close

Вход

Забыли?

вход по аккаунту

?

Barium polytitanate dielectric resonators for microwave wireless communication

код для вставкиСкачать
INFORMATION TO USERS
This manuscript has been reproduced from the microfilm master. UMI
films the text directly from the original or copy submitted. Thus, some
thesis and dissertation copies are in typewriter face, while others may be
from any type of computer printer.
The quality of this reproduction is dependent upon the quality of the
copy submitted. Broken or indistinct print, colored or poor quality
illustrations and photographs, print bleedthrough, substandard margins,
and improper alignment can adversely affect reproduction.
In the unlikely event that the author did not send UMI a complete
manuscript and there are missing pages, these will be noted.
Also, if
unauthorized copyright material had to be removed, a note will indicate
the deletion.
Oversize materials (e.g., maps, drawings, charts) are reproduced by
sectioning the original, beginning at the upper left-hand comer and
continuing from left to right in equal sections with small overlaps. Each
original is also photographed in one exposure and is included in reduced
form at the back of the book.
Photographs included in the original manuscript have been reproduced
xerographically in this copy. Higher quality 6” x 9” black and white
photographic prints are available for any photographs or illustrations
appearing in this copy for an additional charge. Contact UMI directly to
order.
UMI
A Bell & Howell Information Company
300 North Zed) Road, Ann Arbor MI 48106-1346 USA
313/761-4700 800/521-0600
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Barium P olytitan ate D ielectric R esonators for
M icrowave W ireless C om m unication
A Thesis
Presented to
T he Academic Faculty
by
YVen-yi Lin
In P artial Fulfillment
of th e Requirem ents for th e Degree
D octor of Philosophy in Ceram ics Engineering
G eorgia Institute of Technology
June 1997
Copyright c 1997 by VVen-yi Lin
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UMI Number: 9735422
Copyright 1997 by
Lin, Wen-yi
All rights reserved.
UMI Microform 9735422
Copyright 1997, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
300 North Zeeb Road
Ann Arbor, MI 48103
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Barium P olytitanate D ielectric R esonators for
M icrowave W ireless C om m unication
Approved:
Dr. R obert F^-'S’p e ra ^ ;C h airm an
Dr. Thom as R. Shrout
Dr. Rosaxio A. G erhadt
Dr. Joe K. Cochran. Jr.
Dr. D. Norman Hill
D ate Approved
S~/ / f /
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Acknowledgem ents
I would like to express my sincere g ratitu d e to my advisor Dr. R obert F. Speyer
for his su p p o rt and guidance throughout the course of this work. I would also
like to th a n k Dr. Thom as R. Shrout a t T he Pennsylvania S tate University for
his su p p o rt in my research on doped barium p o ly titan ate. The technical help in
processing and m easurem ents of dielectric resonators from Dr. Wesley S. Hackenberger a t Penn S tate is also highly appreciated. I would like to thank Dr. Rosario
A. G erh ard t for her very useful discussion and insights in electronic m aterials.
T he useful com m ents and suggestions from Drs. Joe K. Cochran and D. Norman
Hill are also appreciated. Special th an k s are due to Dr. Jen-Yan Hsu who has
been very helpful in my academic pursuit through the years, ap art from being a
terrific friend.
I enjoyed my work and life at The M aterials Research L aboratory at The
Pennsylvania S tate University, w ith the help and friendship from Dr. Sei-Joo
iii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Jang, Dr. Clive A. R andall, Shoko Yoshikawa, Dr. M ing-Jen P an, M urali Lakshm an. B eth A.M. Jones, M ark McNeal and the technical staff. I also had several
pleasant visits to the M aterials Research L aboratory at IT R I, Chu-Tong, Taiwan
and the help from Dr. VVang and Mr. Shen is highly appreciated. I have had a
great tim e at Georgia Tech w ith the friendship and assistance from quite a few
people: Drs. J. Lee. T .J. Hwang, Y.Y. Su, S.K. Sundaram , H.H. Shin. C.K. Lee.
G. Agarwal. G. Villalobo. as well as Y. B erta, J. W itt, K. Meyers, R. Morano. J.
Lee. D. Lee. J. Cagle. Y.D. Kuan. Y.M. Hsu, staff members, and friends in other
labs and schools.
I would like to express m y sincere and grateful thanks to my parents, sisters,
brother and the rest of my family in Taiwan, who have su p p o rted and encouraged
me throughout my life. W ith o u t them , I would not have been here. The patience,
encouragem ent, and lab o rato ry assistance from my dearest wife - Su-ming Hung
has been the most im portant and valuable support during my years of graduate
studies. To her and my fam ily w ith love and gratitude.
iv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Contents
A ck n ow led gem en ts
iii
List o f Tables
viii
List o f Figures
xi
S u m m ary
xii
C h ap ter
1 In tro d u ctio n
1.1
1
Review of Pertinent L ite r a tu r e ................................................................
2
1.1.1
Physics of Microwave Dielectric P r o p e r ti e s ............................
2
1.1.2
Macroscopic Microwave P roperties
.........................................
12
1.1.3
Microwave Properties, Chem istry, and M a te ria ls ..................
18
1.1.4
Conventional and Shrinkage R ate Controlled Sintering
23
. .
V
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2 E xp erim en tal P rocedure
2.1
28
Processing of Barium P o ly t it a n a te s ......................................................
2.1.1
28
B aTi409 and Zr4+- an d Sn4+-D oped B a2T i90 2o Microwave
R eso n a to rs........................................................................................
28
2.1.2
Shrinkage R ate C ontrolled S in te rin g .........................................
29
2.1.3
Therm al Processing of B aT i40 9 and Undoped and Sn4+Doped Ba2Tig02o ...........................................................................
2.1.4
Rapid Therm al Processing of Undoped Monophase BaoTigOoo 31
2.2
M icrostructure O bservation and Image A n a ly s is ...............................
32
2.3
Phase and Therm al A n a ly se s....................................................................
33
2.4
Dielectric Property M e a s u r e m e n t..........................................................
34
3 R esu lts and D iscu ssion
3.1
36
Dielectric Properties of B aT i4Og and Zr4+- and Sn4+-Doped BaoTigOoo
Microwave R e s o n a t o r s ..............................................................................
3.2
3.3
51
Therm al Processing of B aT i40 9 and Undoped and Sn4+-D oped
Ba2Ti90 2 o ......................................................................................................
3.4
36
Microwave Dielectric P roperties of M icrostructure-Controlled B a2T i902 o
R eso n a to rs......................................................................................................
64
Fabrication of Undoped Single-Phase Ba2T i90 2o via R apid T h e r­
mal P r o c e s s in g ............................................................................................
4
30
C onclusions and R ecom m end ation s
vi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
74
83
B ib liograp h y
85
V ita
90
vii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
List o f Tables
3.1 D ensity and Microwave Properties of B arium P o ly titan ates . . . .
47
3.2
Porosity and average grain size of 1.64%Zr specim ens. TD stands
for theoretical density. 15 g samples were heat tre a te d in a MoSi2
furnace, while 0.5 g specimens were heat treated in th e RCS dilatometer. In furnace heat treatm ents, specimens were exposed to an oxy­
gen flow rate of 200 cm3/m in (unless otherwise indicated). *Sin58
tered a t an oxygen flow rate of 600 cm 3/m in ........................................
3.3
D ensity and microwave properties of BaoTigOao- Indicated dielec­
tric constants and quality factors were m easured a t room tem per­
ature. *Sint.ered a t an oxygen flow rate of 600 cm 3/m in ...................
60
Phases Formed A fter Various H eat T re a tm e n ts ...................................
66
3.4
viii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
List of Figures
1.1
Schematic diagram of polarization mechanisms in ceramics, (a)
Electronic, (h) Ionic, (c) O scillatory dipoles.........................................
4
1.2
Polarization mechanisms in dielectrics as a function of frequency.
5
2.1
A cylindrical dielectric specim en is placed inside a microwave cav­
ity for microwave dielectric property m easurem ents in reflection
mode..................................................................................................................
35
Relative proportion of B a2T i9O20 as a function of ZrO o or Sn02
substitution, for specimens pre-reacted at 1200°C for 4 h. Val­
ues were determ ined via th e ratio of the m ost intense XRD peak
height of Ba2Tig02o to th e sum of the m ost intense peak heights
of Ba2Tig02o and B aTi4 0 g..........................................................................
38
Secondary electron images of th e 0.82%Zr com position heated at
1390°C for (a) 6 and (b) 16 h. (c) B ackscatted image of the
2.46%Zr specimen sintered for 6 h. Black regions in the upper
left of (c) correspond to T i0 2 : while black regions a t the center
and right of the m icrograph are pores. Light grey regions in the
upper left of (c) are B aTi4Og, and th e m atrix phase is Ba2TigO20-
39
3.1
3.2
3.3
The effects of tin oxide additions and sintering tim e on dimensional
densities and dielectric constants in the microwave frequencv range
(3 G H z)..................................................................................................................40
3.4
Dimensional densities and dielectric constants of ZrOg-doped com­
pacts, sintered at 1390°C for 6 and 16 h. as a function of additive
concentration..................................................................................................
42
Effects of dopants and soak tim e on the quality factor at 3 GHz. .
43
3.5
ix
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.6
Influence of tin and zirconium oxide substitutions on quality fac­
tor of B a2Tig0 2 o as a function of tem perature. B aT i40g is also
included. All specimens were sintered a t 1390°C for 6 h ...................
44
Influence of tin and zirconium oxide substitutions on the frequency
drift (relative to room tem perature) and tem p eratu re coefficients
(slopes of lines) of specimens sintered a t 1390°C for 6 h ...................
46
M icrostructures of 1.64%Zr specimens after first zone RCS rates
at (a) 3r (b) 1. and (c) 0.5 % /m in ............................................................
53
Densification and tem perature profiles of 1.64%Zr specimens as
a function of tim e. D otted lines represent setpoint densification
schedules. G rey lines represent setpoint tem p eratu re schedules
assigned to furnace heat treatm en ts.........................................................
54
3.10 (a) 0.5 g 1.64%Zr specimen after a first zone RCS ra te of 0.5 % /m in
to 92% of theoretical density, and a subsequent second zone RCS
rate of 0.01 % /m in to 99% of theoretical density, (b) 15 g speci­
men of the same com position as (a) after furnace heat treatm ent
schedules em ulating the tem perature profile of the RCS schedule.
(c) Sam e as (a) but w ith a second zone RCS rate of 0.1 % /m in.
(d) Sam e as (b) but em ulating the tem perature profile of the RCS
schedule in (c)................................................................................................
56
3.11 1.64%Zr specimen showing the presence of significant grain bound­
a ry /trip le point porosity after heat treatm ent a t 4 °C /m in to 1390°C
and held until the RCS algorithm recognized a term inal shrinkage
equivalent to 99.9% of theoretical density (10.4 h ).............................
59
3.12 DTA and TG traces of raw batch m aterials BaCO.-j. TiOo. and the
two combined in m olar ratio of 18.2B aC 0 3 -81.8T i0 2 - heated in air
at 10°C /inin....................................................................................................
65
3.7
3.8
3.9
3.13 DTA and DTG (visually sm oothed time derivative of TG signal)
traces of the B a0 -T i02 and B a0 -Sn0 2-T i0 2 system s. Asterisks
represent m axim um tem peratures prior to quench for XRD analysis. 68
3.14 D ilatom etry traces (expansion and tem perature derivative of ex­
pansion) of calcined/pre-reacted (975°C. 6h) pressed powder pel­
lets heated at 3 °C /m in ................................................................................
x
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
70
3.15 M icrostructures of polished sections of sintered specimens heat
treated at 1360°C for 5 h. (a) B a0 -T i0 2 , (b) BaO-TiOg-SnCV
D ark regions w ith w hite edges are porosity, while black regions
are T i0 2 ...........................................................................................................
3.16 XRD pattern s of specimens (a) heated a t 5 °C /m in to 1250°C and
held for 1 h. (b) heated at 500°C /m in to 1250°C and held for 3
min. (c) heated a t 500°C /m in and held at 1250°C for 1 h. and (d)
heated at 500°C /m in to 1250°C and held for 2 h. o Ba2Tig0 2 o- °
B aT i4Og,
T i0 2 ..........................................................................................
3.17 Polished section of a specimen heated a t 5Q 0°C/m in to 1250°C and
soaked for 2 h: (a) Secondary' electron image, where small T i02
grains appear as black regions d istributed in a (grey) indistinguish­
able m ixture of B a2Tig02o and B aT i40g. T h e w hite regions are
pores where the w hite rings are from charging effects, (b) Back
scattered image of the same m icrostructure showing needle-like
BaoTigC^o (dark gray) dispersed in th e B aT i4Og (light grey) m a­
trix .....................................................................................................................
3.18 Polished section of a specimen heated at 5 °C /m in to 1250°C and
soaked for 2 h: (a) Secondary electron image, (b) Back scattered
electron image. C orrelation between phases an d phase contrast is
the same as th a t in Figure 3.17.................................................................
3.19 Proportions of B a2Tig02o and BaTi40g m easured from XRD rel­
ative peak intensities (circles) and SEM image analyses (triangles)
3.20 Relative am ounts of Ba2TigO20 for sam ples h eated a t 1250°C for 2
h. followed by various soaking periods a t 1390°C. Triangle, square,
and filled triangle are specimens heated a t 500, 50. and 5°C /m in.
respectively, via image analysis. Circle, diam ond, and filled circle
are specimens heated a t 500. 50, and 5 °C /m in . respectively, via
relative XRD peak intensities....................................................................
Reproduced with permission of the copyright owner. Further reproduction prohibited w ithout permission.
Summary
T h e technology advancement of wireless commimication has been m ade possi­
ble in part w ith recent advances in m iniaturization of microwave circuits by
using high-perm ittivitv. tem perature-stable, low-loss dielectric resonators.
An
im portant dielectric resonator m aterial is BagTigOgo because of its ou tstan d in g
microwave dielectric properties. However. BagTigOgo has been a difficult phase
to form w ithout dopants. D isagreem ent about the ability to form phase-pure
BagTigOgo has been reported in th e literature. The objective of this thesis was
to stu d y the fabrication of BagTigOgo as well as other barium p o ly titan ate. using
various therm al schedules and chem ical modifications. T he optim ization of m i­
crowave dielectric properties, developm ent of m icrostructure, and reaction mech­
anism s amongst starting m aterials were also researched. T h e work is presented
as follows.
xii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1. D ielectric P ro p erties o f B aT i4Og and Zr4+- and Sn4+-D o p ed B a 2 T i 9
0
M icrow ave R esonators
T he effects of solid solution additives, nam ely Zr and Sn, their concentration,
and therm al processing schedide on m icrostructure evolution and microwave
properties of barium polytitan ates were studied.
Dielectric resonators of
high quality factor (13900 a t 3 GHz), dielectric constant (39.3), and near
zero tem perature coefficient of resonance frequency (1.3 p p m /°C betw een
20-60°C) were successfully fabricated.
