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Structural and Microwave Dielectric Properties of Ceramics of Ca(1-x)Nd2x/3TiO3

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Structural and Microwave Dielectric Properties of Ceramics of
Ca(1-x)Nd2x/3TiO3
A thesis submitted to
The University of Manchester for the degree of
Doctor of Philosophy
In the faculty of Engineering and Physical Sciences
Year of Submission
2012
Robert Lowndes MEng
(Materials Science and Engineering)
Materials Science Centre
School of Materials Science
University of Manchester
Grosvenor Street
Manchester
M13 9PL
ProQuest Number: 10030828
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Table of Contents
Abstract ...............................................................................................................................................6
Declaration ..........................................................................................................................................7
Copyright Statement ...........................................................................................................................8
Acknowledgements.............................................................................................................................9
Abbreviations ....................................................................................................................................10
List of Figures ....................................................................................................................................11
List of Tables .....................................................................................................................................16
1 Introduction ...................................................................................................................................18
1.1 Applications and Key Properties .............................................................................................18
1.2 Historical Perspective..............................................................................................................18
2 Literature Review ...........................................................................................................................22
2.1 Origin of Microwave Dielectric Behaviour ..............................................................................22
2.1.1 Polarisation in Materials ..................................................................................................22
2.1.2 Relative Permittivity.........................................................................................................25
2.1.3 Dielectric Losses (Q x f) ....................................................................................................26
2.1.4 Temperature Coefficient of Resonant Frequency............................................................28
2.2 Applications and General Research Objectives for Microwave Dielectric Ceramics ..............29
2.3 Control of Microwave Dielectric Properties ...........................................................................31
2.3.1 Composition .....................................................................................................................31
2.3.2 Microstructure and Texture .............................................................................................32
2.3.2.1 Porosity .....................................................................................................................32
2.3.2.2 Secondary Phases......................................................................................................33
2.3.2.3 Dark Core Formation ................................................................................................34
2.3.2.4 Grain Size..................................................................................................................35
2.3.2.5 Texture ......................................................................................................................36
2.3.2.6 Twin Domains ...........................................................................................................37
2.3.2.7 Antiphase Domains ...................................................................................................42
2.3.3 Engineering of the Crystal Lattice ....................................................................................43
2.3.3.1 Residual Stress ..........................................................................................................43
2.3.3.2 Cation Ordering.........................................................................................................43
1
2.3.3.3 Octahedral Tilting .....................................................................................................45
2.4 Review of Microwave Dielectric Properties of Ceramics ............................................................48
2.4.1 Review of MgTiO3 Microwave Dielectric Ceramics ..............................................................48
2.4.2 Review of CaTiO3 based Microwave Dielectric Ceramics.....................................................50
2.4.2.1 CaTiO3-MgTiO3 Composites ..........................................................................................50
2.4.2.2 CaTiO3-RE(Ga, Al)O3 ......................................................................................................51
2.4.3 Complex Perovskites based on Calcium...............................................................................52
2.4.3.1 Structures and Microwave Dielectric Properties of A-site Modified CaTiO3 Ceramics.52
2.4.3.2 Structure and Microwave Dielectric Properties of B-site Modified CaTiO3 Ceramics ..54
2.4.3.2.1 Ca(B1/3B2/3)(1-x)TixO3 ...............................................................................................54
2.4.3.2.2 Ca(B1/2B1/2)(1-x)TixO3 ..............................................................................................55
2.4.3.3 Combined Doping on both A-site and B-site.................................................................55
2.5 Objectives of the Present Study ..............................................................................................55
3 Experimental Methods...................................................................................................................57
3.1 Sample Preparation ................................................................................................................57
3.1.1 Powder Preparation .........................................................................................................57
3.1.2 Special Preparation Conditions ........................................................................................58
3.1.3 Sample Preparation for Characterisation ........................................................................60
3.2 Characterisation Techniques ..................................................................................................60
3.2.1 Particle Size Analysis ........................................................................................................60
3.2.2 Pellet Densification ..........................................................................................................61
3.2.3 X-Ray Diffraction ..............................................................................................................62
3.2.3.1 Theory .......................................................................................................................62
3.2.3.2 Rietveld Analysis ......................................................................................................65
3.2.4 Scanning Electron Microscopy and Electron Microprobe Analysis..................................65
3.2.5 Transmission Electron Microscopy ..................................................................................67
3.2.6 Aberration Corrected Microscopy ...................................................................................68
3.2.7 Raman Spectroscopy ........................................................................................................69
3.2.8 Dielectric Property Measurements ..................................................................................70
4 Starting Powder and Calcined Powder Characterisation ...............................................................72
4.1 Starting Powders .....................................................................................................................72
4.1.1 Calcium Carbonate (CaCO3) .............................................................................................72
4.1.2 Neodymium Oxide (Nd2O3) ..............................................................................................73
4.1.3 Titanium Oxide (TiO2) .......................................................................................................73
2
4.1.4 Manganese Oxide (Mn2O3) ..............................................................................................74
4.1.5 Magnesium Oxide (MgO) .................................................................................................75
4.2 Calcined Powder Analysis .......................................................................................................77
4.2.1 Phase Development .........................................................................................................77
4.2.2 Particle Sizes.....................................................................................................................78
4.3 Analysis of Calcined Powders in the MgTiO3-Ca0.61Nd0.26TiO3 system ....................................79
4.3.1 Phase Development .........................................................................................................79
4.3.2 Particle Size Analysis ........................................................................................................80
4.4 Attrition Milling of CaTiO3 .......................................................................................................82
4.4.1 Particle Size Analysis ........................................................................................................82
4.4.2 Scanning Electron Microscopy .........................................................................................83
4.4.3 Phase Development .........................................................................................................83
5 Determination of the Room Temperature Structures of Ca(1-x)Nd2x/3TiO3 Ceramics .....................85
5.1 Introduction ............................................................................................................................85
5.2 Conventional Laboratory X-Ray Diffraction ............................................................................85
5.2.1 Phase Development .........................................................................................................85
5.2.2.1 Structure of Ceramics from CaTiO3 to Ca0.61Nd0.26TiO3 .............................................87
5.2.2.2 Structures of Ceramics with Compositions from Ca0.52Nd0.32TiO3 to Ca0.1Nd0.6TiO3..88
5.2.2.3 Tilt System in Ceramics with Monoclinic Structure ..................................................93
5.2.2.4 Cation Vacancy Ordering ..........................................................................................94
5.3 Synchrotron X-Ray Diffraction ................................................................................................95
5.3.1 Structure Determination ..................................................................................................95
5.3.2 Octahedral Distortion ....................................................................................................103
5.3.3 Cation Vacancy Ordering................................................................................................106
5.4 Room Temperature Microstructure of Ca(1-x)Nd2x/3TiO3 Ceramics ........................................106
5.4.1 Grain Size .......................................................................................................................106
5.4.2 Twin Domains.................................................................................................................109
5.5 Transmission Electron Microscopy .......................................................................................112
5.5.1 Twin Domains.................................................................................................................112
5.5.2 Antiphase Domains ........................................................................................................113
5.5.3 Cation Vacancy Ordering................................................................................................115
5.6 Raman Spectroscopy .............................................................................................................117
5.6.1 Mode Parameters ..........................................................................................................117
5.6.2 Rotational Raman Spectroscopy ....................................................................................119
3
5.6.3Cation Vacancy Ordering ................................................................................................122
5.7 Aberration Corrected Scanning Transmission Electron Microscopy ....................................122
5.8 Microwave Dielectric Properties...........................................................................................126
5.8.1 Relative Permittivity.......................................................................................................126
5.8.2 Temperature Coefficient of Resonant Frequency..........................................................127
5.8.3 Quality Factor (Q x f) ......................................................................................................128
6 Structure Sequence in Ca(1-x)Nd2x/3TiO3 Ceramics ........................................................................132
6.1 Introduction ..........................................................................................................................132
6.2 General Information .............................................................................................................132
6.2.1 X-ray Diffraction .............................................................................................................132
6.2.2 Raman Fitting Procedure ...............................................................................................133
6.3 Structure Sequence of Ca0.79Nd0.14TiO3 .................................................................................134
6.3.1 Variable Temperature X-ray Diffraction.........................................................................134
6.3.2 Raman Spectroscopy of Ca0.79Nd0.14TiO3 ........................................................................139
6.4 Structure Sequence of Ca0.7Nd0.2TiO3 ....................................................................................142
6.5 Structure Sequence of Ca0.61Nd0.26TiO3 .................................................................................145
6.5.1 Variable Temperature X-ray Diffraction.........................................................................145
6.5.2 Variable Temperature Raman Spectroscopy .................................................................149
6.6 Structure Sequence of Ca0.52Nd0.32TiO3 .................................................................................152
6.6.1 Variable Temperature X-ray Diffraction.........................................................................152
6.6.2 Raman Spectroscopy of Ca0.52Nd0.32TiO3 ........................................................................158
6.7 Structure Sequence of Ca0.43Nd0.38TiO3 .................................................................................161
6.8 Structure Sequence of Ca0.1Nd0.6TiO3 ....................................................................................164
6.8.1 Variable Temperature X-ray Diffraction.........................................................................164
6.8.2 Raman Spectroscopy of Ca0.1Nd0.6TiO3 ...........................................................................169
6.9 Trends in Structural Phase Transitions .................................................................................171
6.9.1 Transition Diagram of Ca(1-x)Nd2x/3TiO3 ...........................................................................171
6.9.2 Effect of the Transitions on the Microstructure of Ca(1-x)Nd2x/3TiO3 ..............................174
7 Control of Domain Density in Ca(1-x)Nd2x/3TiO3 Microwave Dielectric Ceramics ..........................175
7.1 Introduction ..........................................................................................................................176
7.2 Densification .........................................................................................................................176
7.3 Structure ...............................................................................................................................176
7.4 Microstructure ......................................................................................................................179
7.4.1 Scanning Electron Microscopy .......................................................................................179
4
7.4.2 Transmission Electron Microscopy ................................................................................182
7.5 Raman Spectroscopy .............................................................................................................185
7.6 Microwave Dielectric Properties...........................................................................................186
8 Effect of Composition and Cooling Rate on the Microwave Dielectric Properties of (1-x)MgTiO3xCa0.61Nd0.26TiO3 ..............................................................................................................................190
8.1 Introduction ..........................................................................................................................190
8.2 Composition ..........................................................................................................................190
8.2.1 Densification ..................................................................................................................190
8.2.2 Phase Development .......................................................................................................191
8.2.3 Microstructure ...............................................................................................................193
8.2.4 Microwave Dielectric Properties....................................................................................196
8.3 Effect of Cooling Rate on the Microwave Dielectric Properties of 0.8MgTiO30.2Ca0.61Nd0.26TiO3 .......................................................................................................................201
8.3.1 Microstructure ...............................................................................................................201
8.3.2 Phase Development .......................................................................................................202
8.3.3 Raman Spectroscopy ......................................................................................................204
8.3.3.1 Effect of Cooling Rate on the Raman Spectra ........................................................204
8.3.3.2 Confocal Raman Spectroscopy ...............................................................................206
8.3.4 Synchrotron XRD ............................................................................................................209
8.3.4 Microwave Dielectric Properties....................................................................................214
9 General Discussion, Conclusions and Suggestions for Further Work ..........................................217
9.0 General Discussion ................................................................................................................217
9.1 Conclusions ...........................................................................................................................220
9.1.1 Structure and Microwave Dielectric Properties of Ca(1-x)Nd2x/3TiO3...............................220
9.1.2 Spark Plasma Sintering of CaTiO3 ...................................................................................222
9.1.3 (1-x)MgTiO3-xCa0.61Nd0.26TiO3 .........................................................................................223
9.3 Suggestions for Further Work ...............................................................................................223
10 References .................................................................................................................................225
5
Abstract
Ca(1-x)Nd2x/3TiO3 and MgTiO3-Ca0.61Nd0.26TiO3 composite ceramics were prepared
by the mixed oxide route and characterised in terms of their structure, microstructure and
properties. Ceramics sintered at 1450-1500oC achieved better than 95% of the theoretical
density. X-Ray diffraction (XRD) revealed that Ca(1-x)Nd2x/3TiO3 ceramics were single
phase for all compositions. For x ≤ 0.39 the structure was Pbnm with lattice parameters of
a = b = √2ac and c = 2ac and a tilt system of a-a-c+. Compositions with x ≥ 0.48 could be
better described by a C2/m structure with lattice parameters of a = b = c = 2ac. Scanning
electron microscopy (SEM) revealed that the ceramics had grain sizes in the 5-70 µm
range with abnormal grain growth for Nd3+ rich compositions. Images revealed that the
twin domains in CaTiO3 were needle shaped and on addition of Nd3+ the domain
morphology becomes more complex. The needle domain morphology returns for
Ca0.43Nd0.38TiO3. High resolution electron microscopy (HAADF-STEM and electron
diffraction) was used to probe cation-vacancy ordering (CVO) in the lattice. It was found
that there was no CVO for x < 0.48 whilst at x = 0.48 there was evidence of a transition to
a short range CVO. A transition to long range ordering is almost complete for the
Ca0.1Nd0.6TiO3. The structural characteristics of Ca(1-x)Nd2x/3TiO3 ceramics as a function of
temperature were investigated using in-situ XRD and Raman spectroscopy. All
compositions were found to have the same structure across the entire temperature range.
The Raman spectroscopy as a function of temperature indicated a possible transition with
similar characteristics to a Curie temperature in a ferroelectric ceramic. The transition
temperature was dependent on the cation ordering with the ceramics with greatest degree
of disorder having the lowest transition temperature. The microwave dielectric properties
of the samples were measured by a cavity resonance method in the 2-4GHz range. The
relative permittivity (εr) was found to decrease from 180 for CaTiO3 to approximately 80
for Ca0.1Nd0.6TiO3 with an exponential dependence between the composition and the
property. The temperature coefficient of resonant frequency (τf) ranged from +770ppmK-1
for CaTiO3 to +200ppmK-1 for Ca0.1Nd0.6TiO3. The Q x f for CaTiO3 was found to be
6000GHz and this increased to a maximum of 13000GHz for Ca0.7Nd0.2TiO3. After the
Ca0.7Nd0.2TiO3 composition, the Q x f decreased to approximately 1100GHz for
Ca0.1Nd0.6TiO3. The εr and τf were found to be mainly dependent on the composition of the
ceramics whilst the Q x f value was more complex being dependent on the width of the
twin domains in the grains. CaTiO3 samples fabricated by spark plasma sintering at 1150oC
and above achieved better than 95% of the theoretical density. XRD revealed only a single
phase with an orthorhombic Pbnm structure at room temperature and a tilt system of a-a-c+.
SEM confirmed that the samples were single phase with grain size between 500nm-5µm.
Transmission electron microscopy (TEM) of specimens sintered at 1150oC showed
evidence of both (011) and (112) type domains. The τf of the ceramics was shown to be
dependent on the volume of the unit cell, in agreement with the Bosman-Havinga
equations. The ceramic sintered at 1150oC showed improvement in the Q x f value
compared to samples prepared by conventional sintering. The structure, microstructure and
properties of composite ceramics based on the MgTiO3-Ca0.61Nd0.26TiO3 system were
investigated. Optimum properties were achieved at a composition of 0.8MgTiO30.2Ca0.61Nd0.26TiO3 with τf = -0.1ppmK-1, Q x f of 39000GHz and εr of 25.4. XRD
revealed the presence of 3 phases including Ca0.61Nd0.26TiO3, MgTiO3 and MgTi2O5. The
grain size of the ceramics was typically 5µm. The Q x f value was sensitive to the cooling
rate and these changes could be related to changes in the vibrational properties of the
lattice through changes in the lattice parameters.
6
Declaration
No portion of this work referred to in this thesis has been submitted in support of an
application for another degree or qualification of this or any other University or other
institute of learning.
7
Copyright Statement
1.
The author of this thesis (including any appendices and/or schedules to this thesis)
owns any copyright in it (the “Copyright”) and s/he has given The University of
Manchester the right to use such Copyright for any administrative, promotional,
educational and/or teaching purposes.
2.
Copies of this thesis, either in full or in extracts, may be made only in accordance
with the regulations of the John Rylands University Library of Manchester. Details of these
regulations may be obtained from the Librarian. This page must form part of any such
copies made.
3.
The ownership of any patents, designs, trade-marks and any and all other
intellectual property rights except for the Copyright (the “Intellectual Property Rights”)
and any reproductions of copyright works, for example graphs and tables
(“Reproductions”), which may be described in this thesis, may not be owned by the author
and may be owned by third parties. Such Intellectual Property Rights and Reproductions
cannot and must not be made available for use without the prior written permission of the
owner(s) of the relevant Intellectual Property Rights and/or Reproductions.
4.
Further information on the conditions under which disclosure, publication and
exploitation of this thesis, the Copyright and any Intellectual Property Rights and/or
Reproductions described in it may take place is available from the Head of School of
Materials (or the Vice-President) and the Dean of the Faculty of Life Sciences, for Faculty
of Life Sciences’ candidates.
8
Acknowledgements
I would like to begin my acknowledging the contribution of the following people for whom
without their help this thesis would not have been possible
Professor Robert Freer for initiating this project and for his guidance throughout my PhD
studies
Dr Feridoon Azough for his guidance on the preparation and microwave property
measurements of dielectric ceramics
Dr Marco Deluca (Institute for Structural and Functional Ceramics, Montanuniverstät
Leoben, Austria) for assistance with the temperature dependent Raman spectroscopy and
the Electron Microprobe Analysis
COST Action MP0904 “Single and Multiphase Ferroics and Multiferroics with Restricted
Geometries” for funding to travel to Montanuniverstät Leoben, Austria
Dr Alan Harvey and Mr Michael Faulkner for guidance concerning electron microscopy
Ms Judith Shackleton and Mr Gary Harrison for assistance with X-Ray Diffraction
measurements
Professor Robert Cernik for advice regarding the Rietveld refinement of X-Ray diffraction
data
Dr David Iddles (Powerwave Ceramics Division, Wolverhampton, UK) for microwave
property measurements and supply of raw powder materials
Dr Zhe Zhao (Technical University of Stockholm) for access to the spark plasma sintering
furnace
Finally I would like to thank my family (mother, father and brother) and all of my friends
who have provided support and encouragement along the way
9
Abbreviations
Units of Measurement
m = metres
mm = millimetres
µm = microns
nm = nanometres
Å = Angstroms
GHz = gigahertz (frequency)
AU/ arb units = arbitrary units
Dielectric Measurements
εr = relative permittivity
ε = dielectric constant
tan δ = dielectric losses
f = resonant frequency
Q = reciprocal of dielectric losses
Q x f = product of Q and resonant frequency
τf = temperature coefficient of resonant frequency
τε = temperature coefficient of the dielectric constant
Characterisation Techniques
CuKα = Copper Radiation Source
EDX = Energy Dispersive X-ray spectroscopy
EMPA = Electron Microprobe Analysis
HAADF = High Angle Annular Dark Field
HRTEM = High Resolution Transmission Electron Microscopy
SEM = Scanning Electron Microscopy
STEM = Scanning Transmission Electron Microscopy
TEM = Transmission Electron Microscopy
WDS = Wavelength Dispersive Spectroscopy
XRD = X-ray Diffraction
Compositions
BZN = Ba(Zn1/3Ta2/3)O3
CTLA = CaTiO3-LaAlO3
10
List of Figures
Figure 1.1: (a) Typical geometries of microwave dielectric resonators and (b) dielectric resonators
in an air filled cavity (reproduced from [15]) ....................................................................................20
Figure 2.1: Polarisation mechanisms in dielectric materials (reproduced from Moulsen and
Herbert [22]) .....................................................................................................................................23
Figure 2.2: Dielectric spectroscopy of materials [22] .......................................................................24
Figure 2.3: Parallel plate capacitor with (i) vacuum and (b) dielectric ceramic between the metallic
plates (reproduced from [22]]) .........................................................................................................25
Figure 2.5: Dielectric constant and dielectric losses as a function of frequency for (Zr, Sn)TiO4 and
Ba(NiTa)O3-Ba(ZrZnTa)O3 (reproduced from Wakino [25]) ..............................................................27
Figure 2.6: Q x f value as a function of relative permittivity (after Ohsato [28]) .............................30
Figure 2.7: Microwave dielectric properties of CaTiO3-NdAlO3 (reproduced from [11]) .................31
Figure 2.8 Relative permittivity and Q value as a function of densification (reproduced from [25])
..........................................................................................................................................................33
Figure 2.9: Secondary phases in Ba3(Co0.7Zn0.3)Nb2O9 (reproduced from Hughes et al. [40]) ..........34
Figure 2.10: Dielectric losses in the 4.2-250K range for MgO dielectric spheres [43] ......................35
Figure 2.11: Transmission electron micrograph of twin domains in CaTiO3 (reproduced from
Kipkoech et al [54]) ...........................................................................................................................37
Figure 2.12: Refinement of high temperature neutron diffraction data on the basis of (i)
orthorhombic Pbnm and (ii) orthorhombic Cmcm (reproduced from [59]).....................................39
Figure 2.13: Phase transition temperatures as a function of Sr/Fe doping of CaTiO3 (after [62, 64])
..........................................................................................................................................................40
Figure 2.14: Electron diffraction patterns of (112) and (110) type domains in CaTiO3 (reproduced
from [20, 53]) ....................................................................................................................................41
Figure 2.15: Antiphase domain boundaries in Perovskites (reproduced from Wang and
Liebermann [20])...............................................................................................................................42
Figure 2.16: X-ray diffraction spectra of Ba(Zn1/3Ta2/3)O3 as a function of annealing time
(reproduced from [70]) .....................................................................................................................45
Figure 2.17: Ideal structure of CaTiO3 Perovskite with A site cation (Ca) in blue and oxygen in red.
Ti atoms are in the centre of the octahedra (reproduced from [68]) ..............................................46
Figure 2.18: τε as a function of tolerance factor (reproduced from Reaney et al. [75]) BaxSr1x(Zn1/3Nb2/3)O3 (BSZN), BaxSr1-x(Mg1/3Ta2/3)O3 (BSMT), BaxSr1-x(In1/2Ta1/2)O3 (BSIN), Ba(Nd1/2Ta1/2)O3
(BNdT), Ba(Gd1/2Ta1/2)O3 (BGT), Ba(Y1/2Ta1/2)O3 (BYT), Ba(Y1/2Nb1/2)O3 (BYN), Ba(Ca1/3Ta2/3)O3
(BCaT), Sr(Ca1/3Ta2/3)O3 (SCaT), Ba(Co1/3Ta2/3)O3 (BCoT), Sr(Co1/3Ta2/3)O3 (SCoT), Sr(Zn1/3Ta2/3)O3
(SZT), Sr(Ni1/3Ta2/3)O3 (SNiT), Ba(Ni1/3Ta2/3)O3 (BNiT), Ba(Mn1/3Ta2/3)O3 (BMN), Ba(Mn1/3Nb2/3)O3
(BMnN), Ba(Mg1/3Nb2/3)O3 (BMN) Sr(Mg1/3Nb2/3)O3 (SMN), Ba(Ni1/3Nb2/3)O3 (BNiN), Sr(Ni1/3Nb2/3)O3
(SNiN), Ba(Co1/3Nb2/3)O3 (BCoN)........................................................................................................48
Figure 3.1: Schematic diagram of a spark plasma sintering furnace (reproduced from [121]) ........58
Figure 3.2: Schematic diagram of laser diffraction for particle size analysis equipment (reproduced
from ISO13320 [122]) .......................................................................................................................61
Figure 3.3: Schematic diagram of Bragg’s law (reproduced from Cullity [123]) ...............................63
Figure 3.4: Segment of temperature control program for high temperature x-ray diffraction .......64
11
Figure 3.5: Interactions of the electron beam with solid sample in the scanning electron
microscope (reproduced from Goodhew et al [126]) .......................................................................66
Figure 3.6: Principle of operation of wavelength dispersive spectroscopy in the electron
microprobe analyser (reproduced from Goodhew et al [126]). .......................................................67
Figure 3.7: Optics of a transmission electron microscope (reproduced from Williams and Carter
[127]) .................................................................................................................................................68
Figure 3.8: Schematic of an scanning transmission electron microscope (reproduced from [127])69
Figure 3.9: Diagram showing setup for microwave dielectric property measurements (reproduced
from Sheen [129]) .............................................................................................................................71
Figure 4.1: X-ray diffraction spectra of CaCO3 ..................................................................................72
Figure 4.2: X-ray diffraction spectra of TiO2......................................................................................73
Figure 4.3: Scanning electron micrographs of (a) CaCO3 (Scale bar = 20µm) (b) Nd2O3 (Scale bar =
1µm) (c) TiO2 (Scale bar = 2µm) and (d) MgO (Scale bar = 2µm) ......................................................74
Figure 4.4: X-ray diffraction spectra of Mn2O3 (* denotes MnO2 phase) ..........................................75
Figure 4.5: SEM micrograph of Mn2O3 (scale bar = 2µm) .................................................................75
Figure 4.6: Particle size analysis of (a) CaCO3 (b) Nd2O3 (c) TiO2 (d) MgO and (e) Mn2O3 ................76
Figure 4.7: Typical X-ray diffraction spectra of calcined powders of Ca(1-x)Nd2x/3TiO3 ......................77
Figure 4.8: Scanning electron micrograph of calcined powder of Ca0.61Nd0.26TiO3 (scale bar 2µm).78
Figure 4.9: Particle size analysis of the calcined powders of Ca0.61Nd0.26TiO3 ..................................79
Figure 4.10: X-ray diffraction spectra of 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 calcined powder ...............80
Figure 4.11: Particle size analysis of 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 .................................................81
Figure 4.12: Scanning electron micrographs of calcined powders of MgTiO3-Ca0.61Nd0.26TiO3 (a)
0.2MgTiO3-0.8Ca0.61Nd0.26TiO3 (b) 0.4MgTiO3-0.6Ca0.61Nd0.26TiO3 (c) 0.6MgTiO3-0.4Ca0.61Nd0.26TiO3
and (d) 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 (scale bar 2µm) ....................................................................81
Figure 4.13: Particle Size analysis of attrition milled CaTiO3 as a function of milling time...............82
Figure 4.14: Scanning electron micrograph of attrition milled and freeze dried CaTiO3 (Scale bar =
1µm) ..................................................................................................................................................83
Figure 4.15: X-ray diffraction spectra of attrition milled and freeze dried CaTiO3 ...........................84
Figure 5.1: X-ray diffraction spectra of Ca(1-x)Nd2x/3TiO3 using Cu Kα radiation .................................86
Figure 5.2: Refinement of the X-ray diffraction spectra of Ca0.1Nd0.6TiO3 on the basis of (A)
orthorhombic Pbnm (B) orthorhombic P222 and (C) orthorhombic Amm2 (D) monoclinic P2/m ..90
Figure 5.3: X-ray diffraction spectra of Ca0.1Nd0.6TiO3 refined on the basis of monoclinic C2/m
structure............................................................................................................................................91
Figure 5.4: Magnified region of the X-ray diffraction spectra of Ca(1-x)Nd2x/3TiO3 ((242) index for
monoclinic C2/m structure and (312) index for orthorhombic Pbnm structure) .............................92
Figure 5.5: Rietveld refinement of (i) Ca0.61Nd0.32TiO3 and (ii) Ca0.52Nd0.32TiO3 on the basis of
orthorhombic Pbnm and monoclinic C2/m ......................................................................................93
Figure 5.6: Schematic illustration of the structure of Ca0.1Nd0.6TiO3 using [100] projection ............94
Figure 5.7: X-ray diffraction spectra of Ca(1-x)Nd2x/3TiO3 obtained using synchrotron sources (a)
CaTiO3 (b) Ca0.7Nd0.2TiO3 (c) Ca0.61Nd0.26TiO3 (d) Ca0.52Nd0.32TiO3 and (e) Ca0.1Nd0.6TiO3 ...................98
Figure 5.8: Evidence of octahedral tilting in (a) Pbnm ceramics and (b) C2/m ceramics ...............102
Figure 5.9: Evidence of peaks related to antiphase domain boundaries in CaTiO3 ........................102
Figure 5.10: Octahedral distortion and tolerance factor as a function of composition in the Ca(1x)Nd2x/3TiO3 system ..........................................................................................................................104
12
Figure 5.11: Low magnification SEM images of Ca(1-x)Nd2x/3TiO3 as revealed by thermal etching (a)
Ca0.79Nd0.14TiO3 (b) Ca0.61Nd0.26TiO3 and (c) Ca0.1Nd0.6TiO3 (scale bar = 20µm for (a) and (b), (c) =
10µm ...............................................................................................................................................107
Figure 5.12: Grain growth rate as a function of driving force for grain growth (reproduced from
[136]) ...............................................................................................................................................108
Figure 5.13: Grain size as a function of composition ......................................................................109
Figure 5.14: High magnification images of twin domains in Ca(1-x)Nd2x/3TiO3 as revealed by chemical
etching (a) CaTiO3 (b) Ca0.79Nd0.14TiO3 (c) Ca0.7Nd0.2TiO3 (d) Ca0.52Nd0.32TiO3 (e) Ca0.43Nd0.38TiO3 (f)
Ca0.1Nd0.6TiO3 (scale bar 20µm).......................................................................................................110
Figure 5.15: Domain widths as a function of composition .............................................................111
Figure 5.16: Electron microprobe analysis maps of Ca0.79Nd0.14TiO3 ..............................................111
Figure 5.17: Transmission electron micrographs of twin and antiphase domains in (a)
Ca0.61Nd0.26TiO3 (scale bar 0.5µm) and (b) twin domains in Ca0.52Nd0.32TiO3 (scale bar = 1µm) –
Courtesy of Dr Feridoon Azough .....................................................................................................112
Figure 5.18: [010] Zone axis selected area electron diffraction patterns for twin boundary region
shown in Figure 5.18a – Courtesy of Dr. Feridoon Azough ............................................................113
Figure 5.19: Transmission Electron Micrographs of antiphase domains in (a) Ca0.7Nd0.2TiO3 (left,
scale bar = 200nm) and (b) Ca0.52Nd0.32TiO3 (right, scale bar = 400nm). Courtesy of Dr. Feridoon
Azough. ...........................................................................................................................................114
Figure 5.20: Electron diffraction patterns of Ca(1-x)Nd2x/3TiO3 viewed in the [010] direction for (a)
CaTiO3 (b) Ca0.52Nd0.32TiO3 and (c) Ca0.1Nd0.6TiO3. Courtesy of Dr Feridoon Azough .......................116
Figure 5.21: Raman spectra as a function of composition for Ca(1-x)Nd2x/3TiO3 ..............................118
Figure 5.22: Raman spectra of Ca0.61Nd0.26TiO3 from three different locations..............................119
Figure 5.23: Raman spectra from four different rotation angles of Ca0.79Nd0.14TiO3 (A) 0o (B) 50o (C)
100o and (D) 150o ............................................................................................................................120
Figure 5.24: Angular dependence of the intensities of 330 and 528 Raman modes for
Ca0.79Nd0.14TiO3 ................................................................................................................................121
Figure 5.25: HAADF images for Ca(1-x)Nd2x/3TiO3 (a) [110] zone axis of CaTiO3 (b) [001] zone axis of
Ca0.61Nd0.26TiO3 (c) [110] zone axis of Ca0.52Nd0.32TiO3 and (d) [010] zone axis of Ca0.1Nd0.6TiO3
(courtesy of B. Schaffer)..................................................................................................................123
Figure 5.26: (a) Bright field STEM image and (b) noise filtered image of Ca0.1Nd0.6TiO3 (courtesy of
B. Schaffer) ......................................................................................................................................124
Figure 5.27: (a) [001] Zone axis HAADF of region of Ca0.1Nd0.6TiO3 (b) EELS map for area labelled
spectrum image and (c) False colour EELS map for Ca0.1Nd0.6TiO3 with Ca2+ represented by green
spots, Nd3+ in blue and Ti4+ in red (courtesy B. Schaffer)................................................................125
Figure 5.28: Microwave dielectric properties as a function of composition for Ca(1-x)Nd2x/3TiO3 ...126
Figure 5.29: Phase diagram of La2O3-TiO2 system (reproduced from MacChesney and Sauer [91])
........................................................................................................................................................129
Figure 6.1: Typical refinement of X-ray diffraction spectra of Ca0.79Nd0.14TiO3 including peaks from
Al2O3 sample holder (blue vertical lines) ........................................................................................133
Figure 6.2: X-ray diffraction spectra of Ca0.79Nd0.14TiO3 in the 25-775oC range showing peaks from
the Al2O3 sample holder ( ) and the perovskite main phase .......................................................134
Figure 6.3: Lattice parameters as a function of temperature for Ca0.79Nd0.14TiO3 with the
orthorhombic Pbnm structure (a) a and b axes (b) c-axis ..............................................................135
Figure 6.4: Tilt angles as a function of temperature for Ca0.79Nd0.14TiO3 ........................................138
13
Figure 6.5: Raman spectra as a function of temperature for Ca0.79Nd0.14TiO3 ................................140
Figure 6.6: Magnified Image of 450-550 cm-1 Region of Raman Spectra for Ca0.79Nd0.14TiO3 at (a)
185oC and (b) 205oC ........................................................................................................................141
Figure 6.7: Peak widths as a function of temperature for Ca0.79Nd0.14TiO3.....................................142
Figure 6.8: Raman spectra for Ca0.7Nd0.2TiO3 as a Function of Temperature .................................143
Figure 6.9: Magnified portion of the Raman spectra of Ca0.7Nd0.2TiO3 at (a) 265oC and (b) 285oC 144
Figure 6.10: Width of 330 cm-1 peak as a function of temperature ...............................................145
Figure 6.11: X-ray diffraction spectra of Ca0.61Nd0.26TiO3 as a function of temperature ................146
Figure 6.12: Lattice parameters as a function of temperature for Ca0.61Nd0.26TiO3........................147
Figure 6.13: Octahedral tilt angles as a function of temperature for Ca0.61Nd0.26TiO3 ...................148
Figure 6.14: Raman spectroscopy of Ca0.61Nd0.26TiO3 from -195oC to 600oC ..................................150
Figure 6.15: Magnified region of the variable temperature Raman spectra of Ca0.61Nd0.26TiO3 at (a)
145oC and (b) 165oC ........................................................................................................................151
Figure 6.16: Width of 330cm-1 peak as a function of temperature for Ca0.61Nd0.32TiO3 .................152
Figure 6.17: Variable temperature X-ray diffraction spectra for Ca0.52Nd0.32TiO3...........................153
Figure 6.18: Lattice parameters as a function of temperature for Ca0.52Nd0.32TiO3........................154
Figure 6.19: Octahedral tilt angles as a function of temperature for Ca0.52Nd0.32TiO3 ...................156
Figure 6.20: Width of the 330cm-1 peak as a function of temperature ..........................................157
Figure 6.21: Raman spectra of Ca0.52Nd0.32TiO3 as a function of temperature................................159
Figure 6.22: Magnified portion of the Raman spectra of Ca0.52Nd0.32TiO3 at (a) 285, (b) 305 and (c)
325oC ...............................................................................................................................................160
Figure 6.23: Width of the 330cm-1 peak as a function of temperature for Ca0.52Nd0.32TiO3 ...........161
Figure 6.24: Raman spectra as a function of temperature for Ca0.43Nd0.14TiO3 ..............................162
Figure 6.25: Magnified Raman spectra of Ca0.43Nd0.38TiO3 at (a) 465, (b) 485 and (c) 505oC .........164
Figure 6.26: X-ray diffraction spectra of Ca0.1Nd0.6TiO3 as a function of temperature ...................165
Figure 6.27: Lattice parameters as a function of temperature for Ca0.1Nd0.6TiO3 ..........................166
Figure 6.28: Octahedral tilt angles for Ca0.1Nd0.6TiO3 as a function of temperature ......................168
Figure 6.29: Raman spectroscopy as a function of temperature for Ca0.1Nd0.6TiO3 .......................170
Figure 6.30: Peak widths as a function of temperature for the (a) 469 and (b) 531cm-1 peaks of
Ca0.1Nd0.6TiO3...................................................................................................................................171
Figure 6.31: Transition temperatures as a function of composition in Ca(1-x)Nd2x/3TiO3.................173
Figure 6.32: Scanning electron micrographs of Ca0.61Nd0.26TiO3 heated to (A) 150, (B) 200, (C) 250
and (D) 400oC (scale bar = 10µm) ...................................................................................................174
Figure 6.33: Scanning electron micrographs of Ca0.61Nd0.26TiO3 cooled from 400oC to (A) 300, (B)
250, (C) 200 and (D) 150oC ..............................................................................................................175
Figure 7.1: X-ray diffraction spectra of CaTiO3 fabricated by spark plasma sintering at three
different temperatures ...................................................................................................................177
Figure 7.2: Scanning electron micrographs of CaTiO3 fabricated by spark plasma sintering (a)
sintered at 1150oC (scale bar 5 µm), (b) sintered at 1300oC (scale bar 5 µm) (c) sintered at 1450oC
(scale bar 20 µm) and (d) sintered at 1450oC (scale bar 500 µm) ..................................................180
Figure 7.3: High magnification image of twin domains in CaTiO3 sintered at 1300oC showing
interaction angles between domains (scale bar = 2µm).................................................................181
Figure 7.4: Transmission Electron Micrograph of CaTiO3 fabricated by spark plasma sintering at
1150oC (scale bar = 200nm) ............................................................................................................183
14
Figure 7.5: Selected area electron diffraction patterns of (a) Region A (b) Region B along the
zone axis..........................................................................................................................................183
Figure 7.6: Raman spectra of CaTiO3 sintered at three different temperatures ............................185
Figure 7.7: Typical deconvolution of Raman spectrum of CaTiO3 sintered at 1150oC into individual
peaks ...............................................................................................................................................186
Figure 8.1: Density as a function of composition for the (1-x)MgTiO3-xCa0.61Nd0.26TiO3 system ...191
Figure 8.2: X-ray diffraction spectra of (1-x)MgTiO3-xCa0.61Nd0.26TiO3 as a function of
composition ....................................................................................................................................192
Figure 8.3: Scanning electron micrographs of (1-x)MgTiO3-xCa0.61Nd0.26TiO3 as a function of
composition (a) 0.2MgTiO3-0.8Ca0.61Nd0.26TiO3 (b) 0.4MgTiO3-0.6Ca0.61Nd0.26TiO3 (c) 0.6MgTiO30.4Ca0.61Nd0.26TiO3 and (d) 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3. Scale bar is 10µm................................194
Figure 8.4: EDX spectra of 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 showing (a) MgTiO3 from grey contrast
grain and (b) Ca0.61Nd0.26TiO3 from white contrast grain ................................................................195
Figure 8.5: Microwave dielectric properties of (1-x)MgTiO3-xCa0.61Nd0.26TiO3 as a function of
composition (a) τf (b) εr and Q x f....................................................................................................198
Figure 8.6: Scanning electron micrographs of 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 as a function of
cooling rate (a) cooling rate of 300oC/hr (b) cooling rate of 60oC/hr and (c) 15oC/hr. Scale bar is
20µm ...............................................................................................................................................202
Figure 8.7: X-ray diffraction patterns of 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 as a function of cooling rate
........................................................................................................................................................204
Figure 8.8: Raman spectra as a function of cooling rate in the 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 system
........................................................................................................................................................205
Figure 8.9: Raman spectra as a function of penetration depth into sample for (a) grain of MgTiO3
and (b) grain of Ca0.61Nd0.26TiO3 ......................................................................................................208
Figure 8.10: Synchrotron X-ray diffraction patterns for 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 as a function
of cooling rate .................................................................................................................................210
15
List of Tables
Table 1.1: Microwave Dielectric Properties of = 0 Ceramics ........................................................19
Table 2.1: Effect of B site bond valence on cation ordering (after Davies et al [68]) .......................44
Table 2.2: Tilt symbols, reflection types and conditions for perovskite octahedra tilting
(reproduced from Glazer [73-74] ......................................................................................................47
Table 2.3: Microwave Dielectric Properties of MgTiO3 Ceramics with Different Additions
(reproduced from [21]) .....................................................................................................................49
Table 3.1: List of powders used in ceramic preparation ...................................................................57
Table 3.2: List of Compositions prepared .........................................................................................59
Table 4.1: Structures of secondary phases in Ca(1-x)Nd2x/3TiO3 calcined powder ..............................78
Table 5.1 – Lattice parameters for ceramics in the system Ca(1-x)Nd2x/3TiO3 ....................................87
Table 5.2a: Lattice parameters, atomic coordinates and site occupancies of Ca(1-x)Nd2x/3TiO3
ceramics with Pbnm structure ..........................................................................................................99
Table 5.3: Octahedral distortion and tolerance factor as a function of composition ....................104
Table 5.4a: Bond lengths as a function of composition for the ceramics with the Pbnm structure
........................................................................................................................................................105
Table 5.4b: Selected bond lengths for ceramics with the C2/m structure .....................................105
Table 5.5: Grain size as a function of composition in Ca(1-x)Nd2x/3TiO3 ...........................................108
Table 5.6: Microwave dielectric properties of Ca(1-x)Nd2x/3TiO3 ceramics measured at 2-3GHz .....127
Table 6.1: Lattice parameters as a function of temperature for Ca0.79Nd0.14TiO3 with the
orthorhombic Cmcm structure (square markers for the a-axis, diamond markers for the b-axis and
triangle markers for the c-axis) .......................................................................................................136
Table 6.2: Atomic coordinates, site occupancies and thermal parameters for Pbnm form of
Ca0.79Nd0.14TiO3 at 775oC .................................................................................................................137
Table 6.3: Octahedral tilt angles for Ca0.61Nd0.26TiO3 as a function of temperature .......................149
Table 6.4: Lattice parameters as a function of temperature for Ca0.52Nd0.32TiO3 ...........................155
Table 6.5: Octahedral tilt angles as a function of temperature for Ca0.52Nd0.32TiO3 .......................157
Table 6.6: Lattice parameters of Ca0.1Nd0.6TiO3 as a function of temperature ...............................167
Table 6.7: Octahedral tilt angles as a function of temperature for Ca0.1Nd0.6TiO3 .........................169
Table 7.1: Structural details of CaTiO3 ceramics fabricated by conventional and spark plasma
sintering. Estimated standard deviations are in brackets. .............................................................178
Table 7.2: Octahedral tilt angles in CaTiO3 fabricated by SPS.........................................................178
Table 7.3: Mean domain widths for CaTiO3 ceramics fabricated by conventional and spark plasma
sintering ..........................................................................................................................................182
Table 7.4: Microwave dielectric properties of CaTiO3 as a function of sintering temperature ......187
Table 8.1: Lattice parameters as a function of composition for MgTiO3 in (1-x)MgTiO3xCa0.61Nd0.26TiO3 ..............................................................................................................................193
Table 8.2 Lattice parameters as a function of composition for Ca0.61Nd0.26TiO3 in (1-x)MgTiO3Ca0.61Nd0.26TiO3 ................................................................................................................................193
Table 8.3: Composition of each grain by EDX analysis....................................................................196
Table 8.4: Estimated and measured microwave dielectric properties of (1-x)MgTiO3xCa0.61Nd0.26TiO3 ..............................................................................................................................197
16
Table 8.5: Lattice parameters as a function of cooling rate ...........................................................203
Table 8.6: Summary of assignment of modes of vibration for 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 as a
function of cooling rate...................................................................................................................206
Table 8.7: Proportions of each of the phases in 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 ceramics as a
function of cooling rate...................................................................................................................210
Table 8.8a: Summary of lattice parameters, atomic coordinates, site occupancies and temperature
factors for MgTiO3 as a function of cooling rate. ............................................................................211
Table 8.8b: Summary of lattice parameters, atomic coordinates, site occupancies and temperature
factors for Ca0.61Nd0.26TiO3 as a function of cooling rate ................................................................212
Table 8.9: Thermal expansion coefficients for MgTiO3 and Ca0.61Nd0.26TiO3 determined by neutron
diffraction [156] and X-ray diffraction respectively (from chapter 6) ............................................214
Table 8.10: Microwave dielectric properties of 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 at different cooling
rates. Measurement frequency was approximately 3.5GHz. .........................................................215
17
1 Introduction
1.1 Applications and Key Properties
Microwave dielectric ceramics are used as components in the filter units of
communication systems to produce high quality signals by removing unwanted sidebands
using a resonance technique [1]. Examples of technologies that apply this concept include
Radar, GPS patch antennas and mobile telephony including the base stations and handsets
[2]. The design of new microwave dielectric materials is guided by three criteria that were
recently updated by Freer and Azough [3]. The first is that the material should have a high
relative permittivity to minimise the size of the resonator component. This criterion is
based on Equation 1.1:
(1.1)
√
(D = size factor and
is the relative permittivity). The relative permittivity is usually
restricted to values between 20-100 to take into account for other restrictions applied to the
material. The second criterion is that the Q x f of the material should be as high as possible.