The solubility of Sn in B a2Tig0 2 o
was higher than th a t of Zr bu t b o th facilitated formation of phase-pure
BaoTigOjo resonators. Ba2Ti90 2 o formed m ost easily w ith low d o pant con­
centration (0.82 mol%). most impressively for ZrOo substitutions. E xtended
heat treatm ent (16 vs. 6 h a t 1390°C) resulted in volatilization of grain
boundary liquid phase, leading to more porous resonators, having corre­
spondingly lower perm ittivities. Increasing dopant concentration resulted in
m inor increases in quality factor, w ith Zr-doping leading to slightly higher
values (maximum: 13900). Increasing m easurem ent tem perature degraded
th e quality factor, most precipitously for BaTljOg. The tem p eratu re coeffi­
cient decreased w ith increasing Z r 0 2-substitution. but was largely unaffected
by S n 0 2 concentration. Excess tita n ia in a batch w ith no dopants did not
form phase-pure Ba2T i902o, and dem onstrated degraded microwave proper-
x iii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2o
ties.
2. D ie le c tric P r o p e r tie s o f M ic r o s tr u c tu r e - C o n tr o lle d B a 2T i g 0 2o R e s ­
o n a to r s
Time-efficient therm al schedules for sintering Zr0 2 - and S n 0 2-doped B a2T i902 o
resonators to minimum porosity were developed using a shrinkage ra te con­
trolled dilatom eter. T he sintering schedules were chosen so as to circum vent
pore formation via grain bo u n d ary /trip le point liquid phase volatilization.
A densification rate (0.5 % /m in ) for the early stages of sintering which m in­
imized intragranular porosity was chosen. For the later stages of sintering,
a densification rate (0.01 % /m in) which minimized specimen slum ping via
liquid phase perm itted sintering to high density. These schedules were suc­
cessfully upscaled to heat treatm en t in a conventional furnace. The dielectric
constants, quality factors, and selected tem perature coefficients of 0.82 mol%
and 1.64 mol% SnOo-. and 1.64 mol% Z r0 2-doped monophase BaoTigO^o are
reported.
3. T h e r m a l P r o c e s s in g o f B a T ijO g a n d U n d o p e d a n d Sn'1+- D o p e d
B a 2T i g 0 2o
Sn4+-doped and undoped barium polvtitanat.es pellets were sintered a t 1360
and 1390°C for 5 h. T hough batched to form Ba2Tig02o- a tw o-phase mi-
x iv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
crostructiire of BaTi4Og and TiOo formed from the undoped system . Doping
w ith 1.64 mol% S n 0 2 stabilized B a2Tig02 o and formed a single-phase mi­
crostructure. D ilatom etry studies im plied th a t SnC>2 additions facilitated a
greater fraction of reaction to occur in the solid sta te . Interm ediate chemical
reactions amongst the startin g m aterials to form B a2T i902 o and B aTi4Og
were identified as a function of tem perature.
4. Fabrication o f U n d op ed M on op h ase B a 2 TigO 20 via R apid T herm al
P rocessin g
Ba2Tig02o com pacts were reaction sintered from a pressed powder m ixture
of B a T i0 3 and T i0 2 . w ithout solid solution additives. Specimens heated
using an infrared furnace a t 500°C /m in to 1250°C for 2 h developed a mi­
crostructure w ith ~ 6 4 vol% Ba2T i90 2 o- Phase-pure (98 vol%) Ba2T ig 0 2o
then formed after soaking at 1390°C for 8 h.
Lower heating rates (e.g.
o°C /m in) fostered diffusional agglom eration of T i 0 2. leading to preferred
initial form ation of B aTi40 9. T he work also showed th a t a significantly
longer soak period (24 h) a t 1390°C was required to form 83 vol% Ba2T ig 0 2o
relative to BaTi40 9 via conventional sintering.
xv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 1
Introduction
T h e development of dielectric resonators for telecomm unications has seen a n ex­
ponential growth in the past two decades.
This technology advancem ent has
been m ade possible in p art w ith recent advances in m iniaturization of microwave
circuits by using high-perm ittivity. tem perature-stable, low-loss dielectric res­
onators. Dielectric resonators can function as oscillators, amplifiers, filters, and
tu n ers in communication circuits. A variety of applications utilizing these rela­
tively low-cost ceramics have been developed, for example, personal com m unica­
tion system s, global positioning system s, and personal digital cellular system s.
1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.1
1.1.1
R eview o f P ertinent L iterature
P hysics o f M icrow ave D ielectric P rop erties
Sim ilar to a wave traveling on a string, an electrom agnetic wave traveling from
a dielectric to air may exhibit reflection a t the dielectric-air boundary due to
the difference between the indices of refraction of air and th e ceramic. The re­
flected electrom agnetic waves also achieve resonance at certain frequencies (where
nodes also form at the dielectric-air interfaces). This concept of resonance will
be exploited in later paragraphs.
In dielectrics, positive and negative charges (such as cations and anions) form
local electric fields and dipole m om ents, defined as the product of the electric
charges and the distance between th e charges. W hen an external electric field is
applied to the dielectrics, the electric charges are displaced so th a t the dipoles
are torqued by the external field: in this case, the dielectrics are said to be polar­
ized. As the electric field intensity increases, polarization also increases, i.e.. the
polarization is directly proportional to the electric field and the constant of pro­
portionality is termed the polarizability. Four prim ary polarization mechanisms
may occur in dielectrics under an applied field, namely, electronic, ionic, dipole,
and interfacial polarizations. Dipole polarization can further be divided into po­
larizations of oscillatory dipoles (also called Stevels deform ation polarization[l])
2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and cation dipoles. A schem atic representation of selected polarization mecha­
nisms is displayed in Figure 1.1. Owing to the m obility of th e charged species,
each polarization m echanism in an alternating external electric field can only
operate up to certain frequencies, as shown in Figure 1.2. As can be seen from
the figure, in th e microwave frequency range (gigahertz) th e dielectric constant
is independent of frequency and only electronic polarization, ionic polarization,
as well as Stevels deform ation polarization can occur in the dielectric in response
to an external field a t microwave frequencies (Figure 1.2). T hus only these three
mechanisms are reviewed below: Electronic polarization is due to the relative
displacem ents of their center of positive charges w ith respect to the center of
the negative charges of an ion subjected to an external a ltern atin g electric field.
Ionic polarization originates in the displacement of positive and negative ions
in an electrom agnetic field from their centrosym m etric positions. Stevels defor­
m ation polarization involves the rotational displacement of anions w ith respect
to cations, resulting in a net dipolar orientation in the direction of the applied
field. However, since Stevels polarizability is generally small relative to the sum
of electronic an d ionic polarizabilitiesfl] it is sometimes neglected.
Because of th e aforem entioned polarization mechanisms, m ore electric charge
can be stored in dielectrics (compared to vacuum) for a given potential drop
across the m aterial because a field is set up in the m aterial via polarization which
3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(b)
o-A/WV-#
(c)
Figure 1.1: S ch em atic diagram o f polarization m echanism s in ceram ics,
(a) E lectronic.
Ionic, (c) O scillatory dipoles.
4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(1>)
Dielectric Constant
Interfacial
Electronic
Cation Dipoles
Ionic
Stevels
3
0
3
6
9
12
15
Log Frequency (Hz)
Figure 1.2: Polarization m echanism s in dielectrics as a fun ction o f frequency.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
18
opposes the external field. T he ratio of the charge Q m aking up th e external field
to the voltage V across the dielectric is the capacitance C :
where e is th e perm ittivity. A is the area, and d is th e thickness. T he ratio of p er­
m ittivity of a m aterial to th a t of free space e0 is term ed th e relative p erm ittiv ity er
or equivalently, the dielectric constant. The relation between dielectric constant
and the aforementioned polarizabilities is given in Clausius-M osotti equation:
£r ~
1 _
+ Ckj + Qrf +
er + 2 ~
a in
3e0
'
1
where a ei. a ,. a>/. and q,„ are the electronic, ionic, dipole, and interfacial p olar­
izabilities, respectively.
Using classical theory of absorption and dispersion1, the electronic polarizability is calculated based on force balance equation:
—e E = rnx 4- 2Timrjx + /.r ,
'D isp e rsio n e q u atio n relates energy to wave num ber.
(j
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(1-3)
where m is the m ass of oscillators, x is the second tim e derivative of the distance
x between a pair of oscillators, x is the first tim e derivative of x, f is the force
constant, e is the electron charge, E is the externally applied electric field, and
7 is the dam ping factor (the origin of dam ping factor is discussed later). For a
periodic external field.
E = E 0 exp(jujt),
(1.4)
where E 0 is a constant, j = \ f —i. ui is the angular frequency, and t is time,
the distance between a pair of oscillators can be derived and the corresponding
electronic polarizabilitv is thus.
A'e2
— up
- - 4^ ; iV +7^
(1-5>
where N is the concentration of oscillators, and ve\a is the frequency of electron
resonance where dispersion in the visible and ultraviolet range occurs.
Equa­
tion 1.5 indicates th a t more electrons or a smaller dam ping factor result in higher
electronic polarizabilitv. Classical theory shows th a t to ta l electronic polarizability is the sum of the contributions of all electrons in an atom and of all atom s
in the dielectric[2]. In the quantum theory of dispersion, the H am iltonian of a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
system of bounded electrons in a uniform and periodic field is considered; th e so­
lution to the Schrodinger equation is then used to calculate the dipole m om ent.
A pplication of boundary conditions to the dipole m om ent equation leads to the
electronic polarizability. Kirkwood applied a wave function of a specific form[2]
in the quantum theory and found th a t electronic polarizability is determ ined
m ostly by valence electrons and is higher for ions of higher atomic weights (e.g.
<^e/Zr-<+ > &ei Ti-*+)- and higher for anions th an cations (e.g. a ei F- > cte[ /<-+).
Also, electronic polarizability is higher for a m aterial w ith a smaller band gap
between the valence and conduction bands.
The theory of lattice oscillations is based on th e Netwon's second law: the
combined forces of elastic force bonding the ions and elect rod ynamic force (which
takes the electrom agnetic field into account) cause the ions to accelerate/decelerate.
The theory shows th a t the ionic polarizability increases w ith decreasing volume
of an ion pair Vj an d reduced mass /ic. according to
e2
Qi =
~ ~t / 7( u2l
I'cVi
rT
- aJ2)
(L 6 )
where i/io is the frequency of ion resonance where dispersion in the infrared range
occurs and //.c = m xm 2 / ( ^ 1 + w.o). where m x and ra 2 are the masses of the ion
pair, respectively. W hen b oth electronic and ionic polarizations are considered.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
effective charge e* m ay be used to represent their sum. i.e.,
ze*x = zex + pei,
where 2 is the num ber of charges and pe\ is the electronic polarization.
(1.7)
The
effective charge is proportional to the difference between th e polarizabilities of
positive and negative ions. In solid solutions, Vegard’s law is obeyed['2]. i.e.. the
effective charge is directly proportional to the concentration of the solute.
The quality factor can be approxim ated as the inverse of th e dielectric loss fac­
tor ( ta n 5). defined as the ratio of the imaginary part of th e perm ittivity to the
real part of the perm ittivity. M any factors affect the dielectric loss. According
to the classical dispersion theory[2],[3], dielectric loss at microwave frequencies is
prim arily due to the dam ping factor of a Lorentz oscillator (which, for example,
satisfies Equation 1.3). T he factor is ascribed to the overlapping of electron clouds
of cations and anions[2j. In solid dielectrics, the dam ping factor is related to the
coupling of the oscillators and depends on the anharm onicity of the bond forces
and on the ratio of the radii of th e cations and anions[4],[5]. The anharm onicity
assumes nonlinearity of the equilibrium forces versus displacem ent of ions from
their centrosym m etric positions. The anharm onicity is inversely proportional to
9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the ratio of the defined frequency2 to the frequency where a linear relation be­
tween restoring force and displacem ent occurs; the aforem entioned ratio increases
w ith the reduced mass. T h e origin of the damping factor can be found in lattice
im perfections (in addition to anharm onic interaction), e.g.. im purities, disloca­
tions. and grain boundaries[6]. Using th e classical theory[2]. the dam ping factor
m ay be calculated from th e infrared spectrum as the ratio of the half w idth of
th e m axim um of the transverse optical mode spectrum to the frequency of this
mode.
For an electrom agnetic wave sustained inside a dielectric resonator, th e half
wavelength of the standing wave a t th e lowest possible frequency can be ap­
proxim ated as the specimen diam eter. Waves propagating in a dielectric have
a sh o rter wavelength than in vacuum, the value of which is determ ined by the
index of refraction and Snell’s law. Thus, resonance frequency is a function of
relative perm ittivity (since the index of refraction is related to the perm ittivity)
and sam ple dimension3, i.e..
fo
\ de l ~ D e ^
(L8)
2T h e d efined frequency describes th e v ib ra tio n a l sp e c tru m of the solid as a w hole a n d m ay b e e x p e rim e n ta lly
d e te rm in e d by e q u a tin g the vib ratio n en erg y w ith th e cohesion energy (b o n d in g energy- p e r b o n d ).
•*Frequency d o e s not depend on th e m edium in w hich wave pro p ag ates b u t only c e rta in frequencies can
re so n ate in th e m edium .
10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where f Q and c are, respectively, the resonance frequency and velocity of light in
free space, Ad is the wavelength of the stan d in g wave in th e dielectric, and D is
the diam eter of the dielectric. T he differentiation of E quation 1.8 w ith respect
to tem perature gives rise to the tem p eratu re coefficient of resonance frequency:
TC/ = —O.STCf —a£,
(1.9)
where T C f is the tem perature coefficient of p erm ittivity (th e slope of the perm it­
tivity vs. tem perature plot), and a L is th e linear therm al expansion coefficient.
T he perm ittivity tem p eratu re coefficient m ay be determ ined by differentiating
the Clausius-M osotti relation (Equation 1.2) w ith respect to tem p eratu re and
thus.
( 1. 1 0 )
where a is polarizability and T is tem perature. The su b stitu tio n of E quation 1.10
into Equation 1.9 gives rise to the relation am ongst tem p eratu re coefficient of
resonance frequency, dielectric constant, therm al expansion coefficient, polariz­
ability. and tem perature.
11
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.1.2
M acroscopic M icrowave P rop erties
At the macroscopic level, electric and m agnetic phenomena are described by
Maxwell’s equations:
( 1. 11)
( 1. 1 2 )
V ’ D = p,
(1.13)
V • B = 0.
(1.14)
where E is the electric field intensity. H is the magnetic field intensity. D is
the electric flux density. B is the m agnetic flux density. J is the electric current
density, p is the electric charge density, and y is
^ 4- Jr in rectan g u lar coor­
dinates. In microwave comm unication applications, transverse electric waves (T E
mode) are often used, characterized by the presence of a longitudinal m agnetic
field and no variation in the azim uthal direction. For these modes in rectangu­
lar coordinates. E ; = 0 and H- is a solution to the wave equation. Using the
aforem entioned T E wave characteristics, proper boundary conditions, an d the
Helmholtz equation.
12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
V 2tf_- = - k 2H z,
(1.15)
where k is the wave number, Maxwell’s equation can be solved for geom etric
configurations for two common m ethods to m easure microwave properties. In
the post resonance m ethod[7],[8] a cylindrical dielectric resonator is placed be­
tween two parallel brass plates. Inside the resonator, a solution of the Helmholtz
equation in cylindrical coordinates is
V\ (r) = A \ J 0{k\r)s\n.T]z.
(1-16)
where the subscript 1 denotes inside the resonator. A \ is a constant. J 0 is the
Bessel equation4 of the first kind.
7/
=
i;2
p
/
= 1 .2 ,3 ......
,2..-,
2
A., = u) lie ! — r]
(1-17)
(1.18)
where L is the specim en height. I is the longitudinal variations of the field along
■*Bessel functions c an b e w ritten in series form a n d a re th e so lu tio n s to th e Bessel differential e q u atio n ,
derived from th e wave E q u atio n 1.20 using th e m ethod of v ariable se p a ra tio n .
13
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the z-axis, eY is th e perm ittivity of the resonator, [i is th e perm eability, and a;
is the resonance frequency which is determined by identifying the frequency at
which T E m ode wave resonates in the frequency spectrum . Using th is solution
and Maxwell equation in cylindrical coordinates,
— V x E \ ( r ) = H \(r).
(1.19)
ijJ j.L
the m agnetic field density inside the resonator can be derived as a function of r.
Similarly. Ho(r) can be calculated. The boundary condition of continuity of the
tangential com ponents of the field at the resonator-air interface gives rise to the
following characteristic equation for an isotropic m aterial:
J°(«) =
TI
U
where a = a k\. 3 =
'
pK otf)
I
n 9m
(U-0)
a is the radius of the resonator, J 0(a) and J i ( a ) are
the Bessel functions of th e first kind of orders zero an d one. respectively, and
K 0(3) and K \ ( 3 ) are the modified Bessel functions of th e first kind of orders
zero and one. respectively, a and 3 are dependent on th e resonator geometry,
the resonance wavelength, and dielectric properties, according to th e following
equations.
14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where er is the dielectric constant. A0 is th e resonance wavelength in free space,
and vp is the phase velocity in the resonator, according to the following equation:
From the measured resonance frequency, specim en dimension and E quation 1.22.
3 can he calculated. Using a com puter program , a is then num erically derived
from 3 and the transcendental Equation 1.20. er in tu rn can be obtained from
E quation 1.21. Q uality factor is derived from the inverse of ta n 8. Ivobayashi et
al. [S] later proposed a technique for m easuring the effective surface resistance of
the coupling brass plates to improve th e accuracy of loss tangent m easurem ent.
Microwave properties of high-perm ittivity and low-loss m aterials can also be
m easured inside a m etallic enclosure of high electrical conductivity. T he deriva­
tion above can also be applied to determ ine the dielectric properties w ith this
m ethod, using new boundary conditions. T he to ta l power loss P is expressed as
15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the sum of the losses in the load P^ an d resonator Pr which follows th e equation
below
Pr = P R + PD + Pc,
(1.24)
where PR is th e radiation loss, P q is th e dielectric loss, and Pc is th e conduction
loss in the m etal surface. Three quality factors have to be considered in this
system , nam ely th e loaded quality factor Q l , th e external quality factor Q e. and
the unloaded quality factor Q u (referred to as quality factor throughout this text
unless specified). T he loaded quality factor of a resonance system is defined as
(1.25,
where W is the stored energy of the electrom agnetic field in the resonance system .
Correspondingly, unloaded and ex tern al quality factors can be expressed as
fl. =
0
(1.26)
. - ^
.
(1.27,
1G
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
respectively. Intuitively, the unloaded quality factor is the one m easured in the
absence of any loading effects caused by th e external circuitry.
However, the
quality factor of a resonator can not be m easured w ithout coupling to other
circuitry. Hence, the loaded quality factor is expressed as
Ql
Q
u
(L28)
+ Qe '
In practice, the loaded quality factor can be calculated from the resonance fre­
quency divided by the resonance peak w idth at
10 log
1 + 10s " / 10
dB.
(1.29)
where S n is the input reflection coefficient which is th e power ratio of the reflected
signal to the incident signal entering port 1 in a tw o-port test device. Since the
coupling coefficient i3c. defined as the ratio of the unloaded quality factor to the
external quality factor, is also a function of th e reflection coefficient, th e unloaded
quality factor can be derived according to th e following equation.
Qu = Q l ( 1 + 3 C),
(1.30)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and for undercoupling.
1 _ io 5u/20
,3c= 1 + 10-W2°-
^ ‘31^
while for overcoupling.
1 + io 5ll/2°
ft =
(L32>
T em perature coefficient can be calculated from the experim entally determ ined
tem peratures and resonance frequencies, using the following equation:
(!•» )
=
where f T and f r< are the resonance frequencies at T f and Tj. respectively.
1.1.3
M icrowave P ro p erties, C hem istry, and M aterials
Several microwave resonator m aterials have been developed in recent years. How­
ever. no m aterial is far superior th a n the others. A highly a ttra c tiv e m aterial is
(Zro.8Sno.2)Ti0 4 whose crystal stru ctu re is of an a P b 02 -type, space group Pbcn.
18
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
w ith a phase transition tem peratu re 1130°C. It has a dielectric constant of 38.
quality factor of 8400 at 7 GHz, and a tem p eratu re coefficient of -0.1 ppm /°C [9].
Though, the Sn su b stitution slightly lowers the dielectric c o n stan t[10], it has
a tem perature coefficient of resonance frequency reduced to near zero [ll],[12]
and an improved quality factor[11],[13]. It was speculated th a t the quality fac­
to r improvement was a result of the inhibited long range Zr-Ti ordering by Sn
substitution[14], while other research suggested the quality factor increase was
linked to the effect of Sn on the short-range ordering or local cation and an­
ion coordinations[lO]. Difficulties associated w ith processing of (ZrSn)TiO.( have
been reported[15]. A draw back of using this ceramic is the difficulty in m achining
the sintered pellets to desired dimensions.
A nother popular microwave ceramic adopts a complex perovskite stru ctu re in
the form of A(Bi/3E2/3)0.3 where A is B a or Sr, B is Ni. Ca. Zn. Mg. Co or Zr. and
E is Ta or Nb. Ba(Zn.Ta)C>3 has a high quality factor (10000 at 7 GHz), dielectricconstant, (29). and a near-zero tem p eratu re coefficient (1 ppm/°C)[16]. Unlike
the effeers of ordering on quality factor of (Z rS n )T i0 4. the ordering of B site
ions of complex perovskite reportedly increased quality factor[17]. Later, Desu
et al. proposed th a t the quality factor im provem ent, even after the com pletion
of ordering, was related to zinc oxide volatilization[18]. In another s tu d y [19], Sn
for Mg and Ta substitutions resulted in a near zero tem perature coefficient of
19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
resonance frequency w ith a lower quality factor and dielectric constant. Partial
substitu tio n of Zn and Ta w ith Zr accelerated the sintering and improved the
quality factor[16]. However, the sintering process still requires higher tem perature
(1500-1600°C) and prolonged soak times (20 h) for ordering of Zn and Ta ions[l6].
A nother unavoidable disadvantage of using this microwave ceram ic in designing
a lightweight device is its higher density (7.7 g /cm 3) relative to o ther material
candidates.
A can d id ate m aterial for dielectric resonators is B aT i4Og because of its high
dielectric constant and quality factor (38 and ~ 10000 a t 4 GHz. respectivelv[20]).
Ba2T ig 0 2o has also received attention for its good microwave properties, quality
factor (10000 at 4 GHz) and dielectric constant (39.8)[18].
Ba2T ig 0 2o. how­
ever. has a rep o rted tem perature coefficient of 2 p p m /° C [l8], which is closer
to zero th a n B aT i4Og (14 ppm /°C ). This makes B a2T ig 0 2o a more favorable
choice.
W hile B aT i4Og adopts an orthorhombic P n m n crystal structure[21].
Ba2T ig 0 2o resembles a hexagonal close-packed cell[22] of B a2+ and 0 2~ with
T i‘,+ in octahedral sites. This pseudo-hexagonal arrangem ent has a nine layer
stacking sequence w ith a prim itive triclinic cell. Eight barium ions reside in a
triclinic cell; four of them are 12-coordinated by oxygen while the other four
have a vacancy occurring a t the adjacent barium sites. T his crystal structure
plays an im p o rtan t role in the dielectric properties, which in tu rn obey the di-
20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
electric dispersion equation, as described by Tam ura et al. [9]. T he loss factors
of these microwave dielectrics are determ ined by dam ping constants which are
related to the anharm onic term s in th e po ten tial energy of the crystal. G rzinic
et al.[23] suggested th a t this Ba-vacancy-Ba sequence facilitated dielectric prop­
erties which were b etter than the oth er barium polytitanates. However, an o th er
study[22] pointed out th a t B a e T in O ^ an d Ba4T ii303o do not have superior di­
electric properties, though they have m ore barium vacancies p er unit cell. F urther
investigation of microwave properties by analyzing far-infrared reflection spectra
using the dielectric dispersion equation was apparently ham pered by the complex
crystal stru c tu re of Ba-iTigC^o- (Zro.8Sno.2)T i0 4 and A (B !/3E 2/3)03 (perovskite)
have sim pler structures and thus, have been studied more extensively for the
theoretical prediction of their dielectric properties at microwave frequencies.
BaoTitjC^o has been a difficult phase to form w ithout dopants. There is also
disagreem ent about the ability to form phase-pure Ba2Tig02o[24].[25].[26].[27],
Jonker et al.[24] reported th at the form ation of Ba2Tig02o could not be achieved
w ithout stabilizing dopants such as tin and zirconium oxides. In addition to these
additives. Yu et al.[27] studied the effects of AI2O3 and Bi203 on th e form ation
of Sn-doped Ba2TigC>2o- They reported th a t alum inum and bism uth oxides en­
hanced the form ation of monophase B a2TigO 20- but they did not consider the
fact th a t tin oxide, one of their common additives, has been shown to function
21
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
as the stabilizing agent for BagTigC^o- Several different form ation mechanisms
of BaoTigOoo based on doped system s have been proposed[25].[26],[27]. It is of
practical and academic interest to fabricate undoped phase-pure BagTigOgo as
the quality factor is speculated to be higher w ithout substituted ions, which may
be regarded as im purities. In previous attem p ts, the formation of BaoTigOgo in
this form through conventional sintering at 10°C /m in was not possible[28]. Yoon
et al. also reported th a t a m ixture of Ba2TigO20 and B aTi4Og was dispersed in
m icrostructures after sintering a t 1400°C for 6 h[29].
T in for titan iu m ion substitutions have been used in the form of SnOo and
BaSnO .3 in several studies[28]. [29], [30],[31]. [32] to stabilize Ba2Tig02o and their
microwave properties have been studied.
The substitution of T i+4 w ith S n +4
lowered the tem perature coefficient w ithout significantly degrading the dielectric
constant[33]. As a result, a num ber of patents on Sn+4 doped BaoTigOoo have
been aw arded [33]. [34].
Xd203 additions led to the form ation of BaN d2T i5 0 io[35] (tem p eratu re coeffi­
cient: 93 ppm /°C . dielectric constant: 80, and quality factor: 3500 at 3 G H z[l2]).
Consequently, the overall specimens showed an increased tem perature coefficient
and dielectric constant and a lowered quality factor. Nomura et al.[36] reported
th a t the quality factor could be improved w ith the doping of 0.5-1 mol% \ I n a c t­
ing as an oxidizing agent. No significant change of dielectric constant and tem22
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
peratiire coefficient due to Mn substitution was observed. A nnealing a t 1000°C
for 24 h further increased the quality factor. In addition to th erm al processing,
chem ical treatm en t also affected the microwave properties. O ’B ryan et al. re­
p o rted th a t the quality factor of B aT i4Og and BagTigOao ceram ics was improved
g reatly by leaching Ba-rich com pounds in the pre-reacted pow der w ith HC1[37].
A ddition of up to 5 mol% Sr+2 reportedly stabilized Ba2Tig02o[38]. A lthough the
zirconium ion also has stabilizing effects[24],[28] .[31] the microwave properties of
Zr'l_r-doped Ba2T i902o have not been reported in the literatu re as extensively as
the S n l+-doped.
1.1 .4
C on ven tional and Shrinkage R ate C ontrolled S in terin g
Solid sta te sintering involves three stages, namely, initial, interm ediate, and final
stages. In the initial stage the first 2% of densification occurs. B eneath a concave
surface, the concentration of vacancies is higher th an th a t b en eath a flat or convex
surface.
To reduce surface free energy, vacancies may be tran sp o rted from a
concave surface via lattice and boundary diffusion. As a result , pores are rounded,
particle surfaces are sm oothed, and bond grows at the contact points between
particles, leading to the form ation of necks. The shrinkage w ith tim e t in the
initial stage for uniform ly packed spherical particles may be described by the
following equation[39],
23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AL
L0
( K D v ls Vvt \ m
I k BT d n )
(1.34)
where L 0 is the length of the green compact. A L is the length change during ini­
tial sintering. K is a constant dependent on th e geometry. D v is the diffusivity of
the vacancies of volume Vv, j s is the surface tension. k B is the B oltzm an constant.
T is tem perature, d is the grain diam eter, n is a constant (3 if surface diffusion
predom inates), and m is a constant in the range of 0.3-0.5. This equation indi­
cates shrinkage is influenced by various param eters am ongst which tem p eratu re
and particle size can be controlled experimentally. Shrinkage is very tem p eratu re
dependent because the diffusivity varies exponentially w ith tem perature. Sm aller
particles result in the same m agnitude of shrinkage in shorter time.
In the interm ediate stage, m ajor densification (up to ~ 92%) takes place as the
dim ension of necks increases and open pores channel along three grain junctions
shrink. Slow grain grow th is also observed. Sintering in this stage also depends
on the param eters in Equation 1.34. Diffusion across grain boundaries causes the
boundaries to be displaced at a velocity ?/(, according to the following.
n
r2
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(1.35)
where 77 and r -2 are the principle radii of the grain boundary curvature and Mb
and 7b are th e mobility and surface tension of th e grain boundary, respectively.
U nder the pull of grain boundary, pores may m igrate by m eans of mass tran sp o rt
across the pores. The condition for pore attach m en t depends on the ratio of
mobilities of pores Mp and grain boundary, volume fraction of pores, and pore
radius rp. Pore m igration by surface diffusion m ay be expressed as,
A/p =
KDa
Tr$
(1 .36 )
where K is a constant and D s is surface diffusivity. This equation indicates th a t
small pores m igrate faster th an large ones. This is because sm aller pores have a
higher curvature driving force and sm aller m ean diffusion distance.
In the final stage, the densification rate rapidly decreases as pores are closed
and larger grains grow at the expense of sm aller grains.