The Q value of the material is the reciprocal of the dielectric loss tangent,
, and f is
the resonant frequency of the material. The Q x f value is a measure of the selectivity of
the resonator to a specified frequency. The final criterion is that the material should have a
temperature coefficient of resonant frequency
that is as close to zero as possible. The
determines the stability of the dielectric behaviour as a function of temperature.
1.2 Historical Perspective
The concept of using ceramic dielectric resonators was introduced by Richmeyer in
1939 [4]. However, it was not until the 1960’s with the measurement of the microwave
dielectric properties of TiO2 was it possible to realise the potential for miniaturization of
18
resonator components [5]. Until the 1960’s, the only dielectric resonator components that
were available were large air filled cavities. The use of TiO2 allowed a size reduction by a
factor of ten due to the relative permittivity of TiO2 being 100 times that of air (  r = 100
(TiO2) and  r = 1 (air)) [1]. Although TiO2 has a high relative permittivity (  r = 100) and
low dielectric losses (Q x f = 50000GHz) [6], widespread commercial deployment is not
worthwhile since that TiO2 has a large positive temperature coefficient of resonant
frequency
= +450ppmK-1. The large positive
would cause the dielectric behaviour to
drift should the temperature change during operation and measures should be taken to
stabilise the dielectric behaviour as a function of temperature.
The temperature stability of microwave dielectric ceramics can be improved by the
combination of two or more materials with opposite polarity values of
. Early examples
of the application of this concept was by the combination of CaTiO3-CaZrO3 and SrTiO3SrZrO3 which typically achieved properties of  r = 29-35 and Q x f from 4000GHz to
13300GHz [7]. Several studies [8, 9] have used CaTiO3 as a base material due to its high
 r = 180 and moderate Q x f of 6000GHz [10] in combination with a negative temperature
coefficient of resonant frequency to stabilise the dielectric behaviour as a function of
temperature. CaTiO3-NdAlO3 is an example of a CaTiO3 based material suitable for
commercial deployment with properties of  r = 45 Q x f = 45000GHz and
= 0 ppm K-1
[11]. Other similar compositions are based on similar formulae are listed in Table 1 along
with other key compositions. Dielectric resonators can be made into different geometries to
suit the purpose of the component and examples include toroids, spheres and cubes (see
Figure 1.1)
Table 1.1: Microwave Dielectric Properties of
= 0 Ceramics
Composition
r
Q x f (GHz)
Reference
0.94MgTiO3-0.06CaTiO3
20
68000
[9]
Ca0.7Nd0.3Ti0.7Al0.3O3
45
45000
[11]
Ba(Zn1/3Ta2/3)O3
29
150000
[12]
Ba(Mg1/3Ta2/3)O3
24
300000
[13]
Ba6-3xR8+2xTi18O54
80-90
8000-13000
[14]
19
Figure 1.1: (a) Typical geometries of microwave dielectric resonators and (b)
dielectric resonators in an air filled cavity (reproduced from [15])
1.3 Current Study
Cation deficient microwave dielectric ceramics have been studied as one
component of many different composite materials for resonator applications [16-18].
Although this is the case, there are few studies relating to the base material and in
particular how twin domains affect the microwave dielectric properties. The Q x f value of
Ca(1-x)Nd2x/3TiO3 rises from 6000GHz in CaTiO3 to 15000GHz for Ca0.61Nd0.26TiO3 and
then falls to around 1000GHz for Nd2/3TiO3 [19]. It is not entirely clear why the ceramics
in the solid solutions have higher properties than each of the end members. The primary
objectives of the investigation were to determine the relationship between the structure,
microstructure and properties of ceramics based on Ca(1-x)Nd2x/3TiO3. In chapter 5, the high
resolution structural properties of Ca(1-x)Nd2x/3TiO3 at room temperature are determined
using synchrotron X-ray diffraction (XRD) and scanning transmission electron microscopy
(STEM). These structural properties will then be used to explain the differences in the
microstructure which lead to the change in the microwave dielectric properties. In chapter
6, the structural properties of Ca(1-x)Nd2x/3TiO3 at elevated temperature has been
investigated in detail by Raman spectroscopy and by in-situ diffraction techniques in order
to find a mechanism for microstructure changes observed in these ceramics.
It is well known that CaTiO3 undergoes two structural transitions on cooling to
room temperature after sintering and that the strain from these transitions is relieved by
twinning [20]. It is thought that the presence of twin domains may reduce the microwave
20
dielectric properties, with the change in orientation acting as a source of phonon scattering.
Chapter 7 describes the effect of domains on the microwave dielectric properties of
CaTiO3 ceramics, dense ceramics were produced by spark plasma sintering at temperatures
below the measured transition temperatures in order to avoid the formation of twin
domains.
The effect of processing route on the microwave dielectric properties of MgTiO3
was studied by Ferreira et al. [21] It was found that the microwave dielectric properties
could be improved by cold isostatic pressing of the powders prior to sintering of the
pellets. The improvement in the microwave dielectric properties was attributed to a
reduction in the internal stress state of the ceramics. The study in question only inferred
that there was a reduction in the internal stress and did not make any measurements to
prove that this was the case. In the present investigation the work of Ferreira et al. [21] is
revisited in chapter 8 by measuring the internal stress state in Ca0.61Nd0.26TiO3 and
0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 ceramics by synchrotron X-Ray diffraction. The internal
stress state of the samples was varied by slow cooling to room temperature after sintering.
21
2 Literature Review
2.1 Origin of Microwave Dielectric Behaviour
2.1.1 Polarisation in Materials
Materials that exhibit dielectric behaviour respond to an applied electric field with
polarisation of the chemical bonds in the material [22]. On the application of an electric
field to a metallic material the electrons are mobile causing an electric current. However in
ionic and covalently bonded materials the electrons that could occupy the conduction band
are in the valence band hence prohibiting any current flow. In response to the application
of an electric field the electron clouds in a chemical bond are distorted by a magnitude
according to Equation 2.1.
(2.1)
Where p = polarisation, q = magnitude of charge and x = the distance separating the
charges. There are a 4 modes by which polarisation can occur in oxide materials including:
1. Electron cloud distortion which occurs at frequencies greater than 1017Hz
2. Polarisation of ions is where the cations and anions in the lattice move to form a
dipole
3. Dipolar polarisation where molecules are aligned relative to each other and form
dipoles
4. Diffusional polarisation is where charge carriers move through the lattice until
stopped by defects such as grain boundaries. This mechanism is the slowest mode
of polarisation and is only important at frequencies below 1kHz
These polarisation mechanisms are illustrated graphically in Figure 2.1. Not all of these
mechanisms of polarisation are available across the entire frequency range. If the
22
frequency of the applied electric field is sufficiently high then a particular mechanism of
polarisation will stop (Figure 2.2) because there will be insufficient time for the dipole to
respond to changes in the electric field.
Figure 2.1: Polarisation mechanisms in dielectric materials (reproduced from Moulsen
and Herbert [22])
23
Figure 2.2: Dielectric spectroscopy of materials [22]
The behaviour of a dielectric ceramic under an applied electric field can be
modelled by considering a parallel plate capacitor (Figure 2.3). When an electric field, E, is
applied across the two plates, opposite charges separate such that one plate becomes
positively charged and the other becomes negatively charged. The capacitance (C) of a
parallel plate capacitor is given by Equation 2.2:
(2.2)
(where q = charge and V = voltage). Equation 2.2 assumes that the capacitor is constructed
from two parallel metallic plates separated by a vacuum. When a piece of dielectric
material is placed between the two plates, the polarisation of the dielectric material will
increase the charge stored on the plates. The capacitance can then be written in terms of
Equation 2.3:
(2.3)
24
(where
is the relative permittivity,
is the permittivity of free space, A is the area of
the metallic plates and d is the separation between the plates)
Figure 2.3: Parallel plate capacitor with (i) vacuum and (b) dielectric ceramic between
the metallic plates (reproduced from [22]])
2.1.2 Relative Permittivity
The relative permittivity of a material is how much an electric field can penetrate
into a material compared to the permittivity of free space and can be defined in terms of
Equation 2.4.
(2.4)
where
is the relative permittivity,
-12
is the permittivity of the material and
is the
-1
permittivity of free space (8.85x10 Fm ). In microwave dielectric materials the relative
permittivity is important for the miniaturization of the resonator component as
demonstrated by Equation 2.5:
(2.5)
√
Where
is the wavelength of the lattice vibration,
photon and
is the wavelength of the microwave
is the relative permittivity.
25
2.1.3 Dielectric Losses (Q x f)
The Q x f of microwave dielectric ceramics is measured from width of the
resonance peak at 3dB as illustrated in Figure 2.4 [22]. The narrower the peak becomes the
lower the dielectric losses of the ceramic. The dielectric losses have four separate
components including heat loss, dielectric loss, conduction loss and radiation losses. If a
cavity method is used then the radiation losses can be ignored due to the shielding
provided by the cavity. Otherwise the total loss is given by Equation 2.6:
(2.6)
where Q0 = total losses, Qd = dielectric losses, Qc = losses by conduction and Qr = losses
by radiation. There are two sources of dielectric losses in ceramics; the dielectric losses of
the perfect crystal lattice are known as intrinsic losses whilst losses from defects are known
as extrinsic losses. The intrinsic dielectric losses may be estimated by spectroscopic
methods such as Fourier Tranform Infrared Spectroscopy (FTIR) [23]. Important factors
that contribute to the extrinsic dielectric losses in materials are defects such as point
defects, domain boundaries, grain boundaries, porosity, impurities and secondary phases
[24]. These sources of dielectric loss can be minimised by the careful processing of the
ceramics.
Figure 2.4: Measurement of the width of the resonance peak at 3dB [22]
26
The dielectric losses can be described in terms of the resonant frequency of the
ceramic according to Equation 2.7.
(2.7)
Where
and
T
is the damping constant of the infrared active modes,
is the angular frequency
is the resonant frequency. Analysis of this equation suggests that as the resonant
frequency is increased the value of
will decrease. Wakino [25] confirmed this
analysis by measuring the frequency dependence the dielectric losses of (Zr, Sn)TiO 4 and
Ba(NiTa)O3-Ba(ZrZnTa)O3 (Figure 2.5). It is seen that whilst the dielectric constant of the
ceramic does not change with frequency, the value of
decrease of the
(1/
is seen to decrease. The
as a function of frequency means that the product of the Q value
) and the resonant frequency, f, is approximately constant over a wide range of
frequencies. This product (Q x f) can therefore be used as a figure of merit to enable
comparison between different materials with similar processing conditions.
Figure 2.5: Dielectric constant and dielectric losses as a function of frequency for (Zr,
Sn)TiO4 and Ba(NiTa)O 3-Ba(ZrZnTa)O3 (reproduced from Wakino [25])
27
2.1.4 Temperature Coefficient of Resonant Frequency
The temperature coefficient of resonant frequency is a measure of how much the
dielectric behaviour changes as a function of temperature. It is therefore important to have
a
value that is as close to 0 as possible so that the performance of the device does not
drift should the operating temperature change. The
coefficient of the dielectric constant
is related to the temperature
and the linear thermal expansion coefficient (
)
by Equation 2.8.
(
)
(2.8)
Bosman and Havinga [26] derived expressions for the value of
by differentiating the
Clausius-Mosotti equation with respect to temperature.
(2.9)
Where:
( )
(2.10)
(
) ( )
(2.11)
(
)
(2.12)
And
(
= total polarizability, V = volume, T = temperature, P = pressure,
permittivity and
= relative
= temperature coefficient of the dielectric constant). Each of the terms
in this equation describes a change in dielectric behaviour as a function of temperature. As
a result of the thermal expansion of the lattice there is a reduction in the concentration of
bonds that can become dipoles and this is described by term A in the equation. Although
there is a reduction in the concentration of particles available for polarization as the lattice
expands, the increase in volume enables an increase in the polarizability of a given bond
28
(term B). The final term, term C, represents the change in polarizability as a function of
temperature.
2.2 Applications and General Research Objectives for Microwave Dielectric
Ceramics
Since the year 2000 there has been a rapid development in mobile telephone
technologies. Current mobile telephone devices available include a wide variety of
applications in addition to the traditional function of making telephone calls. Such
applications have included internet browsing capability, video recording devices, short
messaging service (SMS), video games, high memory capacity for storage of personal
media such as downloaded music and movies and personal organiser. It has only been
possible to add all of these applications due to the materials development that has led to the
miniaturisation of device components. As miniaturisation has been a common theme in the
development of components for mobile telephones over the past decade, it is likely that
miniaturisation is going to be a common theme for the decade to come. Two other themes
that are likely to dominate research into ceramics for the foreseeable future are reducing
the carbon footprint of ceramic fabrication and to ensure supply of components by
avoiding the use of oxides which are in short supply [27].
Ohsato [28] plotted the relative permittivity vs the Q x f value for many of the
published properties of tungsten-bronze and perovskite microwave dielectric ceramics. In
addition to the raw data, the approximate specifications for millimetre-wave, mobile
telephone handset and base stations were also plotted (see Figure 2.10). The base stations
require high Q x f value so the relative permittivity (and therefore size) must be reduced to
ensure the resonator is highly selective to the target signal. This target frequency is dictated
by the system in use but this is usually in the 900-2200MHz range [2]. In the handsets of
the mobile telephone systems it is more important to minimise the size of the component in
order to minimise the size of the device at the expense of selectivity. A typical material
would need a relative permittivity of approximately 80 to 100 and an example of a material
which meets such requirements is Ba4Nd9.33Ti18O54 [29, 30]. Similar requirements are
needed for satellite communication system such as GPS. The mass of the components must
be minimised in order to save on the fuel getting the satellite into orbit via a spacecraft and
to reduce the fuel consumption to keep the satellite in orbit [2].
29
Figure 2.6: Q x f value as a function of relative permittivity (after Ohsato [28])
Given that there are different requirements for the base stations, handsets and
satellites of communications systems, it is necessary to have different classes of
microwave dielectric ceramics to accommodate the different requirements. For the low
permittivity, high Q x f ceramics for millimetre wave applications examples include
monolithic ceramics such as Al2O3 [31] and forsterite (Mg2SiO4) [32]. Typical properties
include relative permittivities between 5-10 and high Q x f (150000-600000GHz). Another
family of microwave dielectric ceramics with slightly higher permittivity than the silicate
ceramics are the MgTiO3 ceramics. The typical microwave dielectric properties of MgTiO3
ceramics are εr of 17 and Q x f of 56000GHz but can greatly improved by adjustment of
the processing conditions to around 166000GHz [9]. Another major class of microwave
dielectric ceramics that cover a wide variety of microwave dielectric properties are
ceramics based on the mineral perovskite. The permittivity of such ceramics can range
from low-moderate of 20 for the rare Earth aluminates [33] up to 180 for CaTiO3 [10].
Equally, the Q x f shows a wide variety of values ranging from 6000GHz for CaTiO3 to
56000GHz for the rare Earth aluminates.
30
2.3 Control of Microwave Dielectric Properties
2.3.1 Composition
It is possible to control the microwave dielectric properties of ceramics through
composition adjustments in terms of major compositional additions or through minor
additions of dopants or sintering aids. The starting point in the design of a suitable
dielectric resonator is to consider how two or more ceramics can be combined to achieve a
composition that exhibits stable dielectric behaviour as a function of temperature.
Typically the
can follow either a (i) linear (for composite materials ) or (ii) logarithmic
dependence as a function of composition (for solid solutions) and approximate values of
new materials can derived if the
values of the end members are known. An example of a
perovskite based system that follows a logarithmic relationship between the ceramic
composition and
in the
is the CaTiO3-NdAlO3 system as shown in Figure 2.7 [11]. The trend
is that there is a rapid decrease with the addition of 10 wt% NdAlO3 with the
falling from 800ppmK-1 to 200ppmK-1 and tuning through 0 ppmK-1 can be achieved
with 30 wt% NdAlO3. Further additions of NdAlO3 only have a minimal effect on the
value.
Figure 2.7: Microwave dielectric properties of CaTiO3-NdAlO3 (reproduced from
[11])
31
2.3.2 Microstructure and Texture
2.3.2.1 Porosity
A common feature of ceramics is the presence of porosity both in grains and at the
grain boundaries of the samples. It is important to reduce the porosity to a minimum in
order to maximise the
of the ceramic and hence minimise the size of the filter
components. The reason for the presence of porosity causing a reduction in
pores are filled with air which has
= 1. The
is that the
of most microwave dielectric ceramics
follow the Lichteneker logarithmic mixing rule (Equation 2.13) which means that pores do
not add to the permittivity since ln 1 = 0. The porosity in the microstructure can be
eliminated by increases in the sintering time and temperature and by the addition of
sintering aids. Sintering aids are substances with low melting points relative to the
sintering temperature and these liquid phases wet the grain boundaries [34]. Once the grain
boundaries are wet by the liquid phases material can quickly pass from grain to grain via
the network formed by the liquid phase. Effective sintering aids for CaTiO3 perovskites
include Al2O3 [35] and B2O3 [36].
(2.13)
(where
ceramic 1,
is the relative permittivity of the composite ceramic,
is the relative permittivity of ceramic 1 and
is the mole fraction of
is the relative permittivity of
ceramic 2)
32
Figure 2.8 Relative permittivity and Q value as a function of densification (reproduced
from [25])
2.3.2.2 Secondary Phases
Many microwave dielectric ceramics use Zn2+ as an element in the formulation [11,
37-40].
For example, to achieve optimal densification ceramics based on
Ba3(Co0.7Zn0.3)Nb2O9 (BCZN), sintering temperatures in excess of 1300oC are required
[40]. Above the temperature of 1300oC, Zn2+ is volatile resulting in evaporation from the
surface of the ceramic leading to the formation of Ba8ZnNb6O24 [40]. Further evaporation
of the Zn2+ will lead to the formation of Ba4Nb5O15 and these phases have a needle
morphology. The concentration of the Zn-deficient phases increases with extended
processing times due to the evaporation being diffusion controlled. It has been shown that
the Q x f of the BCZN can be improved as a result of the presence of these phases as the
surface of the ceramics is where the interaction between the microwave photon and the
lattice occurs.
33
Figure 2.9: Secondary phases in Ba 3(Co0.7Zn0.3)Nb2O9 (reproduced from Hughes et al.
[40])
2.3.2.3 Dark Core Formation
The Q x f of Ti based ceramics are known to degrade as a result of the reduction of
Ti4+ to Ti3+ during sintering [41-42]. The key characteristic of ceramics containing Ti3+ is
the presence of a dark core in the ceramic pellets. The properties of the ceramics are
degraded as a result of the presence of different charges which change the vibration
properties of the lattice. Templeton et al. [6] studied the effect of minor additions of
dopants such as MnO to prevent the reduction of Ti4+. They found that the dopants caused
the creation of Ti interstitial defects which compensated for the charge distribution. This
process can be described by Equation 2.14
Mn2+ + Ti3+ = Mn3+ + Ti4+
(2.14)
This effect can also occur in compounds containing TiO2 as well as TiO2 as a monolithic
compound. A study of microwave dielectric ceramics based on BaTi4O9 and Ba2Ti9O20
found that even low concentrations of defects from reduction processes could substantially
degrade the Q value [41-42].
34
2.3.2.4 Grain Size
There has been considerable debate over whether the grain size affects the
properties of microwave dielectric ceramics [43]. It could be argued that the grain size
should affect the properties because the boundary could reasonably be expected to scatter
phonons and hence increase the dielectric loss [23-24]. It is often difficult however to
separate out a series of different variables including ferroelectricity, twin domain
boundaries, cation ordering, secondary phases and porosity [23-24, 43]. There is evidence
that the differences in the Q x f values of single crystal and polycrystalline microwave
dielectric ceramics are due to the grain size of the materials. In single crystals of Al 2O3 the
Q x f in the direction perpendicular to the [001] direction is 1170000GHz and parallel to
the [001] direction it is 1890000GHz [44]. The Q x f of polycrystalline Al2O3 ceramic is
370000GHz [45]. Breeze et al. [43] studied the dielectric properties of spheres that were
either single crystal orientated such that a single grain boundary was either parallel or
perpendicular to the measurement waveguides. They found that there was no significant
difference in the dielectric properties for any of these materials and they concluded that
grain boundaries do not affect the microwave dielectric properties. This situation is
somewhat artificial because most materials for which there are known dielectric properties
have many more grain boundaries that cannot be considered impurity free and clean.
Figure 2.10: Dielectric losses in the 4.2-250K range for MgO dielectric spheres [43]
35
It was originally thought that the effect of grain size on microwave dielectric
properties is that a ceramic with a smaller grain size would contain a greater concentration
of impurities [46]. The presence of impurities on the microwave dielectric properties was
investigated by Wakino et al. [47] on the (Zr, Sn)TiO4 system. It was found that the Q x f
value decreased from 46200GHz to 18900GHz as a result of the presence of Fe2O3 in the
starting powders. It was later postulated by Iddles et al. [48] that the presence of Fe2O3 was
compensated by electrons as displayed in the Kroger-Vink reaction shown in Equation 15:
(2.15)
The Q x f could subsequently be restored to 49000GHz by the addition of Nb2O5 powder
by prevention of the formation of excess electrons. An alternative route to prevention of
dielectric loss due to impurities is to leach the impurities from the powders [49] or use a
sol-gel chemical route [9].
2.3.2.5 Texture
The effect of preferred grain orientation on the microwave dielectric properties of
Ba4RE9.33Ti18O54 (RE = Nd or Sm) [50, 51] and CaTiO3 [52] has been investigated by the
groups of Ohsato and Wada [50-52]. Ba4RE9.33Ti18O54 is an ideal system to exploited
anisotropy of dielectric behaviour because of its highly anisotropic structure with lattice
parameters of a = 12.2Å, b = 22.4Å and c = 7.7Å [50-51]. Hot forging and tape casting
with template particles are the two main routes that have been employed in the fabrication
of anisotropic microwave dielectric ceramics. It was found that the Q x f value of CaTiO 3
could be improved from 6000GHz to 9000GHz by using inducing texture to samples [52].
This improvement in the properties was attributed to the reduction in the dielectric losses
from grain boundary scattering but it is likely that other factors improve the microwave Q
x f. The template particles were made by a microchemical conversion route which involves
the addition of Bi2O3 and KCl to produce highly anisotropic plate shaped particles that will
become orientated in the [001] direction on tape casting. In order to remove the additions
to achieve the desired particle shape it is required to wash the powders in HNO3 and H2O
to remove the Bi2O3 and KCl respectively. It is possible that during this process any
36
impurities that are usually present in CaTiO3 will be removed and hence the Q x f value
will be increased.
2.3.2.6 Twin Domains
Twin domains occur as a result of phase transitions on cooling to room temperature
after any heat treatment processes applied to the ceramic material [20, 53]. The structural
transitions are accompanied with a high degree of lattice strain and this must be
accommodated by a suitable mechanism (twinning, dislocations or cracking) to relieve this
strain [20]. In CaTiO3 perovskites the predominant mechanism of relieving transformation
strain is through twinning of the grains (see Figure 2.11) [54]. If the strain accompanying
the phase transition cannot be relieved by twinning then dislocations will be formed and
cracking will occur if further strain is generated. The relationship between two adjacent
domains is a change in the orientation of the crystal lattice and a boundary is formed
between the two domains [55]. This allows for the domains to be observed using electron
microscopy in combination with a suitable etching or orientation contrast imaging
mechanism.
Figure 2.11: Transmission electron micrograph of twin domains in CaTiO 3
(reproduced from Kipkoech et al [54])
37
The general consensus from the literature is that there are two phase transitions that
are known to cause the formation of twin domains in the microstructure. The first
transition is from cubic
̅
to tetragonal I4/mcm at approximately 1573K and the
second is from the tetragonal structure to orthorhombic Pnma at 1307K [56-57]. Other
studies have suggested that there is an intermediate orthorhombic Cmcm phase between
the tetragonal and orthorhombic phases [58-59]. Guyot et al [58] used drop calorimetry to
investigate the structural transitions on cooling to ambient temperature in CaTiO3 and
suggested three possible phase transitions. These transitions include an orthorhombic
Pbnm to orthorhombic Cmcm in addition to the orthorhombic to tetragonal I4/mcm and
tetragonal I4/mcm to cubic
̅
transitions. The study by Guyot et al. [58] did not
present any structural information from diffraction techniques but came to their
conclusions by assuming the phase transitions would be similar to those observed in
CaGeO3. Kennedy et al. [60] suggested there was no reason for perovksites to experience a
transition to orthorhombic Cmcm in their study of SrZrO3. However, the same author was
able to assign an orthorhombic Cmcm structure between the orthorhombic Pbnm and
tetragonal I4/mcm structures to the patterns of CaTiO3 at temperatures in the 1000-1300oC
range [59].
It is possible to suppress the tetragonal I4/mcm to orthorhombic Pbnm in CaTiO 3
by the additions of either Sr on the A site [61-63] or Fe on the B site [64] of the perovskite
structure. Qin et al [62] and Ball et al [63] studied the effect of composition on the phase
transition temperatures for the Ca(1-x)SrxTiO3 ceramics. It was found that the phase
transition temperatures decreased in a linear trend with increasing strontium content. A
typical structure sequence in this system is the structure sequence for Ca0.6Sr0.4TiO3 was
cubic
̅
to tetragonal I4/mcm at 800oC, tetragonal I4/mcm to orthorhombic Bbmm
(an alternative axes setting for Cmcm) at 500oC and finally transforming to orthorhombic
Pbnm at 400oC [62]. These structural phase transitions are much lower compared to
CaTiO3 which has transition temperatures of 1300oC for the cubic to tetragonal transition
and 1100oC for the tetragonal to orthorhombic transition.
38
Figure 2.12: Refinement of high temperature neutron diffraction data on the basis of
(i) orthorhombic Pbnm and (ii) orthorhombic Cmcm (reproduced from [59])
39
Figure 2.13: Phase transition temperatures as a function of Sr/Fe doping of CaTiO 3
(after [62, 64])
Wang and Liebermann [20, 53] have used in-situ transmission electron microscopy
to explore the orientation relationships of twin domains resulting from the phase transitions
in perovskite materials. They found that there are three types of twin domains that arise as
a result of the phase transitions including (i) reflection twins on the (112) and (110) planes
of the orthorhombic structure (ii) mirror operations about the {110} and {100} cubic
planes and (iii) 90o twins about the [001] direction. Each of the twinning mechanisms are
associated with one of the two structural transitions that occur on cooling to ambient
temperature. The (112) type planes have been associated with the transition from cubic
̅
to tetragonal I4/mcm whilst the (110) and [001] twins are associated with the
transition from tetragonal I4/mcm to orthorhombic Pbnm. Schematic diagrams of the
electron diffraction patterns of the (112) and (110) type twin boundaries are shown in
Figure 2.14 and provide a useful method for distinguishing between the different types of
domains. The (110) type domain boundary will produce electron diffraction patterns with
splitting of the spots (such as the (200)) away from the centre of the diffraction pattern.
40
The (112) type twin also have a distinctive diffraction pattern with apparent cubic
symmetry when the crystal is viewed down the [ ̅ ] zone axis and a hexagonal
arrangement of spots when viewed down the [
̅ ] axis. When viewed in bright field mode
the (112) type twins appear as lamellar intersecting at an angle of 120 o and (110) type
twins intersect at an angle of 90o.
Figure 2.14: Electron diffraction patterns of (112) and (110) type domains in CaTiO 3
(reproduced from [20, 53])
The mechanisms of how the twin domains arise were described by Wang and
Liebermann [20, 53] for MgSiO3. For the (112) type twin domains, the initial distortion is a
small rotation of the oxygen octahedra about the [001] direction of the primitive cubic unit
cell. Each of the TiO6 units parallel to the initial unit is rotated by the same angle whilst the
next unit in the sequence is rotates by the same amount but in the opposite direction. The
resulting symmetry of the unit cell is tetragonal with the exact space group symmetry being
dependent on the composition of the ions but is typically I4/mcm (CaTiO 3) or P4/mbm for
MgSiO3. There is a similar mechanism of rotations for the formation of the (110) type twin
domains. The oxygen octahedra rotate along the [110]pc axis such that the structure
transforms from tetragonal to orthorhombic Pbnm or other structure with lower symmetry.
41
2.3.2.7 Antiphase Domains
Antiphase domains occur when two separate sets of A-site cation displacements
form out of phase and grow until they meet and form an antiphase boundary.
Wondratschek and Jeitschko [55] proposed that the formation of antiphase boundaries can
only form if the resultant structure is a subgroup of the parent structure. An example of a
material that only has antiphase domain boundaries is the Cu3Au alloy. At high
temperature, the atoms are disordered and the alloy has a face-centred cubic structure
(
̅ ) whilst at low temperature the alloy is ordered and has the primitive cubic
̅
structure. It is the loss of translational symmetry from the face centred to primitive cubic
structures that causes the antiphase boundaries. Antiphase domains tend to be curved in
contrast to twin domains which tend to be planar defects. Antiphase domains are also
found in perovskite ceramics such as CaTiO3 and MgSiO3 as studied by Wang and
Liebermann [20, 53] using transmission electron microscopy. They found that the
appearance of antiphase domains was only dependent on the diffraction condition g = hkl
where l is an odd number and not on the use of bright or dark field imaging modes.