Small pores shrink
to a lim ited size or disappear while pores larger th a n grains shrink relatively
slowly. T he diffusion paths for pore shrinkage depend on where the pores are
located. Pores on grain boundary can be elim inated by lattice or grain boundary
diffusion, while pores w ithin grains can only be removed by lattice diffusion. For
continued densification. the location of pores becomes a critical issue because
lattice diffusion is generally so slow th a t the annihilation of pores is unachievable
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
w ithin a reasonable tim e span; thus, pores are trapped. Based on this, a twozone shrinkage rate-controlled sintering (RCS) has been developed. In th e first
zone, a fast shrinkage ra te was selected so th a t time-effective neck form ation and
grow th between particles can be achieved. Following th a t, a slow shrinkage ra te
was applied in order to keep pores a ttach ed to th e grain boundary and thereby
elim inate them.
For microwave ceramics, sintered com pacts of m axim um density are desirable
to achieve a higher dielectric constant. In o ur previous work, Zr4+- or Sn4+-doped
Ba^TigO^o com pact density decreased w ith extended soaking at the sintering tem ­
p e ra tu re (1390°C). as a grain boundary liquid phase formed and volatilized over
tim e. Thus, optim um sintering of this com position is com plicated by th e require­
m ent of sintering periods long enough for elim ination of the porosity between
particles in the com pact, yet short enough to minimize introduction of porosity
via liquid phase volatilization. Control of th e grain boundary velocity is also
needed so th a t pores are not swept into grains during sintering. Though this can
be easily achieved by using a lower heating rate, longer processing tim e would be
required, which in tu rn would facilitate porosity via liquid phase volatilization.
A shrinkage rate controlled dilatom eter is a useful tool for achieving m ax­
im um densification w ithin the shortest, tim e.
Under rate-controlled sintering,
furnace power is adjusted as instructed by a feedback control algorithm to main2G
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tain a desired shrinkage rate. Using RCS, tem perature profiles are deduced w hich
guarantee continued progress in densification. thereby minimizing the tim e and
tem perature (therm al activation) a t which grain growth can occur[40]. O ur ra te
controlled dilatom eter uses an infrared radiation furnace which has d em o n strated
impressive therm al responsiveness, an d is capable of considerable control over th e
sintering process[41|. Previous studies[41] using this device were lim ited to spec­
imens of ~ 0 .5 g. The current stu d y used shrinkage rate controlled sintering to
deduce therm al schedules which were program m ed in a conventional furnace to
form optim ized m icrostructures. These m icrostructures were then correlated to
microwave properties.
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 2
Experim ental Procedure
2.1
2.1.1
P rocessing of B arium P olytitan ates
B aT i4Og and Zr4+- and Sn4+-D op ed B a 2 TigC>2o M icrow ave R es­
onators
Raw m aterials of B aC 03 (electronic grade) and T i02 (anatase. electronic grade)
were hatched to form B aT ^O g. and doped compositions of B a2Tig0 2 o- For these
compositions. TiOg was su b stitu ted w ith 0.82. 1.64. and 2.46 mol% ZrC>2 or
Sn0 2 - An additional com position of Ba2Tig02o w ith 1.64 mol% excess TiC>2 was
prepared. The powders were mixed w ith deionized w ater and a dispersing agent
in plastic bottles w ith ZrC>2 grinding media overnight. T he slurries were then
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
dried and calcined/pre-reacted at 1200°C for 4 h. Pre-reaction was also initially
attem pted a t 1150°C for 4 h. T he powders were th en re-milled in deionized water.
Fifteen g of pow ders sam ple were uniaxially pressed into 22.5 mm diam eter pellets
and sintered by heating a t 1390°C for 6 and 16 h in flowing oxygen.
2.1.2
Shrinkage R a te C ontrolled Sintering
Pellets of 0.5 g each were uniaxially pressed in a 6.25 mm diam eter die. then
stuffed in evacuated rubber sleeves and isostatically pressed under 70 M Pa. Spec­
imens were placed in the rate controlled sintering dilatometer[41] and initially
heated at 100°C /m in to 1050°C. which was ~100°C below the onset of densificafion. T he ra te controlled sintering algorithm th en took over, using setpoint
shrinkage rates of 0.5. 1. or 3 % /m in. Heat tre a tm e n t was term inated after the
specimen dim ension reached 92% of theoretical density (4.615 g /cm 3[42]. based
on monophase E^TigO-^o w ith no dopants).
Based on m icrostructural observation, an optim um shrinkage ra te was selected
for the RCS first zone. Specimens were then sintered at the selected first zone
shrinkage rate, followed by sintering at a lower second zone shrinkage ra te of 0 .1.
0.02 or 0.01 % /m in to a term inal density of 99% of the theoretical density.
T em peratures m easured by the thermocouple disk[40] were calibrated based
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
on the m elting points of silver an d B aT i40g. Because of the lim ited uniform hot
zone w ithin the radiant-heating RCS dilatom eter. green pellet size was restricted
to 6.25 mm diam eter x ~ 2 .6 m m thickness (~0.5 g). However, for microwave
property m easurem ents. 22.6 m m diam eter x ~ 16.5 m m thickness (~ 1 5 g) pow­
der sam ples were required. For sintering of these large specimens, a conventional
MoSio bottom loading box-type furnace was pre-heated to 1500°C. It was then
opened, and the 15 g pellets were placed on a Zr02 setter w ith Zr02 powder on its
surface. The bottom -loading furnace was then closed over a ~ 2 min period (see
results section). The specim ens were then heated in a continuous flowing oxygen
environm ent (200 cm3/m in ). under m ultiple heating ram p and hold schedules,
selected to em ulate tem p eratu re schedules from an RCS study. For com parison
w ith conventional sintering schedules, specimens were also heated a t 4 °C /m in to
1390°C and soaked for 6 or 10.4 h in flowing oxygen at 200 or 600 cm 3/m in . T he
flowing oxygen was for the purpose of sustaining titanium cations in the 4 + state.
2.1.3
T herm al P ro cessin g o f B a T i40 9 and U n d op ed and Sn'l+-D o p ed
Ba2TigO20
Raw m aterials were B aC O .3 (electronic grade), TiC>2 (anatase. electronic grade),
and Sn02 (electronic grade). Two batches of powders in mol%: 18.2BaCO.(81.8Ti02 and 18.2BaCO.3-80.2TiO2-1.6SnO2. were prepared. The powders were
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
mixed w ith distilled w ater and dispersing agent in plastic b o ttles w ith Z r 0 2 balls
for 8 hours. T he slurries were then dried for 12 h a t 45°C and th en calcined
by heating at 20°C /m in to 600°C. then 40°C /m in to 975°C, and holding a t th a t
tem perature for 6 h. T h e powders were wet mixed using zirconia m edia again
w ith PVA and D arvan for 24 h. 5.8 g of powders were uniaxially pressed into
pellets and sintered at 1360 and 1390°C for 5 h on a Zr0 2 plate.
2.1.4
R apid T h erm al P rocessin g o f U ndoped M on op h ase B a 2T i9O20
Raw m aterials of BaTiC>3 (electronic grade) of 0.6 fim average particle size, and
T i 0 2 (anatase. electronic grade) of 0.6 //.m average particle size, were batched to
form Ba2T i9O20. T h e pow der was mixed with distilled w ater and an am m oniabased dispersing agent (Darvan) in plastic bottles w ith Z r 0 2 grinding m edia
overnight. The slurry was then dried for 48 h at 80°C. T he particle size dis­
tribution of the as-m illed powder was examined using a particle size analyzer
(M icrotrac II. Leeds & N orthrup Co., St.
Petersburg, FL). T he pow der was
uniaxially pressed into pellets and soaked at 1250°C for 2h, using heating rates
ranging from 5°C /m in to 500°C/m in. using conventional and inffared[41] fur­
naces. Varying soaking tim es were applied to determ ine th e progress in form ation
of Ba2Ti9 0 2o- Some pellets were exposed to second heat, tre a tm e n ts at 1390°C
(pre-heated \Io S i2-elem ent furnace) for 8, 16. and 24 h to foster the form ation of
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Btl^TigOgo-
2.2
M icrostructure O bservation and Im age A nalysis
T he m icrostructure along the specim en cross section was exam ined using scanning
electron microscopy (S-800. field emission scanning electron microscopes. Hitachi.
L td.. Tokyo. Jap an ). Owing to m inute atom ic weight differences. BaaTigOoo and
B aT i40g could not be distinguished using secondary electron images. However,
th e contrast between the two phases was ad eq u ate in back scattered images. To
determ ine the volume fraction of T i0 2 - secondary electron images were used so
th a t porosity was elim inated from analysis of black T i02 regions.
The micrographs were digitally scanned into bit-m ap com puter files (30 pix­
els/cm ) and the contrast of phases were analyzed using a software w ritten for
this purpose w ith Microsoft Visual Basic.
For each pixel of the scanned im­
age. an averaged (grey-scale) value of the red. green, and blue com ponents were
used to determ ine an eight bit value (0-black to 255-white). A cutoff value was
then assigned to differentiate the phases (BaTi.iOg-light shaded. B a2Tig0 2 o-dark
shaded). The ratio of the pixels w ithin a specified greyscale range to th e pixels
w ithin the specified ranges for b oth phases was calculated as the volume fraction
of a particular phase. Average grain sizes were determ ined from the m ean dis-
32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tance between intercepts of com puter-generated arb itra ry lines across 500 grains
on digital images of the micrographs.
2.3
P h ase and Therm al A n alyses
X -ray diffraction (12054 X-ray diffraction unit, Phillips Electronic Instrum ents
Co.. M ount Vernon, NY) was used for phase analysis w ith a step size of 0.015°
and a sam pling tim e of 1 or 3 seconds. T he relative am ounts of BaaTigOoo and
B aT i409 were calculated from the intensities of their most intense diffraction
peaks ((220) and (121). respectively). T he background level from which peak
heights were determ ined was established based on an average of the noise level
for 28 values showing a level band of lowest background intensity.
The weight change during a soak period at 1390°C was monitored, utilizing
a therm ogravim etric analyzer (Sim ultaneous therm al analyzer. Netzsch Inc.. Ex­
ton, PA). T he STA were also used to detect the reactions which occurred during
heating of the raw materials. Sintering of calcined (pre-reacted) powders was
m onitored using a dilatom eter (O rton A utom atic Recording Dilatom eter. W est­
erville. OH).
33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.4
D ielectric P rop erty M easurem ent
The sintered pellets were cut perpendicular to the cylindrical axis to form p a r­
allel faces and their side walls were ground. The microwave properties of th e
TEow mode of these pellets were m easured a t 3 GHz. using a Hewlett Packard
8510C network analyzer. T he unloaded quality factor of a specim en w ithin th e
microwave cavity of brass coated w ith silver was measured from th e reflection co­
efficient and peak width; A schem atic diagram of experim ental fixture is shown
in Figure 2.1.
The drift of resonance frequency w ith tem perature was measured using a m i­
crowave cavity of invar alloy in a vacuum oven. Only specimens of high quality
factor and relative perm ittivity were evaluated for their tem perature coefficient.
The Kobayashi met,hod[8] was applied to m easure the dielectric constants, where
brass conducting plates ~ 6 tim es the specimen diam eter were located on u p p er
and lower radial surfaces, and th e plates were electrically connected.
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Brass cavity
with silver
coating
Cylindrical
microwave
ceramic
Specimen
holder
Netv vork
Ana yzer
Frequency
Synthesizer
F igu re 2.1: A cylind rical d ielectric sp ecim en is placed inside a m icrow ave ca v ity for m icrow ave
d ielectric p rop erty m easurem ents in reflection m ode.
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 3
R esults and D iscussion
3.1
D ielectric P roperties o f BaT^Og and Zr4+- and Sn4H~D op ed B a 2 Ti<)O20 M icrow ave R esonators
P re-reacting the 0.82 mol% Z r 0 2-su b stitu te d com position (henceforth referred to
as 0.82%Zr) at 1150°C (holding for 4 h) showed th a t m ostly B aT i4Og formed.
Pre-reacting the composition at 1200°C and holding for 4 h led to the forma­
tion of Ba-jTigOoo and BaTi4 0 g; m inute am ounts of B aC O .3 and T i02 were also
identified. These phases were identified in all SnC>2- and Z rC V substituted sam ­
ples. pre-reacted a t 1200°C. Pre-reaction of the 0.829oZr com position resulted in
significantly greater stabilization of B a2Tig02 o. th an when the sam e concentra-
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tion of SnOo was used (Figure 3.1). T he relative percentages of Ba2T ig 0 2o after
this heat treatm en t decreased w ith increasing concentration of S n 0 2. This was
also markedly the case for the Z r 0 2-su b stitu ted sam ples, w ith the exception of
the highest concentration (2.46%Zr). For the powder batched to form B aT i40 9 ,
this pre-reaction heat treatm ent formed B aTi4Og as well as retaining traces of
BaCC>3 and T i 0 2: no Ba2T ig 0 2o was detected. B a2T ig 0 2o, B aT i4C>9. and traces
of BaCOg and T i 0 2 were detected in the h eat-treated b atch w ith excess T i 0 2.
After sintering at 1390°C for 6 or 16 h, monophase B a2T ig 0 2o was observed in
all specimens doped with tin and zirconium ions; an exception was the 2.46%Zr
specimens, which were composed of Ba2T ig 0 2o. B aT i4Og. T i 0 2. and Z r 0 2. Based
on relative XRD intensities, the longer soak period (16 h) for this latter compo­
sition decreased the relative proportion of Ba2T ig 0 2o (to B aTi4Og). The pel­
let batched to form BaTi4Og formed only th a t phase, as expected. The speci­
mens batched w ith 1.64% excess tita n ia developed a m ixture of Ba2T ig 0 2o (32%).
B aT i4Og. and T i 0 2. Figure 3.2a and b shows th a t the porosity increased (in size
and frequency) w ith sintering time for 0.82%Zr. The porosity was clearly located
at grain boundaries, and not necessarily a t triple points. U nreacted tita n ia was
present in the 2.46%Zr specimens, which also showed higher porosity th an the
0.82%Zr specimens heat-treated for the same tim e period.
Figure 3.3 shows th a t the dimensional density of the sintered pellets increased
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
70
•£ £ , 60
8.
O
°
fN
o o
£ .2 50
40
30
20 L
0.5
1.5
2
2.5
Mole Percent Substitution
Figure 3.1:
R elative proportion o f BaoTigOoo as a function o f ZrOo or SnOo su b stitu tio n ,
for speciincn.s pro-reacted at 1200°C for 4 h.
V alues were d eterm in ed via th e ratio o f the
m ost in tense X R D peak height o f BaoTigOoo to the sum o f th e m o st in ten se peak heights o f
BaoTigOoo and BaTLjOg.
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F igure 3.2: S econ d ary electron im ages o f the 0.82% Zr com p osition h eated at 1390°C for (a) G
and (1>) 1G h. (e) B ack seatted im age o f th e 2.4G%Zr sp ecim en sintered for G h. Black regions
in the upper left o f (e) correspond to TiO o. w hile black regions at th e cen ter and right o f the
m icrograph are pores. Light grcv regions in th e upper left o f (c) are BaTi-jOg. and the m atrix
phase is BaoTigOoo-
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39.6
39.4
16 h
-♦-j
4.58
c
ec
•+ -»
C/5
c 39.2
o
U
o
n
-t—>
o
4.56
.32
0)
5
4.54
38.8
38.6
0.5
Dimensional Density (g/cm3)
4.6
4.52
1.5
2
2.5
3
M ole Percent Tin Oxide
Figure 3.3: T h e effects o f tin oxid e ad d ition s and sintering tim e on dim ensional d en sities and
d ielectric co n sta n ts in the m icrow ave frequency range (3 G H z).
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
w ith increasing SnOo content, while the dielectric co n stan t decreased, for both
soak periods. A longer soak period, e.g. 16 h vs. 6 h. fostered a decrease in the
density and dielectric constants. As shown in Figure 3.4, the 1.64%Zr samples
(6 and 16 h) showed m axim a in dimensional densities.
W ith increasing ZrC>2
substitution, the dielectric constants followed the tren d of dim ensional density:
an exception was th e lower density 2.46%Zr specimen soaked for 16 h which
exhibited the highest dielectric constant.
Figure 3.5 shows the quality factors as a function of d o p an ts and sintering time
at 1390°C. T he quality factors of specimens sintered for 6 h increased m oderately
from 11900 to 12900 as SnC>2 content was increased from 0.82 to 1.64%. and
remained largely unchanged for the 2.46%Sn pellets.
For these sam ples, the
soak period had no significant influence on the quality factor.
Increasing the
Zr doping level from 0.82 to 1.64% improved the quality factor to a m axim um
m easured (13900). T he quality factor then degraded precipitously in th e 2.64%Zr
specimens, especially for the long soak period. Figure 3.6 shows th a t the quality
factor of all Sn-doped and the 0.82%Zr specimens, sintered for 6 h. decreased
by about 14% as th e m easurem ent tem perature increased from 25 to 117°C. The
other pellets w ith ZrC>2 substitutions exhibited a greater dim inution in quality
factor with increasing tem perature. A reduction in excess of 50% in th e quality
factor was m easured in the B aTqO g specimen over the tem p eratu re span studied.
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40.6
4.54
-£ 40.2
4.52
CO
t/5
o 39.8
6h
4.5
o
'5 39.4
4.48
o
—
<D
16 h
Q
38.6
4.46
4.44
16 h
38.2
0.5
2.5
Dimensional Density (g/cm3)
4.56
4.42
Mole Percent Zirconia
F igure 3.4: D im ensional d en sities and d ielectric co n sta n ts o f Z r 0 2 -d o p cd com p acts, sintered at
1390°C for G and 1G h. as a function o f a d d itive concentration.
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
14000
6h
12000
Quality Factor
Sn 16 h
10000
8000
6000
4000
16 h
2000 L
0.5
1
2
Mole Percent Dopant
1.5
2.5
Figure 3.5: E ffects o f d o p an ts and soak tim e on the q u a lity factor at 3 G H z.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3
14000
1.64%Zr
13000
12000
4—
»
11000
0.82%Sn
j j 10000
£
9000
§
8000
2.46%Sn
' 82%Zr
1.64%Sn
7000
2.46%Zr
6000
5000
20
40
60
80
100
120
Temperature (°C)
Figure 3.6: Influence o f tin and zirconium o xid e su b stitu tio n s on q u a lity factor o f BaoTigOoo
as a function o f tem perature. BaTLjOg is also in cluded. All sp ecim en s w ere sintered at 1390°C
for 6 li.
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T he effects of dopants on th e tem p eratu re coefficient of resonance frequency
axe shown in Figure 3.7. The te m p e ratu re coefficient (slope) decreased w ith zirconia additions, whereas trends were not as defined w ith increasing tin oxide
concentration. Amongst all doped specim ens, the minimum tem p eratu re coeffi­
cient (0.1 pp m /°C between 25 to 60°C) was m easured in the 2.46%Zr specim ens,
while th e 0.82%Zr specimens showed th e maximum (7.0 pp m /°C between 97117°C). T em perature coefficients, as well as other microwave property results are
sum m arized in Table 3.1.
Pre-reaction heat treatm ent a t 1150°C showed th at m ostly B aTi4Og formed,
im plying th a t in the process of reaction of batch constituents. B aTi4Og formed
first, which then further reacted w ith TiC>2 over time to form B a2T ig0 2 o- It is
postulated th a t BaTi4Og has a higher solubility for large cation replacem ent of
T i4+ th a n does BaoTigC^o at 1250°C. If this is the case, higher doping concen­
tratio n s would resist conversion to B a2Tig02 o since some of the soluble dopant
would have to be rejected. O ur previous work[43] has shown th a t form ation of
BaoTigC^o w ith no doping requires significantly more time (and a soaking tem per­
a tu re of 1390°C): the dilation of the B aT i4Og unit cell via small concentrations of
dopants appears to facilitate reaction w ith TiC>2 to most rapidly form B a2TigO20
at 1390°C.
Re-milling the heat-treated pow der facilitated mixing of the phases initially
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
550
500
450
400
^
Zr 0.82%
350
S. 300
Sn 0.82%
a,
^
250
Sn 1.64%
< 200
150
100
Sn 2.46%
Zr 1.64%
Zr 2.46%
100
120
Temperature (°C)
F igure 3.7: Influence o f tin and zirconiu m oxid e su b stitu tio n s on th e frequency drift, (relative
to room tem perature) and tem perature coefficients (slopes o f lines) o f sp ecim en s sin tered at
I390°C for G h.
4G
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Tabic 3.1: Density and Microwave Properties of Barium Polvtitanates
Specimen.
Density
Sintering
(g /cm 3)
Dielectric Constant
Quality Factor
Temperature Coefficient
at 3 GHz
(ppm /°C )
Time
20-60°C
60-97°C
97-119° C
0.82%Sn. 6h
4.53
39.5
11900
1.8
3.8
4.5
1.64%Sn. 6h
4.59
39.1
12900
1.3
3.1
4.2
2.46%Sn. 6h
4.59
38.8
12900
1.4
2.8
3.7
0.82%Sn. 16h
4.53
39.1
11600
l.64%Sn. 16h
4.56
38.8
12700
2.46%Sn. 16h
4.58
38.7
13100
0.82%Zr. 6h
4.48
39.1
12400
4.5
6.2
7.0
1.64%Zr. 6h
4.56
39.3
13900
2.3
2.8
4.2
2.467c Zr. 6h
4.50
38.8
8600
0.1
1.7
2.6
0.82%Zr. 16h
4.44
38.4
12300
l.64%Zr. I6h
4.51
39.1
13800
2.469cZr. I6h
4.46
40.8
3000
1.647cTi. 6h
4.49
40.2
2100
l.64%Ti. 16h
4.49
38.3
3300
BaTi-tOg. 6h
4.37
37.2
13900
21.4
18.1
14.0
BaTi-iOg. 16h
4.34
36.9
13800
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
formed, e.g. B aT i4Og. and the unreacted T i0 2 - Sintering a t 1390°C for 6 and
16 h resulted in form ation of monophase BajTigC^o for all substituted compo­
sitions. except the 2.46%Zr batch which still contained unreacted ZrOo. This
indicates th a t the solubility of Sn4+ in Ba2Tig02 o was higher than th at of Zr4+.
T his can be a ttrib u te d to th e smaller ionic size of the tin ion. compared to zir­
conium. for substitu tio n into T i4+ positions w ith less distortion. The com plete
solubility of the dopant levels of tin oxide in this work agree with other recent
invest igations[29j.
An excess of TiC>2 in the batch did not prom ote th e form ation of Ba2Tig02 o
after heat-treatin g at 1390°C for 6 h. Instead, it resulted in m ultiple-phase spec­
imens composed of Ba2TigO20: B aTi4Og, and T i0 2 - T he persistence of B aTi4Og
corresponds to th e lack of the influence of su b stitu tio n al solid solution ions.
B aT i4Og and TiC>2. having a lower density th an B a2Tig0 2 o- led to sintered spec­
imens of lower overall density. All specimens sintered a t 1390°C for 6 h in the
current study had either equal or higher densities th a n those after the 16 h soak­
ing period. Higher porosity was apparent in the m icrostructures soaked for 16 h
(Figure 3.2). In addition, therm ogravim etric analysis showed a linear weight loss
w ith time (0.044 wt.% per hour) during an identical therm al schedule w ith a 16
h soak. Above the incongruent, m elting tem perature of B aT i4Og (1432°C). TiC>2
is in equilibrium w ith liquid phase. D opant additions likely locally lowered the
48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
liquid-forming tem perature below 1390°C. Such a grain boundary liquid phase
then volatilized over time, leaving increased porosity. T his is corroborated by th e
shape and location of pores in Figure 3.2b.
The increasing dimensional density of specim ens sintered for b o th soak periods
w ith increasing Sn02 content corresponds to the su b stitu tio n of titan iu m ions
w ith heavier tin ions, where the m ass of th e unit cell was increased more th a n
its volume was dilated.
T he same explanation m ay be used in the Zr-doped
specim ens. An exception was the over-doped 2.46%Zr case, where lower density
second phases lowered the overall dim ensional density.
The dielectric constant decreased w ith increasing soak period (for a given
com position), with the exception of 2.46%Zr. T he porosity formed w ith the 16
h soak introduced low dielectric constant vapor gaps in the m aterial, decreasing
th e overall dielectric constant. For th e 2.46%Zr sam ple, after soaking for 16 h at
1390°C. a more significant percentage of T i02 was detected by XRD (as com pared
to after 6 h). The dielectric constant of T i 0 2 (~100[20j) is appreciably higher
th a n Ba2Tig02o- Thus, the excess T i0 2 content in the 2.46%Zr sam ple soaked
for 16 h was responsible for the high m easured dielectric constant.
W ith increasing Sn doping, the dielectric constant decreased, agreeing well
w ith other work[29]. Since the electron cloud for th e larger Sn4+ is more polarizable[2]
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
th a n T i4+, SnC>2 substitutions would be expected to increase dielectric constant.
Since the opposite effect was observed, it follows th a t the decreased ionic po­
larization associated w ith the larger Sn ion[6] was the cause of the decreased
m easured dielectric constant. In contrast, the increase in dielectric constant w ith
ZrC>2 additions (up to 1.64%) implies dominance of the electronic contribution
to the dielectric constant.
Soaking tim e showed a distinct effect on sintered density, b u t minimal effect on
the quality factor except for the overdoped specimen. Dielectric loss is known to
be only m inim ally influenced by levels of porosity, since pores contain vapor which
do not contribute to energy loss unless m oisture is trapped inside the pores[9].
However, the quality factor is strongly dependent on the condensed phases present
in the m icrostructures. The degradation of quality factor in 2.46%Zr specimens
m ay be a ttrib u te d to dielectric losses via anharm onicities associated w ith bound­
aries between m ultiple phases[6]. W hen specimens were heated for microwave
property m easurem ent, therm al agitation disturbed the harm onic resonance of
the oscillators (electron clouds and ions), leading to a reduction in th e quality
factor.
T he observed higher tem perature coefficient of BaTi4Og th a n th a t of B a2Tig0 2 o
agrees w ith the literature[20]. The 2.46%Zr sample, heat-treated for 6 h did not
form an appreciable volume percent of TiC>2 second phase: T i 0 2 would have oth50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
erwise been expected to contribute to a significant rise in the specim en tem per­
a tu re coefficient (tem perature coefficient for T i 0 2: 400[20]). T hough the quality
factor of undoped B aTi40g was th e highest, its resonance frequency and quality
factor were also the most sensitive to tem perature change am ongst all specimens.
Therefore, application of B aT i40g would be lim ited to a tem perature-stable en­
vironm ent. such as base stations for microwave broadcasting.
3.2
M icrow ave D ielectric Properties o f M icrostructureC ontrolled B a 2 TigO 20 R esonators
A fter calcination/pre-reaction of all compositions at 1200°C for 4 h. B a2T ig 0 2o
and B aT i4Og formed, and m inute am ounts of BaCOg and T i 0 2 were also iden­
tified.
Based on relative XRD peak intensities, a higher volume percent of
Ba2TigO20 formed with the lower S n 0 2 concentration. M onophase B a2T ig 0 2o
was observed in all specimens after rate controlled and conventional sintering.
D ilatom etry of green pellets (using a constant heating rate) showed the onset
of sintering to be at ~1150°C. Therefore. 1050°C was selected as th e tem pera­
ture for RCS to begin. Assuming isotropic shrinkage, a 16.1% linear shrinkage
(92% of theoretical density) was specified as the switchover from first to second
zone shrinkage rates, and a 19.0% linear shrinkage (99% of theoretical density)
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
was calculated to be the point of term ination of RCS. These were based on the
measured dimensional green densities (~54% ).
T he m icrostructures of specimens of different com positions after the same
therm al treatm ent showed no visible difference. The m icrostructures of 1.64%Zr
specimens after first zone RCS rates of 3, 1 or 0.5 % /m in are shown in Figure 3.8.
Plate-like grains appear either in cross-sectional view as needles, or in direct view
as large equiaxed grains. Intragranular porosity is increasingly apparent w ith
higher RCS rates. Intragranular pore frequencies of 6800, 4400. and 1300 m m ' 2
were m easured from m icrographs for the 3. 1, and 0.5 % /m in rates, respectively.
Based on the minimum of intergranular porosity m easured in th e m icrostruc­
ture. the 0.5 % /m in RCS schedule was selected for the first zone of two-zone
RCS schedules. Figure 3.9 shows th a t a short period (32 min) of exposure at a
high tem perature (~1370°C) was required for rapid densification following the
first zone RCS setpoint rate. A near-instantaneous tem p eratu re drop of 100°C
resulted from fiunace power adjustm ents by the feedback control algorithm as
the shrinkage rate switched to the lower values of 0.02 or 0.01 % /m in. The lower
the setpoint shrinkage rate, the greater the oscillation of shrinkage and specimen
tem perature about their respective setpoints: peak to peak tem p eratu re oscilla­
tions for the 0.01% /m in RCS rate were ~35°C . Based on the tem p eratu re profiles
from the three RCS schedules, the grey lines in the figiue were deduced and used
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
c
F igu re 3.8: M ierostructures o f l.G4%Zr sp ecim en s after first zone RCS rates at (a) 3. (b) 1.
and (<•) 0.5 % /m in.
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1400
1000
0.5 %/min.
0.1 %/min
800
600
0.5 %/min,
0.02 %/min->
0.5 %/min,
0.01 %/min
400
-16
-20
Temperature (°C)
1200
200
0
100
200
Time (min)
300
400
Figure 3.9: D cn sifieation and tem perature profiles o f 1.64%Zr sp ecim ens a s a function o f tim e.
D otted lines represent setp oin t densifieation schedules. G rey lines represent setp o in t tem pera­
ture schedules assigned to furnace heat treatm ents.
54
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
for furnace heat treatm en t of larger (15 g) specimens. As th e second zone shrink­
age ra te was doubled from 0.01 to 0.02 % /m in. the h eat-treatin g tem p eratu re
changed from a constant 1260°C to a positive slope (0.16 °C /m in ), sta rtin g at
1260°C and ending a t 1292°C. A sh arp er increase in slope is ap p aren t for th e 0.1
% /m in RCS second zone rate.