Figure 2.15: Antiphase domain boundaries in Perovskites (reproduced from Wang and
Liebermann [20])
42
2.3.3 Engineering of the Crystal Lattice
2.3.3.1 Residual Stress
Since that the Q x f of the ceramics is strongly dependent on the vibrations of the
crystal lattice it is important to consider the effect of residual stress on the microwave
dielectric properties. Ferreira et al. [9] studied the effect of a variety of processing
conditions on the microwave dielectric properties of MgTiO3-CaTiO3 ceramics. They
found that improved Q x f value could be obtained by the reduction in the internal stress by
both uniaxially pressing the powders followed by cold isostatic pressing. The presence of
internal stress is likely to be due to the different thermal expansion coefficients of the two
phase material. Yoo et al [65] found that the Q x f of MgTiO3 ceramics decreased from
220000GHz to 150000GHz when the cooling rate was increased from 1oC/hr to an air
quench. The changes in the properties were attributed to an increase in the dislocation
density causing an increase in the lattice strain. More recently Lee et al. [66] studied the
effect of B2O3 additions on the lattice distortion and microwave dielectric properties of
Ba(Zn1/3Ta2/3)O3. They found that the addition of B2O3 shifted the internal stress state from
compressive to tensile and that there was little change in the internal stress state with
additions of more than 0.25wt% B2O3. They found that the Q x f value decreased with
increases in the B2O3 additions despite the lower stresses and increased degree of 1:2
ordering.
2.3.3.2 Cation Ordering
Cation ordering has been established as probably the most important factor in the
determination of the Q x f of microwave dielectric ceramics. The explanation for this is
that an ordered lattice maximises the distance between cations and reduces the internal
strain in the lattice [67]. The degree of ordering can be measured by using the intensity of
the peaks associated with the formation of a superlattice. In perovskites where the ordering
occurs on the B site this can be determined using Equation 2.16. [12]
43
⁄
[(
√[(
⁄
)]
(2.16)
)]
Where S = the order parameter, I100, I110 and I012 (obs) are the observed intensities for the
(100) (110) and (012) diffraction peaks respectively and I100, I110 and I012 (order) are the
predicted intensities of the same peaks if the lattice is perfectly ordered. The order
parameter varies from 0 for the disordered lattice to 1 for a perfectly ordered lattice.
As the perovskite structure is tolerant to substitutions of different sizes and charges
[68], it is obvious that there are different mechanisms of achieving ordering of the cations.
The ordering in perovskites is often given a notation based on the number of ions required
to complete the ordered structure. For example, Ba(Zn1/3Ta2/3)O3 is given a notation of 1:2
as the ordering is formed by 2 Ta ions for every Zn ion. Davies et al [68] summarised the
different ways ordering can be achieved in perovskites and whether ordering has been
observed in these systems (Table 2.1).
Table 2.1: Effect of B site bond valence on cation ordering (after Davies et al [68])
A Site Valence
1:1 Order
1:2 Order
2:1 Order
1:3 Order
A1+
*
*
Not Possible
*
A2+
A3+
*
or
**
*
indicates mechanism of ordering has not been reported
**
indicates that no ordering was found for investigations of systems based on this formula
The order parameter is usually improved by increasing the amount of time and
kinetic energy available for diffusion of cations. This may be achieved by increasing the
sintering temperature and time, the addition of an annealing process after sintering and by
slower cooling to room temperature. Azough and Freer [69] studied the effect of cooling
rate on the Q x f value of (Zr0.8Sn0.2)TiO4 using transmission electron microscopy and XRay diffraction. They found that the Q x f could be improved from 15000GHz to
44
54000GHz when the cooling rate was varied from an air quench to slow cooling at 1oC/hr.
The change in the degree of ordering was monitored by the observation of the superlattice
peaks in the electron diffraction patterns obtained in the TEM. Kawashima [70]
investigated the effect of annealing time on the microwave dielectric properties of BZT
using X-ray diffraction. The annealing time was varied from 2h to 120h and it was found
that there was an increase in the splitting of the (422) and (226) diffraction peak which was
attributed to an increase in the cation ordering.
Figure 2.16: X-ray diffraction spectra of Ba(Zn1/3Ta2/3)O3 as a function of annealing
time (reproduced from [70])
2.3.3.3 Octahedral Tilting
The ideal structure of perovskite ceramics is the A site cation sits in the centre of
the unit cell with the B site cations occupying the corner positions (see Figure 2.16). The B
site cations are surrounded by six oxygen anions and there are various tilting mechanisms
of these octahedra. According to Megaw [71], the perovskite structure has three
components; the first of these is the tilting of the anion octahedra, second, the displacement
of the A-site cations and finally the distortion of the octahedra. Glazer [72-73] formalised
the notation for the description of the octahedral tilt by consideration of the magnitude and
45
directions of the tilts. The octahedra can either be tilted in phase, antiphase or with no
tilting and these are symbolised by the +, – or 0 superscripts respectively. The
crystallographic axis along which the tilting occurs is denoted by the symbols a, b or c and
the magnitudes of the tilts and if two axes have the same tilts then two of the same symbol
may be used. For example, the a-a-c+ tilt notation means that there are equal antiphase tilts
about the a and b axes and an in phase tilting of the octahedra about the c axis which is of
different magnitude to the a and b axes. The different tilt conformations that the oxygen
octahedra have an effect on the peak present in the x-ray diffraction pattern and these
peaks are summarised in Table 2.2.
Figure 2.17: Ideal structure of CaTiO 3 Perovskite with A site cation (Ca) in blue and
oxygen in red. Ti atoms are in the centre of the octahedra (reproduced from [68])
46
Table 2.2: Tilt symbols, reflection types and conditions for perovskite octahedra tilting
(reproduced from Glazer [73-74]
Tilt Symbol
Reflection Type
Condition
a+
Even-odd-odd
k # l, 013, 031
b+
Odd-even-odd
h # l, 103, 301
c+
Odd-odd-even
h # k 130, 310
a-
Odd-odd-odd
k # l, 131, 113
b-
Odd-odd-odd
h # l, 113, 311
c-
Odd-odd-odd
h # k, 131, 311
The tilting of the oxygen octahedra is important in the temperature dependence of
the dielectric properties of perovskite ceramics. Reaney et al. [74-76] investigated the
effect of distortion on the temperature coefficient of resonant frequency of microwave
dielectric ceramics. Three key regions of behaviour were identified including large τε with
in-phase or anti-phase tilting, small τε for anti-phase tilted and negative τε for untilted
structures (Figure 2.17). The distortion of the lattice can be quantified through the use of
Goldschmidt’s tolerance factor
(2.17)
√
(where t = the tolerance factor, RA is the ionic radius of the A site ion, RB is the ionic
radius of the B-site ion and RO is the ionic radius of oxygen). A tolerance factor of 1
indicates that there is no difference in the sizes of the A and B-site cations whilst any
deviation from unity indicates an increase in the distortion of the lattice. As the difference
between the sizes of the cations becomes larger, the more likely the ceramic will crystallise
into a different structure such as ilmenite as with the case of MgTiO3. The change in the
resonant frequency as a function of temperature is dependent on how much the tilting of
the oxygen octahedra changes. Given that the oxygen octahedra will move less with
increasing distortion, this means that there will be a smaller change in the resonant
frequency and hence smaller change in
.
47
Figure 2.18: τε as a function of tolerance factor (reproduced from Reaney et al. [75])
BaxSr1-x(Zn1/3Nb2/3)O3 (BSZN), Ba xSr1-x(Mg1/3Ta2/3)O3 (BSMT), BaxSr1-x(In1/2Ta1/2)O3
(BSIN), Ba(Nd 1/2Ta1/2)O3 (BNdT), Ba(Gd 1/2Ta1/2)O3 (BGT), Ba(Y 1/2Ta1/2)O3 (BYT),
Ba(Y1/2Nb1/2)O3
Ba(Co1/3Ta2/3)O3
Sr(Ni1/3Ta2/3)O3
(BYN),
(BCoT),
(SNiT),
Ba(Ca1/3Ta2/3)O3
Sr(Co 1/3Ta2/3)O3
Ba(Ni 1/3Ta2/3)O3
(BCaT),
(SCoT),
(BNiT),
Ba(Mn1/3Nb2/3)O3 (BMnN), Ba(Mg1/3Nb2/3)O3 (BMN)
Sr(Ca 1/3Ta2/3)O3
Sr(Zn 1/3Ta2/3)O3
Ba(Mn 1/3Ta2/3)O3
(SCaT),
(SZT),
(BMN),
Sr(Mg1/3Nb2/3)O3 (SMN),
Ba(Ni1/3Nb2/3)O3 (BNiN), Sr(Ni 1/3Nb2/3)O3 (SNiN), Ba(Co 1/3Nb2/3)O3 (BCoN).
2.4 Review of Microwave Dielectric Properties of Ceramics
2.4.1 Review of MgTiO3 Microwave Dielectric Ceramics
MgTiO3 is an attractive material to combine with CaTiO3 because of the negative τf
of -56ppmK-1 and high Q x f of 56000GHz [9] when made by the conventional mixed
oxide route. When CaTiO3 and MgTiO3 are combined it is possible to achieve properties of
εr = 21, Q x f = 56000GHz and τf = 0ppmK-1 [9]. This value can be enhanced by changing
from the conventional mixed oxide route to a Pechini method as studied by Ferreira et al
48
[9] which substantial improves the Q x f value to approximately 160000GHz but has little
effect on the relative permittivity or the τf of the ceramics. The improvement of the Q x f
can be attributed to the removal of impurities at the grain boundaries or those that sit in the
crystal lattice and can disrupt lattice vibrations. Slight improvements to the Q x f can be
made by small additions of Nb5+ to the MgTiO3 base phase. Ferreira et al [21] found that
the Q x f could be improved from 166400GHz to 166900GHz with addition of 1at% Nb5+
but when this is increased to 2at% Nb5+ the Q x f rapidly decreases to 53600GHz. Similar
results are achieved with similar doping levels of Fe3+ and La3+ whilst doping with Co2+ or
Cr3+ produce less severe falls in the Q x f value. The results of these papers are
summarised in Table 2.3.
Table 2.3: Microwave Dielectric Properties of MgTiO3 Ceramics with Different Additions
(reproduced from [21])
Composition
Q x f (GHz)
MgTiO3
17
166400
MgTiO3-0.5% Nb5+
17.7
166240
MgTiO3-1% Nb5+
17.7
166960
MgTiO3-2% Nb5+
16.9
53600
MgTiO3-1% La3+
18.1
47000
MgTiO3-1%Cr3+
17.4
119400
MgTiO3-1%Fe3+
17.5
55950
MgTiO3-1%Co2+
17.4
137940
A recent study by Kuang et al [77] investigated the effect of Ta5+ additions on the
microwave dielectric properties of MgTiO3 ceramics. It was found that small amounts of
Ta5+ (< 2mol%) increased the Q x f value from 100000GHz to approximately 110000GHz.
The change in the Q x f value was attributed to Ta5+ compensating for the generation of
oxygen vacancies formed as a result of Ti4+ reduction. Other papers have revisited the
compositions listed in Table 2.3. For example, Li et al [78], achieved very high Q x f of
49
244500GHz for (Mg0.95Co0.05)TiO3 prepared by reaction sintering. Reaction sintering is
where the raw powders are mixed, pressed and sintered without an intermediate calcination
step. The particle size remains small and the reactivity of the particles and it may be
possible to control the properties by altering the microstructure. Similar high Q x f values
were also observed in Mg0.95Zn0.05TiO3 [79]
The crystal structure of MgXO3 (X = Ti, Si) is of considerable interest to both
materials scientists and geologists because these materials are important in microwave
frequency devices and are minerals that are found in the Earth’s mantle [53, 80-82]. The
structure of the MgXO3 (X = Ti, Si) is ilmenite and has a rhombohedral structure with the
̅ space group symmetry at room temperature and pressure [80-82]. A common problem
that occurs during the fabrication of MgTiO3 ceramics by the mixed oxide route is the
formation of secondary phases due to segregation of the different oxide components in the
system [83]. If there is deficiency of MgO then the secondary phase will be MgTi 2O5
whilst Mg2TiO4 will be formed if the MgO is in excess. The structure of MgTi2O5 [81] is
orthorhombic Bbmm whilst Mg2TiO4 has a structure of Fd3-mz [83]. There have been
several research papers into producing a single phase MgTiO3 ceramics [78, 84]. In
addition to reaction sintering [78] phase analysis results have been achieved been using
alternative precursor powders in the fabrication of MgTiO3 such as substituting (MgCO3)4Mg(OH)2-5H2O for MgO [84]. Only properties for MgTiO3 composite ceramics were
reported so it is difficult to draw direct comparisons between different reports on the
properties of MgTiO3.
2.4.2 Review of CaTiO3 based Microwave Dielectric Ceramics
2.4.2.1 CaTiO3-MgTiO3 Composites
MgTiO3 can be used as a component to tune the
of CaTiO3 through zero and to
increase the Q x f. The crystal structures of MgTiO3 is rhombohedral
̅ whilst the crystal
structure of CaTiO3 is orthorhombic Pbnm which means that there is a composite
microstructure containing two or more separate phases. Ferreira et al. [9] have shown that
the microwave dielectric properties of CaTiO3-MgTiO3 composites are sensitive to the
50
processing route used in the fabrication of the ceramics. For a composition of 0.04CaTiO 30.96MgTiO3, the Q x f of the ceramics made by the mixed oxide route was 56000GHz
whilst when the ceramics were made by a Pechini method the Q x f was increased to
85600GHz [9]. The effect on the processing route on the relative permittivity of the
ceramics is less profound. For the composition of 0.04CaTiO3-0.96MgTiO3 the relative
permittivity of the mixed oxide ceramics was 18.2 whilst the ceramics made by the Pechini
method had a relative permittivity of 19.1. The improvements in the microwave dielectric
properties of the ceramics due to the use of the Pechini route was attributed to the
reduction in the impurities present in the ceramics. Most of the recent work on CaTiO3MgTiO3 has focused on reducing the sintering temperature of the ceramics. Sintering aids
that have been used include ZnO-B2O3-SiO2 [85], ZnO [86] V2O5 [87] and Bi2O3 [88]. For
example, the properties were found to be improved to 18.9 for the εr and the Q x f to
69000GHz compared to 17 and 56000GHz respectively [9]. The improvements in the
properties were attributed to improvements in the densification and reduction in secondary
phases at a sintering temperature of 1300oC.
2.4.2.2 CaTiO3-RE(Ga, Al)O3
A common component used for tuning the τf closer to zero is to use rare earth
aluminate ceramics as they have τf values which are negative and, with the exception of
GdAlO3 have moderately high Q x f (>40000GHz) [33]. An initial study by Suvorov et al
[90] determined that 30 mol % of the rare earth aluminate was required to tune the τf close
to zero. The results from this initial study were promising with a mid-range set of
properties of
increasing the
~ 45, Q x f of 40000GHz and
being approximately 0ppmK-1. A way of
of a ceramic is to introduce a different ion with a higher polarizability to
Al3+ and Ga3+ is an ideal candidate for this because of its similar ionic radius to Al3+. It was
found that the relative permittivity and
was not significantly affected by the total
substitution of Ga for Al but the Q x f was moderately reduced. For example
Ca0.7Ti0.7La0.3Al0.3O3 the Q x f is 30000GHz and this falls to 27000GHz when Ga is used
and the explanation for the reduction in the properties is the formation of an
inhomogeneous microstructure [89].
51
The studies that followed the initial investigations of Suvorov et al. mostly
involved improving the processing conditions required to produce dense ceramics. In the
initial study, long calcination times (20 hours) and high sintering temperatures (>1400 oC)
and times (>10 hours) were required. Ravi et al. [35] found that by adding 0.25wt% Al2O3
to the calcined powders, it was possible to reduce the calcination and sintering times to 4
hours without compromising the densification or properties of the ceramics. A second
possibility to reduce the processing temperatures and times by reducing the particle size by
extending the milling time. Zheng et al [90] used attrition milling to minimise the particle
size of powders based on CaTiO3-LaGaO3 prior to calcination. It was found that the use of
attrition milling introduced a pyrochlore secondary phase of La2Zr2O7 that was formed as a
result of contamination from the milling media used. It is thought that this phase may
contribute to degradation of the Q x f of CaTiO3-LaGaO3 which emphasises the need for
careful processing of powders to ensure optimal properties.
2.4.3 Complex Perovskites based on Calcium
The perovskite structure is known to be tolerant to additions on both the A and Bsites [68] and this offers opportunities for tuning of the microwave dielectric properties of
CaTiO3. The following sections describe some of the studies that have been undertaken
and the properties that can be achieved in these systems.
2.4.3.1 Structures and Microwave Dielectric Properties of A-site Modified
CaTiO3 Ceramics
The high τf and low Q x f of CaTiO3 are the key factors that prevent it being from
commercially deployed alone. It is possible to tune the τf closer to zero by introducing
cation vacancies into the lattice. One of the first reports on the dielectric properties of
cation deficient rare earth ceramics was made by MacChesney and Sauer [91] on the
La2O3-TiO2 system. They found that for the target phase of La2/3TiO3 the phase
decomposed into La2Ti2O7 and La4Ti9O24. The microwave dielectric properties of
La2/3TiO3 were later investigated by Suvorov et al [92] and it was found that the properties
were severely degraded by the presence of the La2Ti2O7 and La4Ti9O24 phases. A number
52
of compounds have been used to stabilise the La2/3TiO3 phase and prevent the formation of
La2Ti2O7 and La4Ti9O24. Such additions have included CaTiO3 [93], NiO [94], LaAlO3
[95] and by modification of the oxygen deficiency [96]. La has been swapped for Nd [15,
97] or Sm [98-99] and details of some of the studies will be described below.
There have been several reports on the crystal structure of Ca (1-x)Ln2x/3TiO3
ceramics. For Nd based ceramics both Yoshii [96] and Yoshida et al [15]. reported an
orthorhombic Pmmm structure based on lattice parameters of a = ac b = ac and c = 2ac.
Other structures that have been reported include orthorhombic Cmmm and monoclinic
C12/m for Nd2/3TiO3 stabilised with NdAlO3 [101]. Kagomyia et al [102] suggested on
orthorhombic structure from the X-ray diffraction patterns of Na(1-x)Nd2x/3TiO3 but did not
attempt to assign a spacegroup to this structure. Azough et al. [103] used high resolution
TEM and synchrotron XRD to study the spacegroup of 0.9La2/3TiO3-0.1LaAlO3. They
found that the structure of this ceramic could be best described in terms of an orthorhombic
Cmmm structure with all three axes doubled due to octahedral tilting. In a later study
[104], it was found that sharing of the 4g sites was a mechanism for the mitigation of strain
from phase transformations in these materials.
For other rare earth cation deficient materials there is appears to be a general trend
in the position of the peak in the microwave dielectric properties. In Ca(1-x)Sm2x/3TiO3 the
peak in Q x f can be found at x = 0.6 with a Q x f of 15000GHz which rapidly decreases
for x > 0.6 [98-99]. The change in the properties of Ca(1-x)Sm2x/3TiO3 ceramics is perhaps is
the easiest to explain due to the formation of Sm2Ti2O7 at this composition [98-99]. It is
not so clear why Ca(1-x)Nd2x/3TiO3 ceramics have a peak in the Q x f whilst Ca(1x)La2x/3TiO3
ceramics show and increase followed by a region of no change in the Q x f
value [93]. There is an disorder-order transition for Ca(1-x)La2x/3TiO3 with ordering
increasing for large additions of La3+ which may explain some of the changes in the Q x f
value [105] However there is only minimal increase in the Q x f with increase in the order
parameter.
The cation deficient rare earth ceramics have also been extensively used in
composite microwave dielectric materials. Huang et al. have studied many different
examples of Ca(1-x)Ln2x/3TiO3-MTiO3 composite ceramics including M = Mg, (Mg-Zn)
53
[106] or (Mg-Co) [107], Ln = Sm or La [108-109] and by changing the stoichiometry of
the MTiO3 phase to M2TiO4 [110] They have also done a considerable amount of work on
lowering the sintering temperature of these materials by the addition of sintering aids such
as B2O3, V2O5, ZnO or CuO [111-114]. Although it is useful to lower the sintering
temperature of these ceramics without seriously degrading the properties some of the
results in these studies do not seem realistic. The most interesting results from these studies
is the dependence on the Q x f on the sintering temperature. Although it is likely that Q x f
would be degraded by porosity it is unlikely that a 30oC difference in the sintering
temperature would have an appreciable effect on either the cation ordering or the porosity
to give a 30000GHz increase in the Q x f value.
2.4.3.2 Structure and Microwave Dielectric Properties of B-site Modified
CaTiO3 Ceramics
2.4.3.2.1 Ca(B1/3B2/3)(1-x)TixO3
Fu et al [115] used (Mg1/3Ta2/3) on the B-site of the perovskite structure to tune the
microwave dielectric properties of CaTiO3. Whilst CaTiO3 (CT) has a low Q x f value of
6000GHz [10], Ca(Mg1/3Ta2/3)O3 (CMT) has a much higher Q x f value of 60000GHz
[116]. Initial additions of CMT caused the Q x f to fall to approximately 1000GHz for 30%
addition before rising to 60000GHz for pure CMT. The rate of increase of the Q x f as a
function of composition slowed after additions of 65% CMT. Monitoring of the peak
widths of the Ag Raman mode of CMT-CT revealed that in the same range of compositions
there was an increase in the ordering of the cations in the lattice. Although the ordering
degree is increased, it is thought that the ordering is still over a short length range (i.e.
ordering over a few nanometres). Huang et al [117] studied the similar system of CaTiO3Ca(Mg1/3Nb2/3)O3 but did not find the same trend in the Q x f value as Fu et al [116] but
did not present any Raman spectroscopy to compare the two systems.
54
2.4.3.2.2 Ca(B1/2B1/2)(1-x)TixO3
The effect of CaTiO3 additions on the structural and microwave dielectric
properties of Ca(Al1/2Nb1/2)O3 were investigated by Levin et al. [118]. In particular they
used high temperature diffraction techniques to explore the order-disorder transitions in the
structure. They found that Ca(Al1/2Nb1/2)O3 remained ordered up to 1650oC but the
transition temperature is rapidly depressed by the addition of CaTiO3. The optimal value of
the Q x f was 48400GHz and was achieved for a composition of 0.33CaTiO30.67Ca(Al0.5Nb0.5)O3. According to the neutron diffraction and Raman experiments, this is
the maximum amount of CaTiO3 which can be added to Ca(Al0.5Nb0.5)O3 without forming
a disordered arrangement of cations in the lattice.
2.4.3.3 Combined Doping on both A-site and B-site
Zheng et al [119-120] have explored the ordering in a variety of CaTiO3 based
ceramics including solid solutions with additions of NdAlO3, LaGaO3, Sr(Mg1/3Nb2/3)O3,
CaZrO3 and other ceramics using Raman spectroscopy. At room temperature,
Sr(Mg1/3Nb2/3)O3 has a hexagonal
̅
structure with an 1:2 ordered arrangement of the
Mg2+ and Nb5+ cations giving 9 modes in the Raman spectra. It was found that the width of
the mode at 825cm-1 increased with additions of CaTiO3 indicating a disruption in the long
range ordering of the cations. It was postulated that the disruption of the long range
ordering and the subsequent presence of short range is responsible for the degradation of
the Q x f value. Kipokoech et al [54] investigated the effect of CaTiO3 additions on the
microwave dielectric properties of La(Mg1/2Ti1/2)O3 (LMT). It is was found that there a
complete solid solution across the whole composition range but the presence of 1:1
ordering of the Mg/Ti ions was only detected for up to 30% additions of LMT.
2.5 Objectives of the Present Study
The mechanisms that affect the microwave dielectric properties of Ca(1-x)Nd2x/3TiO3
have not been fully established by reports previously published in the scientific literature.
In the course of this investigation, the structural properties of Ca(1-x)Nd2x/3TiO3 will be
55
determined using high resolution techniques including synchrotron X-ray diffraction and
high resolution transmission electron microscopy. In order to make correlations between
the microstructure and the microwave dielectric properties, scanning electron microscopy
will be used to determine the role of twin domains. The microstructures of perovskite
microwave dielectric ceramics are known to be dependent on the structure sequence on
cooling to room temperature. The structure sequence in Ca(1-x)Nd2x/3TiO3 will be explored
using a combination of Raman spectroscopy and X-ray diffraction. The role of internal
stresses on the microwave dielectric properties of ceramics is not well established and this
will be explored through the fabrication of composite ceramics of MgTiO3 and
Ca0.61Nd0.26TiO3
56
3 Experimental Methods
3.1 Sample Preparation
3.1.1 Powder Preparation
All samples were prepared using the conventional mixed oxide route from high
purity metal oxide powders which are listed in Table 3.1. MgO and Nd2O3 powders are
known to be hygroscopic and were dried at 900oC for 6 hours prior to weighing. Starting
powders were weighed according to the desired stoichiometry and mixed in polypropylene
bottles for 24 hours using propan-2-ol and ZrO2 milling media. Slurries were dried at 85oC
for 24 hours prior to calcination at 1100oC for 4 hours in air. After calcination but prior to
sintering powders were re-milled for 24 hours and any minor additions to the composition
were made at this stage. Powders were pressed into pellets with initial dimensions of
20mm diameter and 12mm thickness using a uniaxial hydraulic press operating at a
pressure of 25MPa. Conventional sintering of the powders was at 1450oC-1500oC Vecstar
(Chesterfield, UK) box furnace equipped with a CAL9500 temperature controller (Hitchen,
UK) for 4 hours in air and the heating rate was kept at 180oC/hr. Samples were
subsequently cooled to room temperature at rates of 15oC-300oC/hr.
Table 3.1: List of powders used in ceramic preparation
Powder Name
Chemical Formula
Supplier
Purity (wt%)
Calcium Carbonate
CaCO3
Solvay
99.5
Neodymium Oxide
Nd2O3
AMR Limited
99.9
Titanium Oxide
TiO2
Tronox
99.9
Magnesium Oxide
MgO
Alfa Aesar
99.9
Manganese Oxide
Mn2O3
Sigma Aldrich
99.5
57
3.1.2 Special Preparation Conditions
Samples for spark plasma sintering require a small particle size (<1µm) and a
narrow particle size distribution to ensure powders are sufficiently reactive to aid
densification in short periods of time (< 10 minutes) [Z Zhao, private communication]. In
this study powders for spark plasma sintering were prepared by attrition milling of the
calcined powders using an attrition mill (Union Process, USA). The calcined powder was
crushed using an agate pestle and mortar to aid the dispersion of the powder in deionised
water. A further aid to dispersion was by the use of Dispex N40 (BASF, Germany).
Powders were milled using 1mm diameter zirconia beads for 24 hours with milling rate of
400rpm. After milling the slurry containing the powder was separated from the zirconia
milling media by passing the slurry through a sieve and washing of the beads with
deionised water. The slurry was frozen using liquid nitrogen and dried under vacuum. The
progress of the attrition milling was monitored using particle size analysis. The dried
powders were spark plasma sintered using a Dr Sinter 2050 (Sumitomo Coal Mining Co.,
Tokyo, Japan) at temperatures in the 1150-1450oC for 10 minutes at a pressure of 50100MPa.
Figure 3.1: Schematic diagram of a spark plasma sintering furnace (reproduced from
[121])
58
Table 3.2: List of Compositions prepared
Composition
Additives
Sintering
Cooling Rates
Temperatures
CaTiO3
0-1wt% TiO2
1100-1500oC
180oC/hr (Conventional)
200oC/min with 100MPa
Pressure (SPS)
Ca0.79Nd0.14TiO3
0.25wt%
1500oC
180oC/hr
1500oC
180oC/hr
1450oC
15-300oC/hr
1450oC
180oC/hr
1450oC
180oC/hr
1450oC
180oC/hr
1450oC
15-300oC/hr
1450oC
180oC/hr
1450oC
180oC/hr
1450oC
180oC/hr
Mn2O3
Ca0.7Nd0.2TiO3
0.25wt%
Mn2O3
Ca0.61Nd0.26TiO3
0.25wt%
Mn2O3
Ca0.52Nd0.32TiO3
0.25wt%
Mn2O3
Ca0.43Nd0.38TiO3
0.25wt%
Mn2O3
Ca0.1Nd0.6TiO3
0.25wt%
Mn2O3
0.8MgTiO3-
0.25wt%
0.2Ca0.61Nd0.26TiO3
Mn2O3
0.6MgTiO3-
0.25wt%
0.4Ca0.61Nd0.26TiO3
Mn2O3
0.4MgTiO3-
0.25wt%
0.6Ca0.61Nd0.26TiO3
Mn2O3
0.2MgTiO3-
0.25wt%
0.8Ca0.61Nd0.26TiO3
Mn2O3
59
3.1.3 Sample Preparation for Characterisation
Discs of approximate thickness of 1-2mm were cut from the pellets using an
Accutom diamond cut off wheel and then prepared for characterisation. For conventional
X-Ray Diffraction analysis (XRD) samples were ground on 240, 400, 800 and 1200 grade
SiC grinding papers for approximately 2 minutes per grinding stage. For Scanning Electron
Microscopy (SEM), flat plate synchrotron XRD and Raman spectroscopy the samples were
ground in the same manner as the samples for XRD and then subsequently polished using
6µm and 1µm diamond pastes. Final polishing was with Oxide Polishing Suspension
(OPS) for 15 minutes prior to etching in a hot solution of 80% H2SO4 in water to reveal
domain and grain boundaries. Samples for Transmission Electron Microscopy were
prepared by both the mechanical thinning and crushing method. For the crushing method,
samples were ground into a fine powder using an agate pestle and mortar and dispersed in
chloroform. The suspension of chloroform and ceramic particles was added drop-wise to
3mm copper grids with holey carbon film. The thinning method consisted of three stages
of which the first was grinding a 1mm slice of a given composition to a thickness of
approximately 200µm using P240, 400, 800 and 1200 grade SiC papers. The thinned
samples were washed in acetone and dimpled to an approximate thickness of 30µm.
Samples were mounted onto molybdenum grids and final perforation was using argon ion
milling (Gatan PIPS)
3.2 Characterisation Techniques
3.2.1 Particle Size Analysis
The particle size analysis technique is based on the fact that the angle at which the
light is scattered from a particle is related to the size of the particle. As the particle size is
decreased then the scattering angle will increase and the intensity of the scattered light on
the detector will decrease. It is important to check the particle size of the powders used in
ceramic processing because the particle size affects the reactivity of the system and is a
factor controlling the grain size of the final microstructure. The particle size analysis of the
starting and calcined powders was performed using a Malvern Mastersizer Microplus
equipped with a HeNe laser emitting light of wavelength 632.8nm. Powders were
60
dispersed in water and Dispex N40 was used as the dispersant to ensure representative
samples were used. The sizing of the particles was based on using approximate refractive
indices of the powders and the stated detection limit was between 0.05µm-550µm. Given
that the particle size analysis software assumes a perfectly spherical particle in the
calculations of the particle size, the particle shape was assessed using scanning electron
microscopy.
Figure 3.2: Schematic diagram of laser diffraction for particle size analysis equipment
(reproduced from ISO13320 [122])
3.2.2 Pellet Densification
The densification of the ceramic pellets was assessed using a geometrical method
including the mass and dimensions of the samples. The mass was measured using an
Ohaus Adventurer Pro balance accurate to ± 0.001g and the dimensions using a
micrometer accurate to ± 0.001mm. The density was subsequently calculated using
Equation 3.1:
(3.1)
Where m = mass and V = volume of cylinder
where r = sample radius and t =
sample thickness. The densities of the pellets were compared to the theoretical density of
the samples in order to assess the degree of porosity in the sample. The theoretical density
61
of a given composition is calculated from Equation 3.2 using the lattice parameters as
measured by XRD.
(3.2)
Where Z = number of formula units per unit cell (Z = 4 for CaTiO3) M = mass of 1
formula unit V = unit cell volume and NA is Avogadro’s constant (6.023x1023 atoms/mol)
3.2.3 X-Ray Diffraction
3.2.3.1 Theory
The main use of X-Ray diffraction (XRD) is to determine the structure of
crystalline materials. X-ray photons interact with matter and for the majority of scattering
angles there is destructive interference due to the wave like nature of photons. In some
cases there is constructive interference from the crystallographic planes and this results in
peaks in x-ray intensity on the detector. There will only be constructive interference if the
path difference between diffracted photons from two adjacent planes is an integral number
of wavelengths. The spacing between the planes can be determined by Bragg’s law
(Equation 3.3) and taking into account for the peak position and radiation source
wavelength. The position of the peaks in the diffraction pattern depends on the structure,
lattice parameters and symmetry of the crystalline material and the intensities of the peaks
are determined by the scattering power of the atoms. Information that may be obtained
from X-ray diffraction patterns of perovskites includes the composition of specimens and
the structure of the phases including tilt system and the presence of anti-phase domains.
62
Figure 3.3: Schematic diagram of Bragg’s law (reproduced from Cullity [123])
(3.3)
where n = order of the plane,
two planes and
is the wavelength of the radiation, d is the spacing between
is the scattering angle
When electrons are accelerated by a magnetic field to close to the speed of light
emission of radiation in the X-ray region of the electromagnetic spectrum can occur. The
advantage of using synchrotron XRD analysis is that highly accurate lattice parameters and
atomic coordinates can be determined due to the superior quality of diffraction patterns
compared to conventional laboratory X-ray sources. The improvement in the resolution
allows increased accuracy in the determination of the splitting, positions, widths and
relative intensities of the peaks in the diffraction spectra. The increase in quality is due to
the selection of a single wavelength using a monochromator and the high flux of photons
incident on the detector. The high flux of X-ray photons in a synchrotron is provided by
undulator and a collimator produces a beam with a small divergance.
The X-ray diffractometer used in this study for room temperature structure
determination was a Philips Automated Powder Diffractometer (APD) using a Cu X-Ray
radiation source with wavelength of 1.54096Å. The scan range was between 10-85o 2Θ
63
with a step size of 0.05o 2Θ and a counting time of 18.5s/step. Post scanning analysis
included phase determination using Philips X’Pert High score plus and refinement of the
lattice parameters using Rietveld refinement (TOPAS 4.2) [124, 125]. For synchrotron
analysis samples were ground, polished and etched (see section 3.2.4) or crushed into a
fine powder. The fine powders were packed into a boron glass capillary prior to
synchrotron analysis. All synchrotron studies were carried out at the I11 beamline at the
Diamond light source in Harwell, Oxfordshire, UK and the wavelength used was in the
0.825992-0.827442Å
range.
For
the
temperature
dependent
measurements
the
diffractometer used was a Philips X’PERT equipped with an area detector and an Anton
Paar furnace attachment. A polished sample was placed in a 15mm diameter and 1mm
deep Al2O3 crucible and aligned to the correct height by a slitting method. The slitting
method involves moving the height of the sample holder up until the intensity of the beam
is 50% of the maximum beam intensity emitted by the Cu anode. The temperature range in
this experiment was between 25-775oC in steps of 50oC with a heating rate of 10oC/min.
The sample was held at a given temperature for 10 minutes to equilibrate prior to scanning
between angles 20-85o 2Θ for a duration of 45 minutes.
Figure 3.4: Segment of temperature control program for high temperature x-ray
diffraction
64
3.2.3.2 Rietveld Analysis
Rietveld refinement is a method of analysing the structural characteristics of
materials by a non-linear least squares approach [124] and TOPAS 4.2 [125] is an
implementation of the principles of Rietveld refinement using a graphical user interface
(GUI). Refinement of the diffraction spectra was by using the structures reported in the
literature and modifying the input to match the exact nature of the material being
examined. For example, Ca0.1Nd0.6TiO3 has not been studied in this exact form before so it
was required that the crystallographic information file (CIF) of Nd2/3TiO3-NdAlO3 was
modified to suit the purposes of this study. The Lorentz-Polarisation factor and the number
of background functions were fixed at 17 and 5 respectively for radiation from a copper
anode and 90 and 20 respectively for synchrotron radiation. The Philips APD X-ray
diffractometer has variable divergence slits with an irradiated length of 12mm and the
effect of this was taken into account in the refinement of the X-ray diffraction spectra.
3.2.4 Scanning Electron Microscopy and Electron Microprobe Analysis
The scanning electron microscopes used in this study were the Zeiss EVO60
VPSEM or the Philips XL30 FEGSEM both operating at an accelerating voltages of 820kV. To reveal features of the microstructure of the ceramics, specimens were either
thermally or chemically etched. Thermal etching was at a temperature approximately
200oC below the sintering temperature of the specimen for 12 minutes. Chemical etching
of the samples was by warm 80 vol% H2SO4-20 vol% H2O for approximately 30 seconds.
Specimens for SEM examination were mounted on aluminium stubs using carbon leit tabs.
Due to the low electrical conductivity of the samples, a carbon coating was applied and
earthed using Acheson Silver electrodag paint to prevent charging. From the SEM images
it was possible to determine the grain and domain sizes and to examine the different phases
present in the microstructure.
Electron microprobe analysis was performed at the University of Leoben, Austria
using polished and carbon coated samples. The microscope was a JEOL JXA-8530F
65
operating at an acceleration voltage of 15kV with a probe current of 10nA with X-Rays
detected using a wavelength dispersive analyser. The calibration standards used in this
study were ilmenite for Fe and Mn, NdSi for Nd content, apatite for Ca, and a rutile
standard for Ti content. Two types of analysis were performed including spot analysis and
mapping analysis in which an area of approximate dimension 120 x 120µm was surveyed.