A ttem pts to em ulate the 100°C /m in initial heating rate using the conventional
furnace initially involved pre-heating the furnace to 1500°C, opening the furnace
and placing the specimens, and then closing the furnace to im m ediately expose
the specimens to nearly the startin g setpoint tem perature (corresponding to the
tem perature in the RCS dilatom eter a t the onset of RCS). This generally resulted
in therm al shock-induced cracks in the sintered com pacts. Fabrication of un­
cracked sintered specimens required closing the furnace more gradually (~ 2 min).
At the point of closing, the furnace tem p eratu re was ~1200°C. and was heated
at 20°C /m in to the tem perature corresponding to the onset of RCS. Furnace
tem perature then dutifully followed the aforementioned RCS-based tem p eratu re
schedule. Specimen cooling after the heat treatm ent schedule was com plete was
at the rate of furnace cooling w ith no power applied to the furnace (12 min from
1390 to 900°C).
Figure 3.10 shows densified m icrostructures after 0.5 % /m in first, zone RCS
rate. 0.1 or 0.01 % /m in second zone rates, and furnace heat treatm en ts em ulating
55
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F igure 3.10: (a) 0.5 g 1.04%Zr specim en after a first zone R C S rate o f 0.5 % /m in to 92% o f
th eoretical density, and a su bsequ en t second zone RCS rate o f 0.01 % /m in to 99% o f theoretical
density, (b) 15 g sp ecim en o f th e sam e com p osition as (a) after furnace heat treatm en t schedules
em u latin g the tem perature profile o f the RCS schedule, (c) S am e as (a) but w ith a second zone
RCS rate o f 0.1 % /m in . (d) S am e as (b) but em u lating th e tem p era tu re profile o f the RCS
schedu le in (c).
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the tem p eratu re schedules resulting from these RCS rates. T h e m icrostructures
from RCS dilatom eter and furnace h eat treatm en ts appear largely identical; how­
ever. image analysis shows th a t th e furnace h eat-treated specim ens had larger
average grain sizes and lower volume percent porosities. Porosities and average
grain sizes for 1.64%Zr specimens for a variety of RCS and tem perature sched­
ules are shown in Table 3.2.
T em perature controlled sintering to 99.9% of
theoretical density required an extended (10.4 h) soak a t 1390°C. yet resulted in
a higher volume percent porosity th a n the same heat treatm en t w ith a shorter
soak period.
Figure 3.11 shows the m icrostructures of this specimen.
G rain
b o u n d a ry /trip le point porosity is apparent in an otherw ise fully densified microstructure. T he furnace heat treatm en t of 4°C /m in to 1390°C w ith a 6 h soak
was used based on prior trial-and-error experience in optim ized densification of
this com pound. The volume percent porosity after this heat treatm en t was lower
th a n specim ens heat treated in the RCS dilatom eter. though the average grain
size was larger. These m icrostructures showed no sensitivity to oxygen flow rate.
Table 3.3
lists dimensional densities and microwave properties of sintered
specim ens utilizing a conventional furnace (using an oxygen flow rate of 200
cm3/m in . unless otherwise indicated).
The 1.64%Zr com position showed the
highest quality factor of the three compositions. H eat treatm en t corresponding
to th e lower (0.01% /min) second zone rate for the 1.64%Zr specimens yielded a
57
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T ab le 3.2: P orosity and average grain size o f 1.64% Zr sp ecim en s. T D stands for theoretical
density. 15 g sam ples were heat treated in a MoSio furnace, w hile 0 .5 g specim ens were heat
treated in th e RCS dilatom eter. In furnace heat trea tm en ts, sp ecim en s were exp osed to an
oxygen flow rate o f 200 cm 3/m in (unless otherw ise in d ica ted ). *Sintered at an oxygen flow rate
o f GOO cm 3/m in .
Mass
Sintering Schedule
(e)
Porosity
Grain Size
(vol%)
(/im)
0.5 g
0.5% /min to 92% TD
10.2
5.12
0.5 g
1%/min to 92% TD
10.1
4.95
0.5 g
3%/min to 92% TD
10.4
5.07
0.5 g
0.5%/min to 92% TD . 0.01% /min to 99% TD
3.4
3.92
0.5 g
0.5%/min to 92% TD . 0.02% /min to 99% TD
3.1
3.59
0.5 g
0.5%/min to 92% TD , 0 .1%/min to 99% TD
6.9
4.13
15 g
0.5%/min to 92% TD . 0.01%/min to 99% TD
1.2
4.04
15 g
0.5%/min to 92% TD . 0.02% /min to 99% TD
2.7
4.10
15 g
0.5%/min to 92% TD . 0.1%/min to 99% TD
5.9
4.24
0.5 g
•l°C/min to 1390°C. 10.4 h soak, to 99.9% TD
4.5
5.79
15 g
4°C /m in to 1390°. 6 h soak
0.8
5.05
15 g*
4°C /m in to 1390°C, 6 h soak
1.1
5.11
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.11: 1.04%Zr sp ecim en sh ow ing th e presence o f sign ifican t grain b ouudarv/t.riple point,
p orosity after heat treatm ent, at 4 °C /m in to 1390°C and held until th e RCS algorithm recog­
nized a term inal shrinkage equivalent to 99.9% o f theoretical d en sity (10.4 h).
59
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.3: D en sity an d m ierow ave properties o f BaoTigO^o- In dicated d ielcetrie co n sta n ts and
quality factors were m easu red a t room tem perature. *Sintcrcd at a n o x y g en flow rate o f COO
cm 3/m in .
Specimen
Sintering
Density
Schedule
Dielectric
Quality
Temperature
Constant
Factor
Coefficient
at 3 GHz
(ppm /°C )
(g/cm 3)
0.82%Sn
0.5. 0.02% /min
4.47
39.4
11900
l.64%Sn
0.5. 0.02% /min
4.53
38.9
12700
l.64%Zr
0.5. 0.02% /m in
4.54
39.1
13800
0.82%Sn
0.5. 0.01% /m in
4.52
39.6
11800
1.64%Sn
0.5. 0.01% /min
4.57
39.2
13000
l.64%Zr
0.5. 0.01% /min
4.56
39.5
13900
0.827cSn
4°C /m in
4.51
39.5
12000
l.64%Sn
4°C /m in
4.58
39.4
12900
1.6-l7cZr
4°C /m in
4.55
39.4
13900
0.82%Sn*
4°C /m in
4.52
39.7
11900
l.64%Sn*
4°C /m in
4.57
39.3
12800
1.64%Zr*
4°C /m in
4.55
39.5
13900
20-60° C
60-97° C
97-119°C
2.2
2.7
4.0
2.1
2.8
4.2
2.3
2.5
3.9
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
slightly higher quality factor. T he specim en w ith the 4°C /m in heating to 1390°C
w ith a 6 h hold schedule m atched this value. Increasing SnC>2 concentration from
0.82 to 1.64% (using the same therm al schedule) generally showed increased final
densities and quality factors, while the dielectric constants slightly decreased.
Stable resonance frequencies w ith tem p eratu re (2-4 pp m /°C ) were obtained. As
the m easurem ent tem perature increased, the tem perature coefficient of resonance
frequency increased, while the quality factor decreased (the la tte r is not shown
in the table). Oxygen flow rate showed no influence on microwave properties of
these specimens.
Two RCS zones were separately optim ized. For the first RCS rate, the most
rapid densification rate was sought which would not facilitate pore breakaway
from moving grain boundaries, sweeping pores into the grains. Such intragranular porosity was more frequently observed w ith increasing first zone RCS rate,
and thus the 0.5 % /m in schedule was selected. Since a rapid RCS rate in the
la tte r stages of sintering would require elevated tem peratures[40]. a lower sec­
ond RCS rate was required which would facilitate sintering below tem peratures
a t which appreciable liquid phase would form (Ba2Tig02 o decomposes into T i 0 2
and B aT i4Og at 1420°C. where th e B aT i4Og melts incongruentlv at 1432°C[20|).
The on-ofF-tvpe shrinkage and specim en tem perature oscillations (Figure 3.9)
becam e more significant with decreasing setpoint shrinkage rate. These could
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
have been a tte n u a te d to some degree by optim ization of proportional, integral,
and derivative control param eters. In converting th e tem p eratu re histories from
RCS to the heating profiles for furnace sintering of larger specimens, such tem ­
p e ra tu re oscillations were not interpreted to be required, and therefore visually
averaged heating curves were deduced (plotted as th e grey lines in th e figure). The
m icrostructures from the RCS dilatom eter. and those from tem p eratu re schedule
em ulation in the furnace were encouragingly sim ilar. W hen the furnace heating
schedules em ulating RCS schedules were com pleted, the slower furnace cooling
provided some additional time for the specimens to slightly further densify. Con­
sequently. porosity decreased and average grain size slightly increased. Further,
the non-oscillating therm al schedule in the furnace would foster uninterrupted
densification. facilitating a greater degree of pore elim ination.
Theoretical density was based on I^ T ig O a o w ith no additives. A ssuming th at
1.64%ZrOo su b stitutions for TiOo caused no change in volume, the theoretical
density of the su b stitu ted com pound would be 4.64 g /cm 3. In this case, the
(99%) setpoint density used at the end of RCS (99%) would have corresponded
to 98.4% of this theoretical density. This would im ply th a t a 1.6 vol% porosity
should have been measured. M easured porosities ranging from 3.2 to 6.9% were
observed. T his variation can be justified based on variability in m easured green
density or specim en slum ping (creep) via grain bo u n d ary liquid phase.
02
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Such
specimen slum ping is especially considered to be a factor in the 0.1% /m in second
zone schedide. This would have formed th e greatest volume of eutectic liquid
phase because of the higher tem peratures required to sustain the rapid second
zone RCS rate. T he presence of porosity in the specimen which was specified to
sinter to 99.9% was a ttrib u te d to volatilization of liquid phase in an otherw ise
well-densified m icrostructure.
The therm al schedule of heating a t 4 °C /m in to 1390°C and soaking for 6 h
was derived by extensive trial and error in previous w ork[44]. This schedule used
no heat treatm ent shut-off point corresponding to reaching 99% of theoretical
density. This perm itted tim e for further densification and grain growth, but not
so much tim e to allow an increase in porosity via volatilization of liquid phase.
Using the schedule dictated by RCS, a significantly shorter heat-treatm ent period
(6.9 h plus furnace cooling, as com pared to 17.4 h for the 4°C /m in schedule) and
lower tem peratures (1370/1260°C versus 1390°C) were required to form th e sam e
m icrostructure w ith the sam e optim ized microwave properties.
RCS analyses
also avoided the tim e associated w ith trial and error heat treatm ent schedules
and m icrostm cture characterization.
The observed increase in density and quality factor, and decrease in dielectric
constant w ith increasing Sn-doping level agrees well w ith our previous w ork[45].
Com pared w ith titan iu m ions, tin ions are heavier bu t sim ilar in size; therefore.
G3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the density increased w ith concentration as a result of negligible enlargem ent of
the unit cell. R eduction in quality factor w ith increasing m easurem ent tem per­
ature can be a ttrib u te d to increasing therm al agitation of th e oscillators. The
quality factor was generally independent of therm al schedule (i.e. m icrostruc­
ture): increasing volume percent porosity decreased the dielectric constant but
did not affect the quality factor[9],[4o]. The lim ited variation in grain size did
not affect the quality factor, as was expected in some literature[29]: inconsistent
bonding at grain boundaries was suggested to cause dam ping, in tu rn increasing
dielectric loss.
3.3
T herm al P rocessing o f B a T i^ g and U n d op ed and
S n 1+-D o p ed B a 2TigO 20
Therm al analyses of the startin g powders are shown in Figure 3.12. STA schedules
were halted a t 780. 920. 1020. 1175. and 1280°C (after 5 m in hold) and the
quenched specimens were analyzed using XRD (Table 3.4).
Therm al effects
in these specimens were not of high intensity, hence baseline noise is clearly
apparent.
E ndotherm onsets at 810 and 970°C appear for b o th com positions
containing BaG '03. T hey correspond to the 7-/?. and 0 -a polym orphic phase
transform ations in BaCOs[46]. The TG trace for B a C 0 3 alone shows th at weight
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A
310
o
305
*-»
300
•
o
x
w
295
o
6
290
<D
-C
o
T3
C
285
W
v
Specimen Weight (mg)
BaCO
500
600
700
800
900
1000
1100
1200
280
1300
Temperature (°C)
Figure1 3.12: D T A and T G traces o f raw batch m a teria ls B aC 0
3
, TiC>2 , and th e tw o com bined
in m olar ratio o f 18.2B aC O .v8l.8T iO o- heated in air a t 1 0 °C /m in .
G5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Tablr 3.4: Phases Formed After Various Heat Treatments
Temp(°C)
Systems
Major Phases
Minor Phases
Traces
BaTiOs
—
Tim e (min)
780, 120
TiC> 2 (o:), BaC 0
BaO-TiC> 2
780. 120
BaO-TiOa-Sn 0
920. 5
BaO-Ti0
2
T i0
2
3
(<*). B aC 03
Sn 0
- BaTiOs
BaTi 4 Og
T i 0 2 (a ), BaCC>3 ,
2
2
—
Ba4Tii303o
BaTiOs
920. 5
Ba 0 -T i 0
2
-Sn 0
2
T i0
2
(or), BaCOs,
BaTi4
0
g, SnOs
Ba4Tii3O30
BaTiC > 3
975. 5
BaO-Ti0
T i0
2
2
BaTLjOg
(q ). BaTiOs,
Ba4Tii303o
BaCOs
975. 5
Ba 0 -T i 0
2
-SnC> 2
T i0
2
BaTi4
(a ). BaTiOs.
0
g
Ba4 T i 1 .1 O.-io
BaCOs
975. 360
BaO-Ti0
975. 360
Ba 0 -T i 0 2 -Sn 0
1010. 5
BaTiOs, TiO s (ct)
2
2
BaO -T i0 2
BaTiO s, T i 0
SnOs.
2
(q)
BaTi4 0 g
—
BaTi40g. BasTigOso
SnOs
BaTi4 0 g
Ba4Tii3O30
BaTi4
Ba4Tii303o-
BaTiOs. TiO s (a ).
BaCOs
1010. 5
Ba 0 -T i 0 2 -Sn 0
2
BaTiOs- T i 0
BaC 0
1076. 5
BaO-Ti0
1076. 5
Ba 0 -T i 0 2 -Sn 0
1280. 5
1280. 5
2
2
B aO -T i0 2
Ba 0 -Ti 0
2
-SnC> 2
2
(a ),
0
g
SnOs
3
B aT i03
TiOa (/3), BaTi40g
Ba4Tii3O30
BaTiOs
Ti 0
2
( 3 )- BaTi4 0 g
Ba4Tii303o
BaTiOs
Ti 0
2
(3). BaTi.|Og
Ba4Tii3O30
B aT i 0
T i0 2 (3). BaT i40g.
BaiTii.iOso
3
BasTigOso
1360. 300
BaO-TiOi
TiOa (3)
—
BasTigOso
—
—
BaTuO g
T i0 2 (3)
—
BagTigOgo
—
—
BaTi 4
0
g
(cross section)
1360. 300
Ba 0 -Ti 0 2 -Sn 0
2
(cross section)
1390. 300
BaO-TiO;
(cross section)
1390. 300
Ba 0 -T i 0
2
-Sn 0
2
(cross section)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
loss has no correlation to the polym orphic transform ation endotherm s: a broad
decom position to BaO. startin g a t ~1000°C is apparent. In contrast, th e onset
of weight loss for the BaC0 3 -T i02 m ixture is recorded at tem p eratu res as low
as 600°C. This weight loss correlates well w ith the onset of observed BaTiC>3
from XRD of a sample heat treated to 780°C. The endotherm onset at 1020°C
corresponds to a surge in weight loss and a sharp increase in B aT i03 based on
relative XRD peak heights. XRD showed th a t no BaO (or B a(O H )2) formed at
any of the analyzed quench tem peratures.
The therm al effects of tin oxide additions to the batch are shown in Fig­
ure 3.13. These additions had little effect on the tem peratures of reactions or
the corresponding phases formed as indicated by XRD of specimens h eat-treated
up to 1280°C. S n 0 2 additions facilitated com plete conversion from B aT i03 to
B a2T ig 0 2o after an extended soak at 1360°C. W ithout S n 0 2 additions. BaTi.t0 9
and residual T iO -2 were detected. The sam e phases were observed for those sam ­
ples h eat-treated to 1390°C.
For the pellets w ithout S n 0 2 additions, th e bottom surface in contact w ith zirconia plates during heat treatm ent developed different phases th an those observed
in the cross section. The bottom surfaces were mainly composed of Ba2T i90 2o
as well as traces of B a T i^ g and T i02 while the top surface (exposed to air) had
no detectable Ba2Tig0 2o.
G7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.01
Ba-Ti-Sn-O
C/5
-
0.01
£
tEj
T3
Ba-Ti-0
•o
500
600
-
0.02
-0.03
700
Temperature (°C)
Figure 3.13: D T A an d D T G (v isu ally sm ooth ed tim e d erivative o f T G signal) traees o f the
B aO -T iO o and B aO -S nO o-T iO o system s. A sterisks represent m axim u m tem peratures prior to
quench for X R D an aly sis.
68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.14 shows d ilatom etry traces of the two com positions. T he onset of
sintering in both systems was a t 1000°C; however, the in itial ra te of sintering was
suppressed in the B a0 -T i0 2 -Sn0 2 system . A second surge in sintering occurred
w ith a maximum rate at 1350°C for th e B a0 -T i02 system . This surge was present
but a tten u ated in the Ba0 -T i0 2 -Sn02 system.
M icrostructures of the B a0 -T i02 and B a0 -T i02 -Sn02 specimens, heat treated
at 1360°C for 5h are shown in Figures 3.15 a and b. respectively. No difference
was visible in the m icrostructures of the Ba0 -T i0 2 -Sn02 specim ens heat treated
at 1390°C (not shown). A subtle difference in the BaO-TiOo specimen after heat
treatm ent at 1390°C was removal of m inute pores (~ 0.5 fim ). T in oxide additions
resulted in m icrostructures w ith increased porosity in the sintered m aterial. Black
grains in Figure 3.15 a were shown via energy dispersive spectroscopy to be T i 0 2.
It is interpreted th a t B aTiO s diffusion barrier shells form ed around T i02 par­
ticles. The shells formed by solid sta te reaction of BaCO s particles in contact
w ith anatase particles via:
B a C O s + T i0 2 == B a T iO s + C O 2
BaTiO s coatings on BaCOs are less likely since the release of the C O 2 product
wnuld tend to fragment the coatings. Since no BaO w-as observed in XRD traces of
powdered samples heat treated to various tem peratures (m arked in Figure 3.12).
69
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
B a-Ti-0
5 -10
o.
X
-2000
a -15
Ba-Ti-Sn-0
-20
-4000
-25
-30
600
700
800
900
-6000
1000 1100 1200 1300 1400
Coefficient of Expansion (ppm/°C)
2000
Temperature (°C)
F igure 3.14:
D ilatornctry traces (expansion and tem perature derivative o f ex p a n sio n ) o f
calcin ed /p re-rea ctcd (975°C . Oh) pressed powder p ellets h eated at 30C /n iin .
70
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.13: M ierostruetures o f polished sectio n s o f sin tered sp ecim en s heat treated at 13G0°C
for 5 h. (a) B aO -T iO o. (h) BaO -T iO o-SnO o. D ark regions w ith w h ite edges are porosity, w hile
hlaek regions are TiOo-
71
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the T G traces in Figures 3.12 and 3.13 are good indicators of the pace of B aT i03
formation. T he surge in weight loss associated w ith the broad endotherm onset
at 1020°C implies particulating of the coated an atase particles, m otivated by
expansion m ism atch between coating and host particle, in tu rn providing fresh
TiOa surface for reaction w ith as yet unreacted BaCOa.
Tin oxide additions did not alter the crystalline phases formed after heat
treatm ents up to 1280°C. The JC PD S d a ta for BaSnOa shows a unique p attern
which was at no tim e detected. This indicates th a t tin m ust have entered into
solid solution w ith titan iu m in the d etected barium tita n a te phases (predomi­
nantly BaTiOa and m inor am ounts of B aT i4Og). T in oxide additions fostered
formation of the as-batched Ba2Tig02 o stoichiom etry: the deform ation of the
unit cell by this su b stitu tio n clearly stabilized the Ba2T ig02 o stru ctu re. Jonker
and Kwestroo[24] sta te d th a t the phase could only be formed w ith su b stitu tio n
of small concentration of SnOa or ZrOa for TiOa. This was later confirmed by
O 'B ryan et al.[26]. Besides, tin and zirconium oxides, Yu et a l.[27] reported th a t
AI2O3 and Bi203 stabilized BaaTigOao- However, all of their m ixtures contained
S n 0 2 and therefore, such a conclusion is not w arranted w ithout fu rth er study
using a system w ithout Sn02 additions.
In contrast to these results. Ba2Tig0 2 o form ation w ithout solid solution ad­
ditions was reported by Wu et al.[25] who calcined their batch at 1100°C for 3
72
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
h and then sintered a t 1400°C for 6 h. This resulted in a m ix tu re of E^T igC ^o
and B a T i^ g . Phase pure B a2Tig02 o was reported[25] to be form ed by reaction
of raw m aterials mixed by a coprecipitation m ethod.
T here is no im plication from STA results or from the p ertin en t binary phase
diagram [47].[48] th a t a liquid phase had formed up to 1300°C. Hence the bariatita n ia com pounds detected after therm al processing up to this tem p eratu re
formed by solid state reaction. D ilatom etry traces of pre-reacted pellets showed a
second surge in sintering ra te startin g a t ~1300°C. X-ray diffraction (Table 3.4)
showed th a t the com pounds present in the pellets of pre-reacted powders were pre­
dom inantly B aTiO .3 and T iC V Based on the Ba0 -T i02 phase diagram[47].[48].
these two com pounds should react to form interm ediate com pounds and a liquid
phase a t tem peratures above 1317°C. T he aforementioned second surge in sin­
tering ra te is thus correlated to the onset of liquid phase form ation. This fluid
phase fills pores as well as facilitates reaction between grains of different phases.
More rapid sintering is indicated in the BaO-TiC^-SnOg system in the tem per­
atu re range 1200-1300°C (Figure 3.14). This implies th a t su b stitu tio n of Sn4+
for T i4+ forms a product phase (Ba2Tig02 o) which does not im pede further solid
state reaction between B aT iO .3 and T i0 2 - As a result, there is a lower fraction
of reactan ts rem aining at th e tem perature where eutectic liquid forms between
B aTiO .3 a n d T i02 (1317°C). Thus, a lower quantity of liquid phase would be
73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
expected to form in the B a0 -T i02 -Sn02 system as com pared to the Ba0 -T i02
system. T he higher fraction of fluid phase in the B a0 -T i0 2 system would explain
the observed lower porosity. It is believed th a t more rap id heating of pre-reacted
powders to tem peratures in excess of 1317°C will discourage solid-state reaction,
allowing more liquid phase to form as an interm ediate product in the form ation
of Ba2T i902o-
3.4
Fabrication o f U ndoped S ingle-P hase l^ T ig C h o via
R apid T herm al P rocessing
The as-milled powder m ixture showed a near-G aussian particle size distribution
where 98% of the particles were less than 6 fim . No ZrC>2 was d etected in the
XRD p a tte rn of the as-milled powder. As shown in Figure 3.16. B aT i4Og was
detected after sintering a t 5°C /m in to 1250°C w ith a 1 h soak. T he sam e phase
was detected from the specim en heated a t 500°C /m in to 1250°C. held for 3 min.
No BaoTigOoo was detected in either of these samples. However, as the soaking
time increased to 1 h (for a heating rate of 500°C /m in). B a2Tig02 o was detected.
Relative peak intensities imply an increased fraction of B a2Tig0 2 o after a 2 h
soak. T he location of the peak of maximum intensity for TiC>2 (rutile) overlaps
with the peaks of Ba2Tig0 2 o and B a T i^ g . O ther rutile diffraction peaks fall
74
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
20
25
30
35
Two Theta (degrees)
F igu re 3.1C: X R D p attern s o f specim ens (a) heated at 5 ° C /n iin to 1250°C and held for 1 h.
(h ) h eated at 5 0 0 °C /m in to 1250CC and held for 3 m in. (e) heated at 5 0 0 ° C /m in and hold at
1250°C for 1 h. and (d) heated at 50 0 °C /m in to 1250°C and held for 2 h. o I3a2T i g 0 2o. o
BaTLiOo- A T i 0 2.
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
outside the 29 scanned range.
The presence of unreacted TiC>2 is clearly indicated in SEM m icrostructures
(e.g. Figures 3.17 and 3.18) as black (low atom ic mass) regions in secondary elec­
tro n images. These T i02 grains were distributed along w ith porosity (secondary
electron images), as well as I^ T ig C ^ o and B aT i4Og (back scattered electron
images).
T he m icrostructure corresponding to th e lower heating rate showed
a greater volume percent of unreacted TiCfy A gglomerations of TiOo regions
were enhanced in size by the lower heating rates: the large agglom erate size af­
ter heating a t 5°C /m in was ~ 8 0 fim . as com pared to ~ 1 0 //.m after heating at
500°C /m in. These micrographs typify the trend of decreasing T i02 agglom erate
size w ith increasing heating rate.
For the specimens soaked at 1250°C for 2 h. increased heating rate from 5
to 500°C /m in fostered an increased fraction of B a2Tig02o (Figure 3.19). from
12 to 64 vol%. T he scatter in th e d a ta is clearly g reater with analysis using
relative XRD peak heights as com pared to the use of image analysis from SEM
m icrographs.
Figure 3.20 shows th a t after rapid therm al processing, reaction of residual
B aT i40 9 w ith T i 0 2 formed 98 vol% Ba2T ig 0 2o after 8 h of soaking at 1390°C.
However, specimens slowly heated a t 5°C /m in to 1250°C required 24 h of soaking
7G
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F igu re 3.17: Polished se ctio n o f a sp ecim en heated at 5 0 0 °C /m in to 1250°C and soaked for 2 h:
( a ) Secondary’ electron im age, w here sm all TiOo grains appear as black regions d istrib uted in a
(grey) in distingu ish able m ixtu re o f Ba^TigOoo and BaT^O?). T h e w h ite regions are pores w here
th e w h ite rings are from charging effects, (h) Back scattered im age o f th e sa m e m icrostructure
sh ow in g needle-like BanTigOoo (dark gray) dispersed in the BaTi^Og (ligh t grey) m atrix.
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.18: P olished section o f a sp ecim en heated at 5 ° C /in in to 1250°C and soaked for 2 h:
(a) Secondary electron im age, (h) B ack scattered electron im age. C orrelation b etw een phases
and phase contrast is th e sam e as th at in Figure 3.17.
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.8
c
o
0.6
ts
o
o (N
a, o
o Os
H 0.4
<D
CQ
-2 o
<D
C*
0.2
0
100
200
300
400
500
Heating Rate (°C/min)
Figure 3.19: P ro p o rtio n s o f BaoTiqOgo and BaTi.iC >9 m easured from X R D relative p eak in ten ­
sities (circles) and S E M im age an alyses (triangles).
79
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.8
0
5
10
15
20
25
Soaking Time (h)
Figure 3.20: R elative a m ou n ts o f BanTigOgo for sam ples h ea ted a t 1250°C for 2 h. followed Invarious soak ing p eriods a t 1390°C . Triangle, square, and filled trian gle are sp ecim en s heated
at 500. 50, and 5 °C /m in . resp ectively, via im age analysis. Circle, d ia m o n d , an d filled circle are
specim ens h eated at 500, 50, and 5 °C /m in , respectively, v ia rela tiv e X R D p eak in ten sities.
80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a t 1390°C to achieve 87 vol% of BagTigOgoU nder rapid heating, the average grain size of T i02 (after soaking a t 1250°C
for 2 h) was the. same as th e sta rtin g particle size. However, th e agglom erates
under slow (e.g. 5°C /m in) heatin g were roughly an order of m agnitude larger.
Such agglom eration was m otivated by reduction of interfacial area by shrinking
of sm aller (larger surface to volume ratio) T i02 grains, while larger ones grew,
bo th via lattice diffusion. C orresponding to the lower heating rates, significantly
more tim e was allotted for such diffusional processes. In previous work[28|. soak­
ing T i0 2-B aT i0.3 com pacts a t 975°C for extended tim es (~ 6 h) readily formed
B aT i4Og. but resulted in form ation of no Ba2Ti90 2 o- O th er work[48] m ade a simi­
lar observation after soaking at 1125°C for 6 h. The B a2Tig02o phase only appears
to form at tem peratures approaching its incongruent m elting at 1420°C. Thus,
under slow heating rates, diffusion of T i02 through the lattice can co n trib u te to
agglom eration of this phase, w ithout facilitating form ation of B a2T i902 oA fter slow heating, the larger T i02 agglomerations are (com paratively) more
stable, as w*ell as less distrib u ted in the m icrostructure (resulting in g reater av­
erage diffusion distances between reactants). Hence form ation of Ba2T i90 2o by
2 B a T i40 g + TiOg — y B a2T ig02o
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(3.1)
occurs more sluggishly. T he needle-like Ba2T ig 0 2o phase which forms after slow
heating (w ith a 2 h soak at 1250°C) is less frequent, b u t of significantly larger size
(Figures 3.17 and 3.18). This results from th e extended tim e for reaction local
to a T i 0 2 agglom erate, and the plentiful supply of T i 0 2 reactant, creating large
B a2T ig 0 2o grains. However, the less frequent presence of T i 0 2 grains resulted in
less frequent form ation of B a2T ig 0 2g grains.