Scanning electron microscopy involves exposing a sample to a focussed beam of
electrons under vacuum. There are several interactions that can occur on exposure to the
beam including the generation of secondary electrons, electrons backscattered from the
sample surface and x-rays (see Figure 3.6) [128]. The electrons that are backscattered from
the sample are able to give atomic number contrast and hence can be used to determine the
number of phases because heavier elements will scatter electrons more than lighter
elements. The topographic contrast mechanism arises because secondary electrons are
generated only in the upper 2nm of the surface of the sample. Another application of the
backscattered electrons is orientation contrast to image twin domains.
Figure 3.5: Interactions of the electron beam with solid sample in the scanning
electron microscope (reproduced from Goodhew et al [126])
Chemical analysis of the sample can be performed using the X-rays generated from
the interaction of the sample with the electron beam. The X-rays are generated as a result
of electrons undergoing transitions between energy levels of the atom. The energies of the
X-rays are characteristic of the electron orbital and element from which they originate.
This technique is known as energy dispersive spectroscopy and is the chemical analysis
method employed by the Zeiss EVO60 SEM VPSEM at Manchester. The electron
66
microprobe analyser works on the principle of allowing only a specified wavelength of Xray radiation to be detected. X-rays emitted by the sample are diffracted by a curved crystal
onto the detector as illustrated in Figure 3.7.
Figure 3.6: Principle of operation of wavelength dispersive spectroscopy in the
electron microprobe analyser (reproduced from Goodhew et al [126]).
3.2.5 Transmission Electron Microscopy
Transmission electron microscopy is a useful technique for studying perovskites
because of the possibility of imaging the sample using different orientations. This ability is
useful because it allows for the imaging antiphase domain boundaries which only appear in
contrast in given orientations. It also allows for the orientation relationship at the twin
walls to be determined through the use of selected area electron diffraction. The
mechanism of operation of the TEM is the emission of high energy electrons from a
tungsten or LaB6 filament by passing a high voltage (200-300kV) through the filament.
The electrons are focussed into a thin beam using a condenser lens before passing through
the sample. The contrast in the image can be enhanced using an objective aperture or a
diffraction pattern of the region can be observed using a selected area diffraction aperture.
The selected area diffraction patterns are useful for determining how two adjacent twins
are related because the diffraction pattern of the boundary region will be a superposition of
the diffraction patterns of the individual twins. The transmission electron microscopes used
67
in this study were the Philips CM200 and the Tecnai G2 FEGTEM operating at 200kV and
300kV respectively. Samples were secured in a double tilt holder using a beryllium ring
and manipulated such that the sample was aligned to one of the major zone axes.
Figure 3.7: Optics of a transmission electron microscope (reproduced from Williams
and Carter [127])
3.2.6 Aberration Corrected Microscopy
The resolution of TEM is chiefly limited by aberrations of the lenses used to focus
the electrons into a narrow beam. Spherical aberration is where the electrons are too
sharply diffracted near to the edge of the lens and this causes blurring of the image. An
advantage of a technique called high angle annular dark field (HAADF) imaging is that it
allows for Z contrast imaging. In this technique the intensity of a spot on a lattice image is
proportional to the mean atomic number in a given column of atoms. Using this technique
it is possible to directly observe the distribution of cations and vacancies in the lattice. The
atomic columns rich in heavier atoms will appear as bright spots whereas columns rich in
lighter atoms or vacancies will appear dark. The aberration corrected microscopy was
performed at Daresbury Laboratory in Warrington UK, using SuperSTEM 2. SuperSTEM
68
2 is a Nion Ultrastem 100 equipped with a C6 astigmatism correction and operating at an
accelerating voltage of 100kV. The SuperSTEM 2 unit is fitted with a UHV Enfina EELS
spectrometer for recording of atomic resolution EELS linescans.
Figure 3.8: Schematic of an scanning transmission electron microscope (reproduced
from [127])
Electron energy loss spectroscopy involves the measurement of the energy of the
electrons that have been transmitted through the sample. The features of an EELS spectra
is the zero loss peak corresponding to the electrons that have not lost any energy and the
phonon peak which corresponds to the energy lost due to lattice vibrations. The remaining
peaks correspond to energy losses that are characteristic of the chemical composition of an
element. When EELS is used with atomic resolution it is possible to determine the
dominant element in a given atomic column [128]
3.2.7 Raman Spectroscopy
The Raman microscopes used in this study were the Renishaw Raman Microscope
using the 632.9nm line of a HeNe laser or a Jvon-Horiba using the 632.9 nm line of a
HeNe laser. Each result was the sum of three spectra collected for 10s over the 1501500cm-1 range and the laser beam was focussed onto polished samples using either a x50
69
(spot size = 4µm) or x100 (spot size = 1µm) objective lens. For the in-situ measurements
of Raman spectra as a function of temperature using a Linkam THMSG600 temperature
stage operating in the temperature range of 77-873K and spectra were measured every
20K. For the dependence of the intensity on the angle of rotation of the sample stage, cross
polarizers were used and the spectra were taken every 10o between 0-360o rotation.
Raman spectroscopy is a technique for the investigation of the vibrational modes of
matter using the measurement of inelastic scattering of photons in and around the visible
light portion of the electromagnetic spectrum. On interaction with matter, the electric field
component of the photon will distort the electron clouds of the matter. This distortion will
only have a Raman active effect if there is a change in the polarizability of the matter as a
result of the interaction. Raman spectroscopy can be used to investigate a variety of
different effects in matter including composition transitions, structural transitions including
cation order-disorder transitions and changes in the nature of bonding. The intensity and
width of Raman peaks are also sensitive to the orientation of the crystallite and the
presence of internal stresses respectively. The information that can be obtained from
Raman spectroscopy is important for the understanding of changes in microwave dielectric
behaviour as both involve the vibration of the lattice. By monitoring changes in the peak
positions and peak widths of the Raman spectra it is possible to monitor the changes in the
bonding of the structure which is a key factor in the determination of the microwave
dielectric properties.
3.2.8 Dielectric Property Measurements
All microwave dielectric property measurements were made using a silver coated
aluminium cube cavity of 25mm in length. The samples were placed in the cavity on either
polyether-ether-ketone or Al2O3 supports and property measurements were made in the 24GHz range. The resonant frequency (TE011 mode) and Q value of the samples was
measured using a Hewlett Packard 8720ET network analyser. Using the Q and the resonant
frequency it was possible to obtain values for the relative permittivity and the Q x f value
of the samples. The temperature coefficient of resonant frequency was determined by the
measurement of the resonant frequency using the cavity method in the -10oC to +60oC
range.
70
Figure 3.9: Diagram showing setup for microwave dielectric property measurements
(reproduced from Sheen [129])
71
4 Starting Powder and Calcined Powder Characterisation
4.1 Starting Powders
4.1.1 Calcium Carbonate (CaCO3)
The CaCO3 powder was white in its as received state and its stated purity was
99.50%. Analysis of the X-Ray diffraction spectra (Figure 4.1) revealed that the powder
was single phase CaCO3 with a rhombohedral structure and
space group symmetry.
The lattice parameters were refined using TOPAS 4.2 and were found to be a = 4.989Å and
c = 17.066Å respectively. SEM examination of the powder revealed that the CaCO 3
particles (Figure 4.3(a)) were mostly cuboids with a possible bimodal distribution of
particle sizes with sizes ranging from 2μm to 20μm. Agglomeration of the particles was
also observed. The particle size analysis confirms the findings of the SEM analysis
showing three modes in the particle size distribution. There are modes at 0.21μm, 0.39μm
128
306
036
n
312
211
122
214
208
030
20
217
202
024
018
116
110
113
006
012
104
and 33.9μm and 90% of the particles are below 50.77μm.
Figure 4.1: X-ray diffraction spectra of CaCO3
72
4.1.2 Neodymium Oxide (Nd2O3)
The Nd2O3 powder was lilac in colour in its as received state with a stated purity of
99.9%. Nd2O3 is known to be hygroscopic and the powder changes to a white colour when
water and carbon dioxide is adsorbed. All measurements of the Nd2O3 powder were
therefore made on powders dried for 900oC for six hours. The Nd2O3 powder has a
structure of hexagonal
and Nd(OH)3 was detected as a secondary phase The particle
size distribution is shown in Figure 4.6(b) and shows a trimodal distribution with peaks at
0.2µm, 0.8 µm and 6.15 µm respectively. The characteristics of the particles are confirmed
by the scanning electron microscopy shown in Figure 4.3(b).
4.1.3 Titanium Oxide (TiO2)
The Titanium Oxide powder was white in its as received state and had a purity of
99.7%. The SEM micrograph is shown in Figure 4.3(c) which reveals that the individual
particles had an approximate size of 1μm. The XRD pattern for the TiO2 powder is shown
in Figure 4.2. The XRD pattern reveals that the powder contains a single phase which is
Rutile. Rietveld refinement of the XRD pattern yielded lattice parameters of a = b =
4.592(6) and c = 2.958(4) for a crystal structure of P42/mnm.
Figure 4.2: X-ray diffraction spectra of TiO2
73
(a)
(b)
(c)
(d)
Figure 4.3: Scanning electron micrographs of (a) CaCO 3 (Scale bar = 20µm) (b)
Nd2O3 (Scale bar = 1µm) (c) TiO2 (Scale bar = 2µm) and (d) MgO (Scale bar = 2µm)
4.1.4 Manganese Oxide (Mn2O3)
The XRD pattern for the Mn2O3 powder is shown in Figure 4.4. The analysis of the
pattern reveals there are two forms including Mn2O3 and MnO2 present in the powder. The
Mn2O3 form was indexed on the basis of a cubic structure with
space group and the
MnO2 was indexed on the basis of a tetragonal structure with P42/mnm space group. The
SEM micrograph of the Mn2O3 powder is shown in Figure 4.5. The particle size is
approximately 4μm with some agglomeration of the particles. The particle size analysis
shows that there is a bimodal distribution of particle sizes with the first mode at 0.18μm
and the second mode at 3.68μm which is in agreement with the particle size determined in
the SEM micrograph.
74
561
800
741
222
101
400
411
240
332
422
341
251
440
433
442
352
260
451
622
631
444
453
640
633
642
110
211
200
Figure 4.4: X-ray diffraction spectra of Mn 2O3 (* denotes MnO 2 phase)
Figure 4.5: SEM micrograph of Mn2O3 (scale bar = 2µm)
4.1.5 Magnesium Oxide (MgO)
The SEM micrograph for MgO in Figure 4.6 shows what appears to be a bimodal
particle size distribution with some small spherical particles and some large agglomerates.
The particle size analysis for dried MgO powder indicates a bimodal particle size
75
distribution. The first mode has a particle size of 0.18μm and the second mode has a
particle size of 4.50μm. 90% of the MgO particles are below 6.54μm. The X-ray
diffraction pattern of MgO the pattern could be indexed on the basis of a cubic unit cell
with
̅
space group symmetry. The SEM micrograph of MgO is shows particles of
approximate size of 2μm width, 15-20 μm in length and lenticular in shape.
(a)
(c)
(b)
%
0
0.01
100
0.1
1.0
%
%
10
10.0
10
100
90
90
80
80
80
70
70
70
60
60
40
40
40
30
30
30
20
20
20
10
10
10
0
0
0
0.01
0.1
1.0
10.0
100.0
(e)
100
100.0
80
70
60
60
50
50
40
40
30
30
20
20
10
10
Particle Diameter (µm.)
10.0
90
70
100.0
1.0
100
80
10.0
0
0.1
%
10
90
0
0
0.01
Particle Diameter (µm.)
Particle Diameter (µm.)
%
1.0
50
50
(d)
0.1
60
10
50
Particle Diameter (µm.)
0
0.01
100
90
100.0
10
20
0
0.01
0
0.1
1.0
10.0
100.0
Particle Diameter (µm.)
Figure 4.6: Particle size analysis of (a) CaCO 3 (b) Nd2O3 (c) TiO2 (d) MgO and (e)
Mn2O3
76
4.2 Calcined Powder Analysis
The calcined powders were analysed in terms of their particle size, morphology,
structures and compositions as a function of Nd3+ additions.
4.2.1 Phase Development
The X-ray diffraction patterns for compositions in the Ca(1-x)Nd2x/3TiO3 are shown
in Figure 4.7. The patterns reveal that the powders contain the target composition and
several other secondary phases. Analysis of these patterns reveal that the additional phases
include Nd2Ti2O7, TiO2, Nd2/3TiO3 and Nd2O3. The structures of these secondary phases
are summarised in Table 4.1.
16000
Ca0.61Nd0.26TiO3
Nd2Ti2O7
TiO2
Nd2O3
Nd2/3TiO3
200
14000
8000
2000
221
111
4000
210
101
201
211
220
126
218
314
014
113
016
115
210
116
6000
402
040
10000
402
132
134
406 211
326
416
321
232
302
312
331
322
200
251
313
Intensity (AU)
12000
0
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
2θ
Figure 4.7: Typical X-ray diffraction spectra of calcined powders of Ca (1-x)Nd2x/3TiO3
77
Table 4.1: Structures of secondary phases in Ca(1-x)Nd2x/3TiO3 calcined powder
Phase Composition Structure
Space Group a (Å)
b (Å)
c (Å)
Nd2Ti2O7
Monoclinic
P1211
5.456
26.01299
Nd2/3TiO3
Orthorhombic P222
3.83355 3.85201 7.74129
Nd2O3
Hexagonal
P m1
3.8591
TiO2 (rutile)
Tetragonal
P42/mnm
4.60190 4.60190 2.977400
7.677
3.8591
6.0899
4.2.2 Particle Sizes
The scanning electron micrograph of the calcined powder of Ca0.61Nd0.26TiO3 is
shown in Figure 4.8. The image shows with individual particles with size of approximately
0.8µm and agglomerates of these particles are also present. The particle size analysis of the
Ca0.61Nd0.26TiO3 powder is shown in Figure 4.9. The spectra shows two modes; the first is
at 0.31µm and the second is at 2.11µm and these correspond to the individual particles and
the agglomerates respectively.
Figure 4.8: Scanning electron micrograph of calcined powder of Ca0.61Nd0.26TiO3
(scale bar 2µm)
78
Volume (%)
10
100
90
80
70
60
50
40
30
20
10
0
0.01
0
0.1
1.0
10.0
100.0
Particle Diameter (µm.)
Figure 4.9: Particle size analysis of the calcined powders of Ca 0.61Nd0.26TiO3
4.3 Analysis of Calcined Powders in the MgTiO3-Ca0.61Nd0.26TiO3 system
4.3.1 Phase Development
The X-ray diffraction patterns of the calcined powders of MgTiO3-Ca0.61Nd0.26TiO3
as a function of composition. There are 4 phases present in the diffraction patterns
including MgTiO3, MgTi2O5 Nd2Ti2O7 and Ca0.61Nd0.26TiO3.
79
30000
104
121
25000
316 332
286
02 10
134
206
15000
006
220
131
202
024
076
1-2-6
221
1-3-2
230
312
146
306
256
086 224
196
003
101
012
230
115
116
110
Intensity (AU)
20000
10000
5000
0
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
2θ
Figure 4.10: X-ray diffraction spectra of 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 calcined
powder
4.3.2 Particle Size Analysis
The particle size analysis of the calcined powders of MgTiO3-Ca0.61Nd0.26TiO3 is
shown in Figure 4.11. The particle size distributions have two modes with average particle
sizes of 0.29µm and 1.74µm respectively with 90% of the particles being below a size of
2.96µm. There is little difference between each of the compositions made and this is owing
to the calcination temperature being the same for each of the compositions. The SEM
micrographs for the MgTiO3-Ca0.61Nd0.26TiO3 system are shown in Figure 4.12. The sizes
of individual particles are around 1µm in diameter and there appears to be some
agglomeration of the particles. The findings of the SEM analysis are confirmed by the
particle size analysis as described previously.
80
%
10
100
90
80
70
60
50
40
30
20
10
0
0.01
0
0.1
1.0
10.0
100.0
Particle Diameter (µm.)
Figure 4.11: Particle size analysis of 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3
(a)
(b)
(c)
(d)
Figure 4.12: Scanning electron micrographs of calcined powders of MgTiO 3Ca0.61Nd0.26TiO3
(a)
0.2MgTiO 3-0.8Ca0.61Nd0.26TiO3
(b)
0.4MgTiO 381
0.6Ca0.61Nd0.26TiO3
(c)
0.6MgTiO3-0.4Ca0.61Nd0.26TiO3
and
(d)
0.8MgTiO3-
0.2Ca0.61Nd0.26TiO3 (scale bar 2µm)
4.4 Attrition Milling of CaTiO3
4.4.1 Particle Size Analysis
In order for the spark plasma sintering process to be successful it is necessary to
ensure that the average particle size is minimised and that there is a narrow particle size
distribution [Z Zhao, private communication]. The restrictions on the particle size
parameters for spark plasma sintering arise because of the reduced heat treatment time
means that extra particle reactivity is required to ensure densification. Given that the
particle size is a key factor in densification, the particle size of the CaTiO 3 as a function of
milling time has been monitored (Figure 4.13).
3.000
2.500
2.000
10% Percentile
20% Percentile
50% Percentile
1.500
80% Percentile
90% Percentile
1.000
Modal Particle Size
0.500
0.000
0
60
120
180
240
300
360
420
480
540
600
Figure 4.13: Particle Size analysis of attrition milled CaTiO 3 as a function of milling
time
82
4.4.2 Scanning Electron Microscopy
The scanning electron micrograph of attrition milled and freeze dried CaTiO3 is
shown in Figure 4.14. The majority of individual particles appear to be below a size of
1µm and there also appears to be some agglomeration. There is no evidence of neck
formation between the particles and the findings of the SEM are consistent with the
findings of the particle size analysis.
Figure 4.14: Scanning electron micrograph of attrition milled and freeze dried CaTiO 3
(Scale bar = 1µm)
4.4.3 Phase Development
The x-ray diffraction pattern of the attrition milled CaTiO3 is shown in Figure 4.15.
The pattern shows a single perovskite phase of CaTiO3 with a structure of orthorhombic
Pbnm and no secondary phases were detected. The peaks in the diffraction pattern show a
significant broadening compared to the peaks of non-attrition milled powders investigated
in this study. Crystallite size, crystallite strain and instrumental broadening are the three
key factors that contribute to the peak width. Since that all powders were tested on the
83
same instrument so it may be assumed that the instrument broadening has not had a
significant effect on the changes in the peak widths in this pattern.
50000
45000
022
40000
400
30000
25000
312
Intensity (AU)
35000
20000
116
332
141
402
105
133
221
213
310
131
110
111
10000
021
210
103
022
113
122
224
15000
5000
0
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
2θ
Figure 4.15: X-ray diffraction spectra of attrition milled and freeze dried CaTiO 3
84
5 Determination of the Room Temperature Structures of Ca(1-x)Nd2x/3TiO3
Ceramics
5.1 Introduction
The objectives of this chapter are to establish the relationship between the structure
and microwave dielectric properties of Ca(1-x)Nd2x/3TiO3. The first part of the chapter
concerns the determination of the structure through X-ray diffraction techniques including
using synchrotron techniques. Raman spectroscopy will be used to monitor changes in the
strength of bonding and cation-vacancy ordering in the structure. The microstructure will
be evaluated using scanning and transmission electron microscopy. Cations and vacancies
will be directly imaged through the use of aberration corrected high angle annular dark
field microscopy (HAADF) in the scanning transmission electron microscope (STEM).
Finally, the microwave dielectric properties were measured using a cavity resonance
technique.
5.2 Conventional Laboratory X-Ray Diffraction
5.2.1 Phase Development
The X-ray diffraction spectra of Ca(1-x)Nd2x/3TiO3 collected using conventional Cu
Kα radiation are shown in Figure 5.1. All spectra could be indexed on the basis of a single
perovskite phase. No evidence of secondary phases could be found which is in contrast to
the findings of Fu et al [98] who reported small amounts (<4wt%) of TiO2. A possible
explanation for the absence of the TiO2 phase is the difference in the processing conditions
used by Fu et al [98] compared to this study. The samples in the study by Fu et al [98]
cooled at the slower rate of 120oC/hr to 1100oC and then allowed the samples to cool
naturally to ambient temperature whereas this study used a constant cooling rate of
180oC/hr. Another explanation is that the heat treatment of the Nd2O3 powders prior to
initial mixing of the powders changed the chemistry of the powders during the calcination
process. The previous report by Moon et al [129] on the effect of calcination conditions on
85
the microwave dielectric properties of CaTiO3-LaAlO3 has shown that the densification of
ceramics can be adversely affected by the phase analysis of the powders. The La2O3 used
as a starting powder in the preparation of CaTiO 3-LaAlO3 is hygroscopic and reacts with
water to form the La(OH)3 phase. It is thought that if the La(OH)3 is not completely
eliminated, it is this phase that is responsible for the degradation of the density of the
completed products [130]. In the previous study by Fu et al. [98], it was not stated whether
Nd2O3 powders were heat treated prior to mixing of the powders and it is therefore
possible that calcination was incomplete. The incomplete calcination could have affected
the chemistry of the system during sintering leading to the formation of the TiO2 secondary
phase. It is known that for the compositions that are rich in Nd3+ it is possible for the
perovskite phase to decompose into Nd2Ti2O7 and Nd4Ti9O24 as observed by Lee et al
[131]. These phases were not detected in any of the finished products which suggests that
for the solid solution limit is beyond the composition of x = 0.9.
Figure 5.1: X-ray diffraction spectra of Ca(1-x)Nd2x/3TiO3 using Cu Kα radiation
86
5.2.2.1 Structure of Ceramics from CaTiO3 to Ca0.61Nd0.26TiO3
The structure of the samples for CaTiO3 to Ca0.61Nd0.26TiO3 could be indexed on
the basis of the orthorhombic Pbnm structure as previously reported [10, 19, 98] and
structural details for these ceramics are given in Table 5.1. The trend in the lattice
parameters is that the a axis increases in length whilst the b axis decreases as a function of
Nd3+ doping. These changes in structure be attributed to the difference in the sizes of the
Ca2+ (1.34Å) and Nd3+ (1.27Å) ions [132]. The c-axis length increases from 7.652Å for
CaTiO3 to 7.694Å for Ca0.61Nd0.26TiO3 before decreasing for Ca0.52Nd0.32TiO3 and beyond.
Local strains caused by disorder of the cations and vacancies are the likely reason for these
changes (see also section 5.7). The lattice parameters for the ceramics with the
orthorhombic Pbnm structure are approximately a =
b =
c = 2ac (ac is the
lattice parameter of cubic perovskite) indicating that only the c axis is doubled relative to
the cubic form of perovskite. The tilt system for the ceramics with the orthorhombic Pbnm
structure was the a-a-c+ tilt system according to Glazer’s notation [72, 73]. This indicates
that there is equal anti-phase tilting of the oxygen octahedra about the a and b axes and inphase tilting about the c-axis. Glazer [72-73] found that anti-phase tilts about the a and b
axes would give rise to peaks with (hkl) being all odd and that in-phase tilts about the b
axis would give odd-even-odd values of (hkl). The tilt system assignment is confirmed by
the presence of the (133), (313) and (115) peaks for the antiphase tilts and by the (301),
(103) and (105) peaks for the in phase tilting about the c-axis.
Table 5.1 – Lattice parameters for ceramics in the system Ca(1-x)Nd2x/3TiO3
a (Å)
b (Å)
c (Å)
x=0
5.382 (5)
5.446 (4)
7.634 (5)
x = 0.21
5.394 (2)
5.440 (2)
7.652 (3)
x = 0.3
5.399 (5)
5.433 (7)
7.651 (5)
x = 0.39
5.409 (2)
5.434 (2)
7.694 (2)
x = 0.48
7.679 (4)
7.669 (8)
7.679 (5)
x = 0.57
7.674 (9)
7.676 (9)
7.671 (1)
x = 0.9
7.666 (3)
7.665 (3)
7.717 (3)
β (o)
90
90
90
90
90.17 (6)
89.94 (7)
90.05(7)
The ideal crystal system for Ca(1-x)Nd2x/3TiO3 perovskites is a cubic structure with
with the A site cations (Ca/Nd) sitting in the centre of the cube with the Ti cations
87
in the centre of the oxygen octahedra [68]. The tilting of the oxygen octahedra displaces
the A-site cations from their ideal position at the centre of the unit cell. During heat
treatment of the ceramics it is possible for two different configurations of anti-parallel
displacements to meet and form an antiphase domain boundary [55]. The displacement of
the A-site cations can be detected from the XRD patterns in a similar way to the octahedral
tilting by examination of special peaks in the diffraction pattern. These peaks will have
(hkl) with general forms of even-even-odd, even-odd-even and odd-even-even. The
presence of the (221), (210) and (122) peaks in the diffraction patterns confirm s that the
A-site cations are displaced from their normal positions in the centre of the unit cell [7273]. This type of displacement of cations has been observed in other perovskite ceramics
including CaTiO3-LaAlO3 [35] and MgSiO3 [53].
5.2.2.2 Structures of Ceramics with Compositions from Ca0.52Nd0.32TiO3 to Ca0.1Nd0.6TiO3
The initial refinement of the diffraction pattern for Ca0.1Nd0.6TiO3 was on the basis
of the orthorhombic Pbnm structure in accordance with the structure of the CaTiO3 rich
ceramics. The refinement of the data on the basis of this structure was poor and this is
reflected in Figure 5.2. One of the key peaks not adequately accounted for in the structural
model is the peak at a d-spacing of 7.67Å which would correspond to the (001) plane of
the crystal structure. The (001) peak is forbidden in the orthorhombic Pbnm structure as all
peaks must conform to the reflection condition of (00l) where l = 2n and n is any non-zero
integer [133]. The presence of additional peaks suggests a transition to a lower symmetry
structure compared to the symmetry of orthorhombic Pbnm. Zhang et al [101] used group
theoretical analysis to predict the likely structures of materials with compositions similar to
Nd2/3TiO3. It was concluded that the possible structures were C2/m or Amm2 on the basis
of a unit cell doubled in each of the principal crystallographic directions or a P2/m
structure with unit cell dimensions of 21/2 x 2 x 21/2.
88
10
20
30
40
50
60
70
312
130
135
312
042
133
124
220
115
015
202
221
222
113
021
400
001
020
110
002
110
123
023
022
121
021
001
013
111
101
002
001
(B) – P222
80
89
312
004
112
053
062
610
124
044
242
400
411
222
231
300
4-4-1
-
200
102
100
022
(C) – Amm2
10
20
30
40
50
60
70
062
250
024
241
1-1-4
2θ
403
223
222
132
003
002
012
001
220
(D) P2/m
80
Figure 5.2: Refinement of the X-ray diffraction spectra of Ca 0.1Nd0.6TiO3 on the basis
of (A) orthorhombic Pbnm (B) orthorhombic P222 and (C) orthorhombic Amm2 (D)
monoclinic P2/m
Refinement of the Ca0.1Nd0.6TiO3 diffraction data on the basis of the monoclinic
P2/m structure with lattice parameters of a = 21/2ac b = 2ac and c = 21/2ac was unsatisfactory
with several predicted peaks not appearing in the diffraction pattern and poor matching
between predicted and experimental intensities of the peaks. Similar problems were
encountered for the Amm2 structure and therefore these structures can be eliminated as
candidates for the structure of Ca0.1Nd0.6TiO3. The refinements of the diffraction spectra
for Ca0.1Nd0.6TiO3 on the basis of (a) orthorhombic Pbnm (b) orthorhombic P222 (c)
orthorhombic Amm2 and (d) monoclinic P2/m are shown in Figure 5.2. These models have
90
limited success in describing the structure of Ca0.1Nd0.6TiO3 with poor match between the
predicted and actual intensities and positions of the peaks. Refinement of the diffraction
patterns on the basis of the monoclinic C2/m structure was more successful (Figure 5.3).
All the major peaks in the diffraction pattern are accounted for by the model and there is a
good match between the observed and predicted intensities of the peaks. On this basis, the
structure of Ca0.1Nd0.6TiO3 can be better described by the monoclinic C2/m structure in
045 062
443
622
245
244
061
440
441
205
242
430 150
240
241
400
2-2-3
222 -2-2-2
023
003 221
020
021
001
contrast to the work of Yoshida et al [19], who assigned the orthorhombic P222 structure.
Figure 5.3: X-ray diffraction spectra of Ca 0.1Nd0.6TiO3 refined on the basis of
monoclinic C2/m structure
The determination of the composition at which the phase transition occurs began
with the consideration of the positions of the peaks. Figure 5.4 shows 56-62o 2θ region of
the X-ray diffraction spectra of Ca(1-x)Nd2x/3TiO3. Examination of the peaks reveals that the
peaks shift to lower 2θ values for the 0 ≤ x ≤ 0.39 range of compositions followed by an
abrupt shift to higher 2θ values before resuming the shift to the left. This suggests the onset
of the phase transition is somewhere between the compositions of x = 0.39 and x = 0.48.
To confirm the onset of the phase transition, the X-ray diffraction spectra of
Ca0.61Nd0.26TiO3 and Ca0.52Nd0.32TiO3 were refined on the basis of (i) orthorhombic Pbnm
and (ii) monoclinic C2/m (Figure 5.5). Comparison of the refinements reveals that the
orthorhombic Pbnm structure produces the best fit for Ca0.61Nd0.26TiO3 whilst
Ca0.52Nd0.32TiO3 is best described by the monoclinic C2/m structure. This is in contrast to
the work of Fu et al [98] who assigned an orthorhombic Pbnm structure to the
Ca0.52Nd0.32TiO3 material.
91
Pbnm
312 242
C2/m
Figure 5.4: Magnified region of the X-ray diffraction spectra of Ca (1-x)Nd2x/3TiO3
((242) index for monoclinic C2/m structure and (312) index for orthorhombic Pbnm
structure)
92
220 221
220 221
400 2-2-3
213
310
131
400 2-2-3
240
310
131
213
240
241
Ca0.61Nd0.26TiO3 (Pbnm)
312
241
242
312
Ca0.61Nd0.26TiO3 (C2/m)
Ca0.52Nd0.32TiO3 (Pbnm)
242
Ca0.52Nd0.32TiO3 (C2/m)
Figure 5.5: Rietveld refinement of (i) Ca 0.61Nd0.32TiO3 and (ii) Ca0.52Nd0.32TiO3 on the
basis of orthorhombic Pbnm and monoclinic C2/m
5.2.2.3 Tilt System in Ceramics with Monoclinic Structure
The tilt system assignment to the ceramics with the C2/m structure is a-b0c- which
indicates that there are two different antiphase tilts around the a and c axes and no tilt
about the b axis. From the work of Glazer [72, 73], we would expect this tilt systems to
93
produce reflections that have (hkl) values which are odd-odd-odd with (h ≠ l) and (h ≠ k).
Examination of the X-ray diffraction patterns revealed the presence of (113), (311) and
(131), confirming the tilt system proposed. Examination of the indexing of the peaks
reveals the presence of even-odd-even and odd-even-even type peaks suggesting the
presence of antiphase domain boundaries as observed in the compositions in the 0 < x <
0.39 composition range. The structure of Ca0.1Nd0.6TiO3 is illustrated schematically in
Figure 5.6 to show the doubling of the unit cell in each of the principal crystallographic
directions and the tilting of the oxygen octahedra.
Nd1
Nd1
Nd2
Nd2
Nd1
Nd2
Nd1
Nd1
Nd1
Figure 5.6: Schematic illustration of the structure of Ca0.1Nd0.6TiO3 using [100]
projection
5.2.2.4 Cation Vacancy Ordering
Cation ordering in the structure was assessed from the superlattice peaks in the
XRD patterns. Kagomyia et al [102] found superlattice peaks in the diffraction patterns of
NaxNd(2-x)/3TiO3 (using conventional XRD with Cu radiation) at approximately 10o, 35o,
48o, 55o, 60o and 65o. No spacegroup was assigned to these diffraction patterns but the
authors conjectured that the likely structure was orthorhombic. In contrast with previous
studies [102], no significant superlattice peaks were found in the X-ray diffraction patterns
of any of the ceramics investigated with Cu Kα radiation. The most likely explanation for
94
the lack of superlattice peaks in the diffraction patterns of this study is that the superlattice
peaks are too weak to be distinguished from the background of the patterns.
Structural phase transitions and cation-vacany order transitions have been reported
for other perovskite microwave dielectric ceramics. Ca(1-x)La2x/3TiO3 shows a transition
from Pbnm to Ibmm followed by a transition to Cmmm for the compositions richest in
La2/3TiO3 [105]. These structural phase transitions are also accompanied by a shift from
cation-vacancy disorder to order for x > 0.8 with some short range order between 0.7 < x <
0.8. For compositions based on CaTiO3 with rare Earth aluminates, there is typically a
phase transition from the CaTiO3 structure (orthorhombic Pbnm to the structure of the rare
Earth aluminate (typically R3c) for high additions of the aluminate [134]. In contrast to the
behaviour in Ca(1-x)La2x/3TiO3 there is no evidence of long range ordering in the aluminate
based ceramics.
5.3 Synchrotron X-Ray Diffraction
5.3.1 Structure Determination
The synchrotron diffraction spectra for five specimens in the Ca(1-x)Nd2x/3TiO3 are
shown in Figure 5.7. All patterns could be indexed on the basis of a single perovskite phase
with no secondary phases detected. The diffraction spectra of Ca0.1Nd0.6TiO3 shows
asymmetry in the shape of the peaks with broadening being only on the left hand side of
the peak (higher d-spacing end of the peak) (see Figure 5.6e). The origin of the peak
asymmetry is likely to be the result of the nano-chessboard formation observed in section
5.7. The peak asymmetry has been previously observed in the SrLaCuTaO6 double
perovskite where there was complete ordering of the B-site cations in the structure [135].
95
(a)
96
(c)
97
(e)
Figure 5.7: X-ray diffraction spectra of Ca(1-x)Nd2x/3TiO3 obtained using synchrotron
sources (a) CaTiO3 (b) Ca0.7Nd0.2TiO3 (c) Ca0.61Nd0.26TiO3 (d) Ca0.52Nd0.32TiO3 and
(e) Ca0.1Nd0.6TiO3
It was discussed in section 5.3 (regarding the XRD patterns collected using a Cu Kα
radiation) that it is possible to index the diffraction spectra of ceramics with x ≥ 0.48 on a
number of different structures. In order to determine the correct structures in this system,
selected samples were investigated using synchrotron XRD using a wavelength of
0.827442Å. The synchrotron XRD pattern for CaTiO3 produced using the conventional
sintering route is shown in Figure 5.7a. As with previous literature on this material [10, 5657], it was possible to index the pattern on the basis of an orthorhombic Pbnm structure.
The lattice parameters have the general form of a =
,b=
and c = 2ac which
indicates that the c-axis is doubled due to the tilting of the oxygen octahedra. The lattice
parameters, atomic coordinates and site occupancies of all the ceramics examined with
synchrotron X-ray diffraction are summarised in Tables 5a and 5b.
98
Table 5.2a: Lattice parameters, atomic coordinates and site occupancies of Ca(1x)Nd2x/3TiO3
ceramics with Pbnm structure
x
Composition
Space
Group
a (Å)
b (Å)
c (Å)
Ca
x
y
z
Occupancy
Temperature Factor
Nd
x
y
z
Occupancy
Temperature Factor
Ti
x
y
z
Temperature Factor
O1
x
y
z
Temperature Factor
O2
x
y
z
Temperature Factor
0
0.3
0.39
CaTiO3 Ca0.7Nd0.2TiO3 Ca0.61Nd0.26TiO3
Pbnm
Pbnm
Pbnm
5.37911(8)
5.43977(7)
7.64182(10)
-0.00692(7)
0.03554(4)
0.25
1
0.523(3)
N/A
N/A
N/A
N/A
N/A
0
0.5
0
0.247(3)
0.072(2)
0.484(2)
0.25
0.43(2)
0.709(3)
0.289(1)
0.038(1)
0.53(1)
5.40380(2)
5.43797(2)
7.66200(3)
-0.002(6)
0.027(7)
0.25
0.70
0.1(26)
-0.002(7)
0.027(3)
0.25
0.2
0.1(26)
0
0.5
0
0.10(6)
0.067(5)
0.4902(3)
0.25
0.1(3)
0.719(2)
0.2848(2)
0.028(3)
0.1(2)
5.40852(2)
5.43627(2)
7.66541(2)
-0.003(1)
0.0221(7)
0.25
0.61
0.01(31)
-0.00297(2)
0.0221(7)
0.25
0.26
0.01(20)
0
0.5
0
0.08(6)
0.081(6)
0.487(3)
0.25
0.10(4)
0.726(4)
0.281(3)
0.034(3)
0.3(3)
99
Table 5.2b: Lattice parameters, atomic coordinates and site occupancies of Ca(1-x)Nd2x/3TiO3
ceramics with C2/m structure
x
0.48
0.9
Composition
Ca0.52Nd0.32TiO3
Ca0.1Nd0.6TiO3
Space Group
C2/m
C2/m
a (Å)
7.6752(4)
7.6728(2)
b (Å)
7.6707(2)
7.6726(4)
c (Å)
7.6705(5)
7.7218(2)
Beta
90.215(3)
90.004(1)
x
0.253(3)
0.249(3)
y
0
0
z
0.002(3)
0.002(1)
Occupancy
0.52
0.125(1)
Temperature Factor
0.006(3)
0.99(1)
x
0.253(3)
0.249(3)
y
0
0
z
0.002(3)
0.002(1)
Occupancy
0.32
0.875(1)
Temperature Factor
0.006(3)
0.991(1)
x
0.252(3)
0.249(9)
y
0
0
z
0.495(3)
0.500(5)
Occupancy
0.52
0.08(1)
Temperature Factor
0.006
0.99(1)
x
0.252(3)
0.249(9)
y
0
0
z
0.495(3)
0.500(5)
Occupancy
0.32
0.32(1)
Temperature Factor
0.006(3)
0.99(1)
x
-0.012(2)
0.001(6)
y
0.250(2)
0.254(6)
z
0.256(2)
0.266(1)
Ca1
Nd1
Ca2
Nd2
Ti1
100
O1
O2
O3
O4
O5
Temperature Factor
0.006(3)
0.99(1)
x
0
0
y
0.261(8)
0.27(1)
z
0
0
Temperature Factor
0.006(3)
0.99(1)
x
0
0
y
0.207(4)
0.21(1)
z
0.5
0.5
Temperature Factor
0.006(3)
0.99(1)
x
-0.037(1)
-0.04(3)
y
0
0
z
0.21(1)
0.24(1)
Temperature Factor
0.006(3)
0.99(1)
x
0.04(1)
-0.04(3)
y
0.5
0.5
z
0.259(9)
0.27(1)
Temperature Factor
0.006(3)
0.99(1)
x
0.240(6)
0.24(3)
y
0.235(6)
0.24(9)
z
0.203(6)
0.219(7)
Temperature Factor
0.006(3)
0.99(1)
The tilt systems assigned to the ceramics on the basis of spectra collected by
conventional X-ray diffraction are confirmed in the synchrotron X-ray diffraction patterns.
The tilt system for the orthorhombic Pbnm structure is a-a-c+ indicating approximately
equal antiphase tilts about the a and b axes and in-phase tilting about the c-axis. The tilt
system is confirmed by the presence of odd-odd-odd type peaks for the antiphase tilts and
odd-odd-even type peaks for the in-phase tilting about the c-axis [72-73]. The ceramics
with the monoclinic C2/m structure have the a-b0c- tilt system indicating two different
antiphase tilts about the a and c principle crystallographic axes. This tilt system is expected
to give peaks of type odd-odd-odd where (k ≠ l) and (h ≠ k). There is no tilting about the b
principal axis. Figure 5.7 shows the x 2θ region for Ca0.1Nd0.6TiO3 investigated by
101
synchrotron X-ray diffraction confirming the a-b0c- tilt system assignment with the (113),
(131) and (311) peaks respectively.
131
311
1-1-3
2θ
131
113
311
Figure 5.8: Evidence of octahedral tilting in (a) Pbnm ceramics and (b) C2/m ceramics
120
210
Figure 5.9: Evidence of peaks related to antiphase domain boundaries in CaTiO3
102
5.3.2 Octahedral Distortion
The synchrotron data was used to calculate the bond lengths and angles as a
function of composition for the Ca(1-x)Nd2x/3TiO3 ceramics. The lengths of the Ti-O bonds
and the octahedral distortion as a function of composition are shown in Table 5.4. The
octahedral distortions
∑{
̅
̅
[99-100] were calculated using Equation 5.1:
}
Where Ri = the length of a given bond and
(5.1)
is the mean of the bond length of the
octahedra. The octahedral distortion of the TiO6 increases almost exponentially as a
function of composition from 2.71x10-6 for CaTiO3 to 2.83x10-3 for Ca0.1Nd0.6TiO3. This
change in distortion can be related to the different size and charges of the Ca2+ and Nd3+
respectively [132] which can be quantified using the tolerance factor. The tolerance factor
as a function of composition for the Ca(1-x)Nd2x/3TiO3 system is shown in Figure 5.10 and
the values range from 0.966 for CaTiO3 to 0.81 for Ca0.1Nd0.6TiO3. The tolerance factor is
a useful method for estimating the distortion in the lattice caused by two or more different
cations. A perovskite structure having a tolerance factor of unity would not be distorted
and would not exhibit any octahedral tilting; any deviation from unity would cause tilting
and distortion. It is therefore evident that the octahedra distortion derived from the
synchrotron data is consistent with the distortion estimated from the tolerance factor. The
tolerance factor shows a linear trend as a function of composition whereas the octahedral
distortion shows an exponential dependence. It is likely that the structural transition from
orthorhombic Pbnm to monoclinic C2/m is responsible for the difference in the
compositional dependence of these variables.
103
Table 5.3: Octahedral distortion and tolerance factor as a function of composition
Composition (x)
Octahedral Distortion
Tolerance Factor
0
2.713x10-6
0.966
0.3
4.940x10-5
0.914
0.39
1.79x10-4
0.898
0.48
2.2x10-6
0.883
0.9
2.83x10-3
0.81
3.000E-03
0.98
0.96
0.94
2.000E-03
0.92
0.9
1.500E-03
0.88
1.000E-03
0.86
Tolerance Factor
Octahedral Distortion
2.500E-03
0.84
5.000E-04
0.82
0.000E+00
0.000
0.200
0.400
0.600
0.800
0.8
1.000
Composition (x)
Figure 5.10: Octahedral distortion and tolerance factor as a function of composition in
the Ca(1-x)Nd2x/3TiO3 system
Table 5.4a shows the bond lengths for the Ti-O bonds for each of the ceramics with
the Pbnm structure whilst Table 5.4b shows the Ti-O bond lengths for compositions with
the P2/m structure determined using synchrotron X-ray diffraction. The mean bond length
decreases slightly from CaTiO3 to Ca0.7Nd0.2TiO3 and then increases back to 1.954Å for
104
Ca0.61Nd0.26TiO3. This trend in the Ti-O bond lengths was also observed in a previous
study of Ca(1-x)Sm2x/3TiO3 by Yoon et al. [100] but the magnitude of the change in the
bond lengths of Ca(1-x)Sm2x/3TiO3 is much less compared to the change in the bond lengths
of Ca(1-x)Nd2x/3TiO3. There does not to appear to be any significant change in the average
Ti-O bond lengths across the entire of the compositional range in this study. A possible
explanation for this observation is the magnitude of octahedral distortion in the Nd3+ rich
compositions.
Table 5.4a: Bond lengths as a function of composition for the ceramics with the Pbnm
structure
Atom 1
Ti1:0
Mean
Lengths
Atom 2
O1:0
O1:2
O2:0
O2:5
O2:6
O2:3
Bond
CaTiO3
1.951
1.951
1.958
1.958
1.959
1.959
1.956
Bond Lengths (Å)
Ca0.7Nd0.2TiO3
1.950
1.950
1.929
1.929
1.961
1.961
1.947
Ca0.61Nd0.26TiO3
1.967
1.967
1.917
1.917
1.977
1.977
1.954
Table 5.4b: Selected bond lengths for ceramics with the C2/m structure
Atom 1
Ti1:0
Atom 2
O5:3
O2:4
O4:0
O3:0
O1:0
O5:0
O2:0
O2:1
O4:2
O1:1
O5:4
O3:3
O5:7
Bond Lengths
Ca0.52Nd0.32TiO3
1.944
1.956
1.957
1.960
1.971
1.986
2.006
-
Ca0.1Nd0.6TiO3
3.127
1.801
1.992
2.099
2.998
3.155
3.001
105
5.3.3 Cation Vacancy Ordering
As discussed in section 5.2.2.5 (on the diffraction patterns of Ca(1-x)Nd2x/3TiO3)
there appears to be an ordering transition that occurs at approximately the same
composition as the transition to the monoclinic C2/m structure. It was suggested that the
nature of ordering was alternate layers of sites filled with cations and the other layer is
predominantly vacancies. The high quality of the synchrotron data allows refinement of the
occupancies of the crystallographic sites with a high degree of accuracy. The atomic
coordinates and site occupancies derived from synchrotron XRD analysis are shown in
Table 5.4. It is noted that two of the four sites are filled with vacancies and the other two
are empty confirming the layered structure. This layered arrangement of cations and
vacancies has been reported in perovskite materials including Ca(1-x)La2x/3TiO3 [105].
5.4 Room Temperature Microstructure of Ca(1-x)Nd2x/3TiO3 Ceramics
5.4.1 Grain Size
Low magnification SEM images of Ca(1-x)Nd2x/3TiO3 ceramics are shown in Figure
5.11. They confirm that all samples in the compositional range are single phase Ca(1x)Nd2x/3TiO3.
This is in contrast to the previous study on this system Fu et al. [98]; Figure
5.11 shows the grains are generally equiaxed in shape with sizes in the range 5 µm to
55µm with some abnormal grain growth in Ca0.61Nd0.26TiO3 to Ca0.1Nd0.6TiO3. A summary
of the grain sizes as a function of composition are shown in Table 5.6. The grain size
appears to decrease with increasing value of x with the exception of x = 0.57 where there is
a rapid increase in the grain size. The pores are located at both the grain boundaries and
within the grains in all compositions in Ca(1-x)Nd2x/3TiO3, suggesting that the sintering rates
were rapid. When sintering is rapid, the pores do not have sufficient time to diffuse to the
grain boundaries and become trapped within the grains. Grain boundaries are the preferred
location for pores because this minimises the total surface area in the sample.
106
(a)
(b)
(c)
Figure 5.11: Low magnification SEM images of Ca (1-x)Nd2x/3TiO3 as revealed by
thermal etching (a) Ca0.79Nd0.14TiO3 (b) Ca0.61Nd0.26TiO3 and (c) Ca0.1Nd0.6TiO3 (scale
bar = 20µm for (a) and (b), (c) = 10µm
The SEM image of the microstructure of Ca0.1Nd0.6TiO3 (Figure 5.11) shows
abnormal grain growth. The work of Fisher et al. [136, 137] on abnormal grain growth in
perovskite ceramics attributed the strong bimodal grain size distribution to the presence of
facetted grain boundaries. If a grain has an atomically rough interface, atoms may add at
any point along the grain boundary resulting in normal grain growth. Alternatively, if the
grain boundary is facetted then atoms can only add on to the grain at special sites where
the energy barriers are lower than the energy barrier for the facetted interface. Examples of
such sites may include screw dislocations, 2D nuclei and twin domains. Figure 5.9 shows
the grain growth rate as a function of driving force for grain growth including different
type of grain boundaries from the work of Fisher et al. [136, 137] It shows that grain
growth can happen for nearly any driving force but for facetted interfaces there is critical
driving force to initiate grain growth. It should be noted that µc for a facetted interface with
107
defects is less than the µc for a facetted interface without defects. It is possible that the high
concentration of vacancies in the Ca0.1Nd0.6TiO3 system enhances the abnormal grain
growth rate relative to stoichiometric CaTiO3 and ceramics with lower concentrations of
vacancies.
Table 5.5: Grain size as a function of composition in Ca(1-x)Nd2x/3TiO3
Composition
Grain Size (µm)
CaTiO3
48.9 ± 2.45
Ca0.79Nd0.14TiO3
37.3 ± 1.87
Ca0.7Nd0.2TiO3
37.1 ± 1.86
Ca0.61Nd0.26TiO3
31.6 ± 1.58
Ca0.52Nd0.32TiO3
16.0 ± 0.8
Ca0.43Nd0.38TiO3
54.9 ± 2.75
Ca0.1Nd0.6TiO3
13.9 ± 0.7
Figure 5.12: Grain growth rate as a function of driving force for grain growth
(reproduced from [136])
108
70
60
Grain Size (µm)
50
40
30
20
10
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Composition (x)
Figure 5.13: Grain size as a function of composition
5.4.2 Twin Domains
Chemically etched microstructures of Ca(1-x)Nd2x/3TiO3 are shown in Figure 5.14.
Chemical etching has the advantage of revealing some of the sub grain features present in
CaTiO3 based perovskites. In order to assess the dominant twin domain morphology, an
area of approximately 1mm2 was imaged using orientation contrast techniques in the SEM.
For CaTiO3, the dominant morphology is a lamella (Figure 5.14(a)) of variable width to
form a needle shaped domain. On the addition of Nd3+ to give a composition of
Ca0.79Nd0.14TiO3 the domain morphology changes to a variety of geometrical shapes
including triangular and trapezium morphologies (Figure 5.14c). The variety of domain
morphologies present in the microstructures persists until the composition of
Ca0.43Nd0.38TiO3 where the dominant morphology returns to needle shaped lamella (Figure
5.14d).
(a)
(b)
109
Figure 5.14: High magnification images of twin domains in Ca (1-x)Nd2x/3TiO3 as
revealed by chemical etching (a) CaTiO3 (b) Ca0.79Nd0.14TiO3 (c) Ca 0.7Nd0.2TiO3 (d)
Ca0.52Nd0.32TiO3 (e) Ca0.43Nd0.38TiO3 (f) Ca0.1Nd0.6TiO3 (scale bar 20µm)
The twin domain widths were measured using a linear intercept method; domain
width as a function of composition is shown in Figure 5.15. The average domain width
ranged from 1.65µm for CaTiO3 to 4.52µm for Ca0.52Nd0.32TiO3 and subsequently fell to
1.67µm for Ca0.1Nd0.6TiO3. There appears to be a bimodal distribution of twin domain
widths, including grains with a high density of narrow twin domains and other grains with
(d)
a low density of widely spaced domains. It is not clear why the bimodal distribution of
twin domains occurs in Ca0.1Nd0.6TiO3 ceramics. The composition map evaluated using
electron microprobe analysis is shown in Figure 5.16 along with the secondary electron
image for the same area. The EMPA data shows a regular distribution of the Ca, Nd and Ti
atoms in the selected region. The homogeneity of the samples would suggest that the
bimodal distribution of twin domain widths is not related to the distribution of the
elements. It is also not clear why there is a sudden drop in the width of the twin domains
for Ca0.52Nd0.32TiO3.
110
Figure 5.15: Domain widths as a function of composition
Figure 5.16: Electron microprobe analysis maps of Ca 0.79Nd0.14TiO3
111
(a)
(b)
5.5 Transmission Electron Microscopy
5.5.1 Twin Domains
Low magnification transmission electron microscopy images for the Ca(1x)Nd2x/3TiO3
system are shown in Figure 5.18. They reveal the presence of twin domains
and antiphase domain boundaries. The twin domains form to relieve the strain in the lattice
due to the changes in the lattice parameters [20, 53]. Figure 5.19 shows a selected area
electron diffraction pattern for Ca0.61Nd0.26TiO3 in the [010] zone axis. The diffraction
pattern is typical of a (112) type domain as determined by Wang and Liebermann [20, 53]
(a)
(b)
Figure 5.17: Transmission electron micrographs of twin and antiphase domains in (a)
Ca0.61Nd0.26TiO3 (scale bar 0.5µm) and (b) twin domains in Ca 0.52Nd0.32TiO3 (scale bar
= 1µm) – Courtesy of Dr Feridoon Azough
200
112
202
101
000
200
202
200
202
000
002
Figure 5.18: [010] Zone axis selected area electron diffraction patterns for twin
boundary region shown in Figure 5.18a – Courtesy of Dr. Feridoon Azough
5.5.2 Antiphase Domains
Figure 5.19 shows antiphase domains in three Ca(1-x)Nd2x/3TiO3 ceramics. The Xray diffraction data corroborates the findings of the transmission electron microscopy with
the presence of (hkl) peaks of even-even-odd, even-odd-even and odd-even-even.
Wondratschek and Jeitschko [55] theorized that the existence of antiphase domains was
due to the loss of translational symmetry as a result of structural transitions on cooling to
ambient temperature. In Ca(1-x)Nd2x/3TiO3 the antiphase domains form as a result of the
antiparallel displacement of the A site cations from their equilibrium positions causing the
loss of translational symmetry. Antiphase domain boundaries are formed as a result of two
different antiparallel cation displacements growing until they impinge upon each other
[55]. Antiphase domains have been reported for several ceramics with the perovskite
structure including CaTiO3 [20] and lanthanum magnesium niobate [139] and in metallic
materials such as the alloy Cu3Au [140].
113
(a)
(b)
Figure 5.19: Transmission Electron Micrographs of antiphase domains in (a)
Ca0.7Nd0.2TiO3 (left, scale bar = 200nm) and (b) Ca0.52Nd0.32TiO3 (right, scale bar =
400nm). Courtesy of Dr. Feridoon Azough.
114
5.5.3 Cation Vacancy Ordering
Selected area diffraction patterns of Ca(1-x)Nd2x/3TiO3 in the [010] direction are
shown in Figure 5.20. The most striking features in the electron diffraction patterns of
Ca0.52Nd0.32TiO3 to Ca0.1Nd0.6TiO3 are the satellite peaks which are not present in the
CaTiO3 to Ca0.61Nd0.26TiO3 patterns. There are two possible physical mechanisms for the
appearance of these superlattice peaks in the electron diffraction patterns. The first is phase
separation, as observed by Guiton [141] in the Nd2/3-xLixTiO3 Li ion conductor; the second
is the double layer ordering observed in ThNb4O12 crystals [142-143]. Examination of the
patterns for Ca0.1Nd0.6TiO3 reveals that there are no more than four satellite peaks per
reflexion. This eliminates the spinodal decomposition reaction observed in the Nd2/3xLixTiO3
crystal because more than four satellites would be expected, because of the
superposition
of
two
or
more
orientations
of
the
phases.
115
(a)
(b)
200
202
000
002
200
000
202
002
(c)
200
000
202
002
Figure 5.20: Electron diffraction patterns of Ca(1-x)Nd2x/3TiO3 viewed in the [010]
direction for (a) CaTiO 3 (b) Ca0.52Nd0.32TiO3 and (c) Ca0.1Nd0.6TiO3. Courtesy of Dr
Feridoon Azough
116
5.6 Raman Spectroscopy
5.6.1 Mode Parameters
Factor group analysis of the structures identified using X-ray diffraction reveals
that there are a total of 24 Raman active modes for CaTiO3 and 33 for the monoclinic
C2/m structure [134] as shown in Equations 5.2 and 5.3.
7Ag + 5B1g + 7B2g + 5B3g (orthorhombic Pbnm)
(5.2)
16Ag + 17 Bg (monoclinic C2/m)
(5.3)
The Raman spectra for Ca(1-x)Nd2x/3TiO3 are shown in Figure 5.21; peak fitting algorithms
revealed the presence of 11 Raman active modes. The Raman spectra are in good
agreement with earlier Raman spectroscopy studies of CaTiO3 [119-120]. The modes were
assigned in the same way as Zheng et al. [119-120], with modes in the 200-400cm-1 region
of the spectra being attributed to rotations of the oxygen octahedra. The modes at 464cm -1
and 494cm-1 can be attributed to the torsional modes of the Ti-O bond and the mode at
640cm-1 can be attributed to the stretching of this bond. Some of the modes that were
predicted by the group factor analysis were not present in the Raman spectra. They may
not have been visible due to the background function or due to weak changes in
polarisability. For compositions Ca0.43Nd0.38TiO3 and Ca0.1Nd0.6TiO3 there is an additional
mode at around 850cm-1 which suggests that there is a transition to a structure with a lower
degree of symmetry as the orthorhombic Pbnm structure of CaTiO3.
117
Figure 5.21: Raman spectra as a function of composition for Ca (1-x)Nd2x/3TiO3
The modes in the Raman spectra move to lower wavenumbers as a function of
composition in the Ca(1-x)Nd2x/3TiO3 system. Given that the modes shift to lower
wavenumbers indicates that there is a reduction of energy required to change the
polarisability of a particular bond or rotation. The Raman spectroscopy indicates the
possibility of a structural transition near to Ca0.52Nd0.32TiO3 due to the appearance of an
additional mode at approximately 850cm-1. The appearance of an additional mode in
Raman spectroscopy indicates that there is a new way of inducing a change in polarisation
due to the lattice vibrations. It is likely that in the Ca(1-x)Nd2x/3TiO3 system this change
would be due to the structural angle β deviating from 90o. In the orthorhombic system there
are no changes in the lattice parameter that could change the symmetry in any significant
way; therefore there must be an angle change. The angle change causes the extra mode
because it reduces the number of rotational symmetry operations that could be performed
on the unit cell.
118
The relative intensities of the Raman peaks are dependent on the orientation of the
interaction volume relative to the polarisation direction of the laser light. To ensure that
any changes are due to changes in the structure the rotation dependence of the Raman
spectra was measured and also Raman spectra of several different areas of the sample were
investigated. The Raman spectra in Figure 5.22 are the position dependent spectra for
Ca0.61Nd0.26TiO3. It can be seen that there are some small changes in the relative intensities
of the peaks and the peak fitting has shown that the peak centres and widths do not change
significantly. In order to eliminate the effect of composition on the Raman spectra, electron
microprobe analyses were made on the area surrounding the sites of the Raman spectra
acquisition. The EMPA map shows that there is a regular distribution of the key elements
analysed which suggests that the samples are homogeneous. It is therefore safe to assume
that the changes in the Raman spectra are not due to compositional variation. It is likely
that the changes are due to the changes in crystal orientation between each of the points
773
662
325
378
459
471
521
194
229
273
that were sampled.
Figure 5.22: Raman spectra of Ca 0.61Nd0.26TiO3 from three different locations
5.6.2 Rotational Raman Spectroscopy
A useful technique for exploring the nature of the modes in Raman spectra is to
assess the change in the intensity of polarised Raman light as a function of rotation of the
sample stage. An example of the angular dependence of the Raman spectra is shown in
Figure 5.23. The resulting intensity profile is usually of sinusoidal form and the periodicity
of the profile can be used to determine from which crystallographic axis a Raman mode
119
originates. Knowledge of the origin of the Raman modes can be used in the assignment of
the Raman modes and can be useful when considering phase transitions in a given ceramic.
The rotation dependent intensity profiles of the Raman modes of Ca0.79Nd0.14TiO3 (Pbnm
structure) are shown in Figure 5.24. There are two distinct types of intensity profile; the
first is the modes with a periodicity of
The modes with a periodicity of
with
and the second type of intensity profile is
.
originate from the ab plane whilst the intensity profiles
periodicity originate from vibrations along the c-axis [143].
(A)
(B)
(C)
(D)
Figure 5.23: Raman spectra from four different rotation angles of Ca 0.79Nd0.14TiO3 (A)
0o (B) 50 o (C) 100o and (D) 150 o
120
330 Peak, π/2 dependence
528 Peak, π dependence
Figure 5.24: Angular dependence of the intensities of 330 and 528 Raman modes for
Ca0.79Nd0.14TiO3
121
5.6.3Cation Vacancy Ordering
Raman spectroscopy can be used to examine the relative degree of order and
disorder in materials by examination of the width of the Raman active modes. Cation
vacancy disorder in crystal lattices causes broadening in Raman modes because of the
variation in the energies required to cause changes in the polarisability of bonds. For
Ca0.79Nd0.14TiO3 there appears to be some ordering in the lattice due to the sharpness of the
peak at 240cm-1. As further additions of Nd3+ are made the width of the peak at 240cm-1
increases which suggests that the degree of disorder increases. The width of the 240cm -1
peak decreases for large additions of Nd3+ suggesting that the cation vacancy ordering
returns. A possible mechanism for these changes is that for small additions of Nd3+, the
cations can spread evenly throughout the lattice resulting in an ordered structure. As the
amount of Nd3+ is increased a disordered lattice must be formed because all the Nd3+
positions which would result in an ordered lattice have previously been filled. The width of
the Raman modes as a probe of ordering has been used before for microwave dielectric
ceramics. Zheng et al. [119-120] found that a broadening of a peak at 850 cm-1 was
associated with the short range ordering of cations and this was later associated with higher
dielectric losses.
5.7 Aberration Corrected Scanning Transmission Electron Microscopy
High angle annular dark field imaging mode in the aberration corrected scanning
transmission electron microscope may be used to probe cation distributions by Z contrast
imaging. The technique of Z contrast imaging takes advantage of the intensity of the spots
in the image being proportional to the average atomic number (Z) of the species in a given
atomic column. Given that the atomic number of Ca is 20 and 60 for Nd, it should be
straightforward to identify the column rich in Nd and columns that have a significant
number of vacancies. Figure 5.25 shows HAADF images for selected compositions in the
Ca(1-x)Nd2x/3TiO3 system. As Nd3+ is added to CaTiO3, there is no long range regular
distribution of the intensity of the spots which suggests there is no long range ordering of
the cations. This disorder appears to reach a maximum at x = 0.39 where further additions
122
of Nd3+ causes a transition from short range to long range ordering. When the composition
is changed to Ca0.1Nd0.6TiO3 the structure is characterised by the ordering of layers of Nd3+
and Ca2+ cations and the vacancies in the lattice.
Figure 5.25: HAADF images for Ca (1-x)Nd2x/3TiO3 (a) [110] zone axis of CaTiO3 (b)
[001] zone axis of Ca0.61Nd0.26TiO3 (c) [110] zone axis of Ca0.52Nd0.32TiO3 and (d)
[010] zone axis of Ca0.1Nd0.6TiO3 (courtesy of B. Schaffer)
Further confirmation of the formation of an ordered structure can be found in the
bright field SuperSTEM images. Figure 5.26 shows the bright field STEM image and the
FFT obtained from the latter for Ca0.1Nd0.6TiO3. The FFT was subsequently noise filtered
and an inverse FFT was performed to obtain the image in Figure 5.26. The bright field
STEM image shows a series of zig-zag fringes known as microtwins whilst the FFT shows
the presence of the splitting of some of the spots into 4 satellite peaks. The form of
microtwins in this arrangement was described as a nanochessboard pattern by Guiton and
Davies [141] in their study on Nd based ionic conductors. They attributed the patterns in
their images to a decomposition process which is similar to spinodal decomposition. The
patterns observed in Ca0.1Nd0.6TiO3 cannot be attributed to nanoscale phase separation
123
because there are only 4 satellites per diffraction spot in the FFT patterns. It would be
expected that there would be more than 4 satellites for a phase separation process because
of the differences in the lattice parameters of each of the phases. Each of the squares in the
checkerboard pattern corresponds to a different configurations of ordering in the lattice and
the size of these nano-checkerboard squares were found to be 2.4nm from Figure 5.26
Figure 5.26: (a) Bright field STEM image and (b) noise filtered image of
Ca0.1Nd0.6TiO3 (courtesy of B. Schaffer)
The formation of microtwinning was previously studied in Cu3Au alloys [139] and
ThNb4O15 ceramics[142-143]. Yamaguchi et al [140] determined that the microtwins were
due to the long range ordering of cations whilst Labeau et al [142-143] attributed the
pattern formation to alternating layers of Th cations and vacancies. The formation of
microtwins has also been observed in microwave dielectric ceramics including
0.9La2/3TiO3-0.1LaAlO3 where it was found that the density of the microtwins is sensitive
to the cooling rate [104]. This observation was derived from the fact that the intensity of
the additional reflections decreased as function of processing conditons and this in turn led
to an increase in the Q x f value. A similar trend occurs in the Ca(1-x)Nd2x/3TiO3 system
whereby the microtwins are present in Ca0.1Nd0.6TiO3 but absent in Ca0.52Nd0.32TiO3,
which is accompanied by the disappearance of the extra reflections.
Figure 5.27 shows electron energy loss maps for a region of the [010] zone axis of
Ca0.1Nd0.6TiO3; the red spots represent Ti4+, blue spots for Nd3+ and green for Ca2+. The
124
map shows that there is a regular distribution of the Nd3+ on one site and the Ca2+ are
randomly distributed on this site. The EELS mapping therefore confirms the findings of the
bright field and HAADF imaging that there is a well ordered lattice for Ca0.1Nd0.6TiO3.
The EELS spectra and HAADF images (Figure 5.30) also show the disordered nature of
the Ca0.61Nd0.26TiO3 ceramics. The EELS line scan shows that there is no regular
distribution of the intensities of the peaks suggesting that there are different concentrations
of atoms in each of the respective columns.
Figure 5.27: (a) [001] Zone axis HAADF of region of Ca 0.1Nd0.6TiO3 (b) EELS map
for area labelled spectrum image and (c) False colour EELS map for Ca0.1Nd0.6TiO3
with Ca2+ represented by green spots, Nd 3+ in blue and Ti 4+ in red (courtesy B.
Schaffer)
125
5.8 Microwave Dielectric Properties
5.8.1 Relative Permittivity
The relative permittivity as a function of composition is shown in Figure 5.28. It
decreases from 180 for CaTiO3 to 80 for Ca0.1Nd0.6TiO3 and these values are generally
consistent with previous studies [18, 98]. It is generally difficult to exactly ascertain the
microwave dielectric properties of Nd2/3TiO3 due to phase separation but with the data
obtained in this study it is possible to estimate the properties by fitting a curve to the data.
On this basis it was possible to estimate the relative permittivity to be 79 on the basis of an
exponential fit to the data. The trend in the relative permittivity may be explained through
the Clausius-Mossotti equation. The two key terms in this equation are the polarisability of
the lattice and the volume of the unit cell. Given that there is a substantial increase in the
unit cell volume in the course of the structural phase transition, it is likely that this
substantial volume change is responsible for the non-linear pattern in the relative
permittivity.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
800
600
f
400
200
Q x f (GHz)
0
12000
10000
8000
6000
4000
2000
0
150
r
100
50
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Composition (x)
Figure 5.28: Microwave dielectric properties as a function of composition for Ca (1x)Nd2x/3 TiO3
126
Table 5.6: Microwave dielectric properties of Ca(1-x)Nd2x/3TiO3 ceramics measured at 23GHz
x
0
0.21
0.3
0.39
0.48
0.57
0.9
εr
180
101
79.3
87.5
82.8
96.7
78
Qxf (GHz)
5900
8000
13000
12400
7850
3140
1000
τf (ppm/K)
770
295
242
200
-
-
-
5.8.2 Temperature Coefficient of Resonant Frequency
The
for ceramics in the Ca(1-x)Nd2x/3TiO3 decreases from +800 ppm K-1 to +200
ppm K-1 for Ca0.52Nd0.32TiO3 and are close to values previously reported in a number of
studies[18, 98]. The gross non-linear relationship between the
and the composition can
be attributed to changes in the tolerance factor and the octahedral tilting of the perovskite
structure. Reaney et al [74-76] postulated that changes in the tolerance factor t, reflect the
onset of octahedral tilt transitions and hence changes of the
of the ceramics. It is
significant that there is a phase transition from orthorhombic Pbnm to monoclinic C2/m in
this system as this causes the nature of the tilting and distortion of the oxygen octahedra to
change. The tilt angle of the oxygen octahedra will affect the microwave dielectric
properties of ceramics because this will affect the vibrational properties of the lattice
including the resonant frequency. The distortion of the structure will restrict the movement
of the oxygen octahedra including when the temperature of the ceramic is increased. If the
structure is distorted then the change in the tilt angle per temperature increment will be
reduced and hence reducing the temperature coefficient of resonant frequency.
The change in the mobility of the oxygen octahedra on the
of microwave
dielectric ceramics can be related to the equations derived by Bosman and Havinga [26].
(5.5)
127
Where:
(5.6)
(5.7)
And
(5.8)
(
= total polarizability, V = volume, T = temperature, P = pressure,
permittivity and
= relative
= temperature coefficient of the dielectric constant)
The distortion of the oxygen octahedra will affect the volume and total polarisability terms
in this equation. The distortion of the oxygen octahedra will affect the tilting of the
octahedra which will affect the lattice parameters of the ceramics. Glazer [72-73]
demonstrated that the tilting of the oxygen octahedra will lead to the doubling of the lattice
parameter of the untilted cubic structure. The tilt angle will increase as the temperature of
the ceramic is increased which will cause the volume of the ceramic to decrease.
5.8.3 Quality Factor (Q x f)
The Q x f value increases from 6000GHz for CaTiO3 and reaches a maximum of
13000GHz for Ca0.61Nd0.26TiO3 and then decreases to approximately 1000GHz for
Ca0.1Nd0.6TiO3 and these values are shown in Figure 5.28. The trends in the values of the Q
x f are broadly consistent with earlier studies [18, 98] although their absolute values are
slightly lower. When comparing to other similar systems such as Ca(1-x)Sm2x/3TiO3 and
Ca(1-x)La2x/3TiO3 it is apparent that the general trend in the Q x f value is similar to that for
Ca(1-x)Sm2x/3TiO3 but not Ca(1-x)La2x/3TiO3 [93, 99-100]. There are however some
differences between the properties of Ca(1-x)Sm2x/3TiO3 and Ca(1-x)Nd2x/3TiO3 ceramics
including the level of lanthanide doping needed to produce the peak in the properties. The
trends in the properties of the Ca(1-x)Sm2x/3TiO3 [99-100] can be explained by the change in
the phases present in the microstructure whilst the changes in the ordering in Ca (1128
x)La2x/3TiO3
seem to be the most plausible explanation for the changes of properties in this
system [105].
The analysis that follows is similar to that of Fu et al. [98] in their work on as Ca(1x)Nd2x/3TiO3
but the data has been reassessed in light of new information from different
techniques. The presence of porosity and secondary phases in the microstructure of
microwave dielectric ceramics is known to have an influence on the Q x f value. It is
possible to eliminate the influence of variations in porosity between the compositions
because all ceramics reach in excess of 95% of the theoretical density when using similar
processing conditions. Investigations of ceramics based on La2/3TiO3 found that the
presence of phases such as La2Ti2O7 or La4Ti9O24 (see Figure 5.29) caused serious
degradation of the Q x f value [95]. In this study, no analogous secondary phases
(Nd2Ti2O7 or Nd4Ti9O24) were detected using any of the techniques which can give
information on presence and composition of phases. The presence of impurities [48] is
known to degrade the Q x f values of microwave dielectric ceramics. Electron microprobe
analysis of the specimens showed that the ceramics were homogenous although there were
low levels of impurities present. It is unlikely that this is a significant factor in the trends in
the properties of these ceramics.
Figure 5.29: Phase diagram of La 2O3-TiO2 system (reproduced from MacChesney and
Sauer [91])
129
The final microstructure parameter to consider is the presence of boundaries
including the grain and domain sizes of the ceramics. Studies undertaken by Alford et al
[43] have suggested that the grain size does not have a significant effect on the Q x f value
of microwave dielectric ceramics. This result seems counterintuitive because it is expected
that the grain boundaries would scatter the phonons and cause dielectric loss. It has been
shown that the abnormal grain growth which was observed in some of the ceramic sample
does have a significant deleterious effect on the Q x f value of columbite niobates [145].
However, the absence of abnormal grains in the samples with x ≤ 0.39 cannot explain why
there is an increase in the Q x f value in this region. Lowe [138] found that a decrease in
the domain density was responsible for an increase in the Q x f value with decreasing
cooling rate in CaTiO3 ceramics. The analysis of the domain widths as a function of
composition shows that there is an increase in the domain width as a function of
composition from CaTiO3 to Ca0.61Nd0.26TiO3. This is analogous to a decrease in the
domain density as an increased width is an indication that there are fewer domains in the
microstructure and this can easily explain the increase in Q x f in the x ≤ 0.39 region.
The degree of ordering of cations in the lattice is known to have a significant effect
on the Q x f value of B site ordered microwave dielectric ceramics, with Q x f values
reaching up to 300000GHz for Ba(Zn1/3Ta2/3)O3 annealed for times up to 120 hours [13].
The long annealing times allow the distance between similar charges to be maximised and
possibly reduce the internal stress state. Any change in the distribution of charges will
affect the vibrational properties of the lattice and hence affect the Q x f value [67]. The A
site ordering in Ca(1-x)Nd2x/3TiO3 has been investigated using Raman spectroscopy,
HAADF-STEM and XRD techniques and it has been found that upon small additions of
Nd3+, the cations and vacancies in the lattice are disordered and the ordering increases only
after significant additions of Nd3+ (x > 0.48). The maximum ordering is observed in
Ca0.1Nd0.6TiO3 which does not coincide with the highest Q x f values so it is possible to
eliminate the possibility of a disorder-order transition as a mechanism for increasing the Q
x f values.
This study has found a new phase transition from orthorhombic Pbnm to
monoclinic C2/m near to the composition of Ca0.61Nd0.26TiO3. In a study of the effect of
Ni2+ doping level on the microwave dielectric properties of (Mg(1-x)Nix)2Al4Si5O18, Ohsato
130
et al [146] found that there were rapid increases in the Q x f over a small range of
compositions. Through the use of synchrotron radiation techniques it was deduced that the
large increases in the Q x f could be explained by increases in the symmetry of the crystal
structure. Although there is a clear reduction in symmetry on transition from any
orthorhombic structure to any monoclinic structure it is unlikely that this has any effect on
the properties in the present investigation. The change in Q x f per unit composition in the
Ca(1-x)Nd2x/3TiO3 system is much less than the change in Q x f over the same range of
composition in (Mg(1-x)Nix)2Al4Si5O18 [146]. The change in the symmetry on the transition
in monoclinic C2/m also does not explain why there is an increase in the Q x f from
CaTiO3 to Ca0.61Nd0.26TiO3.
The Q x f of a microwave dielectric ceramic is dependent on the formation of
defects and the mechanisms for balancing charges that accompany them. The defect
equations for the incorporation of Nd3+ on the Ca site in CaTiO3 has been described in a
previous study but the phase transition to monoclinic C2/m has not been taken into
account. In the C2/m structure it is the Ca2+ which is incorporated onto the Nd site and this
significantly changes the charge compensation mechanism.
(5.9)
Equation 5.9 shows that the charge compensation mechanism in these ceramics is by the
formation of electron holes which would greatly increase the electrical conductivity. The
interaction between the electric field of the microwave frequency photon and the crystal
lattice, these electron holes would be mobile and increase the dielectric losses of the
ceramic.
131
6 Structure Sequence in Ca(1-x)Nd2x/3TiO3 Ceramics
6.1 Introduction
In chapter 5, it was demonstrated that the Q x f of Ca(1-x)Nd2x/3TiO3 is dependent on
the widths and morphologies of twin domains. It is known that the twin domains originate
from the structural phase transitions on cooling to ambient temperature after sintering [20,
53]. In this chapter, Raman spectroscopy and X-ray diffraction were employed to explore
the structural characteristics of Ca(1-x)Nd2x/3TiO3 on cooling from 600oC to ambient
temperature. The samples examined by Raman spectroscopy were cooled to -195oC to help
to reduce noise and to help in the interpretation of the spectra. Variable temperature
scanning electron microscopy is used to determine whether the changes observed in the
Raman spectroscopy and X-ray diffraction have any effect on the microstructure of the
ceramics. Finally, the structural changes will be used to interpret some of the trends in the
microwave dielectric properties.
6.2 General Information
6.2.1 X-ray Diffraction
The diffraction patterns of ceramics in the Ca(1-x)Nd2x/3TiO3 at room temperature
were indexed on the basis of the structures which were established in chapter 5. There also
appears to be some additional peaks which cannot be attributed to the structure of the Ca (1x)Nd2x/3TiO3
ceramics and nothing suitable could be found in the ICSD database to suggest
an identity for the secondary phase. It is assumed that the additional peaks must be
associated with a component of the furnace attachment and the peaks are shifted
significantly from their usual positions. The most likely component to cause these
additional peaks is the Al2O3 holder in which the sample sits during the course of the
experiment. This conclusion was made after the samples were run without the furnace
attachment and these peaks disappeared from the diffraction patterns. A peaks only model
132
was added in order to take this into account in the Rietveld refinements of the diffraction
pattern to ensure that this did not affect the judgement of any structural changes. A peaks
only model does not contain any structural information for the Al2O3 phase from the
sample holder. The additional peaks were located at 31o, 35o, 45o, 50o, 56o and 63o and
positions were refined to allow for thermal expansion of the sample holder (see example in
Figure 6.1).
Figure 6.1: Typical refinement of X-ray diffraction spectra of Ca 0.79Nd0.14TiO3
including peaks from Al 2O3 sample holder (blue vertical lines)
6.2.2 Raman Fitting Procedure
A standardised procedure was used in order to obtain reliable fitting of the modes
of the Raman spectra as a function of temperature. Given that there are no peaks of interest
above 900cm-1, this region was excluded from the analysis. Equally, there is no meaningful
data below 150cm-1 because of the notch filter used is not able to exclude light close to the
laser line. The background was modelled through the use of a peak which was refined to
take into account for the temperature dependence of the background function. The modes
were fitted using a Voigt model and the positions, widths and intensities of the modes were
refined to fit the spectra.
133
6.3 Structure Sequence of Ca0.79Nd0.14TiO3
6.3.1 Variable Temperature X-ray Diffraction
The X-ray diffraction spectra in the 25-775oC range for Ca0.79Nd0.14TiO3 are shown
in Figure 6.2. The room temperature diffraction pattern was refined on the basis of the
orthorhombic Pbnm structure as established in chapter 5.
116
224
312
310
131
220
221
35000
210
103
022
113
122
021
111
40000
112
110
45000
775oC
725ooC
675oC
625 C
575ooC
525 C
475ooC
425 oC
375 oC
325 C
275ooC
225oC
175oC
125 oC
75 oC
25 C
30000
25000
20000
15000
10000
5000
80
75
70
65
60
55
50
45
40
35
30
25
20
0
2θ
Figure 6.2: X-ray diffraction spectra of Ca0.79Nd0.14TiO3 in the 25-775oC range
showing peaks from the Al2O3 sample holder ( ) and the perovskite main phase
The lattice parameters for Ca0.79Nd0.14TiO3 as a function of temperature are shown
in Figure 6.3. The linear trend in the lattice parameters suggests that the composition is
approximately constant and there is no significant evaporation of atoms on heating. The
lattice parameters have a general form of
. The thermal
134
expansion coefficients were calculated from the gradient of the plots of the lattice
parameters as a function of temperature and the values are 1.67x10-5 K-1 for the a axis,
9.2x10-6 K-1 for the b axis and 1.31x10-5 K-1 for the c axis. The volume expansion
coefficient was 4.11x10-5 K-1. The thermal expansion coefficients are slightly larger than
the thermal expansion coefficients of CaTiO3-LaAlO3 but the lattice parameters are
generally consistent with the work of Ravi et al. [147]
Figure 6.3: Lattice parameters as a function of temperature for Ca 0.79Nd0.14TiO3 with
the orthorhombic Pbnm structure (a) a and b axes (b) c-axis
The tilt system of the ceramics across the entire temperature range is a-a-c+,
consistent with the tilt system assigned to the ceramics in chapter 5.The assignment of the
tilt system is confirmed by the presence of odd-odd-odd (k ≠ l) type peaks such as the
(131) and the (113) and odd-odd-even type peaks such as the (130) and (310) peaks.
135
Table 6.1: Lattice parameters as a function of temperature for Ca0.79Nd0.14TiO3 with the
orthorhombic Cmcm structure (square markers for the a-axis, diamond markers for the baxis and triangle markers for the c-axis)
Temperature (oC)
a (Å)
b (Å)
c (Å)
25
5.391(2)
5.434(2)
7.649(3)
75
5.395(2)
5.435(2)
7.652(3)
125
5.402(2)
5.440(2)
7.657(3)
175
5.405(3)
5.442(2)
7.666(4)
225
5.407(3)
5.442(3)
7.668(4)
275
5.413(3)
5.444(3)
7.673(5)
325
5.417(2)
5.447(2)
7.679(3)
375
5.423(2)
5.451(2)
7.686(3)
425
5.425(3)
5.452(3)
7.690(4)
475
5.431(2)
5.456(3)
7.697(3)
525
5.436(4)
5.458(3)
7.700(5)
575
5.440(2)
5.462(2)
7.706(3)
625
5.443(3)
5.464(3)
7.711(4)
675
5.449(2)
5.468(2)
7.719(2)
725
5.460(3)
5.470(3)
7.718(4)
775
5.464(3)
5.472(3)
7.726(4)
The atomic coordinates, site occupancies and temperature factors for the
Ca0.79Nd0.14TiO3 are given in Table 6.2. The atomic coordinates have been used by
Kennedy et al [59] to monitor changes in the octahedral tilt angles as a function of
temperature. The tilt system of Ca0.79Nd0.14TiO3 is a-a-c+ indicating that the octahedral tilt
angles about the a and b axes are equal with a unique tilt angle about the c-axis. The tilt
angles can be calculated for Pbnm perovskite ceramics by considering the deviation of the
second oxygen site (O2) from the ideal position of (0.75, 0.25, 0). To quantify the
distortion it is necessary to define three variables of u, v and w which can be calculated
from the atomic coordinates as follows: (0.75-u, 0.25+v, w). The tilt angles can then be
calculated through Equations 6.1 and 6.2:
136
In-phase tilt angle
where
(6.1)
Antiphase tilt angle
(6.2)
The tilt angles for Ca0.79Nd0.14TiO3 in the 25-775oC range are graphically represented in
Figure 6.4. The general trend of a slight decrease in the tilt angles about the a and b axes as
a function of temperature and is in agreement with the findings of Kennedy et al. [60].
There is no discernible trend about the c-axis as a function of temperature. The exact
values are however slightly higher (approximately 0.5o) than the values obtained for
CaTiO3 [60] which is most likely due to the smaller size and different ionization state of
Nd3+ compared to Ca2+ [131].
Table 6.2: Atomic coordinates, site occupancies and thermal parameters for Pbnm form of
Ca0.79Nd0.14TiO3 at 775oC
Site
x
Y
z
Ca1
-0.006(1) 0.025(5) 0.25
0.79 0.44(5)
Nd1 -0.006(1) 0.025(5) 0.25
0.14 0.44(5)
Ti1
0
0.5
1
0.44(5)
O1
0.055(3)
0.486(2) 0.25
1
0.44(5)
O2
0.712(2)
0.294(1) 0.048(1) 1
0.44(5)
0
occ
B
137
Figure 6.4: Tilt angles as a function of temperature for Ca 0.79Nd0.14TiO3
138
Table 6.3: Octahedral tilt angles as a function of temperature for Ca0.79Nd0.14TiO3
Temperature
a-axis and b-axis tilt (o)
c-axis tilt (o)
25
11.5 ± 0.58
12.7 ± 0.64
75
10.9 ± 0.55
17 ± 0.85
125
10.8 ± 0.54
17.2 ± 0.86
175
11.4 ± 0.57
13.5 ± 0.68
225
11 ± 0.55
14.4 ± 0.72
275
10.1 ± 0.51
14.2 ± 0.71
325
9.8 ± 0.49
16.2 ± 0.81
375
10 ± 0.5
14.2 ± 0.71
425
10 ± 0.5
14.6 ± 0.73
475
9.5 ± 0.48
14.5 ± 0.73
525
9.6 ± 0.48
15.7 ± 0.79
575
9.7 ± 0.49
14.8 ± 0.74
625
9.5 ± 0.48
14.6 ± 0.73
675
9.7 ± 0.49
13.6 ± 0.68
725
9.8 ± 0.49
13.3 ± 0.67
775
8.5 ± 0.42
14.5 ± 0.73
6.3.2 Raman Spectroscopy of Ca0.79Nd0.14TiO3
The Raman spectra for Ca0.79Nd0.14TiO3 in the temperature range -195oC-600oC are
shown in Figure 6.5. The spectra taken at -195oC shows 14 modes at 176, 219, 243, 286,
294 340, 294, 339, 379, 463, 472, 500, 531, 642, and 786 cm-1 and the modes can be
assigned to rotations of the oxygen octahedra, torsion of the oxygen octahedra and
stretching of the Ti-O bonds. The modes shift to lower wavenumbers as a function of
temperature indicating that it becomes easier to change the polarisability of a given bond.
Examination of the modes in the Raman spectra taken at 225-265oC shows changes in the
modes parameters including the relative intensities of the modes (see Figure 6.6). The
changes in the relative intensities are most pronounced for the 470 and 520 cm-1 peaks
139
relative to the peak at approximately 500 cm-1. The intensity of a Raman active mode is
dependent on several factors including the incident intensity of the laser light, the
concentration of a given dipole and the Raman cross-section. The decrease of the intensity
of the peak at 463cm-1 suggests that there is a decrease in the number of dipoles as a
641
463
472
500
531
339
379
177176
219
243
286
293
function of temperature.
858K
758K
658K
558K
458K
358K
258K
158K
Figure 6.5: Raman spectra as a function of temperature for Ca 0.79Nd0.14TiO3
140
(a) 185oC
(b) 205oC
Figure 6.6: Magnified Image of 450-550 cm-1 Region of Raman Spectra for
Ca0.79Nd0.14TiO3 at (a) 185oC and (b) 205 oC
The peak widths as a function of temperature are shown in Figure 6.7. There is a
sudden increase in the widths of the peaks at approximately 200oC until returning to the
familiar linear trend after 300oC indicating that there is a significant decrease in the
ordering in the lattice. The gradual broadening of the peaks after the sharp transition in
peak width is due to increases in temperature causing increased vibration of atoms. The
possible scenarios causing these changes will be discussed in detail in section 6.9.
141
Figure 6.7: Peak widths as a function of temperature for Ca 0.79Nd0.14TiO3
6.4 Structure Sequence of Ca0.7Nd0.2TiO3
The Raman spectra for Ca0.7Nd0.2TiO3 in the -195-600oC range is shown in Figure
6.8. The spectra are similar to those observed for Ca0.79Nd0.14TiO3 suggesting that the
structural characteristics are similar for each of the two materials. At cryogenic
temperatures there are 12 modes in the spectra. As with the Ca0.79Nd0.14TiO3 spectra, the
modes shift to lower wavenumbers indicating that it is easier to change the polarisability of
the dipole. At approximately 285oC, there are the same changes in the relative intensities of
the modes as observed in Ca0.79Nd0.14TiO3. This suggests that there is an octahedral tilt
transition at this temperature.
142
781
650
411
459
472
500
533
338
377
239
283
4.0
858K
3.5
758K
Raman Intensity [AU]
3.0
658K
2.5
558K
2.0
458K
1.5
358K
1.0
258K
0.5
158K
0.0
200
300
400
500
600
700
800
900
1000
Wavenumber [cm-1]
Figure 6.8: Raman spectra for Ca 0.7Nd0.2TiO3 as a Function of Temperature
The 425-550 cm-1 region of the Raman spectra as a function of temperature for
Ca0.7Nd0.2TiO3 are shown in Figure 6.9. The spectra in this region show three distinct
modes corresponding to the torsion of the O-Ti-O bonds along the c-axis of the unit cell.
When the temperature is increased to approximately 285oC, the mode at approximately
450cm-1 disappears in the same way as it does in Ca0.79Nd0.14TiO3. The disappearance of
the mode at 450cm-1 therefore indicates that Ca0.7Nd0.2TiO3 is also undergoing a similar
transition to Ca0.79Nd0.14TiO3. All peaks in the spectra shift to lower wavenumbers as a
function of temperature in linear fashion. The shift to lower wavenumbers indicates that it
becomes easier to change the polarisability of the dipoles associated with these modes. The
likely reason for the increase in the polarisability is the extra volume due to the thermal
expansion of the crystal structure and the extra energy available from the increase in the
temperature of the sample.
143
Figure 6.9: Magnified portion of the Raman spectra of Ca 0.7Nd0.2TiO3 at (a) 265 oC and
(b) 285 oC
The peak width of the mode at 338cm-1 as a function of temperature are shown in
Figure 6.10. There is a sharp increase in the peak widths which begins at approximately
245oC which coincides with the changes in the relative intensities. The completion of the
transition occurs over the same number of temperatures as Ca0.79Nd0.14TiO3.
144
Figure 6.10: Width of 330 cm -1 peak as a function of temperature
6.5 Structure Sequence of Ca0.61Nd0.26TiO3
6.5.1 Variable Temperature X-ray Diffraction
The X-ray diffraction spectra of Ca0.61Nd0.26TiO3 from room temperature to 800oC
are shown in Figure 6.11. No secondary phases were detected and there is no evidence of
any phase transitions as a function of temperature. The spectra were indexed on the basis
of the orthorhombic Pbnm structure with lattice parameters of general form
. The tilt system of the Ca0.61Nd0.26TiO3 is a-a-c+ as established
in chapter 5 and this is confirmed by the (131), (113) and (311) type peaks in the X-ray
diffraction spectra. The thermal expansion coefficients were calculated to be 0.00007K-1,
0.00006K-1 and 0.00009K-1 along the a, b and c principal crystallographic axes
respectively.
145
Intensity (AU)
116
105
133
224
312
213
310
131
221
103
022
210
111
20000
113
122
220
112
021
25000
775oC
725ooC
675 C
625ooC
575 C
525oC
o
475
25oCC
425ooC
375 C
325oC
275ooC
225 C
175oC
125ooC
75 C
25oC
15000
10000
5000
0
20
30
40
50
60
70
80
2θ
Figure 6.11: X-ray diffraction spectra of Ca 0.61Nd0.26TiO3 as a function of temperature
The lattice parameters plotted in Figure 6.12 appear to begin to converge towards
the upper end of the temperature range that was tested in this investigation. The
convergence of the a and b lattice parameters suggests that the structural phase transition to
tetragonal I4/mcm could be beginning in this temperature range. It is not clear why there is
a spike in the lattice parameters at 625oC. The octahedral tilt angles for Ca0.61Nd0.26TiO3 as
a function of temperature are shown in Figure 6.13. The angles are lower than those
calculated for Ca0.79Nd0.14TiO3 but decrease with temperature in the same fashion.
146
Figure 6.12: Lattice parameters as a function of temperature for Ca 0.61Nd0.26TiO3
147
Figure 6.13: Octahedral tilt angles as a function of temperature for Ca 0.61Nd0.26TiO3
148
Table 6.3: Octahedral tilt angles for Ca0.61Nd0.26TiO3 as a function of temperature
Temperature (oC)
a-axis
c-axis
25
7.6 ± 0.38
14.8 ± 0.74
75
7.7 ± 0.39
14.7 ± 0.74
125
7.8 ± 0.39
14.9 ± 0.75
175
7.2 ± 0.36
15.1 ± 0.76
225
7.2 ± 0.36
14.8 ± 0.74
275
7.4 ± 0.37
14.2 ± 0.71
325
7.1 ± 0.36
14.2 ± 0.71
375
7.6 ± 0.38
13.5 ± 0.68
425
6.6 ± 0.33
15.2 ± 0.76
475
7.2 ± 0.36
14.7 ± 0.74
525
7.7 ± 0.39
12.4 ± 0.62
575
7 ± 0.35
11.1 ± 0.56
625
6.7 ± 0.34
15.1 ± 0.76
675
6.7 ± 0.34
15.1 ± 0.76
725
7.2 ± 0.36
13.9 ± 0.7
775
6.7 ± 0.34
14.1 ± 0.71
6.5.2 Variable Temperature Raman Spectroscopy
The Raman spectra as a function of temperature for Ca0.61Nd0.26TiO3 are plotted in
Figure 6.14. At cryogenic temperatures there are 11 modes consistent with the other
ceramics with the Pbnm structure at room temperature. On reaching approximately 165 oC,
there is a substantial change in the relative intensities of the peaks between 450-550cm-1 in
the same way as Ca0.79Nd0.14TiO3 and Ca0.7Nd0.2TiO3. There is a significant broadening of
the modes as a function of temperature which is due to thermal broadening and an increase
in the disorder in the lattice. The Raman spectra of Ca0.61Nd0.26TiO3 in the 425-550cm-1
range as a function of temperature are shown in Figure 6.15. In contrast to the spectra of
Ca0.79Nd0.14TiO3 and Ca0.7Nd0.2TiO3 there are two distinct modes as opposed to three.
149
Examination of the spectra indicates that this is the case across the entire temperature range
770
656
500
528
457
331
376
235
276
tested.
858K
758K
658K
558K
458K
358K
258K
158K
Figure 6.14: Raman spectroscopy of Ca 0.61Nd0.26TiO3 from -195oC to 600oC
150
(a)
(b)
Figure 6.15: Magnified region of the variable temperature Raman spectra of
Ca0.61Nd0.26TiO3 at (a) 145oC and (b) 165 oC
151
Figure 6.16: Width of 330cm -1 peak as a function of temperature for Ca 0.61Nd0.32TiO3
6.6 Structure Sequence of Ca0.52Nd0.32TiO3
6.6.1 Variable Temperature X-ray Diffraction
The X-ray diffraction spectra for Ca0.52Nd0.32TiO3 are shown in Figure 6.17 and all
patterns could be indexed on the basis of a single perovskite phase with monoclinic C2/m
symmetry. This structure is consistent with the structure proposed in section 5.2 and the
splitting of the peaks at approximately 65o and 75o 2θ is additional evidence for a structural
phase transition between Ca0.61Nd0.26TiO3 and Ca0.52Nd0.32TiO3. In the X-ray diffraction
spectra of Ca0.61Nd0.26TiO3 (Figure 6.12), the peaks at these angles are not split which
suggests a structure with a higher symmetry than C2/m. As a function of temperature for
Ca0.52Nd0.32TiO3, inspection of the key region for detection of phase transitions in this
system reveals that there is no significant change in the splitting of the peaks. As there is
no significant change in the number or splitting of the peaks, it can be confirmed that there
is no phase transition within this temperature range. The lattice parameters of
152
Ca0.52Nd0.32TiO3 as a function of temperature are shown in Figure 6.18. As with all
ceramics so far there is a linear trend in the lattice parameters as a function of temperature
indicating that there is no significant change in the composition due to evaporation of any
of the elements. The thermal expansion coefficients of Ca0.52Nd0.32TiO3 were found to be
245
062
443
424
440
150
242
240
241
2-2-3
103
022
021
020
400
022
1.08x10-5K-1 1.11x10-5 K-1 and 1.27x10-5 K-1for the a, b and c-axes respectively.
775oC
725ooC
675 C
625ooC
575 C
525ooC
475o o C
25 CC
425
375ooC
325oC
275oC
225 C
175oC
125ooC
75 C
25oC
Figure 6.17: Variable temperature X-ray diffraction spectra for Ca 0.52Nd0.32TiO3
The tilt system is a-b0c- indicating two different anti-phase tilts about the a and c
axes and no tilting about the b axis. The peaks in the diffraction pattern confirming the tilt
system assignments were the (113), (311) and the (131). There are no changes in the
number or the splitting of the peaks indicating that it is unlikely that there are any
structural phase transitions in this temperature range for Ca0.52Nd0.32TiO3. There appears to
be some narrowing of the peaks which is an indication of a reduction in the internal
stresses in the sample. The reduction in the internal stresses of the ceramics is likely to be
due to thermal energy input allowing annealing of the ceramics.
153
Temperature (oC)
Figure 6.18: Lattice parameters as a function of temperature for Ca 0.52Nd0.32TiO3
154
Table 6.4: Lattice parameters as a function of temperature for Ca0.52Nd0.32TiO3
a (Å)
b (Å)
c (Å)
β (o)
25
7.670(5)
7.669(10)
7.664(14)
89.85(4)
75
7.675(4)
7.672(9)
7.675(3)
90.18(4)
125
7.679(8)
7.682(9)
7.680(9)
90.11(3)
175
7.682(7)
7.680(8)
7.686(7)
89.88(2)
225
7.685(7)
7.682(7)
7.692(8)
90.11(2)
275
7.691(4)
7.689(5)
7.696(5)
89.89(2)
325
7.693(9)
7.691(9)
7.699(9)
90.09(2)
375
7.701(9)
7.700(9)
7.703(7)
89.92(2)
425
7.707(5)
7.705(6)
7.710(5)
89.90(3)
475
7.708(7)
7.704(3)
7.715(7)
90.04(6)
525
7.715(8)
7.718(7)
7.711(8)
90.06(6)
575
7.718(6)
7.722(7)
7.721(8)
90.01(8)
625
7.731(9)
7.723(9)
7.719(9)
90.08(6)
675
7.747(8)
7.727(6)
7.733(7)
89.89(4)
725
7.730(7)
7.733(7)
7.734(6)
90.02(5)
775
7.732(5)
7.733(5)
7.737(5)
90.01(7)
The antiphase octahedral tilt angles ( ) about the a and c axes for the ceramics with the
monoclinic C2/m structure were calculated using Equation 6.5 and 6.6 [105]. There is no
tilting about the y axis of the structure.
(6.5)
(6.6)
155
Where x(O3) and z(O3) are the x and z coordinates of the O3 oxygen site and x(O4), z
(O4) are the x and z coordinates of the O2 oxygen sites whilst a, b and c are the lattice
parameters of the material. The octahedral tilt angles as a function of temperature are
shown in Figure 6.19. There is no discernible trend in the antiphase tilt angle about the a
axis of the structure whilst the angle about the z axis appears to decrease to a minima then
begins to increase again.
18
16
14
Tilt Angle (o)
12
10
8
6
4
2
0
25
75
125
175
225
275
325
375
425
475
525
575
625
675
725
Temperature (oC)
Figure 6.19: Octahedral tilt angles as a function of temperature for Ca0.52Nd0.32TiO3
(diamond markers represent the antiphase tilts about the x axis and the square markers
represent the antiphase tilt about the z axis)
156
Table 6.5: Octahedral tilt angles as a function of temperature for Ca0.52Nd0.32TiO3
Temperature (oC)
a-axis
c-axis
25
6.5 ± 0.33
15.8 ± 0.79
75
9.2 ± 0.46
14 ± 0.7
125
7.8 ± 0.39
10.4 ± 0.52
175
12.1 ± 0.61
7.8 ± 0.39
225
3.7 ± 0.19
4.4 ± 0.22
275
4.9 ± 0.25
4.4 ± 0.22
325
0.2 ± 0.01
5.6 ± 0.28
375
4.8 ± 0.24
7.3 ± 0.37
425
1.9 ± 0.1
1 ± 0.05
475
9 ± 0.45
3.8 ± 0.19
525
7.9 ± 0.4
6.1 ± 0.31
575
9.7 ± 0.49
3.8 ± 0.19
625
1.3 ± 0.07
1.8 ± 0.09
675
2.6 ± 0.13
1.1 ± 0.06
725
9.6 ± 0.48
8.6 ± 0.43
775
1.2 ± 0.06
0.1 ± 0.01
Figure 6.20: Width of the 330cm -1 peak as a function of temperature
157
6.6.2 Raman Spectroscopy of Ca0.52Nd0.32TiO3
The Raman spectra of Ca0.52Nd0.32TiO3 in the 30-775oC range are shown in Figure
6.21. At cryogenic temperatures there are 12 modes in the spectra In section 5.2 it was
found that the structure of ceramics with x > 0.48 have a monoclinic C2/m structure which
leads to a total of 12 modes in the Raman spectra. The majority of the predicted modes will
be weak due to the small changes in polarisation that are responsible for these modes. The
changes in polarisability are small because the monoclinic tilt angle only deviates from 90o
by a small amount. If structure transformed to a higher symmetry, it would be expected
that the new structure would be orthorhombic Cmmm as was discovered for Ca0.1La0.6TiO3
and 0.9Nd2/3TiO3-0.1NdAlO3 [101]. Group theoretical analysis reveals that there would be
8 modes in the Raman spectra if the structure was to transform to orthorhombic Cmmm.
Examination of the number of modes as a function of temperature suggests that there are
no changes in the number of modes and it is unlikely that there are any structural phase
transitions in this temperature range. This analysis is in agreement with the analysis of the
X-ray diffraction spectra as a function of temperature for Ca0.52Nd0.32TiO3. At 285oC there
are substantial changes in the relative intensities of the peaks suggesting changes similar to
those in Ca0.7Nd0.2TiO3 and Ca0.61Nd0.26TiO3.
158
762
797
627
678
522
400
454
466
314
344
220
246
858K
758K
658K
558K
458K
358K
258K
158K
Figure 6.21: Raman spectra of Ca 0.52Nd0.32TiO3 as a function of temperature
In the analysis of the ceramics that have the orthorhombic Pbnm structure, it was
found that the modes in the 425-550cm-1 range were important in the determination of
changes in structural characteristics. There appears to be similar changes in this same
region but the changes in the relative intensities of the peaks are more subtle and progress
of the transition is over a wider range of temperatures. This is also reflected in the width of
the peak at 314cm-1 where there is no sharp increase in the width in contrast to
Ca0.79Nd0.14TiO3 and Ca0.7Nd0.2TiO3.
159
(a)
(b)
(c)
Figure 6.22: Magnified portion of the Raman spectra of Ca 0.52Nd0.32TiO3 at (a) 285,
(b) 305 and (c) 325oC
160
Figure 6.23: Width of the 330cm -1 peak as a function of temperature for
Ca0.52Nd0.32TiO3
6.7 Structure Sequence of Ca0.43Nd0.38TiO3
The Raman spectra as a function of temperature for Ca0.43Nd0.38TiO3 are shown in
Figure 6.24. At cryogenic temperatures there are 10 modes consistent with the C2/m
structure assigned in section 5.6. From -195oC to approximately 505oC there are no
significant changes in the number of peaks or changes in the relative intensities that persist
over a wide range of temperatures. There are some minor changes in the relative intensities
which may be attributed to changes in the orientation of the crystal. At 505oC, there is a
significant decrease in the intensity of the mode at approximately 520 cm-1 relative to the
mode at 470 cm-1. This transition is consistent with the transitions in the other ceramics
tested in this way.
161
803
754
618
675
524
458
471
322
345
216
858K
758K
658K
558K
458K
358K
258K
158K
Figure 6.24: Raman spectra as a function of temperature for Ca 0.43Nd0.14TiO3
162
(a)
(b)
(c)
163
Figure 6.25: Magnified Raman spectra of Ca 0.43Nd0.38TiO3 at (a) 465, (b) 485 and (c)
505oC
6.8 Structure Sequence of Ca0.1Nd0.6TiO3
6.8.1 Variable Temperature X-ray Diffraction
The X-ray diffraction spectra of Ca0.1Nd0.6TiO3 in the 30-775oC range are shown in
Figure 6.26. Close examination of the splitting of the peaks reveals that there are no
significant changes in this temperature range which suggests that there are no phase
transitions in this temperature range. All diffraction patterns in this temperature range
could be indexed on the basis of the monoclinic C2/m structure with lattice parameters of
the general form of
. The lattice parameters were consistent with
those reported in Section 5.2. The tilt system across the whole of the temperature range
was a-b0c- due to the presence of (113), (311) and (131) type peaks respectively. The lattice
parameters as a function of temperature are shown in Figure 6.27 and there is a clear linear
trend between the lengths of each of the crystallographic axes and temperature. There
appears to be no obvious trend between the monoclinic distortion angle and the
temperature. It is likely that this is due to the small deviation from 90o and insufficient
resolution to adequately resolve small changes in this parameter. The thermal expansion
coefficients for Ca0.1Nd0.6TiO3 were calculated to be 0.0044K-1 for the a axis, 0.0039K-1
for the b axis and 0.0042K-1 for the c axis.
164
062
443
440
423
240
241
150
400
2-2-3
022
222
022
006
021
020
775ooC
725oC
675 oC
625 oC
575 C
525ooC
475 oC
375oC
325oC
275 oC
225 C
175ooC
125 oC
75 C
25oC
Figure 6.26: X-ray diffraction spectra of Ca 0.1Nd0.6TiO3 as a function of temperature
165
7.74
556
Temperature (oC)
Figure 6.27: Lattice parameters as a function of temperature for Ca 0.1Nd0.6TiO3
166
Table 6.6: Lattice parameters of Ca0.1Nd0.6TiO3 as a function of temperature
a (Å)
b (Å)
c (Å)
β (o)
25
7.666(6)
7.664(6)
7.713(6)
90.03(3)
75
7.671(5)
7.670(5)
7.719(5)
90.03(3)
125
7.675(6)
7.673(6)
7.722(6)
90.04(3)
175
7.679(6)
7.677(5)
7.726(5)
90.04(3)
225
7.681(3)
7.681(3)
7.719(3)
89.95(2)
275
7.686(4)
7.684(4)
7.733(4)
90.04(2)
325
7.689(5)
7.678(4)
7.737(4)
90.04(2)
375
7.693(5)
7.692(5)
7.741(5)
90.03(2)
425
7.697(5)
7.696(5)
7.747(5)
89.97(2)
475
7.702(4)
7.700(4)
7.750(4)
90.03(3)
525
7.704(5)
7.703(4)
7.754(4)
89.97(3)
575
7.710(4)
7.710(3)
7.760(3)
89.98(2)
625
7.715(5)
7.714(4)
7.766(4)
89.97(3)
675
7.719(5)
7.719(4)
7.719(5)
89.96(3)
725
7.725(6)
7.726(5)
7.777(6)
89.96(4)
775
7.728(4)
7.736(5)
7.782(5)
89.93(3)
The octahedral tilt angles as a function of temperature for Ca0.1Nd0.6TiO3 are shown
in Figure 6.28. For the antiphase tilt about the a axis of the structure there is a sharp
decrease in the octahedral tilt angles between room temperature and 225 oC whilst after
225oC there seems to be a more random dependence with temperature. For the antiphase
tilt about the c-axis there appears to be a weak linear dependence with increasing
temperature. There are no studies in which the octahedral tilt angles of Ca0.1Nd0.6TiO3 have
been studied as a function of temperature. There is however a few studies where previous
data may be used to calculate these angles or angles have been quoted in the discussion of
the data. Zhang et al. [101] found that the tilt angles of 0.9Nd2/3TiO3-0.1NdAlO3 were 6.8o
(antiphase about the a-axis) and 5.0o for antiphase tilting about the c-axis. Both these
values are higher than the angles calculated for Ca0.1Nd0.6TiO3, most likely the result of the
additional Nd, lack of Ca and the different charge and size of Al3+ compared to Ti4+ [132]
167
18
2
16
1.5
14
Tilt Angle (o)
12
1
10
0.5
8
6
0
4
-0.5
2
0
-1
0
100
200
300
400
500
600
700
800
900
Temperature (oC)
Figure 6.28: Octahedral tilt angles for Ca 0.1Nd0.6TiO3 as a function of temperature
(diamond markers represent the antiphase tilts about the x axis and the square markers
represent the antiphase tilt about the z axis)
168
Table 6.7: Octahedral tilt angles as a function of temperature for Ca0.1Nd0.6TiO3
Temperature (oC)
a-axis
c-axis
25
1.2 ± 0.06
0.1 ± 0.01
75
1.6 ± 0.08
2.7 ± 0.14
125
0.8 ± 0.04
0.1 ± 0.01
175
1.2 ± 0.06
2.2 ± 0.11
225
1.4 ± 0.07
2.5 ± 0.13
275
1.1 ± 0.06
1.9 ± 0.1
325
1 ± 0.05
2.2 ± 0.11
375
0.9 ± 0.05
2.4 ± 0.12
425
0.9 ± 0.05
2 ± 0.1
475
0.5 ± 0.03
2.1 ± 0.11
525
1 ± 0.05
0
575
1.1 ± 0.06
2.2 ± 0.11
625
0.6 ± 0.03
2 ± 0.1
675
0.5 ± 0.03
1.1 ± 0.06
725
0.1 ± 0.01
0.2 ± 0.01
775
0.7 ± 0.04
0
6.8.2 Raman Spectroscopy of Ca0.1Nd0.6TiO3
The Raman spectra for Ca0.1Nd0.6TiO3 taken in the 77-800K temperature range are
shown in Figure 6.29. As with the room temperature spectrum of this composition, there
are 8 distinct Raman active modes visible in the spectra across the entire temperature
range. This suggests that there are no significant structural transitions for this composition
and in this temperature range. There are some changes in the relative intensities of some of
the peaks but the magnitude of these changes alters from one spectrum to the next. The
reason for the random variation in some of the relative intensities of the peaks is likely to
be due to thermal expansion causing the Raman laser to sample regions of different
crystallographic orientation such as twin domains. Towards higher temperature (>500 oC)
169
there is a significant weakening of the intensity of the modes at 450-550cm-1 relative to the
other modes in the spectrum suggesting the onset of a phase transition but it does not reach
858
781
584
534
470
329
352
241
completion before 600oC (see Figure 6.29).
858K
758K
658K
558K
458K
358K
258K
158K
Figure 6.29: Raman spectroscopy as a function of temperature for Ca 0.1Nd0.6TiO3
The relative intensities of the peaks in the 450-550cm-1 region did not show any
changes that would suggest any sort of transition as a function of temperature. To confirm
this observation, the widths for the 469 and 531cm-1 peaks were plotted as a function of
temperature in Figure 6.30. In contrast to ceramics with compositions of x ≤ 0.57, there is a
linear trend between the peak widths and the temperature of the ceramic which can be
attributed to thermal vibrations of the lattice. The linear trend appears to confirm that there
are no significant changes in the alignment of the dipoles.
170
Figure 6.30: Peak widths as a function of temperature for the (a) 469 and (b) 531cm -1
peaks of Ca0.1Nd0.6TiO3
6.9 Trends in Structural Phase Transitions
6.9.1 Transition Diagram of Ca(1-x)Nd2x/3TiO3
The transition temperatures observed in the Raman spectra do not appear to be
reflected in the X-ray diffraction data. Firstly, it is reasonable to expect that there may be
some slight temperature difference between different pieces of equipment. The high
temperature stage for the Raman experiments was calibrated using a sample containing
microfluidic inclusions containing carbon dioxide. The first stage of the calibration was to
cool the sample to -100oC and reheat to approximately -60oC which is near to the triple
point of carbon dioxide. It was found that the carbon dioxide inclusions disappeared at
approximately -57.5oC compared to the accepted value of -56.6oC giving a deviation of
0.9oC. The second calibration point was the melting point of water. Observations of an
inclusion containing water found that the thermocouple used recorded the melting point of
water as -0.4oC. The final calibration point was the critical point of water which occurs at
approximately 374oC. The calibration using this property yielded a temperature deviation
of 7.5oC. The calibration of the furnace attachment for the Anton Paar furnace unit was
found to be approximately 1oC. Due to the large difference in the transition temperatures
and good accuracy of the temperature stages used, it is unlikely that any error in
171
temperature measurement is the cause of the changes in the Raman spectra not being
reflected in the X-ray diffraction data.
Given that it has been established that the transition observed in the Raman
spectroscopy is not reflected in the X-ray diffraction data it is necessary to consider the
possible interpretations of the data. The change in the octahedral tilt angles as with
changing temperature was calculated from the X-ray diffraction data. It was found that
there was no consistent relationship between octahedral tilt changes and changes in the
Raman spectra at elevated temperature. The second part of this argument is to dismiss the
possibility that the antiphase boundaries observed in the microstructure disappear at
elevated temperature. It is possible to explain the changes in the number of peaks in the
Raman spectra by arguing that the disappearance of anti-phase boundaries would lead to an
increase in the local translational symmetry of the lattice. It is however not possible to
explain why there are sudden changes in the peak widths around the transition temperature.
The antiphase domain boundaries are known to occur mainly on the (001) and (110) type
planes [20, 53] but it has been shown that the changes in the Raman spectra in this study
mostly originate from vibrations along the (100) and (010) axes.
It is also possible that there is a change in the polarization state in the lattice in the
range of temperatures where transitions are observed. CaTiO3 based ceramics are classified
as incipient ferroelectrics [148]. These materials do not undergo have a Curie temperature
where ferroelectric behaviour is lost above this temperature. However, it is possible for a
ferroelectric phase to be created by the presence of impurities, elastic strains and electric
fields present in the ceramic sample [148]. For example, Lemanov [149] found that
CaTiO3 undergoes an incipient ferroelectric to ferroelectric transition when 30% of PbTiO3
is added. It is possible given the addition of Nd3+, Mn2O3 and the presence of localised
strains in some samples (see section 5.2) that the CaTiO3 based ceramics could become
ferroelectrics with Nd3+ additions. Given that ceramics in Ca(1-x)Nd2x/3TiO3 are likely to be
ferroelectrics at room temperature, it is also likely that the changes observed as a function
of temperature represent the Curie temperature of the ceramic. The changes observed in the
Raman spectra of Ca0.79Nd0.14TiO3 to Ca0.61Nd0.26TiO3 are consistent with the loss of
ferroelectric order as the peaks with the increase in the peak widths. The changes in the
Raman spectra as a function of temperature of Ca0.52Nd0.32TiO3 to Ca0.1Nd0.6TiO3 do not
172
appear to be consistent with ferroelectric behaviour because the peak widths do not
significantly change with temperature. The change in behaviour is likely due to the phase
transition from orthorhombic Pbnm to monoclinic C2/m. The changes in the relative
intensities of the peaks in the Raman spectra as a function of temperature for the materials
with the C2/m require further investigation to determine the nature of these changes.
.It has been found that Ca(1-x)Nd2x/3TiO3 ceramics change from an incipient
ferroelectric state to a ferroelectric state at different temperatures depending on the
composition of the ceramic. A plot of transition temperature as a function of composition
has been plotted in Figure 6.31. As the Nd3+ content is increased there is a decrease in the
transition temperature to a minima for x = 0.39. After this point the transition temperature
increases to a point above the 600oC limit of the hot stage used in the Raman experiment.
In section 5.2 it was shown that the Ca(1-x)Nd2x/3TiO3 ceramics undergo a phase transition
to monoclinic C2/m and a cation-vacancy order-disorder transition at this point. It is likely
that the strain from the cation-vacancy disorder as a function of composition induces the
changes in the transition temperature.
450
Transition Temperature ( oC)
400
350
300
250
200
150
100
50
0
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
Composition (x)
Figure 6.31: Transition temperatures as a function of composition in Ca (1-x)Nd2x/3TiO3
173
6.9.2 Effect of the Transitions on the Microstructure of Ca(1-x)Nd2x/3TiO3
A key question arising from the analysis of the Raman spectroscopy and X-ray
diffraction data is whether the structural changes that are observed are reflected in the
microstructure of the ceramics. Variable temperature scanning electron microscopy was
used to determine whether the microstructure changes significantly with temperature. The
micrographs in Figure 6.32 are the scanning electron micrographs of Ca0.61Nd0.26TiO3
taken at 150, 200, 250 and 400oC in the heating phase of the experiment. The images were
assessed to monitor for any changes in the twin domains including the contrast, the
morphology and the density of the domains. From the images in figure x it is apparent that
there are no significant changes in any of the domains on heating of the samples to 400 oC.
The samples were subsequently cooled and images taken at 300, 250, 200 and 150oC are
shown in Figure 6.34. There are no changes in the contrast, shape or number of the
domains which suggests that any transitions in this range do not have any effect on the
microstructure of the ceramics.
(A)
(A)
(A)
(B)
(C)
(D)
Figure 6.32: Scanning electron micrographs of Ca 0.61Nd0.26TiO3 heated to (A) 150, (B)
200, (C) 250 and (D) 400oC (scale bar = 10µm)
174
(A)
(B)
(B)
(C)
(D)
Figure 6.33: Scanning electron micrographs of Ca 0.61Nd0.26TiO3 cooled from 400 oC to
(A) 300, (B) 250, (C) 200 and (D) 150 oC
175
7 Control of Domain Density in Ca(1-x)Nd2x/3TiO3 Microwave Dielectric
Ceramics
7.1 Introduction
It was proposed by Kipkoech et al [54] that it may be possible to avoid the
formation of twin domains by sintering pellets below the temperatures at which structural
phase transitions that occur in many perovskite materials. It is hoped that by avoiding these
phase transitions the Q x f of microwave dielectric ceramics may be improved because it is
thought that domains cause damping of phonon propagation. Spark plasma sintering has
been shown to be an effective method of lowering the sintering temperature of many
materials including perovskites (see for example [150]). The spark plasma sintering
process is characterised by the simultaneous application of temperature, pressure and
electric field to the pellet [121]. In this chapter, CaTiO3 pellets fabricated by spark plasma
sintering have been characterised in terms of their structure, microstructure and properties.
7.2 Densification
Attrition milling of calcined powders was used to ensure that powders have both a
small average particle size and narrow particle size distribution for optimal reactivity and
densification (see section 4.4). The powders were subsequently sintered at pressures of 50100MPa with temperatures between 1150oC-1450oC for 10 minutes. The heating and
cooling rates were 200oC/min. The densification as a function of sintering temperature
revealed that all the samples reached densities in excess of 95% of the theoretical density
when sintered between 1150oC-1450oC for 10 minutes.
7.3 Structure
Figure 7.1 shows the X-ray diffraction spectra for the samples fabricated by the
SPS process. All patterns could be indexed on the basis of a single perovskite phase with
an orthorhombic Pbnm structure with lattice parameters of approximately a = √2ac b = √2ac
176
and c = 2ac. No secondary phases were detected in the diffraction spectra. There are no
significant changes in the structure as a function of sintering temperature with only minor
changes in the lattice parameters as summarised in Table 7.1. Although there are only
small differences between the lattice parameters of the samples sintered at different
temperatures using SPS there is a significant difference between the SPS and samples
prepared by conventional sintering. This could indicate that there may be change in the
internal stress state of the ceramics. To further investigate possible changes in the internal
stress state the octahedral tilt angles were calculated from the atomic coordinates of the
second oxygen site and these values are summarised in Table 7.2. Both the in-phase and
antiphase tilt angles decrease as the sintering temperature is increased which indicates a
Intensity (AU)
decrease in the distortion of the structure.
2θ
Figure 7.1: X-ray diffraction spectra of CaTiO3 fabricated by spark plasma sintering at
three different temperatures
The tilt system for the CaTiO3 fabricated by spark plasma sintering does not change
from the a-a-c+ that has been reported for CaTiO3 prepared by conventional methods. The
tilt system notation indicates that there is equal antiphase tilting about the a and b
crystallographic axes whilst there is in-phase tilting about the c axis. This tilt system is
177
confirmed by the presence of (113), (131) and (150) type peaks in the X-ray diffraction
spectra. The X-ray diffraction spectra also suggest the presence of antiphase domains being
present in the ceramics from the presence of odd-even-even, even-odd-even and eveneven-odd type peaks in the spectra. Analysis of the diffraction spectra also reveals that
there are changes in the relative intensities of the peaks. In X-ray diffraction analysis this
indicates that there is a change in the degree of texture as there will be a change in the
number of a specific plane orientated to satisfy the Bragg condition. The mechanism for
these changes is likely to be grain boundary sliding which has been observed in other
ceramics fabricated with the aid of applied pressure [151].
Table 7.1: Structural details of CaTiO3 ceramics fabricated by conventional and spark
plasma sintering. Estimated standard deviations are in brackets.
c (Å)
Volume (Å3)
5.442(6) 5.391(7)
7.651(9)
224.46(5)
1300
5.443(4) 5.386(4)
7.650(6)
224.26(2)
SPS
1450
5.449(3) 5.390(4)
7.657(3)
224.88(2)
Conventional
1500
5.440(5) 5.379(3)
7.642(7)
223.61(3)
Processing
Sintering Temperature a (Å)
Route
(oC)
SPS
1150
SPS
b (Å)
Sintering
Table 7.2: Octahedral tilt angles in CaTiO3 fabricated by SPS
Sintering Temperature
In-phase tilt (o)
Anti-phase tilt (o)
1150
8.87 ± 0.44
13.98 ± 0.70
1300
8.21 ± 0.41
10.17 ± 0.51
1400
7.74 ± 0.39
9.28 ± 0.46
1500
(conventional 9.28 ± 0.46
12.11 ± 0.61
sintering)
178
7.4 Microstructure
7.4.1 Scanning Electron Microscopy
The microstructures of CaTiO3 as a function of sintering temperature are shown in
Figure 8.2. The grain sizes range from 0.3 µm to 6 µm as a function of sintering
temperature. The SEM analysis confirms that all samples are single phase in line with the
XRD analysis. The sample sintered at 1150oC at 100MPa for 10 minutes has the best
microstructure because it appears to be crack free. All other samples have a significant
degree of cracking (see, for example Figure 7.2(d)). The cracking could to be due to
thermal shock of the sintered samples due to the rapid heating/cooling rates of 200oC/min.
It is likely that the sample sintered at 100MPa was crack free due to the increased pressure
causing crack closure. An alternative explanation is that the vacuum used in the SPS
process created a reducing atmosphere for the samples which caused oxygen loss. Such
non-stoichiometry has been known to cause cracking in perovskite ceramics [152]. The
pellet sintered at 1150oC is not cracked and therefore it may be assumed that the oxygen
loss at this temperature is insufficient to cause cracking.
179
(A)
(C)
(B)
(D)
Figure 7.2: Scanning electron micrographs of CaTiO 3 fabricated by spark plasma
sintering (a) sintered at 1150 oC (scale bar 5 µm), (b) sintered at 1300 oC (scale bar 5
µm) (c) sintered at 1450 oC (scale bar 20 µm) and (d) sintered at 1450 oC (scale bar 500
µm)
The scanning electron micrographs in Figure 7.2 show that the CaTiO 3 samples
fabricated by spark plasma sintering show that the grains exhibit many twin domains. The
formation of these twin domains were discussed in detail in Chapter 5 but briefly they form
to mitigate the internal stresses caused by the two structural phase transitions on cooling to
room temperature [20, 53]. The morphology of all of the twin domains appears to be
lamellae with parallel twin walls in contrast to the needle shapes reported for the CaTiO3
samples prepared by conventional sintering. The change in the morphology of the twin
domains is likely to be the differences in the processing conditions for conventional and
spark plasma sintering. The needle morphology arises as a result of twin domain healing
during the sintering process and the degree of healing is dependent on diffusion processes
in the material. Since the healing process is driven by diffusion, it is only possible for
180
healing to occur at high temperatures where there is sufficient thermal energy input for
diffusion to occur. The samples prepared by conventional sintering spend more time at
elevated temperatures compared to the samples fabricated by spark plasma sintering. Given
the extended heat treatment, it is reasonable to expect that the conventional samples would
exhibit more twin domain healing than the samples fabricated by spark plasma sintering.
The intersection angle between adjacent twin domains in the CaTiO3 samples
fabricated by spark plasma sintering is illustrated in Figure 7.3. There appears to be only
one type of angle of interaction between intersecting twin domains. This angle is 90o and it
is not clear why there is no evidence of domains intersecting at 120o in either Figure 7.3 or
in lower magnification image in Figure 7.2c. The domains that intersect at an angle of 120o
are characteristic of the (112) type domains whilst the (011) type domains intersect at an
angle of 90o [53]. The mean domain widths as a function of sintering temperature and
processing route are given in Table 7.3. The domain widths for the samples fabricated by
spark plasma sintering are lower than the samples fabricated by conventional sintering as a
result of decreased time for twin accommodation.
Figure 7.3: High magnification image of twin domains in CaTiO 3 sintered at 1300 oC
showing interaction angles between domains (scale bar = 2µm)
181
Table 7.3: Mean domain widths for CaTiO3 ceramics fabricated by conventional and spark
plasma sintering
Processing route
Sintering Temperature
Domain Width (µm)
SPS
1150
0.292 ± 0.01
SPS
1300
0.467 ± 0.02
SPS
1450
0.417 ± 0.02
Conventional
1500
0.868 ± 0.04
7.4.2 Transmission Electron Microscopy
The scanning electron micrographs in Figure 7.4 revealed that there are twin
domains present in the microstructure of the ceramics. It is possible to determine the
domain types using selected area electron diffraction patterns in the transmission electron
microscope and typical micrographs for the sample sintered at 1150oC are shown in Figure
7.4 and the selected area diffraction patterns are shown in Figure 7.5. The selected area
diffraction pattern of the area indicated by (A) in Figure 7.4 is shown in Figure 7.5(A). It is
observed that there is splitting of the spots away from the centre spot of the diffraction
pattern. Previous work by Wang and Liebermann [20, 53] has shown that this type of
pattern is an indication of (110) type domains. The selected area electron diffraction
pattern of the domain wall region in Figure 7.5 (B) appears to be a superposition of two
single domain diffraction patterns with two different alignments of spots. The two different
alignments of spots indicates that there are two different crystallographic orientations
either side of the twin wall and this is consistent with the (112) type domain walls [20, 53].
182
A
B
Figure 7.4: Transmission Electron Micrograph of CaTiO 3 fabricated by spark plasma
sintering at 1150 oC (scale bar = 200nm)
100
000
002
110
010
000
110
Figure 7.5: Selected area electron diffraction patterns of (a) Region A (b) Region B
along the
̅
zone axis
The work of Wang and Liebermann attributed the (112) domains to the cubic Pm3m to tetragonal I4/mcm structural phase transition whilst the (011) type domains were the
result of the tetragonal I4/mcm to orthorhombic Pbnm phase transition [20, 53]. Given that
183
the cubic Pm-3m to tetragonal I4/mcm structural phase transition is at approximately
1300oC, it must be assumed that there are other processes driving the formation of the twin
domains. The most likely parameter that has changed between the conventional and spark
plasma sintering is the application of pressure during the sintering process. The application
of the pressure could either affect the chemistry of the system to the extent that the phase
transition temperature is suppressed below the sintering temperature used. Alternatively,
external sources of stress such as the rapid heating and cooling rates employed or the
release of the pressure applied could change the behaviour of the twin domains.
A recent study by Zhao et al [153] investigated the structural characteristics of
CaTiO3 under non-hydrostatic conditions to 4.7GPa and under hydrostatic conditions to
8.1GPa. In both loading conditions there were no phase transitions recorded for CaTiO3.
Given that the applied pressure in the spark plasma sintering is 100MPa, it can therefore be
assumed that there are no pressure induced phase transitions are affecting the twin domain
formation in CaTiO3. The pressure applied to the pellets during sintering could also change
the temperature of the structural phase transition. The temperature of the structural phase
transitions in CaRhO3 were found to increase with increase in the pressure applied to the
ceramic [154]. Given that the pressure increases the transition temperature it is unlikely
that the pellets will undergo the structural phase transition required to produce a
combination of (112) and (011) type domains.
The three remaining possibilities are the pressure applied during sintering or the
thermal shock due to the spark plasma sintering process. From the evidence in section 7.1
that speculated that the oxygen octahedra were approaching a tetragonal configuration as a
200
result of tensile residual stresses suggests that it is unlikely that the pressure applied is
responsible for this. It would be expected that the pressure applied would cause
compressive residual stresses and this is not consistent with the changes in octahedral
tilting. The second possibility is that there is oxygen loss from the ceramic during sintering
000
which could cause cracking [155]. The oxygen deficiency would cause cracking due to
differences in the lattice parameters of grains with different oxygen stoichiometries. The
final possibility is cracking caused by thermal shock.
Thermal shock is where a
temperature gradient across a material causes cracking either due to low fracture toughness
or low thermal conductivity. Given the rapid heating and cooling rates employed in the
184
SPS process, there is a strong possibility that thermal shock caused cracking of the samples
fabricated in this way.
7.5 Raman Spectroscopy
The Raman spectra for the three samples prepared by spark plasma sintering are
shown in Figure 7.6. Modes were located at approximately 224, 245, 285, 294, 336, 364,
408, 466, 493, 510, 627, 671 and 728cm-1. The peaks can be assigned to the same
vibrational modes given in the previous chapter with modes in the 200-400cm-1 range
being assigned to the rotations of the oxygen octahedra, 400-510cm-1 assigned to the
torsion of the O-Ti-O bond and the modes above 600cm-1 being attributed to the stretching
of the Ti-O bonds. It is interesting to note that all of the modes are shifted to lower
wavenumbers compared to those reported by Zheng et al. [119-120] and the likely
explanation for this is a change in the internal stress state of the ceramics. The peak shifts
from the Raman spectra are consistent with the changes in the octahedral tilting which
were attributed to changes in the internal Raman modes, a sample of the calcined powder
627
671
728
224
245
285
337
364
408
493
509
of CaTiO3 was investigated using Raman spectroscopy.
Figure 7.6: Raman spectra of CaTiO 3 sintered at three different temperatures
185
Raman spectra were taken from five different positions on the CaTiO3 samples
fabricated by spark plasma sintering and the peak parameters for each sample are given in
Table 7.4. There were only minor differences of less than 1 cm-1 in the positions of the
peaks indicating that the samples are likely to be compositionally homogeneous and that
there are no significant stress state changes between the grains. There are also no
significant changes in the relative intensities of the peaks. There are however significant
728
627
671
493
509
224
245
285
337
364
408
differences between each of the different sintering temperatures used.
150000
100000
50000
200
400
600
800
1000
1200
1400
Figure 7.7: Typical deconvolution of Raman spectrum of CaTiO 3 sintered at 1150 oC
into individual peaks
7.6 Microwave Dielectric Properties
The microwave dielectric properties of the CaTiO3 spark plasma sintered ceramics
are listed in Table 7.5. The relative permittivity of the ceramics was in the range of 135160, which is significantly lower than the reported values of the relative permittivity of
CaTiO3 [10]. The densification and the phase analysis of the materials are the most likely
factors to affect the relative permittivity of microwave dielectric ceramics. Given that
neither of these factors change significantly between the two processing routes, it is not
clear why there should be degradation of this property compared to the literature values.
186
Table 7.4: Microwave dielectric properties of CaTiO3 as a function of sintering
temperature
Sintering Temperature
Relative
Q x f (GHz)
τf (ppm K-1)
Permittivity
1150 (SPS)
135.2 ± 6.76
6770 ± 338.5
752 ± 37.6
1300 (SPS)
152.0 ± 7.6
1498 ± 74.9
750 ± 37.5
1450 (SPS)
150.3 ± 7.52
2179 ± 109
749 ± 37.5
1500 (Conventional Sintering)
159.8 ± 7.99
5930 ± 296.5
800 ± 40
For the Q x f, a standard sample of CaTiO3 was used to calibrate for the changes in
sample dimensions on their effect on the Q x f values of the ceramics. The CaTiO 3
standard sample was found to have a Q x f of 5900GHz which is the literature value for
this material [10] and eliminates the effect of sample dimensions on the Q x f. The crack
free sample sintered at 1150oC was found to have a Q x f of 6700GHz± x GHz which is
slightly higher than the reported value of 6000GHz for CaTiO3 fabricated by conventional
sintering (see section 5.8). It is possible to eliminate certain changes in the microstructure
such as the changes in the densification or the phase analysis of the samples. All the
samples reached in excess of 95% of the theoretical density allowing porosity to be
eliminated as the cause for the changes in the properties. Secondary phases have been
known to increase the Q x f of materials such as Ba(Zn1/3Nb2/3)O2-Ba(Ga1/2Ta1/2)O3 [40]
and to decrease the Q x f of cation deficient perovskites such as La2/3TiO3 [95] Given that
all samples were found to be a single phase of CaTiO3 for both conventional and spark
plasma sintering processes, it is possible to eliminate secondary phases being responsible
for changes in Q x f. There is a possibility that there is some contamination from the SPS
process in the form of carbon and species introduced as a result of the reducing
atmosphere. This may be responsible for some of the low Qxf values and it is possible to
perform an annealing procedure in air to check if properties will be restored.
The analysis of the X-ray diffraction spectra revealed that there were changes in the
octahedral tilt angles when the processing conditions are changed from conventional
187
sintering to spark plasma sintering. It was found that the octahedral tilt angles for the
conventionally prepared CaTiO3 were 9.28 and 12.11 for the a/b axes and c-axis
respectively whilst for the spark plasma sintered samples the angles were 8.87 and 13.98.
An important factor that determines the Q x f of the ceramics is vibrational properties of
the crystal lattice of the sample. It is reasonable to expect that the octahedral tilt angles
would affect the vibrational properties of the lattice.
The
values for the CaTiO3 prepared by the conventional and spark plasma
sintering routes are shown in Table 7.5. The
value for the conventional CaTiO3 is
approximately the same as the values reported in the literature but the three samples
prepared by spark plasma sintering are slightly lower. The error in
measurements is
typically 5% and on this basis it is apparent that there is no difference between the
values of the three spark plasma sintered specimens. It is unlikely that the octahedral tilt
angles are also having an effect on the τf of the CaTiO3 ceramics. In section 7.1 it was
found that the octahedral tilt angles of samples prepared by spark plasma sintering were
significantly different compared to the sample prepared by conventional methods. It is well
known that octahedral tilting has a significant effect on the τf in perovskite based
microwave dielectric ceramics. The resonant frequency of the ceramic is dependent on the
structural characteristics as well as composition of the material. In order for the resonant
frequency to change as a function of temperature, it is realistic to expect that this could be
achieved by changing the tilt angles of the oxygen octahedra. There was however no
consistent trend between the octahedral tilt angles and the τf of the samples fabricated by
spark plasma sintering. The τf of the spark plasma sintered samples are nearly the same and
the conventional samples significantly different. Given this, it would be expected that all
samples fabricated by spark plasma sintering would have octahedral tilt angles that are
either higher or lower than the tilt angles for the samples prepared by conventional
sintering techniques. This is not the case as the sample prepared at 1150oC by spark plasma
sintering has higher tilt angles than conventionally sintered CaTiO3 whilst the samples
prepared at 1300oC and 1450oC have lower tilt angles than CaTiO3.
The Raman spectroscopy showed slight shifts in the peaks suggesting a change in
the internal stress state of the spark plasma sintered specimens compared to the
conventional CaTiO3. The slightly lower
values of the spark plasma sintered samples
188
may be attributed to these residual stresses and distortions as a result of the change in the
processing conditions. The changes in the
due to changes in the internal stress state can
be explained analytically through the use of the equations derived by Bosman and Havinga
[26].
(7.1)
(7.2)
Where:
(7.3)
(7.4)
And
(7.5)
In Section 7.2 it was established that there was a shift in the lattice parameters which
indicates that there is a change in the internal stress state of the ceramics fabricated by
spark plasma sintering relative to samples prepared by conventional sintering methods.
This change in the internal stress state affected the volume of the unit cell and this will
affect the magnitude of the term A in Equation 7.3. It is also possible that the change in the
unit cell volume will also affect the polarisability of the bonds in the structure. The
polarisability will increase as a result of the extra volume available for distortion of the
bonds in the perovskite structure.
189
8 Effect of Composition and Cooling Rate on the Microwave Dielectric
Properties of (1-x)MgTiO3-xCa0.61Nd0.26TiO3
8.1 Introduction
The aim of this part of the study is to produce a ceramic based on the composition
of (1-x)MgTiO3-xCa0.61Nd0.26TiO3 with a temperature coefficient of resonant frequency τf
≈ 0ppmK-1 and to study the effect of cooling rate. In total 5 different compositions were
examined for their microwave dielectric properties, composition and microstructure in the
(1-x)MgTiO3-xCa0.61Nd0.26TiO3 series with x = 0.2, 0.4, 0.6, 0.8 and 1.0. The x = 0.2
composition was studied in detail with variation in the cooling rate and additional
investigations by Raman spectroscopy and synchrotron X-Ray diffraction techniques.
8.2 Composition
8.2.1 Densification
All finished products in the (1-x)MgTiO3-xCa0.61Nd0.26TiO3 system reached at least
95% of the theoretical density. Theoretical densities were calculated from the lattice
parameters of each of the phases and a linear relationship between the composition and the
theoretical density was assumed. The relative densities as a function of composition in the
(1-x)MgTiO3-xCa0.61Nd0.26TiO3 system when sintered at 1450oC for 4 hours are shown in
Figure 8.1. Sintered densities appear to decrease by a small amount with increasing
Ca0.61Nd0.26TiO3 content possibly due to the higher sintering temperature of
Ca0.61Nd0.26TiO3 (1450oC) compared to MgTiO3 (1350oC)
190
Figure 8.1: Density as a function of composition for the (1-x)MgTiO3xCa0.61Nd0.26TiO3 system
8.2.2 Phase Development
The X-Ray diffraction patterns of ceramics in the (1-x)MgTiO3-xCa0.61Nd0.26TiO3
system are shown in Figure 8.2. The patterns reveal that there are three distinct crystalline
phases present in the microstructure which includes the phases of MgTiO3 and
Ca0.61Nd0.26TiO3. The third phase is a secondary MgO-TiO2 phase with a composition of
MgTi2O5 which has been observed in previous studies on similar systems [18, 21]. This
secondary MgO-TiO2 phase is likely to originate as a result of segregation of the MgO and
TiO2 after the initial mixing of the powders.
191
146
306
256
131
122
040
202
2
024
076
1-2-6
221
1-3-2
230
110
006
112
230
Intensity (AU)
0.8MT-0.2CNT
0.6MT-0.4CNT
0.4MT-0.6CNT
0.2MT-0.8CNT
2θ
Figure 8.2: X-ray diffraction spectra of (1-x)MgTiO3-xCa0.61Nd0.26TiO3 as a
function of composition (
for MgTiO3,
for Ca0.61Nd0.26TiO3 and
for MgTi2O5)
The XRD patterns were analysed using Rietveld refinement using the TOPAS 4.2
[124] software package to monitor any substantial changes in the lattice parameters. The
structure used for the Ca0.61Nd0.26TiO3 phase in the refinements was the orthorhombic
Pbnm structure with lattice parameters of
where
is the
lattice parameter of the cubic perovskite form. This structure has been described in detail
in sections 5.2 and 5.3. The structure of the MgTiO3 phase is accepted to be rhombohedral
with lattice parameters of a = 5.05Å and c = 13.89Å whereas the structure of the
MgTi2O5 phase is orthorhombic Bbmm with lattice parameters of a = 9.75Å, b = 10.01Å
and c = 3.73Å [81]. The lattice parameters as a function of composition are shown in
Tables 8.1 and 8.2. The lattice parameters do not change substantially as a function of
composition which suggests there is little or no dissolution of the MgTiO3 into the
Ca0.61Nd0.26TiO3 phase. The difference between the structures of the two phases supports
this proposal.
192
Table 8.1: Lattice parameters as a function of composition for MgTiO3 in (1-x)MgTiO3xCa0.61Nd0.26TiO3
Composition (x)
a (Å)
b (Å)
c (Å)
0.2
5.059(4)
5.059(4)
13.92(1)
0.4
5.058(7)
5.058(7)
13.92(2)
0.6
5.058(7)
5.058(7)
13.92(2)
0.8
5.056(3)
5.056(3)
13.92(1)
Table 8.2 Lattice parameters as a function of composition for Ca0.61Nd0.26TiO3 in (1x)MgTiO3-Ca0.61Nd0.26TiO3
Composition (x)
a (Å)
b (Å)
c (Å)
0.2
5.452(7)
5.420(6)
7.686(9)
0.4
5.443(6)
5.412(6)
7.670(9)
0.6
5.451(7)
5.42(5)
7.68(1)
0.8
5.451(7)
5.412(6)
7.669(5)
8.2.3 Microstructure
Figure 8.2 shows the SEM micrographs of (1-x)MgTiO3-xCa0.61Nd0.26TiO3. The
images reveal that dense ceramics are produced when the powders are sintered at 1450 oC
for 4 hours. The microstructures have a number of small pores which are mainly located at
the grain boundaries which indicates good densification of the ceramics. The grain sizes
range from 5 µm to 15 µm and are consistent with the grain sizes of ceramics such as
0.85Mg0.95Zn0.05TiO3-0.15Ca0.61Nd0.26TiO3 [18]. The grain size of single phase
Ca0.61Nd0.26TiO3 is approximately 30µm and this suggests that the grain sizes of the
composite ceramics are inhibited by the presence of the MgTiO3 phase. Z contrast arises in
backscattered electron images as a result in differences in the atomic number of the
elements from grain to grain. On this basis there appears to be two distinct phases present
in the microstructure and in conjunction with the EDX spectra (Figure 8.4) is possible to
deduce that the light contrast phase is Ca0.61Nd0.26TiO3 and the darker contrast phase is
MgTiO3. It is not immediately apparent whether the MgTi2O5 phase is present because
there does not appear to be a third type of contrast. It is unlikely to be possible to
distinguish between the MgTiO3 and MgTi2O5 phases using backscattered electrons
193
because the atomic numbers of the atoms in each of the phases are the same. All grains
have an equiaxed morphology including 0.2MgTiO3-0.8Ca0.61Nd0.26TiO3 where MgTiO3
has inhibited the formation of abnormal Ca0.61Nd0.26TiO3.
(A)
(B)
(C)
(D)
Figure 8.3: Scanning electron micrographs of (1-x)MgTiO3-xCa0.61Nd0.26TiO3 as a
function
of
composition
0.6Ca0.61Nd0.26TiO3
(c)
(a)
0.2MgTiO 3-0.8Ca0.61Nd0.26TiO3
0.6MgTiO 3-0.4Ca0.61Nd0.26TiO3
0.2Ca0.61Nd0.26TiO3. Scale bar is 10µm.
and
(b)
0.4MgTiO 3-
(d)
0.8MgTiO 3-
(A)
194
(B)
Figure 8.4: EDX spectra of 0.8MgTiO 3-0.2Ca0.61Nd0.26TiO3 showing (a) MgTiO 3 from
grey contrast grain and (b) Ca0.61Nd0.26TiO3 from white contrast grain
195
Table 8.3: Composition of each grain by EDX analysis
Weight %
Atomic %
Weight %
Atomic %
O (K line)
42.62
63.01
33.41
65.05
Ca (K line)
N/A
N/A
14.54
11.30
Ti (K line)
39.30
19.41
28.48
18.52
Zn (K line)
N/A
N/A
0.15
0.07
Nd (L line)
N/A
N/A
23.42
5.06
Mg (K line)
18.08
17.59
N/A
N/A
8.2.4 Microwave Dielectric Properties
The relative permittivity and the
values as a function of composition in the (1-
x)MgTiO3-xCa0.61Nd0.26TiO3 system are shown in Figure 8.5. The relative permittivity and
values both decrease in an almost linear fashion with composition and this can be
explained using a simple rule of mixtures.
(8.1)
The relative permittivity decreases as a function of composition from 89.7 for
Ca0.61Nd0.26TiO3 to 25.4 for 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3. The relative permittivity of
MgTiO3 when produced by the mixed oxide route is 17 and for Ca0.61Nd0.26TiO3 it is 89.7.
A summary of the predicted relative permittivities and those determined experimentally are
summarised in Table 8.2. The estimated properties were calculated on the basis of a linear
dependence between composition and microwave dielectric properties assuming there is no
solid solution formation. The data for these properties were taken from Ferreira et al [21]
and section 5.8 of this study. The reason for the deviation between the experimental and
calculated values is the presence of porosity which is well known to degrade the relative
permittivity of microwave dielectric ceramics. There are no studies in which to directly
196
compare the microwave dielectric properties of ceramics in the (1-x)MgTiO3xCa0.61Nd0.26TiO3.
Table 8.4: Estimated and measured microwave dielectric properties of (1-x)MgTiO3xCa0.61Nd0.26TiO3 (calculated using MgTiO3 data from Ferreira et al [21] and properties
reported in section 5.8)
Composition
(x)
Estimate
d εr
Measured
εr
Estimated
Measured
Qxf
Qxf
(GHz)
(GHz)
Estimated τf
-1
(ppmK )
Measured
τf
(ppmK-1)
0.2
31±1.55
25.6±1.28
47300±236
39000±1950
3.6±0.18
1.4±0.07
0.4
45±2.25
35.3±1.87
38600±193
25600±1280
63.2±3.16
71.6±3.58
0.6
59±2.95
47.5±2.38
29900±149
18000±900
122.8±6.14
124±6.2
0.8
73±3.65
56.8±2.84
21200±106
12600±630
182.4±9.12
151±7.55
Composition (x in (1-x)MgTiO3-xCa0.61Nd0.26TiO3
197
Q x f (GHz)
Relative Permittivity
Composition (x in (1-x)MgTiO3-xCa0.61Nd0.26TiO3
Figure 8.5: Microwave dielectric properties of (1-x)MgTiO3-xCa0.61Nd0.26TiO3 as a
function of composition (a) τ f (b) εr and Q x f
The
values decrease from 242 ppm k-1 for Ca0.61Nd0.26TiO3 to 1.4ppm K-1 for
0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 and follow a linear law of mixtures relationship. The
reduction in the τf is the result of the opposite polarity values of each of the end members
in this system. The τf of MgTiO3 is -56ppmK-1 [9] which allows tuning of the τf and the
composition dependence of the τf is shown in Figure 8.5(a). Compared to similar materials
such as 0.9MgTiO3-0.1CaTiO3 [9] the amount of MgTiO3 required to obtain a temperature
stable ceramic is less which allows for higher relative permittivity to be obtained but at the
expense of the Q x f value.
The Q x f values range from 12000GHz for the 0.2MgTiO3-0.8Ca0.61Nd0.26TiO3
composition to 39000GHz for 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 and the values are displayed
in Figure 8.5b. The most widely studied composition in this series is based on 0.8MgTiO30.2Ca0.61Nd0.26TiO3 as this has the
value which is closest to 0 ppm K-1 [16, 106, 112198
115] The values of the Q x f in Figure 8.4 do not agree with the values previously
published studies of similar materials such as Mg0.95Zn0.05TiO3-CaTiO3 [16, 106, 112-115].
The majority of the ceramics cannot be directly compared due to differences in the
composition. The higher Q x f can be attributed to the higher proportion of MgTiO 3 added
to the ceramics by Huang et al. [16] compared to this study and the addition of ZnTiO3.
The addition of more MgTiO3 increases the Q x f because it has a higher Q x f of
56000GHz compared to Ca0.61Nd0.26TiO3 (12600GHz). Additions of ZnTiO3 have also
been shown to improve the Q x f of MgTiO3 from 56000GHz to x GHz depending on the
amount of ZnTiO3. The final possible reason for the differences in the Q x f values is the
processing route employed to fabricate the ceramics. The ceramics fabricated by Ferreira et
al [21] were prepared by a Pechini method as opposed to the mixed oxide route in this
study. The Pechini method is known to produce high quality ceramics with improved Q x f
values as a result of reduction in the concentration of impurities, especially at grain
boundaries [21].
The Q x f value of MgTiO3 produced by the mixed oxide route is 56000GHz and it
would be expected that the 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 composition would have an
approximate Q x f of 47800GHz assuming a linear dependence of the Q x f on the
composition of the ceramic. The difference from what is expected for the Q x f value is
unlikely to be due to the presence of the MgTi2O5 phase because the proportion of this
phase in the microstructure is insufficient (< 5wt %) to have a significant effect on the Q x
f value. The effect of any temperature changes during the course of the measurement can
be ignored because any changes are likely to be too subtle to significantly change the Q x f.
0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 has a small value of
of 1.4 ppm K-1 which gives the
dielectric behaviour good stability should the temperature change. The presence of defects
such as grain boundaries, point defects and twin domains are known to cause reduction in
the Q x f value from predicted values of the microwave dielectric properties [67]. This
deviation however is the difference between theoretical values derived from spectroscopic
data and not predictions based on experimental data of the properties. It can therefore be
assumed that the experimental values take into account some of the differences in
dielectric losses because the presence of defects is already accounted for.
199
It is by the process of elimination that the difference between the experimental and
expected microwave dielectric properties from experimental data is likely to be due to the
presence of residual stresses in the lattice. The residual stress in the structure will change
the d-spacings of the crystal lattice and this will change the vibrational properties of the
lattice. The residual stress will have the most significant effect on the Q x f value if the
magnitude of the stress varies from grain to grain as homogenous d-spacings will not
change the wavelength of the phonon. If the wavelength of the phonon is not changed, it is
not possible for either the resonant frequency or the dielectric losses to change.
200
8.3 Effect of Cooling Rate on the Microwave Dielectric Properties of
0.8MgTiO3-0.2Ca0.61Nd0.26TiO3
8.3.1 Microstructure
All ceramics reached in excess of 95% of the theoretical density when sintered at
o
1450 C for 4 hours and cooled at different rates. The SEM micrographs for 0.8MgTiO30.2Ca0.61Nd0.26TiO3 as a function of cooling rate are shown in Figure 8.5. The images
confirm that the ceramics are dense with small number of pores at the grain boundaries.
The images also confirm that there are two distinct phases are present including MgTiO3
andCa0.61Nd0.26TiO3 but no search was conducted to find MgTi2O5. The grain sizes range
from 5µm to 8µm showing that the grain size does not significantly change as a function of
cooling rate. The grains have equiaxed morphology and this does not change with cooling
rate; there is no evidence of abnormal grain growth.
201
Figure 8.6: Scanning electron micrographs of 0.8MgTiO 3-0.2Ca0.61Nd0.26TiO3 as a
function of cooling rate (a) cooling rate of 300 oC/hr (b) cooling rate of 60 oC/hr and (c)
15oC/hr. Scale bar is 20µm
8.3.2 Phase Development
The XRD patterns for 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 as a function of cooling rate
are shown in Figure 8.6. As with the investigation of different levels of Ca0.61Nd0.26TiO3
additions, all ceramics had three phases present in the microstructure. The patterns show
that the main phases were MgTiO3 and Ca0.61Nd0.26TiO3 with small amounts of the minor
MgTi2O5 phase present. The proportion of each of the phases present is consistent with the
intended composition for the ceramics. The amount of each phase present does not change
significantly with cooling rate. The XRD patterns were refined on the basis of the
structures determined in chapter 5 for Ca0.61Nd0.26TiO3 (Pbnm) and reported in the
literature for MgTiO3 (R3) and MgTi2O5 (Bbmm). The lattice parameters for the
202
0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 ceramics as a function of cooling rate are summarised in
Table 8.5. The lattice parameters are in good agreement with previous studies on the lattice
parameters of each of the phases.
Table 8.5: Lattice parameters as a function of cooling rate
Phase (cooling rate)
a (Å)
b (Å)
c (Å)
MgTiO3 (15oC/hr)
5.053
5.053
13.8
MgTiO3 (60oC/hr)
5.056
5.056
13.9
5.054
5.054
13.9
Ca0.61Nd0.26TiO3 (15 C/hr)
5.411
5.443
7.673
Ca0.61Nd0.26TiO3 (60oC/hr)
5.418
5.447
7.675
Ca0.61Nd0.26TiO3 (300oC/hr)
5.414
5.449
7.674
MgTi2O5 (15oC/hr)
9.745
10.01
3.740
MgTi2O5 (60oC/hr)
9.740
10.07
3.74
MgTi2O5 (300oC/hr)
9.754
10.01
3.739
MgTiO3 (300oC/hr)
o
203
206
316 161 323
286
02 10 02 10
134
086 242
196
146
306
256
Ca0.61Nd0.26TiO3
220
131
122
202
024
076
1-2-6
221
1-3-2
230
321 240 123
210
110
MgTi2O5
Intensity (AU)
003
101
012
230
121
104 104
MgTiO3
15oC/hr
60oC/hr
300oC/hr
2θ
Figure 8.7: X-ray diffraction patterns of 0.8MgTiO 3-0.2Ca0.61Nd0.26TiO3 as a function
of cooling rate
8.3.3 Raman Spectroscopy
8.3.3.1 Effect of Cooling Rate on the Raman Spectra
The Raman spectra of 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 as a function of cooling rate
are shown in Figure 8.7. As there are three phases present in the microstructure, ten
different grains were sampled to try and obtain Raman spectra for each of the phases. Two
distinct grain contrasts were observed using the optical microscope during this experiment.
Raman active peaks were observed at 222, 247, 272, 280, 322, 324, 327, 340, 349, 389,
396, 481 and 710cm-1 and the mode assignments are listed in Table 8.3. The values listed
here deviate typically between 1-5cm-1 and this is likely to be due to stresses present in the
204
crystal lattice [66]. No attempt was made to quantify this stress state as it is difficult to find
637
481
340
349
389
396
222
247
272
280
322
710
peaks related to the Ca0.61Nd0.26TiO3.
15oC/hr
60oC/hr
300oC/hr
Figure 8.8: Raman spectra as a function of cooling rate in the 0.8MgTiO 30.2Ca0.61Nd0.26TiO3 system
205
Table 8.6: Summary of assignment of modes of vibration for 0.8MgTiO30.2Ca0.61Nd0.26TiO3 as a function of cooling rate
Peak Position Assignment of Mode of Vibration
222
Vibration of Mg and Ti along (001) Axis
247-272
MgTi2O5
280
Stretch Breathing of Oxygen Octahedra
322-340
Twisting of the Oxygen Octahedra with the Mg and Ti on the xy plane
349
Twisting of the Oxygen Octahedra with the Mg and Ti on the xy plane
380-396
Vibration of Oxygen
481
Antisymmetric Breathing of Oxygen octahedra with Mg + Ti in xy
637
Antisymmetric Breathing of Oxygen octahedra with Mg + Ti in xy
710
Vibration of Oxygen
The preferred method of measurement of the residual stress in 0.8MgTiO30.2Ca0.61Nd0.26TiO3 microwave dielectric ceramics was to use Raman spectroscopy and to
measure the shift in the modes. The measurements of the Raman spectra of these ceramics
have revealed that there may be an issue in adequately distinguishing between the phases
present in the microstructure. The grain sizes of the ceramics is approximately 5-6µm and
when using a x100 objective lens it should be possible to focus the laser beam on a single
grain and not get a signal from the neighbouring grains. It is however possible that the
Raman laser is penetrating below the surface to a depth greater than the average grain size
and this is part of the reason for not being able to distinguish between the phases. The other
reason for not being able to distinguish between the different phases is the much higher
intensities of the modes of MgTiO3 compared to the modes of Ca0.61Nd0.26TiO3 to the
extent that none of the modes can be resolved.
8.3.3.2 Confocal Raman Spectroscopy
Confocal Raman spectroscopy can be used to probe changes in the structural
parameters of ceramics as a function of depth in materials and to estimate the depth to
which the Raman laser penetrates. The Raman spectra as a function of depth are shown in
Figure 8.8 and each spectra in the figure represents a change in the working distance of
206
1µm. Also, due to the three phase nature of the material, two different contrasts of grain
were assessed. As with the conventional Raman spectra reported in section 8.3.3.1, thirteen
modes were required to fit the spectra and the peak parameters were also in good
agreement. Three modes at 255, 467 and 518 cm-1 disappeared from the spectra as the
sample stage was moved up in the z-direction. The majority of the peaks do not shift
significantly as a function of depth into the sample or if there is any shift it appears to be
random. Given that some modes show a random change and others do not significantly
change, it is not possible to state for certain whether there are any changes in the stress
state of the grains.
Intensity (AU)
714
642
484
518
396
223
255
10000
280
306
327
352
(A)
12000
8000
6000
4000
2000
0
200
300
400
500
Wavenumber
600
700
800
(cm-1)
207
(B)
400
500
714
484
518
300
642
396
9000
223
255
280
306
327
352
10000
8000
Intensity (AU)
7000
6000
5000
4000
3000
2000
1000
0
200
Wavenumber
600
700
800
900
(cm-1)
Figure 8.9: Raman spectra as a function of penetration depth into sample for (a) grain
of MgTiO3 and (b) grain of Ca 0.61Nd0.26TiO3
As the position of the sample stage was moved in the z direction, the absolute
intensity of the Raman modes was reduced and there were some changes in the relative
intensities of the peaks. The change in the relative intensities of the peaks indicates that a
grain boundary has been crossed and that a new grain is being sampled. The changes in the
relative intensity as a function of depth appear to coincide with the grain size of the
ceramics that were tested. For example, the grain size of the 0.8MgTiO30.2Ca0.61Nd0.26TiO3 ceramic cooled at 180oC/hr was approximately 7µm and there is a
change in the relative intensities with the same change in magnitude in the z-direction. The
penetration depth of the Raman laser was determined to be approximately 20-25µm for
each of the grains sampled. There are no studies of the confocal Raman spectroscopy of
0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 that can be used to compare these results.
208
8.3.4 Synchrotron XRD
The synchrotron X-ray diffraction patterns of 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3
cooled at three different rates are shown in Figure 8.9. As with the conventional XRD,
three phases were detected including the phases of MgTiO3 and Ca0.61Nd0.26TiO3 and
MgTi2O5. The relative proportions of each of the phases are also consistent with the target
composition with the amount of MgTi2O5 remaining reasonably constant as a function of
cooling rate. The diffraction patterns were indexed in the same manner as section 8.3.2.
The MgTiO3 phase was indexed on the basis of a rhombohedral
structure whilst
Ca0.61Nd0.26TiO3 and MgTi2O5 were indexed on the basis of orthorhombic Pbnm and
Bbmm respectively.
(A)
003
(B)
209
(C)
Figure
8.10:
Synchrotron
X-ray
diffraction
patterns
for
0.8MgTiO 3-
0.2Ca0.61Nd0.26TiO3 as a function of cooling rate
Table 8.7: Proportions of each of the phases in 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 ceramics as
a function of cooling rate
Cooling Rate (oC/hr) MgTiO3 (%)
Ca0.61Nd0.26TiO3 (%)
MgTi2O5(%)
300
74.8 ± 3.74
25.4 ± 1.27
3.5 ± 0.18
60
77.2 ± 3.86
22.4 ± 1.12
4.1 ± 0.21
15
74.9 ± 3.75
24.9 ± 1.25
3.8 ± 0.19
210
Table 8.8a: Summary of lattice parameters, atomic coordinates, site occupancies and
temperature factors for MgTiO3 as a function of cooling rate.
Cooling Rate (oC/hr)
300 C/hr 60 oC/hr
15 oC/hr
R-3
R-3
R-3
5.05420(6)
5.05444(7)
5.05421(6)
5.05420(6)
5.05444(7)
5.05421(6)
13.9063(3)
13.9072(3)
13.9075(2)
307.64
307.69
307.67
0
0
0
0
0
0
0.3553(5)
0.3557(5)
0.3561(5)
0.840(4)
0.856(4)
1.01(4)
0
0
0
0
0
0
0.1450(3)
0.1449(3)
0.1450(2)
0.840(4)
0.856(4)
1.01(4)
0.315(1)
0.315(1)
0.317(1)
0.0221(2)
0.022(2)
0.0217(1)
0.2461(6)
0.2465(6)
0.2473(4)
0.840(4)
0.856(4)
1.01(4)
o
Space Group
a (Å)
b (Å)
c (Å)
Volume
Mg
Ti
O1
x
y
z
Temperature Factor
x
y
z
Temperature Factor
x
y
z
Temperature Factor
211
Table 8.8b: Summary of lattice parameters, atomic coordinates, site occupancies and
temperature factors for Ca0.61Nd0.26TiO3 as a function of cooling rate
Cooling Rate (oC/hr)
300 C/hr 60 oC/hr
15 oC/hr
Pbnm
Pbnm
o
Space
Group
a (Å)
b (Å)
c (Å)
Volume
Ca
Nd
Ti
O1
O2
x
y
z
Occupancy
Temperature Factor
x
y
z
Occupancy
Temperature Factor
x
y
z
Temperature Factor
x
y
z
Temperature Factor
x
y
z
Temperature Factor
Pbnm
5.4161(2)
5.4449(3)
7.6765(3)
5.4166(3)
5.4466(3)
7.6775(3)
5.4172(2)
5.447(2)
7.6788(3)
226.38
-0.005(2)
0.0283(9)
0.25
0.61
1.24(8)
-0.005(2)
0.028(9)
0.25
0.26
1.24(8)
0
0.5
0
1.24(8)
0.071(7)
0.485(4)
0.25
1.24(8)
0.715(7)
0.284(4)
0.037(4)
1.24(8)
226.5
-0.008(2)
0.027(1)
0.25
0.61
1.18(8)
-0.008(2)
0.027(1)
0.25
0.26
1.18(8)
0
0.5
0
1.18(8)
0.077(7)
0.485(5)
0.25
1.18(8)
0.717(5)
0.283(5)
0.038(3)
1.18(8)
226.58
-0.005(2)
0.0283(8)
0.25
0.61
1.34(7)
-0.005(2)
0.0283(8)
0.25
0.26
1.34(7)
0
0.5
0
1.34(7)
0.072(3)
0.484(4)
0.25
1.34(7)
0.718(4)
0.283(3)
0.033(3)
1.34(7)
In order to establish whether the fabrication of a three phase composite ceramics
has any effect on the internal stress state of each individual phase, the lattice parameters of
the sintered and polished samples were compared with the lattice parameters of crushed
powders. The crushed powders cannot sustain any long range residual stresses because the
connectivity between the grains has been lost. Once the connectivity has been lost the
structure is able to relax and the lattice parameters will be longer if the stresses are
212
compressive and shorter if the stresses are tensile. A comparison of the lattice parameters
of Ca0.61Nd0.26TiO3 (crushed solids), MgTiO3 taken from the work of Weschler et al [81]
and 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 sintered solids shows that there are reasonable
differences (0.01Å) between the lattice parameters of the sintered solids containing
Ca0.61Nd0.26TiO3 and the powders of the same composition (from section 5.3.1). There
appears to be no regular pattern between the cooling rate and the lattice parameters. The
likely reason for this is that the proportions of each of the phases are changing at the same
time.
Another way of determining whether the stress state is changing as a function of
cooling rate is to monitor the changes in the widths of the peaks. There are three key
contributions to the width of diffraction peaks which are the crystallite size, stress state and
instrumental broadening parameters. The width of the peaks will only broaden if the
changes in the lattice parameters are non-uniform because of the distribution of different dspacings in the lattice. In order to accurately measure changes in d-spacing distribution two
assumptions must be made. The first of these is that there are no changes in the
instrumental broadening contribution of the peaks. This is a reasonable assumption as the
same instrument was used for each of the samples and there is an additional advantage of
using a synchrotron source as the instrumental broadening is relatively low compared to
conventional sources. The second assumption is that the crystallite size does not have any
significant contribution to the peak widths. The crystallite size will generally only
significantly affect the width of the peaks if the crystallite size is below 1µm. For MgTiO3,
there are no features such as twin domains which means that the crystallite size is likely to
be the same as the grain size. Given that the grain sizes of all the MgTiO3 samples in this
study are 5µm and above, it is unlikely that the crystallite size is having any significant
effect on the width of the peaks of the MgTiO3. A similar set of arguments can be applied
to the peak widths of the Ca0.61Nd0.26TiO3 phase. Given that there is no nano-checkerboard
pattern at the lattice level of Ca0.61Nd0.26TiO3, it is likely that the smallest diffracting unit
would be a single domain region of a grain. Given that the typical domain width from
section 5.4 was approximately 4 µm, it is also unlikely that the Ca0.61Nd0.26TiO3 phase
would experience any peak broadening from changes in crystallite size.
213
Initial visual examination of the peaks reveals that there are no significant changes
in the width of the peaks in the diffraction spectra for each of the ceramics. This is true
across the whole 2θ range which is important because it would be expected that the peak
broadening would be more sensitive at higher 2θ values. Given that there is no significant
change in the widths of the peaks it can be assumed that there is no change in the
distribution of the spacings of the lattice planes. This does not mean however that there is
no change in a stress state of a uniform nature and this can be assessed through changes in
the lattice parameters.
The changes in the lattice parameters for the composite ceramics compared to the
single phase ceramics has been used to detect changes in the stress state of the ceramics.
The origin of the stresses in these ceramics are likely to be due to differences in the linear
thermal expansion coefficients between each of the phases. The linear thermal expansion
coefficients for Ca0.61Nd0.26TiO3 were reported in chapter 6 whilst the linear thermal
expansion coefficients for MgTiO3 were derived from the lattice parameters reported by
Henderson et al [156]. The linear thermal expansion coefficients are repeated in Table 8.4
for the purpose of the following argument. The thermal expansion coefficients for the a
and b axes of both phases are similar whilst there is a substantial difference in the
expansion coefficient of the c-axis for each phase.
Table 8.9: Thermal expansion coefficients for MgTiO3 and Ca0.61Nd0.26TiO3 determined by
neutron diffraction [156] and X-ray diffraction respectively (from chapter 6)
axis
MgTiO3
Ca0.61Nd0.26TiO3
a (/oC)
0.00006
0.00007
b (/oC)
0.00006
0.00006
c (/oC)
0.0002
0.00009
8.3.4 Microwave Dielectric Properties
The microwave dielectric properties of the 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 are
shown in Table 8.10. The relative permittivity of the ceramics is approximately 26,
214
consistent with the measurements made in section 8.2.4. There is little change as a function
of cooling rate. The likely reason for this is that the density of the ceramics does not
change significantly with cooling rate as the ceramics are of high density with
conventional cooling rates (180oC/hr).
Table 8.10: Microwave dielectric properties of 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 at different
cooling rates. Measurement frequency was approximately 3.5GHz.
Cooling Rate (oC/hr)
εr
Q x f (GHz)
300
26.2 ± 1.31
35000 ± 1750
60
26.5 ± 1.33
43900 ± 2195
15
26.6 ± 1.33
49000 ± 2450
There are significant differences in the Q x f values with decreasing cooling rate for
0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 ceramics. The mechanisms responsible for the changes in
the Q x f are difficult to elucidate in the same way as Ca (1-x)Nd2x/3TiO3. As with Ca(1x)Nd2x/3TiO3,
there are no significant changes in the porosity and all samples are fully
dense. The grain size is also reasonably constant and there are some doubts whether grain
size really affects the Q x f of microwave dielectric ceramics. In section 5.8 of this study, it
was revealed that the Q x f was dependent on the domain widths of the twin domains.
Lowe [138] demonstrated that as the cooling rate is decreased the density of domains in the
microstructure is decreased. It would be expected that the domain density would behave in
the same way in Ca0.61Nd0.26TiO3 given that the domain morphology is significantly
different compared to CaTiO3. It is however unlikely that the twin domain density of the
Ca0.61Nd0.26TiO3 would change enough to produce the change in the Q x f that has been
observed in the MgTiO3 ceramics.
Another well-known physical factor that affects the Q x f is the cation ordering or
cation-vacancy ordering in the case of A-site modified perovskite ceramics. Firstly,
ordering effects are not possible in the MgTiO3 phase because there is only a single
element on each lattice site and therefore there is nothing for Mg or Ti to order with.
Changes in the degree of cation-vacancy ordering are possible in the Ca0.61Nd0.26TiO3
215
phase. Although the Ca0.61Nd0.26TiO3 was found to be highly disordered (section 5.7), it is
still possible that this ordering was improved by slow cooling. It is not certain whether this
process took place as neither the synchrotron X-ray diffraction nor the Raman
spectroscopy showed any evidence of an increase in ordering. The main difficulty
associated with monitoring the changes in the ordering using Raman spectroscopy was the
difficulty in the detection of the Ca0.61Nd0.26TiO3 phase.
The final factor that is known to affect the Q x f is the dielectric losses of the
perfect lattice (intrinsic losses) [67]. It is possible to speculate about the changes in the
intrinsic losses of the lattice by examining the lattice parameters as a function of cooling
rate. Although there is no clear pattern in the a and b axes of the unit cell for either
MgTiO3 or Ca.61Nd0.26TiO3, there is a clear increase in the length of the c-axis for both of
the phases. It is unlikely that this is due to changes in the internal stress state as it would be
expected that one phase would expand and the other would be compressed as a result
whilst there would be no effect on MgTi2O5 because of the relatively low content of this
phase at < 4 wt%. Given that both phases appear to expand it is more likely that the
vibrational properties of the lattice are responsible and that Q x f values are increased as a
result of longer c-axis lengths.
216
9 General Discussion, Conclusions and Suggestions for Further Work
9.0 General Discussion
The effect of processing conditions and composition on the microwave dielectric
properties of Ca(1-x)Nd2x/3TiO3 based ceramics has been investigated using diffraction
techniques, microscopy and spectroscopy. It was found that all ceramics reached in excess
of 95% of the theoretical density when conventionally processed and sintered at 14501500oC and when CaTiO3 was processed by spark plasma sintering (SPS) between 11501450oC. The Ca(1-x)Nd2xTiO3 ceramics were all found to be single phase perovskite with
either the orthorhombic Pbnm or monoclinic C2/m structure depending on the
composition. The a and c lattice parameters of Ca(1-x)Nd2x/3TiO3 increased as a function of
composition whilst the length of the b-axis decreased. These changes were attributed to the
different sizes and charges of the Ca2+ and Nd3+ ions respectively. In contrast, ‘composite’
ceramics of Ca(1-x)Nd2xTiO3 and MgTiO3 were found to be triple phase with the additional
phase of MgTi2O5 being detected by X-ray methods. MgTiO3 and MgTi2O5 were refined
on the basis of their literature structures of rhombohedral R3 and orthorhombic Bbmm
respectively. It was found that there was no clear trend between the lattice parameters and
the composition of the ceramics. There is some evidence of residual stress altering the
lattice parameters as a result of different thermal expansion coefficients of each of the
phases.
The grain sizes of the ceramics ranged from 500nm (CaTiO3, SPS processed) to
100µm for Ca0.1Nd0.6TiO3 whilst composite ceramics based on MgTiO3 had an almost
constant grain size of 8µm regardless of the composition. The grain shape of all (1x)MgTiO3-xCa0.61Nd0.26TiO3 ceramics was equiaxed as were the ceramics with x ≤ 0.39 in
the Ca(1-x)Nd2x/3TiO3 system. For ceramics with x > 0.39, the grains were equiaxed but with
evidence of abnormal grain growth as a result of vacancies driving grain growth. For Ca(1x)Nd2x/3TiO3
the pores were located at grain boundaries and within the bulk of the grain in
contrast to the composite ceramics where the pores were only found at grain boundaries.
SEM examination of the microstructures of the composite ceramics suggested even
distribution of the two main phases of MgTiO3 and Ca0.61Nd0.26TiO3 whilst MgTi2O5 was
difficult to detect by SEM. Chemical etching of Ca(1-x)Nd2x/3TiO3 revealed extensive
217
twinning present in the microstructure. The dominant morphology of the domains was
needle lamellae for CaTiO3 whilst on addition of Nd3+ the domain morphologies became
more complex with domains with multiple walls and evidence of curved domain walls. The
needle lamellae were found to be dominant in ceramics with compositions of x ≥ 0.57. The
domain widths were measured using a linear intercept method and it was found that the
mean domain width for CaTiO3 was approximately 1.653µm. The domain widths increased
with composition to a maximum of 4.12µm for Ca0.61Nd0.26TiO3 and subsequently
decreased to 1.67µm for Ca0.1Nd0.6TiO3. There was a sudden drop in the domain width to
1.34µm for Ca0.52Nd0.32TiO3 which could not be explained.
High resolution synchrotron X-ray diffraction (XRD) and scanning transmission
electron microscopy (STEM) in conjunction with Raman spectroscopy was used to probe
cation-vacancy ordering in the lattice. It was found that for compositions with x ≤ 0.39
there was significant cation-vacancy disorder transitioning to short range order at x = 0.52
and near complete ordering of cations and vacancies with x = 0.9. Transmission electron
microscopy (TEM) investigations found that an ordered superstructure of alternating layers
of cations and vacancies was formed at x = 0.9. The ordered superstructure of a nanochessboard lattice may form as a way of mitigating the stresses induced by regions of
different order parameters. These observations were confirmed by the synchrotron XRD
which showed asymmetric peak broadening, consistent with the formation of a nanochessboard pattern. The significance of these results is that interesting properties in
microwave dielectrics and other materials by controlling assembly on the nano-scale
TEM was used in conjunction with scanning electron microscopy to investigate the
twin domains present in the microstructure of ceramics based on Ca(1-x)Nd2x/3TiO3. It was
found that in both conventionally prepared samples and samples prepared by SPS that both
(112) and (011) type domains are present. It is probable that both types of domains are
present in SPS samples as a consequence of stresses induced by thermal shock rather than
the result of two phase transitions because the sintering temperature is below the
temperature of the cubic to tetragonal phase transition. It was also possible to eliminate the
effect of pressure on the phase transition temperatures.
218
It is known that the domain structure in perovskite ceramics is dependent on the
structural phase transitions on cooling to ambient temperature. X-ray diffraction and
Raman spectroscopy were used to probe the structural characteristics of Ca(1-x)Nd2x/3TiO3
on cooling from 800oC (XRD) and 600oC for the Raman experiments. Changes in the
relative intensities and widths of the peaks suggested that for Ca0.79Nd0.14TiO3 to
Ca0.61Nd0.32TiO3 have ferroelectric ordering at room temperature and undergo a Curie
transition between 200-300oC. It is likely that the reduction in the Curie temperature was
driven by cation-vacancy disorder induced strain. Ceramics with x > 0.39 did not show the
same behaviour; this is likely to be the result of the transition from orthorhombic Pbnm to
monoclinic C2/m. High temperature SEM was used to investigate whether these changes
had any effect of the microstructure; no evidence of any changes were found.
The microwave dielectric properties of the ceramics were measured in the 2-4GHz
range. For Ca(1-x)Nd2x/3TiO3 it was found that the relative permittivity (εr) was primarily
dependent on the composition of the ceramics as the densification was above 95% for all
samples. The temperature coefficient of resonant frequency (τf) was found to be dependent
on the composition and the changes in octahedral distortion that accompany the changes in
composition. The τf ranged from +800ppmK-1 for CaTiO3 to 200ppmK-1 for
Ca0.52Nd0.32TiO3; τf measurements for x > 0.48 were not possible due to low Q x f. The
effect of composition on the Q x f was more complex with a number of factors possibly
having an effect. The Q x f ranged from 6000GHz for CaTiO3 and rose to 13000GHz for
Ca0.7Nd0.2TiO3 and subsequently falling to 1000GHz for Ca0.1Nd0.6TiO3. Three possible
effects were identified including (a) changes in the widths of the twin domains (b)
abnormal grain growth and (c) increases in conductivity as a result of formation of defects.
For changes in domain width, it was found that the pattern of changes in Q x f closely
followed the changes in domain width and a similar effect is observed with abnormal grain
growth. For (c) the increase in conductivity could arise from the formation of electron
holes. In most microwave dielectric ceramics, an increase in the degree in cation ordering
usually leads to enhancement of the Q x f value. In Ca(1-x)Nd2x/3TiO3 it was found that the
best Q x f values did not coincide with the highest degrees of order instead optimum Q x f
was found in ceramics with cation-vacancy disorder.
219
Given that Ca0.61Nd0.26TiO3 has a τf of 242ppmK-1; it is unsuitable for commercial
use because device performance would drift if the operating temperature was changed.
MgTiO3 offers the opportunity to tune the τf through zero to stabilise the performance of
the ceramic. All properties (τf, Q x f and εr) in the (1-x)MgTiO3-xCa0.61Nd0.26TiO3 system
showed a linear dependence with value of x as a result of the formation of composite
ceramics. The optimum properties were found for a composition of 0.8MgTiO30.2Ca0.61Nd0.26TiO3 with εr of 25.4, Q x f of 39000GHz and τf = -0.1ppmK-1. It was argued
that there was an unexplained difference in the predicted and experimentally measured
properties and residual stress was suggested as a possible cause for this deviation. To
modify the internal stress state, samples with the 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3
composition were cooled at different rates after sintering at 1450oC. Synchrotron XRD
analysis did not show any consistent trends in the volumes of the unit cells of each of the
structures so it was not possible to conclude that residual stress was the sole cause of the
deviation between predicted and experimental properties. There was however a consistent
increase in the length of the c-axis of the two main phases. This increase could have
changed the intrinsic properties of the lattice and increased the Q x f to 49000GHz for
samples cooled at 15oC/hr.
9.1 Conclusions
9.1.1 Structure and Microwave Dielectric Properties of Ca(1-x)Nd2x/3TiO3
High density (>95%) microwave dielectric ceramics have been produced by the
mixed oxide route at temperatures of 1450-1500oC. All ceramics were shown to be single
phase materials. The structure of ceramics with x = 0-0.39 could be indexed on the basis of
an orthorhombic Pbnm structure and a new phase transition to monoclinic C2/m beginning
at x = 0.48. The lattice parameters had the general form of a = √2ac, b = √2ac and c = 2ac
for ceramics with the orthorhombic Pbnm structure and a = 2ac b = 2ac and c = 2ac for the
samples with the monoclinic C2/m structure. The tilt system on transition to the
monoclinic structure changed from a-a-c+ to a-b0c-. The grain sizes of the ceramics ranged
from 20 µm for CaTiO3 to 5 µm for Ca0.1Nd0.6TiO3 with evidence of abnormal grain
growth for Nd3+ rich samples. It was found that the twin domain size and morphology
220
changed from needle lamellae for CaTiO3 to a complex array of morphologies for
Ca0.61Nd0.26TiO3 and eventually returning to needles for Ca0.43Nd0.38TiO3. The width of the
twin domains ranged from approximately 1.653µm to 4.123µm for Ca0.61Nd0.26TiO3 before
falling to 1.669µm for Ca0.1Nd0.6TiO3. There was a unexplained drop in the domain width
for Ca0.52Nd0.32TiO3.
High resolution structural analysis was used to examine the ordering of the cations
in the lattice. It was found that for small to moderate additions of Nd2/3TiO3 to CaTiO3 a
disordered distribution of cations arose whereas large additions resulted in an ordered
structure. The nature of the ordered structure was found to be of the double perovskitetype, that is alternating layers of cation rich layers and layers rich with vacancies.
Asymmetry of the peaks in the diffraction spectra for Ca0.1Nd0.6TiO3 suggests the
formation of a nano-chessboard microstructure at the lattice level which was later
confirmed by high resolution imaging techniques. It is of interest to note that the highest Q
x f values obtained in the Ca(1-x)Nd2x/3TiO3 did not coincide with the highest degrees of
cation-vacancy ordering. The synchrotron analysis also revealed that there was a
substantial increase in the distortion of the oxygen octahedra as a result of Nd3+
substitution on the A-site of the perovskite structure. The analysis of the synchrotron X-ray
diffraction indicated that there was a substantial increase in the octahedral distortion as a
function of composition.
Raman spectroscopy was used to probe the bonding and cation-vacancy ordering in
the lattice. The Raman spectra were composed of modes originating from the rotations of
the oxygen octahedra, and the stretching and torsion of the Ti-O bonds. Polarised Raman
spectroscopy was used to determine which crystallographic axis a given mode originated
from. The Raman spectroscopy indicated that the onset of the orthorhombic Pbnm to
monoclinic C2/m transition began at Ca0.52Nd0.32TiO3. Monitoring of the peak widths after
the phase transition confirmed the increase in the cation-vacancy ordering observed in the
high resolution structural analysis.
The structure sequence in six ceramic compositions based on Ca(1-x)Nd2x/3TiO3
were investigated using Raman spectroscopy, four of those were investigated using in situ
high temperature X-ray diffraction. Samples that have the orthorhombic Pbnm structure at
221
room temperature (x ≤ 0.39) were shown to lose their ferroelectric ordering between 200300oC. The temperature at which the phase transitions occurred was shown to be sensitive
to the composition of the ceramic and room temperature structure. The transition
temperatures were not an important factor in the control of the microstructure.
The microwave dielectric properties were determined using a cavity resonance
technique in the 2-4GHz range. The εr decreased from 180 for CaTiO3 to 79 for
Ca0.1Nd0.6TiO3 and was primarily dependent on the composition of the ceramics. The τf
decreased from +800ppm/K for CaTiO3 to 242ppm/K for Ca0.52Nd0.32TiO3; it was not
possible to measure the τf for ceramics with x > 0.48 due to low Q x f affecting the
measurement of the resonant frequency. The τf was found to be dependent on the degree of
octahedral distortion as derived from the synchrotron X-ray diffraction analysis. The Q x f
increased from 6000GHz for CaTiO3 to 13000GHz for Ca0.7Nd0.2TiO3 and subsequently
falling to approximately 1000GHz for Ca0.1Nd0.6TiO3. It was found that the trends in the Q
x f value were closely related to the twin domain widths with the widest domains giving
the best Q x f values. It was also found that abnormal grain growth and electron-hole
formation for charge compensation have an influence on the Q x f.
9.1.2 Spark Plasma Sintering of CaTiO3
Spark plasma sintering was found to be able to reduce the sintering temperature to
1150oC without substantial reduction in density. Grain sizes were found to be in the 500nm
to 5µm range and twin domains were identified in the microstructure. Both (011) and (112)
type domains were found with thermal shock being the reason for both types of domain
despite sintering below the cubic to tetragonal phase transition temperature. The samples
sintered at 1150oC showed a degradation in the εr but with slight improvements in the Q x f
and the τf. The improvement in the τf was attributed to a slight increase in the unit cell
volume whilst changes in the lattice vibrational properties were the possible cause of the
slight increase in the Q x f. The changes in the octahedral tilt angles were the likely cause
of the changes in the intrinsic losses.
222
9.1.3 (1-x)MgTiO3-xCa0.61Nd0.26TiO3
MgTiO3 was added to Ca0.61Nd0.26TiO3 in order to tune the τf towards zero. The
composition with the zero τf was 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 with Q x f of 39000GHz
and εr = 25.4. Investigation of the phase makeup of these samples revealed that there are
three phases present in the microstructure the identity of which are MgTiO3,
Ca0.61Nd0.26TiO3 and MgTi2O5. The structures of these phases were R-3 for MgTiO3,
orthorhombic Pbnm for Ca0.61Nd0.26TiO3 and orthorhombic Bbmm for MgTi2O5. The
relative proportions of these phases are roughly in line with the target composition with
approximately 5wt% of MgTi2O5 present in all compositions. The grain size of the
ceramics was approximately 5 µm for 0.8MgTiO3-0.2Ca0.61Nd0.26TiO3 to 15 µm for
0.2MgTiO3-0.8Ca0.61Nd0.26TiO3 showing that the grain size is heavily inhibited by the
presence of the MgTiO3 phase. Use of the Q x f values of the MgTiO3 (56000GHz) and
Ca0.61Nd0.26TiO3 (13000GHz) was used as a way of predicting values of mixtures of the
two components. This revealed that there was a substantial deviation between the predicted
and measured values of the Q x f of mixtures of up to 8000GHz which is outside of the
error in the measurements. Through the use of synchrotron X-ray analysis it was revealed
there were changes in the lattice parameters which affected the vibrational properties of the
lattice and increased the Q x f value
9.3 Suggestions for Further Work
1. It would be interesting to explore the relative proportions of the different types of
domains present in the microstructures of the ceramics using Raman spectroscopy
and to make orientation maps. This was attempted for the Ca(1-x)Nd2x/3TiO3
compositions using Electron Backscatter Diffraction (EBSD) but reliable analysis
was not possible because (i) the difference in the two or more of the lattice
parameters is less than 2% leading to misindexing of Kikuchi patterns and (ii) the
electron beam causing charging of the ceramics. Full understanding of the relative
proportions of each type of domain may indicate methods of processing ceramics to
improve the microwave dielectric properties.
2. Do other perovskite type microwave dielectrics show similar patterns in dominant
domain structure as a function of compositions and hence exhibit high Q x f as a
223
result? It is rare to find full studies of the dominant domain structure in the
literature and the effect of those domains on the microwave dielectric properties. It
is suggested that the dominant domain structures of other microwave dielectrics
such as CaTiO3-REAlO3 (RE = Nd, Sm or La) and cation deficient ceramics such
as Ca(1-x)La2x/3TiO3 should be studied in order to understand the Q x f values.
3. Modelling of Dielectric Properties and Residual Stresses – it would be useful to
consider modelling local variations in the microwave dielectric properties that arise
due to variations in the internal stress state. It would also be interesting to derive a
set of rules that dictate what processing conditions should be used to optimise the
internal stress state to give enhanced microwave properties
4. Adjustments to the spark plasma sintering of CaTiO3 powders need to be made in
order to avoid cracking of the samples. It is worth considering using higher
pressures and lower cooling rates for crack prevention and avoidance of thermal
shock. It would also be interesting to reduce the sintering temperature below
1100oC to avoid the tetragonal to orthorhombic phase transition and complete avoid
the formation of twin domains. These steps are important to determine which type
of domains have the most significant effect on the microwave dielectric properties.
5. Further investigation of the structure sequence of Ca(1-x)Nd2x/3TiO3 on cooling to
room temperature is required. In particular it is not established what effect adding
Nd2/3TiO3 to CaTiO3 has on the structural phase transition temperatures and the
structures of the ceramics above 1000oC. Full understanding of the structure
transitions may help to understand the microstructures that were observed in section
5.4. The best technique to study the structural characteristics is neutron diffraction
given the high accuracy to which the oxygen positions can be measured. It is
important to measure the oxygen positions to a high accuracy because the
octahedral tilts play a key role in the characteristics of structural phase transitions.
A proposal for access for the high resolution powder diffraction beamline at the
ISIS neutron source has been granted but it is out of scope with respect to time on
this PhD project.
224
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