82
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 4
Conclusions and
R ecom m endations
1. M icrow ave D ielectric P roperties o f BaT ^O g and Zr4+- and S n l+D o p ed B a 2TigO 20 R esonators
Six hours of sintering a t 1390°C was adequate to achieve microwave ceramics
of high density. Longer duration caused density reduction because of slow
volatilization of grain boundary liquid phase. Increased doping concentra­
tions of tin oxide reduced the dielectric loss, stabilized the resonance fre­
quency. and only slightly affected the perm ittivity. Sim ilar microwave prop­
erty im provem ents were observed in the Zr-doped specimens up to 1.64%.
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T he tem perature coefficient decreased w ith increasing Zr content, b u t was
largely unaffected by Sn concentration.
2. D ielectric Properties o f M icrostru ctu re-C on trolled B a 2 TigC>2o R es­
on ators
Low porosity Ba2Tig02o dielectric resonators were successfully fabricated
using two-zone shrinkage rate controlled sintering.
During sintering, fast
first-zone shrinkage rates led to a higher frequency of intragranular pores,
while fast later shrinkage rates resulted in higher porosity because of falsely
indicated densification via specimen slum ping. Heat treatm ent of large spec­
imens using tem perature profiles from RCS schedules resulted in sim ilar mi­
crostructures as the specimens h eat tre a ted in the RCS dilatom eter. T he
microwave dielectric properties of rapidly sintered (RCS-based tem p eratu re
schedules) specimens were com parable to th e fired com pacts from optim ized
conventional sintering. Studies on the effects of o ther dopants will be inter­
esting subjects.
3. T h erm a l Processing o f B a T i 4Og and U n d op ed and S n4+-D o p e d
Ba2Ti9O20
T herm al processing and phase analyses of quenched BaCO.^-TiOo w ith and
w ithout Sn-substitution at various tem p eratu res were studied. Interm ediate
84
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
chemical reactions am ongst the startin g m aterials to form Ba2Tig0 2 o and
B aTi4Og were identified, as a function of tem p eratu re. D ilatom etry studies
implied th a t S n 0 2 additions facilitated a g reater fraction of reaction to occur
in the solid state.
4. F a b r ic a tio n o f U n d o p e d M o n o p h a s e B a 2T ig O 20 v ia R a p id T h e r m a l
P r o c e s s in g
Rapid therm al processing of BaTiO .3 and TiC>2 pressed powders at 500°C /m in
to 1250°C for 2 h in an infrared furnace resulted in a m ixture of B a2Tig02 oBaTi4C>9. and T i 0 2. F urther heat treatm en t a t 1390°C led to 98 vol% phasepure Ba2Tig0 2o from an initial m ixture devoid of any dopant. Heat tre a t­
ment at 5 °C /m in to 1250°C facilitated agglom eration of T i 0 2. This in tu rn
increased th e diffusion distance required for reaction of B aT i40g and T i 0 2
to form B a2Tig0 2 o- In this case, significantly longer soak times at 1390°C
were required to form nearly phase-pure B a2T ig 0 2o- For further stu d y on
fabricating dielectric resonators of this m aterial, a large q u an tity of undoped
single phase B a2T i90 2 o powder is required. T h e microwave dielectric prop­
erties of undoped monophase BagTigOgo also m erit fu rth er investigation.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Bibliography
[1] L.L. Hench and J.K . W est. Principles o f Electronic Ceramics, Jo h n W iley
and Sons. New York 1990.
[2] I. Bunget and M. Popescu, Physics o f Solid Dielectrics, Elsevier Science.
New York 1984.
[3] G. Burns. Solid State Physics. IBM . Y orktown Heights 1985.
[4] C.C. You. C.L. Huang. C.C. Wei. and J.W . Huang, "Improved High-Q
Dielectric Resonator Sintered a t Low Firing Tem perature.’’ Jap. J. Appl.
Phys.. 34 [4A] Part 1. 1911-15 (1995).
[5] J.N . Plendle. Far Infrared Properties o f Solid. Plenum Press. New York
1970.
[6] B.D. Silverman. "Microwave A bsorption in Cubic Strontium T ita n a te .”
Phys. Rev.. 125 1921-30 (1962).
[7] B.W. Hakki and P.D. Coleman, "A D ielectric Resonator M ethod of M ea­
suring Inductive Capacities in the M illim eter Range.” IR E Trans, on M i­
crowave Theory and Tech., M T T -8 [7] 402-10 (1960).
[8] Y. Kobayashi and M. K atoh. "Microwave M easurement of Dielectric P ro p ­
erties of Low-Loss M aterials by th e Dielectric Rod Resonator M eth o d ,”
IE E E Trans, on Microwave. Theory Tech., M T T - 3 3 [7] 586-92 (1985).
[9] H. Tam ura. "Microwave Loss Q uality of (Zro.8Sno.2)Ti0 4.” Am . Ceram..
Soc. Bull.. 73 [10] 92-95 (1994).
86
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[10] R. C hristoffersen. R K . Davies. X. Wei, and T. Negas. “Effects of Sn Sub­
stitu tio n on C ation O rdering in (Zri_xSnT)T i0 4 Microwave Dielectric Ce­
ram ics.” J. Am.. Ceram.. Soc., 77 [6] 1441-50 (1994).
[11] G. W olfram and H.E. Gobel, “Existence Range, S tru ctu ral and Dielectric
P roperties of Zrr T ivS n ,0 4 Ceramics (x + y + z = 2 ),” Mater. Res. Bull.. 16
[11] 1455-63 (1981).'
[12] K. W akino. K. Minai, and H. Tam ura. “Microwave C haracteristics of
(Z r.S n )T i0 4 and B a0 -P b0 -Nd203-T i02 D ielectric R esonators.” J. Am .
Ceram.. Soc... 6 7 [4] 278-81 (1984).
[13] S. H irano. T. Hayashi. and A. H attori. “C hem ical Processing and Mi­
crowave C haracteristics of (Z rS n )T i0 4 Microwave D ielectrics.” J. .4m. Ce­
ram.. Soc.., 74 [6] 1320-24 (1991).
[14] A.E. McHale and R.S. Roth, “Investigation of th e Phase Transition in
Z rT i0 4 and Z rT i0 4-SnOo Solid Solutions.” J. Am.. Ceram.. Soc... 66 [2]
C-18-C-20 (1983).
[15] T. Negas. G. Yeager. S. Bell. N. Coats, and I. M inis. “B aT i4O g/B a2TigO20Based Ceram ics Resurrected for M odern Microwave A pplications.” .4m.
Ceram.. Soc. Bull.. 72 [1] 80-89 (1993).
[16] H. T am ura. T. Konoike, Y. Sakabe, and K. W akino. “Improved High-Q
Dielectric R esonator w ith Complex Perovskite S tru c tu re .” J. A m . Ceram..
Son.. 6 7 [4] C-59-C-61 (1984).
[17] S. Kawashim a. M. Hishada, I. Ueda, and H. Ouchi. “Microwave Loss Qual­
ity of B aZ n1/ 3Ta2/303 Ceramics.” J. Am.. Ceram.. Soc... 66 [6] 421-23 (1983).
[18] S.B. Desu and H.M. O'Bryan. “B aZ ni/3Ta2/303 C eram ics w ith Low Dielec­
tric Loss at Microwave Frequencies.” J. A m . Ceram.. Soc... 68 [10] 546-51
(1985).
[19] H. M atsum oto. H. Tamura, and K. Wakino. “B a(M g,T a)0 3 -B aSn03 HighQ Dielectric R esonator.” J. Am . Ceram.. Soc., 6 7 [4] C-59-61 (1984).
87
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[20] A .J. Moulson and J.M . H erbert. Electroceramics: Materials. Properties,
and Applications, C hapm an and Hall, New York 1990.
[21] K. Lukaszewicz. "Crystal S tructure of B arium T e tra tita ta n te , BaO-TiO-2,"
Rocz. Chem... 31 1111-22 (1957).
[22] P.K. Davies and R.S. Roth, “Defect Intergrow ths in B arium Polytitanates
1. BaoTigO-io/’ J- Solid State Chem.. 71 490-502 (1987).
[23] G. Grzinic. L.A. Bursill. and D .J. Sm ith, “T h e H ollandite-R elated S tru ctu re
of BaoTigOaoC J- Solid State Chem... 4 7 115 (1983).
[24] G.H. Jonker and W. Kwestroo. “T he T ern ary System s BaO-TiC^-SnOo and
BaO-TiOo-Zr0 2 ." J. -4m. Ceram.. Soc... 4 1 [10] 390-94 (1958).
[25] J.-M . Wu and H.-W. Wang. “Factors Affecting the
BaoTigOao-4m. Ceram. Soc... 71 [10] 869-75 (1988).
Formation of
[26] H.M. O ’Bryan. J. Thomson, Jr., and J .K . Plourde. “A New BaO -Ti02
C om pound w ith Tem perature-Stable High P erm ittiv ity and Low Microwave
Loss.’’ J. .4m. Ceram.. Soc.. 57 [10] 450-53 (1974).
[27] J. Yu. H. Zhao. J. W ang and F. Xia, “Effects of AI2O3 and Bi203 on the
Form ation Mechanism of Sn-Doped Ba^TigC^o-" J ■ A m . Ceram.. Soc... 77
[4] 1052-56 (1994).
[28] W.-Y. Lin. R.A. G erhardt, and R.F. Speyer. "Therm al Processing and
Properties of BaTi4Og and Ba2Tig02o.,, su b m itte d for publication in Jo u r­
nal of M aterials Science. 1996.
[29] K.H. Yoon. J.B. Kim, W.S. Kim, and E.S. Kim, “Effects of BaSn03 on
T he Microwave Dielectric Properties of B a2Tig0 2 o-” J- Mater. Res.. 11 [8]
1996-01 (1996).
[30] W.-Y. Lin. R.A. G erhardt. and R.F. Speyer, “Effects of D opants and S ta rt­
ing M aterials on The formation and dielectric P roperties of Ba2Tig02 o-"
presented a t the 98th Annual Meeting of A m erican Ceram ic Society, Indi­
anapolis. Indiana 1996.
88
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[31] W.-Y. Lin and R.F. Speyer, "Fabrication and Dielectric P roperties of P haseP ure BaoTigC^o Microwave R esonators.’’ to be published in th e M RS Fall
Proceeding 1996.
[32] W.-Y. Lin, R.A. G erhardt, a n d R .F. Speyer, “Processing and C h arac te r­
ization of Barium T ita n a te D ielectric Resonators.” presented at th e 97th
Annual M eeting of A m erican C eram ic Society, C incinnati, Ohio 1995.
[33] H.M. O ’Bryan. J.K . Plourde, an d J. Thomson, Jr.. “Dielectric for Mi­
crowave Applications,” U.S. P a te n t: 4563661 (1986).
[34] J. Thomson. Jr.. “M ethods of P roducing Microwave Device,” U.S. P a te n t:
5133129 (1992).
[35] T. Jaakola. J. M ottonen, A. U usim aki. R. Rautioaho. and S. Leppavuori.
“Preparation of Nd-Doped B a2Tig02o Ceramics for Use in Microwave A p­
plications.” Ceram.. Int.. 13 151-57 (1987).
[36] S. Nomura. K. Tomaya. and K. K aneta. “Effects of Mn Doping on th e
Dielectric Properties of Ba2Ti<)0 2 o Ceram ics at Microwave Frequency.” Jap.
J. Appl. Phys.. 22 [7] 1125-28 (1983).
[37] H.M. O ’Bryan. J. Thom son, J r.. and J.K . Plourde, “Effects of C hem ical
Treatm ent on Loss Q uality of Microwave Dielectric Ceram ics.” Ber. Dt.
Keram.. Ges.. 55 [7] 348-51 (1978).
[38] W. Kwestroo and H.A.M. P aping, “T he Systems BaO-SrO-TiOo. B aO C aO -T i0 2. and Sr0 -C a0 -T i0 2 .” J ■Am.. Ceram.. Soc.. 42 [6] 292-99 (1959).
[39] J.S. Reed. Introduction to The Pri.nci.ples o f Ceramic Processing. Jo h n W i­
ley & Sons. New York 1988.
[40] G. Agarwal and R.F. Speyer, “Effect of R ate Controlled Sintering on Mi­
crostructure and Electrical P ro p erties of ZnO Doped w ith B ism uth and
Antimony Oxides.” su bm itted for publication in Journal of M aterials Re­
search. 1996.
89
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[41] VV.S. Hackenberger and R .F. Speyer, “A Fast-Firing Shrinkage R ate Con­
trolled D ilatom eter Using A n Infrared Image Furnace.” Rev. Sci. lustrum...
65 [3] 701-06 (1994).
[42] JC PD S card num ber 40-405, Powder Diffraction File. In tern atio n al C enter
for Diffraction D ata, Pennsylvania. 1991.
[43] W.-Y. Lin and R .F. Speyer, '‘Fabrication of U ndoped M onophase
B a2Tig02o via R apid T herm al Processing,” subm itted for publication in
Journal of M aterials Research. 1996.
[44] W.S. Hackenberger, private com m unication. The Pennsylvania S ta te Uni­
versity. University Park. PA. 1996.
[45] W.-Y. Lin and R .F. Speyer, “Dielectric Properties of Ba2Tig02 o Microwave
Resonators Doped w ith Zirconium and T in Oxides,” su b m itted for publi­
cation in Journal of A m erican Ceram ic Society. 1996.
[46] R.C. Weast. C'RC Handbook o f C hem istry and Physics. CRC Press. Inc..
Ohio 1977.
[47] D.E. Rase and R. Roy,“P hase Equilibria in the System B a0 -T i0 2 . ' J • Am..
Ceram. Sor... 38 [3] 103-13 (1955).
[48] H.M. O 'Bryan and J. Thom son, Jr.. “Phase Equilibria in the TiOo-Rich
Region of the System B aO -T i0 2 ,” J ■ Am . Ceram.. Soc... 57 [12] 522-26
(1974).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
V ita
Wen-yi Lin. a son of Tung-Lian Lin and Sho-chu Hwang, was born in A ugust in
1965 in C hang-H ua City. Taiwan. He atten d ed T atu n g In stitu te of Technolog}'.
Taipei. Taiwan, in 1983 and obtained Bachelor of Science degree in M aterials
Engineering. After two years of compulsory m ilitary service in Taiwanese A rm y
where he served as a platoon leader, in the rank of ju n io r lieutenant, in an
ordnance corp in Hua-lian. Taiwan, he came to the U nited S tates of A m erica and
studied at the New York S ta te College of Ceramics a t Alfred University. Alfred.
New York. He acquired M aster of Science degree in Ceram ics Engineering in
1993. He then came to G eorgia In stitu te of Technolog}'. A tlanta, Georgia, to
pursue his Ph.D. degree. He passed the Ph.D . qualifying exam ination in 1994
with the highest score in the school’s history, according to a faculty m em ber.
Dr. D.N. Hill. In 1996 while th e Olympics was taking place in A tlanta, he spent
the sum m er at The M aterials Research L aboratory at T he Pennsylvania S tate
91
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
University, University P ark, Pennsylvania. To date, he has had one invention
disclosure/provisional p a ten t application, sixteen referred publications and more
th an fifteen conference presentations. He earned his D octor of Philosophy in the
School of M aterials Science and Engineering in 1997.
92
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Документ
Категория
Без категории
Просмотров
0
Размер файла
3 369 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа