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Microwave induced plasmas for the spectrochemical determination of some non-metals

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O rder N u m b er 8914114
Preparation and microwave response o f Y-Ba-C u-O
superconducting materials
Jeong, Dae-Yeong, D.Sc.
The University of Texas at Arlington, 1988
Copyright ©1988 by Jeong, Dae-Yeong. All rights reserved.
UMI
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PREPARATION AND MICROWAVE RESPONSE OF
Y-Ba-Cu-0 SUPERCONDUCTING MATERIALS
The members of the Committee approve the Doctoral
Dissertation of Dae-Yeong Jeong
Truman D . Black
Supervising Professor
Roy S . Rubins
John L. Fry
Suresh C . Sharraa
John R. Reynolds
Dean of the Graduate School
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Copyright ® by Dae-Yeong Jeong 1988
All Rights Reserved
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Dedicated to my family for their support and perseverance.
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PREPARATION AND MICROWAVE RESPONSE OF
Y-Ba-Cu-0 SUPERCONDUCTING MATERIALS
by
DAE-YEONG JEONG
Presented to the Faculty of the Graduate School of
The University of Texas at Arlington in Partial Fulfillment
of the Requirements
of the Degree of
DOCTOR OF SCIENCE
THE UNIVERSITY OF TEXAS AT ARLINGTON
December 1988
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ACKNOWLEDGMENTS
The author would like to express his gratitude, assistance and
support he receivedfrom Dr. Truman D. Black during his entire work for
his Doctor of Science degree at The University of Texas at Arlington.
The
author also expresses a special thanks to Dr. Roy S. Rubins who helped him
to understand the underlying theory of the response of high-Tc super­
conductors to microwaves, and Dr. Glenn Fletcher who helped him to learn
the theory of superconductivity.
Another thanks goes for Dr. S. Krichene
and Dr. John R. Reynolds who did electrical measurements for the whole of
his work, Mr. David
Taylor who helped him all thetime, Mr. Michael
Haji-Seikh who took
SEM pictures, and Mr. WallaceLutesand Mr. Don Miller
who made some apparatus for his work. Another special thanks goes for Dr.
Suresh C. Sharma, Dr. John L. Fry, Dr. Shao J. Wang, Dr. Dilip K. De, Dr.
S. V. Naidu, Dr. John M. Owens, Dr. B. C. Deaton, Dr. Wendell Chen and Dr.
Ron Carter, for their assistance and encouragement. The author also wishes
to acknowledge the contribution of all the professors and staff of the
Physics Department to my education.
Final gratitudes goes to Mr. Rob
Leslie, Mrs. Kari Baum and Mr. Kie-Moon Song for their help to compile the
data and to write this dissertation.
November 18, 1988
v
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ABSTRACT
PREPARATION AND MICROWAVE RESPONSE OF
Y-Ba-Cu-0 SUPERCONDUCTING MATERIALS
Publication No. ______
Dae-Yeong Jeong, D.Sc.
The University of Texas at Arlington, 1988
Supervising Professor:
Truman D. Black
The preparation parameters affecting the physical properties of
Y-Ba-Cu-0 superconducting ceramics were studied by using the conventional
powder technique.
Also their unusual low-field microwave absorptions, as
well as high-field EPR signals, were studied in different magnetic
histories and temperatures.
The important parameters for better
superconducting characteristics are known to be heating temperatures,
atmosphere, pelleting pressure, reactivity with crucible material, cooling
rate and additional annealing.
The low-field signals are interpreted in a
framework of superconducting analog of spin glass in conjunction with the
critical state theory.
The high-field EPR signals seem to appear mainly
due to the presence of nonsuperconducting phases.
vi
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TABLE OF CONTENTS
ACKNOWLEDGMENTS .................................................... v
ABSTRACT........................................................... vi
LIST OF ILLUSTRATIONS............................................... x
LIST OF TABLES....................................................xiii
LIST OF SYMBOLS...................................................xiv
INTRODUCTION........................................................ 1
I.
SOME PHYSICAL PROPERTIES OF YBa2Cu307_5 ....................... 5
1.1
Crystal Structure..................................... 5
1.2
Energy G a p ....................................... ’ . .9
1.3
Specific Heat........................................ 10
1.4
Isotope Effect...................................... 12
1.5
Microstructure...................................... 13
1.6
Effects of Oxygen-Deficiency ........................
1.7
Stability in Environment............................. 17
1.8
Josephson Effects.................................... 18
1.9
Magnetic Properties...................................21
1.9.1
Magnetic Behavior in Conventional Hard
Superconductors ..............................
1.9.2
16
22
Magnetic Behavior in High-Tc Superconductors Superconducting Glass ........................
25
1.9.2.1 Superconducting Cluster Theory.......... 26
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1.9.2.2 Difference in Response Between
Zero-Field-Cooled and Field-Cooled
Samples, and Existence of
Quasi de Almeida-Thouless Line...........29
1. 9.2.3 Decay of Remnant Magnetization...........30
1.9.2.4 Intergranular and
Intragranular Couplings ............... 33
1.9.2.5 Anisotropy in Critical Fields .........
37
1.10 Magnetic Structure................................... 38
II.
IMPORTANT PARAMETERS ON THE PREPARATION OF BULK Y-Ba-Cu-0
SUPERCONDUCTORS.......................................... 41
III.
2.1
Nominal Composition ................................
42
2.
2
2.3
Heating Temperature ................................
2.4
Cooling Rate......................................... 46
2.5
Reaction with Crucible Materials...................... 47
2.6
Additional Annealing................................. 48
2.7
Experiments......................................... 49
2.8
Results and Discussion................................52
Preparation Atmosphere......................... 43
45
MICROWAVE SPECTROSCOPY IN Y-Ba-Cu-0 BASED SUPERCONDUCTING
MATERIALS................................................ 75
3.1
Experimental Set-Up for the Microwave Response
of the Y-Ba-Cu-0 Superconductors...................... 76
viii
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3.2
3.3
IV.
Results............................................ 79
3.2.1
Low-FieldSignals.............................. 81
3.2.2
High-Field EPRSignals........................121
Discussions........................................ 123
CONCLUSIONS............................................. 136
REFERENCES........................................................ 140
ix
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LIST OF ILLUSTRATIONS
1
Crystal Structure of YBa2Cu30y .................................. 8
2
Micrographs for Multi-Phase Sample No. 19 and 20 ..............54,55
3
Micrographs for Multi-Phase Sample No. 21........................ 56
4
Difference in Resistive Superconducting Transition between
Single-Phase and Multi-Phase YBa2Cu307_ g ....................... 60
5
Effect of Annealing on Critical Current in Multi-Phase
YBa2Cu307_£................................................... 61
6
Effect of Excess of Oxygen on Resistive Superconducting
Transition................................................... 63
7
Semiconductor Behavior in Resistance vs. Temperature Due to
Excess of Oxygen.............................................. 64
8
Variation of Resistive Superconducting Transition Characteristics
with Respect to Annealing T i m e ................................. 67
9
Variation of Resistivity at Normal State and Onset of
Superconducting Transition with respect to Annealing Time.........68
10
Variation of Critical Current Density as a Function of
Temperature with Respect to Annealing T i m e ......................69
11
Magnetization Curve for Zero-Field Cooled Sample No. 22........... 71
12
Effect of Trapped Flux on Magnetization of Multi-Phase
YBa2Cu307_£....................................................72
13
Variation of Resistance of YBa2Cu3F30x with Temperature........... 74
14
Schematic Diagram of Ku-Band Spectrometer........................ 77
x
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15
Whole of the Spectra Near Superconducting Transition
Temperature................................................... 80
16
Low-Field spectra for Sample No. 22 Zero-Field Cooled to 77 K..82,83
17
Variation of Peak-to-Peak Signal Height and Width with
Modulation Amplitude ......................................... 85
18
Variation of Peak-to-Peak Signal Height and DC Component of
Absorption with Microwave Power................................. 86
19
Time Dependence of Low-Field Spectra............................ 88
20
Different Sign and Behavior in Spectra for Sample No. 22
Zero-Field Cooled to 77 K ................................. 89,90
21
Low-Field Spectra for Sample No. 52 Zero-Field Cooled to 77 K.
22
Different Sign in Spectra Observed in Sample No. 52 Zero-Cooled
. . 92
to 77 K ....................................................... 93
23
Effect of Sweep Range on Spectra............................. 95
24
Anomalous Increase in Signal Intensity by Repetition of Sweeps . . 96
25, 26 and 27 Effect of Trapped Flux Due to Increased Upper Limit
of Sweep Field.............................. 98,99,100
28
Effect of Trapped Flux Due to Suddenly Applied Field on Spectra. .101
29
Anomalous Sign Change in Spectra Obtained with Suddenly
Applied Field................................................. 102
30
Effect of Trapped Flux on Spectra with Different Sign............ 105
31
Variation of Trapped Flux Due to Suddenly Applied Field with
Temperature...................................................106
32
Effect of Remnant Magnetization Due to Field-Cooling onSpectra.
xi
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.107
33
Effect of Decay of Remnant Magnetization Due to Field-Cooling
Spectra.......................................................109
34
Sudden Sign Change Observed in Sample No. 22 Field-Cooled to
77 K .........................................................Ill
35
Modulated Spectra Due to Decay of Remnant Magnetization Observed
in Sample No. 52 Field-Cooled to 77 K ...........................112
36
Change in Periodicity and Shape in Local Peak Due to Large
Remnant Magnetization..........................................114
37
Enlarged Feature of Local Peak Induced by Decay of Remnant
Magnetization................................................. 116
38
Low-Field Spectra for Sample No. 52 Zero-Field Cooled
to 4.2 K ............................................. 118,119,120
39
Effect of Trapped Flux at Low Temperature on Low-Field Spectra . .122
xii
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LIST OF TABLES
6
1
Physical Constant for YBa2Cu307_g ..............................
2a
Preparation History of Samples.................................. 53
2b
Variation of Resistive Superconducting Transition
Characteristics with Preparation History........................ 53
3
X-Ray Diffraction Data For Single-Phase Sample No. 4 6 ............. 58
4
Variation of Superconducting Property and Transition
Characteristics with Annealing T i m e ............................ 65
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L IST OF SYMBOLS
SYMBOLS RELATED TO ELECTROMAGNETISM
A
- magnetic vector potential
Ap.p
- peak-to-peak height of microwave absorption signal
B
-magnetic induction
B0
- constant in magnetic induction
Bt
-trapped magnetic induction
c
- speed of light
D(Ep) - density of state at Fermi level
e
-charge of electron
Ec
-minimum voltage per meter
EF
-energy at Fermi level
f
-fraction
Gn
- electrical conductance at normal state
H
-magnetic field intensity
H
-threshold field for a critical state
Hac
- ac magnetic field amplitude
Hc
- thermodynamical critical magnetic field intensity
Hci
- lower critical field
Hci
-critical field for onset of superconducting glass
Hq2
• upper critical field
Hm
- amplitude of modulation magnetic field
Hmax
- maximum applied field
xiv
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**mx
- magnetic field for microwave absorption peak
Ho
- constant
fi
- Planck’s cons tant
I
- electrical current
•*dc
- dc component of microwave absorption
*o
- critical current through a junction
Jc
- critical current density
•^co
- critical current density at zero temperature
^max
- maximum current density through a junction
Jn
- Bessel function of order n
JM
- microwave supercurrent density
K
- elastic force constant
M
- magnetization
Mr
- remnant magnetization
m£
- fluxon mass per unit length
n
- free fluxon density
ne
- electron concentration
R
- electrical resistance
%
- Hall coefficient
rP
- ration of A^ to A
S
- phase of area
u
- electrostatic potential energy
V
- dc electric potential
vs
- ac electric potential
XV
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- energy loss per unit volume per cycle due to magnetization
hysteresis
a
- constant
- coherence length
So
- coherence length at zero temperature
K
- Ginzburg-Landau parameter
X
- macroscopic screening length
XL
- London penetration depth
- microwave penetration depth
n
- viscous damping coefficient
$
- magnetic flux
- quantum fluxon
p
- electrical resistivity
p
- magnetic moment
Xac
- ac magnetic susceptibility
*dc
- dc magnetic susceptibility
n
- oscillation angular frequency
u
- microwave angular frequency
WJ
- Josephson oscillation frequency
SYMBOLS RELATED TO THERMODYNAMICS
a3
- coefficient of nuclear quadruple contribution to specific '
C
- specific heat
F
- Helmholtz free energy
xvi
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H
-classical energy Hamiltonian
kB
- Boltzmann constant
T
-temperature
Tc
- superconducting transition temperature
ATC
-transition temperature width
Tcf
-temperature at which resistance becomes zero
Tco
-temperature for onset of superconducting transition
T0
-orthogonal-to-tetragonal transition temperature
Tg
-glass transition temperature
UQ
-activation energy
Z
-classical canonical ensemble
a
-constant or thermal expansion coefficient
ft
-coefficient due to phonon contribution to specific heat
A(T)
- energy gap parameter at temperature T
0j)
-Debye temperature
7
-coefficient of electronic contribution to specific heat
SYMBOLS RELATED TO MATERIALS
d
- distance
D
- thickness
Kc
- fracture toughness
£
- length of path
m
- mass
r
radium
xvii
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v
- volume
6
- oxygen deficiency
xvm
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INTRODUCTION
After the discovery of superconductivity in Hg by Onnes in 1911 [1],
Much research has been done in the intermetallic compounds to increase the
transition temperature (Tc). However, the highest Tc remained 23.3 K in
Nb3Ge [2] until the discovery of La-Ba-Cu-0 based superconducting material
by Bednorz and Muller in 1986 [3], in which the transition onset temper­
ature (Tco) was 35 K.
Originally the superconductivity in the oxide
system was discovered in the Li-Ti-0 system with the Tco = 13.7 K in 1973
by Johnston et al. [4].
Then Sleight et al. [5] discovered a perovskite,
mixed-valent compound BaPb]^.xBix03 with the highest Tc at 13 K.
After the
discovery, two features, mixed-valence and perovskite structure, were
focused to enhance the Tc . After the work of Michel [6] in the mixed
perovskite BaLa^Ck^O^ 4 in 1985, the efforts to enhance the Tc were
shifted to copper-containing compounds, such as metallic LaCu03, because
of the non-degeneracy of the Cu^+ ground state.
With the idea that the
doping of Ba lowers the Fermi energy level and increases the carrier
density at the Fermi level, Bednorz et al. [7] discovered 35 K as Tco by
doping Ba to L^CuO^.
From the Bardeen-Cooper-Shrieffer theory [8], the
enhanced electron-phonon interaction and the increased density of state
result in higher transition temperature.
They also confirmed Meissner
effect [9], which is one of the characteristic phenomena of supercon­
ductivity, and inferred the existence of a superconducting glass state
[10].
After the discovery by Muller and Bednorz, Wu et al. [11] discovered
1
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Y-Ba-Cu-0 based superconducting compound with a Tc higher than 90 K, which
is higher than the boiling temperature of nitrogen (77 K). This break
through to liquid nitrogen temperature opened the gate for a very wide
application because the application of low-Tc superconductor have been
restricted by high cost of liquid He used for keeping the materials at the
superconducting state.
The phase responsible for the high-Tc superconduc­
tivity was YBa2Cu307_£ [12,13,14,15] with the oxygen-deficient orthorhombic perovskite structure [16,17,18,19,20]. However, this material is
unstable because it has oxygen vacancies at (1/2 , 0 , 0) and (0 , 1/2 , 0)
sites.
The Cu-0 chain was believed to play a critical role in the super­
conductivity of YBa2Cu307_j [16,21,22,23], unlikely to the case of
^al.75®a0.25Cu04 which only has Cu-0 planes, for a while until the recent
discovery of a Bi-Sr-Ca-Cu-0 based compound [24,25] which was identified
to be a Bi2Sr2CaCu20g phase [26], and of a Tl-Ba-Ca-Cu-0 based compound
[27] which was identified to be a Tl2Ba2Ca2Cu30^Q phase [28].
It may be
believed that the Cu-0 plane is responsible for superconductivity in the
high-Tc superconducting oxides [29], because Bi2Sr2CaCu20g and Tl2Ba2Ca2CugO^Q have only Cu-0 planes. Therefore, from the historic viewpoint of
the recent high-Tc superconductor, it was even said [29] that one copperoxygen plane produced a Tc of less than 80 K, two 105 K, and three 125 K,
and suggested that the four-plane compound will give 150 to 160 K, and the
10-plane 200 K.
Now many people believe that the room-temperature-Tc
superconductor will be accomplished soon.
The purpose of studying the high-Tc superconductor mainly lies on two
viewpoints-physics and application.
From the theoretical point of view,
although the BCS theory [8] explains the superconductivity in pure metals,
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it fails for the recently developed high-Tc superconductor.
Some of
experimental evidence for its failure are the absence of [30,31,32] or a
small isotope effect [33] and the linear dependence of specific heat on
temperature at temperatures below the Tc [34,35,36],
Many theories to
explain the superconductivity in the high-Tc superconductor have appeared,
including resonant valence bond theory [37], doped Mott insulator [38],
combined phonon-exciton mechanism [39], etc.
However none of these was
verified suitable for the high-Tc superconductivity.
From the application point of view, superconductors are used for
systems which need high field magnets, including magnetic resonance
imaging, particle accelerators, magnetic levitated trains, propulsion
motors, generators, electric power energy storage systems, electrical
transmission line, etc, and for low field applications such as highsensitivity devices and rapid signal process, etc.
However the low value
of critical current density (Jc) and the weak mechanical property of the
high-Tc superconductor are the severe barriers for many application.
In this dissertation, a study of YJ^C^Oy.g will be presented, with
emphasis on the preparation and the microwave response of the bulk
YBa2Cu307_5.
Chapter 1 covers some of its physical properties to give a basic
information characterizing the material.
Chapter 2 covers the important parameters in the preparation of the
bulk material and show some of our results.
Chapter 3 covers the resonant and non-resonant response of the bulk
material to microwaves.
Chapter 4 concludes and summarizes the results and suggests further
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investigations.
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CHAPTER I
SOME PHYSICAL PROPERTIES OF YBa2Cu307_6
The physical properties of the high-Tc superconductors are quite
different from those of the low-Tc ones due to the possibly different
mechanism of superconductivity as that predicted by the BCS theory and to
their ceramic property.
In this chapter, some of the physical properties
of YBa2Cu307_£ will be compared with those of the BCS superconductors.
Some of their characteristic features will be presented, to give a
physical background for understanding the meaning and the significance of
the preparation parameters and the resonant and nonresonant responses to
microwaves.
The list of physical constants which other groups have
already published are shown in Table 1 (a) and (b) . The other important
physical constant not listed in Table 1 (a) and (b) are as follows.
For polycrystalline YBa2Cu307_£ material, it was reported that the
fracture stress was 5,100 psi [59], and the linear thermal expansivity, a ,
was 11.9 x 10'6K _1 [60].
For the single crystal, it was reported [61]
that the fracture toughness, Kc , in (100) and (001) planes was 1.1 ± 0.3
MPam^/2 and the hardness was 8.7 ± 2.4 GPa.
1.1
Crystal Structure
Many researchers have studied the crystallography of YBa2Cu307_g by
using x-ray diffraction (XRD) and neutron scattering.
Neutron scattering
studies give more firm information than the XRD because the x-ray is
insensitive to oxygen due to its small atomic number.
On the other hand,
5
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the neutron beam interacts only with the nuclei of the oxygen due to the
Table 1.
Data for YBa2Cu307_£.
The letters ab and c refer to the
directions in the a-b plane and in the c-axis, respectively.
Aeff, Jc , 7 ,
Hq^, H(j2, I,
neff and p mean the lower and the upper field, coherence
length, effective penetration depth, critical current density, Sommerfeld
constant, Debye temperature, effective carrier concentration and the
normal-state resistivity, respectively.
The numbers in [ ] and (
)
indicates the reference and the temperature where the data is taken,
respectively.
Physical
Constant
Unit
' dHc2 '
Tesla/K
. dT
'
.
T
Ac
Single
ab
Crystal
c
Polycrystalline
3.8 [40]
0.5 [40]
1.3 [42]
3.6 [41]
0.2 [41]
1.9 ± 0.2 [43]
dHcl ‘
Tesla/K
. dT
.
HC2(0)
Hci(O)
£<0)
xeff(°)
7 x 10-4 [14]
T
■■•c
Tesla
240 [40]
222 [41]
160-240 [40]
Tesla
< 0.5 [40]
34 [40]
61.7 [41]
35 [44]
80 - 180 [42]
120 [43]
< 0.5 [40]
5.5 x 10'2 [46]
0.1 [45]
1 x 10-2 [47]
A
31 [40]
23 [41]
31 [44]
4.3 [40]
< 6.3 [41]
5.1 [44]
x 102 A
2.7 [40]
18 [40]
22 [14]
14 [43]
30 [48]
10 [14]
13 - 20 [43]
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7
Physical
Constant
Unit
Jc(0)
x 103 A/cm2
Single
ab
Crystal
c
Polycrystalline
11 [45]
160 (4.5) [48]
3200 (4.5) [48]
7
0-q
nejf
mJ/mole-K2
K
x 1021 cm'3
dp
pfl-cm/K
dT
9 [51]
300 ~ 410 [51]
1.1 [14]
0.2 [49]
7.4 [50]
3 [14]
7±2 [34]
2.77 [35]
400 [34]
439 [36]
440 [52]
1.1 [14, 53]
1.4 [43, 54]
1.5 [55]
1.7 - 2.5 [56]
4 [57]
13 [58]
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8
m
o (4)
©
Fig. 1
Crystal structure of YBa2Cu307.5 (after Beech et al. [20])
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9
small wavelength of the neutron beam [62]. The crystal structure which had
been identified by others [16,17,18,19,20] is shown in Fig. 1.
The crystal structure of YBa2Cu307_£ is known as an orthorhombic
oxygen deficient perovskite different from the layered I^NiF^ structure of
La2_x (Ba,Sr)xCuO^_y [63].
The main feature of the structure is that it is
composed of Cu(I)-0 chains along b-axis and Cu(II)-0 2-dimensional layers
perpendicular to c-axis.
As the value of S increases, the occupancies at
(1/2, 0, 0), (0, 1/2, 0) and 0(4) are randomized [64],
The role of oxygen
will be discussed more detailed in section 1 .6 .
1.2 Energy Gap
The energy gap (Eg or 2A(T)) in the superconductor is the energy
difference between the superconducting state and'nonsuperconducting state,
usually tied around the Fermi energy level in the BCS theory.
Measured
values of gap taken from the various junctions of quantum tunneling and
the far infrared (FIR) spectroscopy in terms of 2A(T)/kgTc at very low
temperature where kg is Bolztman constant, vary from 2 to 13 [65,66,67,
68,69,70,71,72,73,74,75].
However, it is expected that the value of
2A(0)/kgTc is 5 or less, where 2A(0) is the energy gap at 0 K, but higher
than 3.5 which is the weak coupling limit of the BCS superconductor [76],
because it is believed that the strong coupling or any other unknown
mechanism is the case of this high-Tc superconductor.
The energy gap measurement from Josephson tunneling junction is
described by
Gn
Jo
ttA(T)
tanh
2e
A(T)
--2kBT
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(1 .2 .1)
10
where JQ is the maximum Josephson current density, Gn the normal-state
conductance of the junction, A the junction area, A(T) the gap parameter
at temperature T, and e is the electron charge.
through various techniques are inconsistent.
The values of 2A(T)/kBTc
They are 4.8 ± 0.5 from the
point contact of Nb/Y-Ba-Cu-0 [65], 3.2 ± 0.4 from the piezo-driven
microbe [66], 3.9 from the superconductor-insulator-normal metal junction
[67], 4.8 from the brake junction [68] and 13 for the point-contact
junction [69] at the temperature near zero.
From the FIR absorption, the 2A(T)/kgTc is 8 for a single crystal
[70].
For the bulk material, it was determined 2 [71], 3.5 [72], in the
region between 1.6 and 3.4 [73], 3.6 ± 2 [74] and 3.3 [75] at very low
temperature.
It was observed that the gap value decreases with increasing
temperature.
In the BCS theory, the gap parameter A(T) is proportion to
(1 -T/Tc) V 2 [77]>
On the other hand, Polturak and Fisher [78] estimated the energy gap
by using the imaginary part of the ac susceptibility in the YBa2Cu307_£ as
2A(0)/kBTc - 5 ± 0.2.
1.3
Specific Heat
For the low-Tc superconductors, a strong anomaly in specific heat was
observed at Tc , which is a characteristic of the second-order transition
of the BCS superconductivity [39].
When T > Tc , the specific heat shows
the linear dependence on the temperature, i.e.,
C - yT + /3T3
(1.3.1)
where 7 is a coefficient due to the electronic contribution to the
specific heat and f t a coefficient due to the lattice contribution.
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When T
11
< Tc , the lattice contribution is negligibly small, only the electronic
contribution becomes dominant and is exponentially dependent on 1/T, i.e.,
C <x exp(-aA/kgT) ,
(1.3.2)
where C is the specific heat and a is a constant, which implies the
excitation of electrons across an energy gap [62].
For Yl^C^Oy.^, only a weak anomaly was observed at Tc due to the
superconducting transition.
The results of Li et al. [79], Chen et al.
[80] and Collocott et al. [60] showed the linear dependence of the
specific heat on the temperature above and below Tc . They interpreted the
linearity at temperatures below Tc as being due to the existence of the
normal state in part of the sample up to a temperature far below the Tc ,
resulting from the significant contribution of lattice vibrations below
Tc , because the Tc is so high.
Li et al. observed a discrepancy between
the Tc in specific heat anomaly and that in the resistivity and suggested
that the case of granular superconductor is well described by the
percalation model of Duetscher et al. [81].
For a single crystal YBa2Cu307_$, von Molnar et al. [51] reported
that in region of 0 < S < 0.3 and at low temperatures between 2 and 10 K,
C
- - 7 + /3T2 + A3T4,
T
(1.4.3)
where 7 «» 9 mJ/mole K2 , /3 — 0.37 mJ/mole K4 and a coefficient of the
nuclear quadrupole contribution A3 — 1.3 x 10"3 mJ/mole K6. They also
observed the increase in p by inducing oxygen disorder consistent with a
softening of the phonon spectrum in glassy materials.
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12
1.4
Isotope Effect
For the low-Tc superconductor, there was established from experiment
the relation [62]
maTc — constant,
(1.4.1)
where m is the molecular weight of the superconductor and a is a constant.
From the BCS theory,
Tc = 1.14
-1
------
exp
LU
where
D(Ef )
(1.4.2)
J
is a Debye temperature, U an attractive potential, and D(Ep) the
density of state
at the Fermi level [62].
For BCS superconductors, a =
1/2.
ifphonons are related to
the superconductivity of the
Therefore,
material, as is the BCS mechanism where electron-electron coupling occurs
via the phonons,
one should observe the isotope effect.
Batlogg et al.
[30] and Bourne et al.
by substituting ^®0 for
[31] reported no isotope effect
in the YBa2Cu30y.
zur Loye et al. [32]
reported they observed very small isotope effect from their magnetic
susceptibility measurement on BaBig.ysPbg.25^3’ l^l.SS^O.lS^11^ '
Lal 85Sr0 15CUO4 and YBa2Cu30y after replacing
by -^0.
However the
shifts due to the isotope substitution were independent of the mass
through the above four materials. They concluded that there is no or
negligibly small amount of isotope effect in the high-Tc superconductor
and that the electron-phonon coupling is not significant in the high-Tc
superconductor.
However, Morris et al. [33] reported a = 0.019 ± 0.005
for YBa2Cu30y after taking special precautions to avoid errors caused by
sample-to-sample differences.
It means that there exists a phonon-
mediated coupling in the material, even though it is very weak.
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13
1.5
Microstructure
The importance of microstructure in the superconductor lies on the
magnetic behavior, as well as its usual influence on the mechanical
property.
The observed irreversibility of magnetization in the hard
superconductor is directly related to the defects in the specimen which
impedes the movement of magnetic flux.
The penetration of the magnetic
field is well described by the London equation [82],
o" - “
2
V2B
B/AL
(1.5.1)
B(x) = B(0) exp(-x/AL),
> where Al «= (mc2/47rnee2) , m is a electron mass, c speed of light in vacuum,
ne electron concentration, e a electron charge, B(x) the magnetic field
strength at a distance x from the surface of the specimen, and B(0) the
field strength at the surface, and the irreversibility is well explained
by Bean's model [83] based on the flux density inside the sample.
The
effect of the microstructure on the irreversibility of the low-Tc hard
superconductors were illustrated experimentally by many researchers,
including annealing effect on Pb - 8.23 wt%. In alloy by Livingston [84]
in terms of the dislocation and point defect density, the effect of
changing concentration and size of a precipitate in Pb - Bi eutectic
samples by Evetts et al. [85], and the effect of fast neutron irradiation
producing many different types of point defect by Swartz et al. [86].
The effect of the microstructure on the irreversibility and the
critical current density was developed by Kim et al. [87] and others, in
terms of flux slips [88], flux jumps [89], flux pinning, [90,91] and flux
creep [92,93].
It is generally established that the critical current
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14
density depends predominantly on the local microstructure, its degree of
uniformity, and the nature of its characteristic defect structure [94]
which affect the strength of flux pinning.
For the microstructure of YBa2Cu307_£, there are many inconsistent
reports, especially about submicrostructure within the grain.
However
there are certain characteristic features related to the tetragonal to
orthorhombic structural transition and its inherent crystal structure,
which are the domain-type substructures and twins within the grains
[94,95,96,97,98] and the stacking fault along the c-axis [97].
Actually the nature of the domain-like substructure and the twins
seems to be same.
The only difference between the two is occurrence
habits which are {113} for the domain substructure and {110} for the
twins, and therefore their phase-coherency [95].
The cause of the
occurrence of those two is believed to be the shear transformation to
minimize the distortion energy and to accommodate the volume change [94].
Notice that Chen et al. [99] called the twin boundary as an antiphase
boundary, because of discontinuity between oxygen chains and vacancies
across the boundary. Also notice that the twin boundary lies on {110}
planes containing the metal ion, not the oxygen-only plane [96]. Henry et
al. [97] reported the stacking fault along the c-axis and ascribed it to
the high density of defects on the (001) plane due to oxygen disordering
on the plane.
The interpretation was well illustrated by the observation
that as the oxygen content decreased, the stacking fault density was
reduced.
Through almost all of the reports [95], it is estimated that the
average grain size is 1 - 100 f i m and the average spacing between twin
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15
boundaries is 100 A — 1000 A.
The dimensions of the twin may correspond
to the homogeneous superconducting area according to the superconducting
cluster theory of Ebner and Stroud [100].
From the microstructure, four
characteristic phenomena can be expected; the proximity or Josephson
couplings between the grains and between the domain-like substructures (or
twins) on the basis of the work of Ebner and Stroud, and the flux pinning
at the domain boundary and at the grain boundary.
discussed in more detail at Sec. 1.9.2.4.
The couplings will be
Camps et al. [95] described
their expectation that the domain substructure would pin the flux vortices
strongly, the pinning possibly varying as a function of the habit. Ourmazd
et al. [101] concluded that the flux penetrates more in the twin boundary
than in the regular grain substrate and that the twin boundary is also the
free path of the fluxoid motion as determined from their magnetic microstructure study.
Camps et al. [95] also mentioned that the anisotropy of
the upper critical field on the basal planes would lead to pinning on the
basis of the work of Campbell and Evetts [102] , and that pinning at parent
grain boundaries due to anisotropy might be very large, if the oxide
structure is undisturbed to within less than a superconducting coherence
length, £, of the physical boundary [95].
Horovitz et al. [103] developed a theory of "dyadons" which are
collective twin-boundary oscillations and proposed that the change in
specific heat from the T3 dependence to T2 at lower temperature - below 12
K in La^ 35B a o i 5CuO^ and La^ gSrQ2^u®4 [104] - is due to dyadons, and
that the linearity of the normal state resistivity with temperature to as
low as 40 K [1-5,106,107] is due to the low frequency dyadon-electron
coupling.
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16
1.6
Effects of Oxygen-Deficiency
The content of oxygen is directly related to the physical properties
[21,64,108,109,110,111,112] and oxygen disordering in the crystal
structure [16,22,23], and can be controlled by quenching at certain
temperatures [16,113].
The oxygen deficiency through the conventional
powder technique of preparation of YBa2Cu307_g results from the tetragonal
to orthorhombic structural transition occurring at the oxygen deficiency,
S = 0.5 - 0.6 [16,110] and the temperature, Tc = 650 - 750°C [23,108,114],
Among the many reports about the change of physical properties with
oxygen content, that of Cava et al. [21] is mentioned here because they
made the samples by a gettered annealing technique [115] to get the better
uniformity of oxygen deficiency through the samples. The superconducting
transition temperature (Tc) showed the highest point at S = 0 and
decreased like stairway with increasing 6 . The normal state resistivity
(p) showed a minimum at 6 - 0 and increased with increasing 6, with a
local abnormal minimum between 5 = 0 . 3 and S = 0.4.
The semiconducting
behavior in the resistivity began to appear at S = 0.24. In diamagnetic
behavior, the magnetic transition temperature decreased with increasing 5.
However, the maximum diamagnetism appeared not at S = 0, but at S ~ 0.28.
They interpreted that this might be related to the fact that the strongest
flux trapping occurs at other material rather than the material with S «
0. The lattice parameters, a and c increased with increasing S , and b
decreased with increasing S because the oxygen occupancy at (0, 1/2, 0)
site decreases with increasing S at the expense of increasing the
occupancy at (1/2, 0, 0) site.
The a and b become equal at 6 = 0.5 in
which the crystal structure corresponds to the tetragonal perovskite
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17
[108].
Wang et al. [110] report the variation of the Hall coefficient
(Ry), the volume fraction showing the Meissner effect (f) and the
superconducting transition temperature (Tc) with oxygen content.
They
observed that Rjj, f and Tc are insensitive to 8 over the range 0.1 < 8 <
0.5, and concluded that the superconductivity is due to the Cu(II) -0
plane because the increase of 8 results in breaking of Cu(I) - 0 chains.
The tetragonal to orthorhombic structural transition occurs according
to the oxygen content in the YBa2Cu30y.^.
In the orthorhombic structure,
the oxygen atoms are fully ordered at (0 , 1/2 , 0) sites, creating
one-dimensional Cu(I) - 0 chains.
At the transition which corresponds to
5 = 0.5 theoretically [108], the occupancy of the oxygen at the tetragonally equivalent sites, (1/2 , 0, 0) and (0 , 1/2, 0), becomes equal (=
0.25), producing a highly disordered two-dimensional Cu(II) - 0 network.
Jorgensen et al. [16] and Kwok et al. [113] reported the variation of
the Tc ,
p,
lattice constants, Meissner effect and the lengths of Cu(I)
-0(4) and Cu(II) - 0(4) with quenching temperatures and showed that the
quenching at certain temperatures is directly related to the oxygen
content.
1.7
Stability in Environment
The superconducting YBa2Cu30y.g phase is likely to be very unstable
in any environment because of the instability of oxygen content.
Yan et
al. [116] reported that the YBayCuOy is highly sensitive to water and
water vapor through the reaction
2YBa2Cu30y +
3 H2O
-+ Y2BaCu05 + 5CuO + 3Ba(OH)2 + 1/2 02 ,
(1.7.1)
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18
and
Ba(OH)2 + C02 -*• BaC03 + H20,
where Y2BaCu05 is the semiconducting green phase.
(1-7.2)
Rosamilia et al. [117]
related the reaction to the conversion of Cu3+ to Cu2+ in the presence of
water, i.e.
Cu3+ + 1/2H20 -*• Cu2+ + H+ + 1/4 02
(1.7.3)
Barns and Laudise [118] reported that the stability of YBa2Cu3C>7_£ phase
to water does not depend on oxygen content for 0 < S < 1.
They also
reported that the YBa2Cu30y decomposes in water more easily at low pH, but
at high temperature eventually even in strongly basic solutions.
However
the material is stable in alcohol.
To prevent the decomposition of YBa2Cu307_g, it is necessary for this
material to be encapsulated by glass, metal [119] or an organic compound
[118].
1.8
Josephson Effects
The particle tunneling through a junction is usually classified as a
single-electron tunneling between two normal metal (NN junction), a
quasiparticle tunneling between a normal metal and a superconductor, or
between two identical (SS junction) or different superconductors (SS'),
and Josephson tunneling [110] through a SS or SS' junction.
The former
two tunnelings usually use a thicker insulating oxide barrier than a
Josephson junction, to avoid overlapping the wavefunctions of either side
in the barrier.
The current can flow through the junction when a applied
voltage is larger than the potential across the junction.
However, the
Josephson tunneling is the result of overlapping the superconducting
wavefunctions in a very thin barrier, and the current can flow without the
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19
applied voltage across the junction.
effect.
This is known as a dc Josephson
A simple derivation of the Josephson effect was given by Feynmann
et al. [121], which is a case of single point contact junction, as follows
J - JQ sin S,
(1.8.1)
where J is the current density across the junction, J0 the critical
current density given by equation (1.2.1), S the phase difference across
the junction.
For a two identical point-contact junction with a magnetic
field perpendicular to the contacts [122],
J - Jmax sin s
and
(1.8.2)
Jmax= 2J0 cos (*$/%)
(1.8.3)
where S is the phase difference along two point contact, $ the magnetic
flux through the area between the junctions, and
a quantum fluxoid
(= h/2e), where h is Planck's constant, e the charge of a electron.
For a
rectangular thin film junction [122],
sin(7r$/$0 )
J - JQ --------»V$o
and
(1.8.4)
$== BL(A^ + Ag + d) ,
where B is the magnetic field, L the length of junction, A^ and Ag are the
penetration depths and d the barrier thickness.
Ac Josephson effect is that a dc voltage applied across the junction
causes a ac current across the junction and is described by the equation
J = JQ sin
2eV
S(0) - -- t
(1.8.5)
h
where S(0) is the phase difference at a reference time, t = 0, V the dc
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20
voltage across the junction, and t is the time [62].
The Josephson
current response, when both dc voltage, V, and ac source by a microwave
with frequency w and equivalent ac voltage Vs are simultaneously applied
to the junction, as in the usual detection application, is
2eVs
J(t) - JQ
where wj ■= 2 e V / h ,
S (-l)n Jn
n=-»
sin [(Wj - nw)t + S(0)],
(1.8.6)
fiu>
the Josephson oscillation frequency, and Jn is the
Bessel function of order n [123].
When 2eVs = n f t u and S(0) = tt/2, J =
J0Jn (2eVs/7zw) , which is a maximum dc current.
For these junctions, JQ is
proportional to Tc - T for SS junction and to (Tc - T)^/2 for SS' junction
[124].
For the YBa2Cu30y.^ superconductors, the dc and ac Josephson effects,
including macroscopic quantum interference, were observed [65,66,67,68,69,
125,126,127,128,129,130,131,132,134,135,136,137].
Chen et al. [138] and
Kuznik et al. [139] observed an inverse ac Josephson effect.
Kuznik et
al. attributed the effect to great effective capacitance developed in twin
boundaries having a width of only a few atomic layers. They also found
irregular and chaotic I-V characteristics.
All the above references are
the ones that used point-contact, break-junction and SS" junction.
The
YBa2Cu307_g insulating barrier YBa2Cu30y.j film junction has not been
reported, probably due to the difficulty of making the thin insulating
barrier on the surface of YBa2Cu30y_^ material.
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21
1.9
Magnetic Property
In general, the superconductors are classified as two kinds - type I
and type II, according to their response to the external magnetic field.
The type I superconductors shield the external field by the supercurrent
generated within a penetration depth, A, of the surface to keep the
magnetic induction, B, inside superconductor to be zero, and show a
perfect Meissner effect [9], until the external field is reached at a
certain critical field, Hc . At Hc , the superconductor loses the
superconductivity and becomes a normal metal.
The type I superconductor
is also called Pippard [140] superconductor because of the non-local
nature of the response of the current, J, to the magnetic vector poten­
tial, A, when the coherence length, |, is larger than the penetration
depth, A.
The type I superconductor is also called soft superconductor
because of the reversibility of its magnetization.
In the type II
superconductors, the external magnetic field is totally shielded and the
superconductor shows the perfect Meissner effect [9], until a certain
lower critical field, Hc^, is reached.
At Hc^, the external field starts
to penetrate into the surface of the superconductor and converts some part
of the superconducting state into the normal.
Thus the superconductor is
composed of the normal state and the superconducting state.
This state is
called a mixed state or a vortex state, and shows a incomplete Meissner
effect.
As the field is further increased, the superconductor becomes
less superconducting, and become a normal state totally at a certain upper
critical field, Hc2. The response of J to A follows the London equation
[83],
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22
-»
c
-f
J = - ---- A,
(1.9.1)
U n\2
L
where Al *= (mc2/47rne2)^/^, the London penetration depth.
The non-ideal
type II superconductor is also called hard superconductor because of the
irreversibility and hysteresis on the magnetization.
1.9.1
Magnetic Behavior in Conventional Hard Superconductors
Now it is well-known that the irreversible magnetization is related
to the pinning of the magnetic flux on the defects in the superconductor,
even though the nature of the pinning is not cleared yet [102].
The first
theory to explain this irreversibility is the Mendelssohn "sponge" model
[141], which states that the hard superconductor consists of a multiplyconnected internal structure of high critical field material surrounding a
matrix of material with lower (or zero) critical field. With this model,
Abrivkov [142] and Goodman [143] leaded a mechanism favoring high ratio of
Hc2/Hc ■ After them, Bean [83] explained the size-dependent magnetization
commonly observed in hard superconductors by treating the magnetization as
resulting directly from the critical supercurrents, which may be an
intrinsic property of the walls of the sponge in the Mendelssohn model or
a consequence of the gradient of flux lines that exists as flux is driven
into an inhomogeneous mixed-state superconductor.
Bean assumed, as a starting point, that the critical current density,
Jc , is independent of field.
The field, H, within a slab specimen of
thickness D decreases linearly with distance as a consequence of Ampere's
law,
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23
*A-7T
V x H = — Jc
c
(1.9.1.1)
From equation (1.9.1.1), he derived that the macroscopic screening length,
A, is dependent of field and governed by
c H
A = --4tt J c
(1.9.1.2)
Then, he defined the external field at which the field becomes zero in the
center of the slab (A = D/2) as H*.
4x
2tt
H* = — A Jc = — D Jc
c
c
(1.9.1.3)
At this field, the Jc flows through the entire volume of the slab.
The magnetic flux density, which is the volume average of the local
field, is governed by
B - J Hdv/ J dv
and
(1.9.1.4)
4ttM - B -H,
(1.9.1.5)
where dv is a volume element and 4jtM is the average field created by the
induced supercurrents.
lit
H < H* - —
c
D Jc ,
2H*
Hin - - -- z + H
D
(1.9.1.6)
where z is a position inside the sample and varies from zero to
A - DH/2H*.
Therefore
and
When
2?r
H > H* - - D Jc,
c
B = H2 / 2H*
(1.9.1.7)
-4jtM= H - H2/2H*
(1.9.1.8)
2H*
Hin - - -- z + H
D
(o < z > D/2)
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24
B - H - H*/2
and
-4ttM
(1.9.1.9)
- H*/2
(1.9.1.10)
After a field Hmax is applied to a magnetically virginal slab and
then removed, an opposite field gradient is developed at the surface and
hence the surface current is reversed.
When Hmax < H ,
B = H Hmax/2H* ± (H2 - * W ) / 4 H *
The minus signapplied for areverse sweep from
signfor a forward sweep from
(1.9.1.11)
Hmax to -Hmax and the plus
-Hmax to Hmax.When Hmax
> H , and Hmax -
2H* < H < Hmax,
H*
1
B = Hmax - _ (Hmax - H)2
4H*
(1.9.1.12)
for a reverse sweep and
H*
1
B = H -_ -_
2
4H
(Hmax - H)2
(1.9.1.13)
for a forward sweep.
Therefore, the loss of energy per unit volume per cycle, Wn , due to
the hysteresis shown above, is
1
Wh = _ § H dB
4jr
(1.9.1.14)
3
wh “ Hmax/6jrH
(1.9.1.15)
and then for HQ < H*,
and for Hmax »
H"Jc , the loss approaches a linear dependence.
This picture
gives that within the sample, local electric fields exist during the
change of magnetization and that the hysteric loss is the local Joule
heating which is the product of the electric field and the local current
density.
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25
He mentioned that as the current density depends on the field in a
real sample, the previously driven equation should be revised.
Kim et al.
[87] derived the relation between the critical current
density, Jc , and the magnetic induction, B, by the equation
a/Jc - B0 + B
(1.9.1.16)
where a and B0 is constant, from their assumption of the "critical state"
of Bean's model, which states a state at which the whole of the sample
carries a maximum supercurrent determined only by the local magnetic field
on the sample region.
They also described the Jc decreases with increas­
ing field, after the critical state is reached.
The Jc , however, is
independent of magnetic field at low magnetic fields.
With these work,
Anderson [92,144,145] described the motion and creep of the magnetic flux
on the basis of the concept of Abrikosov [142] flux line and of the work
of Kim et al. [87]. Yamafuji and Irie [146] and Labusch [147] pointed out
the role of the elastic interaction of the flux line lattice, in addition
to the vortex-defect interaction.
1.9.2
Magnetic Behavior in High-Tc Superconductors Superconducting Glass
On the contrary with the above-mentioned development for the magnetic
behavior of the low-Tc hard superconductors, it seems that the high-Tc
superconductors have a slightly different magnetic nature.
The main
feature in the magnetic behavior seems to be that of spin glass [100],
which is called "superconductive glass" state by Muller et al. [10].
The
main feature of magnetic behavior in the high-Tc superconductor, in
connection with the spin glass, is the difference between field-cooled
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26
(FC) and zero-field-cooled (ZFC) response [148,149,150,151,152,153], the
existence of a de Almeida-Thouless line [148,149,150,152,154], and
non-exponential time dependence of the remnant magnetization
[151,155,156,157].
1.9.2.1
Superconducting Cluster Theory
Originally the superconducting analog of spin glass behavior was
suggested in superconducting cluster by Ebner and Stroud [100], as a
theory of the diamagnetic response of superconducting composites. Their
composite is composed of isolated clusters of superconducting grains, each
smaller than the penetration depth, embedded in a nonsuperconducting host,
and weakly coupled together to make many superconducting loops by the
proximity effect or Josephson tunneling [120] depending on a electrical
nature of the nonsuperconducting host.
The brief introduction of the spin
glass behavior in superconducting composites, including the high-Tc
superconductors, is as follows.
The ith grain is centered at
A^exp(iS^).
and has a complex energy gap ^
«=
The Hamiltonian for the coupling of the grains is
H >= - 2 J^j cos (S^
(1.9.2.1.1)
ij
Here J^j — (h/2e)Ijj is the coupling energy between grains i and j, where
Ijj is the superconducting critical current between grains i and j , for a
Josephson junction between two identical grains,
7T A(T)
A(T)
tanh
(1.9.2.1.2)
2kBT
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27
where R^j is the resistance at the normal state between grains i and j .
The phase factor, A j j , is
2jt
J
— J A • di.
(1.9.2.1.3)
Here, if the Josephson coupling energy, J-y , is greater than the thermal
energy, kgT, the grains are coupled together [120].
By considering the
phases S as classical variables in the canonical ensemble, the Helmholtz
free energy, F, is
F - - kBT In Z
(1.9.2.1.4)
Z - J (n dSi) exp(-H/kgT).
(1.9.2.1.5)
i
Then, the magnetic moment, p ,
is
' 3F '
fj, = -
(1.9.2.1.6)
3H
T,
the isothermal differential (ac) susceptibility, xac, *-s
3M ‘
Xac “
(1.9.2.1.7)
3H
and the dc susceptibility, Xdc> *-s
M '
(1.9.2.1.8)
*dc =
H
where M is the magnetization, i.e., the magnetic moment per unit volume.
From the equations (1.9.2.1.4), (1.9.2.1.5) and (1.9.2.1.6), the moment,
fi,
of a cluster is
1
2c
S (Xij x I'ij Xy),
ij
(1.9.2.1.9)
where X jj = (X£ + Xj)/2, X y = Xj - Xi, and
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By "frustration" [158] produced by A y , any cluster with closed loops
cannot find a state which simultaneously minimizes all the bond energy at
a finite field.
It only can choose a state among numerous competing
ground states with nearly equal energy, as a true ground state.
As the
magnetic field is changed, the levels of the computing states will cross
each other and the cluster must hop from one configuration to another in
order to find a new ground state.
change in magnetization.
Such hopping will result in an abrupt
Therefore the energy spectrum of the ground
state with the field will consist of many short arcs, with discontinuities
of slope with
as a periodicity.
As the size of the cluster is in­
creased, those discontinuities are smeared out because of compactness of
the competing levels with nearly equal energy.
The consequence of this picture is the existence of metastable states
at low temperatures, because the thermal energy is too small to overcome
an energy barrier.
Therefore, if a ac magnetic field with a frequency
larger than the relaxation rate of the cluster, is applied, Xac measures a
nonequilibrium property, which is larger than Xdc• This difference was
identified in the YBa2Cu3<!)7_g by Ayache et al. [153] . Ebner and Stroud
defined the field
at which Xdc starts to deviate from Xac and the
first flux slip occurs, as
- $0/2S (1.9.2.11), where S is a average
projected area of the loop perpendicular to the applied field.
As a real
composite has a broad distribution of relaxation rates, more of clusters
exhibits non-equilibrium response at high frequency of a external field
than at low frequency.
Therefore, one expects the frequency dependence of
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29
Xac. At high temperature, this frequency dependence will be weaker.
1.9.2.2
Difference In Response Between Zero-Field-Cooled and Field-Cooled
Samples, and Existence of Quasi-De Almeida-Thouless Line
Another version of the existence of metastable states is the
difference between FC and ZFC response.
If the superconducting clusters
are field-cooled slowly enough to allow relaxation through a temperature
range, the resulting state is in equilibrium.
If the clusters are
zero-field-cooled and a magnetic field is suddenly turned on at a fixed
low temperature, the clusters are in a nonequilibrium state because they
need the relaxation time to reach a equilibrium state at that field.
If
one investigates the FC and ZFC response by means of magnetization or
susceptibility versus temperature at a certain magnetic field, there
exists a certain temperature at which the FC response curve deviates from
the ZFC curve.
This temperature is called a glass transition temperature,
Tg(H), at that field H.
On the other hand, if the temperature is fixed
and the magnetic field varies, the superconducting state becomes
superconducting glass state at a certain magnetic field.
This field is
the Hci* at which the superconducting state becomes the superconducting
glass state at that temperature [10,100,159].
The equality of
to Hg^
was identified by Giovannella et al. [160] (1G at 4.2K for La^ 25 Srg ^5
CuO^). Here Hg^ is the field at which the initial part of the low-field
magnetization deviates from a linearity, due to flux-penetration into
-t-
intergranular junctions.
Usually the value of Hg^
or Hc^ was reported
for flux-penetration into intragranular junction [10,159].
Therefore, the
usually observed values are much larger than those reported by Giovannella
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30
et al.
Above Tg, there exists no flux trapping and no hysteresis.
The
relationship between Tg and H is known as Quasi-De Almeida-Thouless line
[161], which distinguishes the ergodic region from the non-ergodic region,
and is given by
H - H0[l - Tg(H)/Tg(0)]T,
where H0 and 7 are constant.
(1.9.2.2.1)
Muller et al. [10] estimated HQ = 1.7 Tesla
and 7 = 1.5 for Ba-doped L^CuOy.g by assuming infinitely slow sweep time
of temperature and Tg(0) = 23 K.
In their sample, the transition in the
resistivity occurred at a temperature range of 35 to 30 K.
For the
YBa2Cu307_5 polycrystalline, H0 = 5.1 ± 0.2 Tesla and 7 = 1.49 ± 0.04
[149], Hq = 0.76 Tesla and 7 « 1.5 [151].
For the YBa2Cu307_5 single
crystal, H0 ■= 6.8 Tesla and 7 « 1.5 [152], H0 = 10.1 Tesla and 7 w 1.5
[154],
1.9.2.3
Decay of Remnant Magnetization
If the superconducting clusters are field cooled to a low temperature
and the field is suddenly turned off, there will remain trapped flux which
slowly decays away as the cluster equilibrates.
The decay of the remnant
magnetization is expected to have nonexponential time dependence or
stretched exponential dependence like that seen in the spin glass [162],
which is characteristic of a broad distribution of relaxation time through
the clusters, in contrast to the exponential decay of an excess of trapped
flux in the flux creep mechanism of usual irreversible superconductors
[87,92,93,95].
Muller et al. [10] reported that for a early short time,
the decay of FC magnetization for Ba doped L^CuO^.g was exponential and
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31
later considerably slow then exponential.
For the YBa2Cu30y_g, Drumheller
et al. [155] reported the stretched exponential increase of ZFC magneti­
zation (this corresponds to the flux penetration, in contrast to expulsion
by phase slip in FC magnetization) with 400 sec. as relaxation time.
Datta et al. [156] observed the non-exponential decay of FC magnetization
at T < 70 K, and the chaotic dependence of a field-cooled and warmed (FCW)
sample at 70 K < T < 90 K.
They ascribed this chaotic decay to nonlinear
dynamics of the trapped flux-lattice melting. Tuominent et al. [151] also
observed the stretched exponential decay of FC and ZFC magnetization.
However, the decay rate of FC magnetization, dM/d(ln t), had a maximum
around 30 K.
As the temperature was decreased or increased from 30 K, the
decay rate was decreased.
They said that this was not the case of either
spin-glass or flux creep, because the decay rate is increased with
increasing temperature at both cases.
Yeshurun and Malozemoff [154],
however, also observed this anomaly at 30 K interpreted it through the
equation from the flux creep model [163],
dM
rJc kBT
------ —
d(ln t)
3c UQ
forcylindricalsample,
(1.9.2.3.1)
where r is the radius and U0 is the activation energy in the absence of
flux gradient.
As Jc is decreased with increasing temperature to Tc ,
dM/d(ln t) is increased and then decreased with increasing temperature,
through competition between the explicity linear T term and the implicity
drop in Jc with increasing temperature.
Tuominen et al. [151] also
reported that as the field was increased, there was a decrease in the
temperature at which the anomalous maximum was found.
They concluded that
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32
this is the difference between the spin glass and the superconducting
glass.
In spin glasses, the magnetic field suppresses the spin glass
phase, i.e., reducing the disorder in the system, by aligning the magnetic
moments, and results in a marked decrease in Tg. In superconducting
glasses, however, the field increases the frustration in the system and
enhances the glassy behavior [148,151].
Yeshurun and Malozemoff [154] reported the strong, anisotropic
magnetic relaxation of the FC and ZFC magnetization in a Yl^C^Oy.^
single crystal and interpreted it by the flux creep.
Jc is larger for the
field parallel to c-axis (H // C) than for that perpendicular to c-axis
(H
C) . The larger dM/d(ln t) for H // C results from the contribution of
larger Jc to eq. (1.9.2.3.1).
Even though larger Jc may mean stronger
pinning, for this case, it means a larger flux gradient, which drives the
flux bundles to hop faster.
From the anisotropy, U0a^
> UQC , where U0a^
and UDC are values in the direction of the a-b plane and of c-axis, they
suggested the role of twin boundaries as pinning centers and UQ =
Hc2£3/q7r.
Using £3 *= £at>2£C [148] where £a^ and £c are coherence length
in the a-b plane and through c-axis, respectively, they estimate U0 = 0.15
eV at low temperature. From the role of thermal activation in Jc on the
basis of flux creep [102],
^c = ^co
kBT
Bdfi
1 - -- In -uo
Ec
(1.9.15)
where d is a distance between pinning centers, fl an oscillation frequency
of a flux line in a pinning wall, and Ec a minimum measurement voltage per
meter, the critical current may be strongly affected by thermally affected
flux creep.
Also they derived that UQ is proportional to (1 - T/Tc)^/^
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33
and 1 - T/Tc is proportional to
(de Almeida-Thouless Line) by using
the clean limit Ginzburg-Landau formulas [164], Hc » 1.73 Hco (1 - T/Tc)
and £ - 0.74
(1 - T/Tc)"^/^, where Hco and £0 are values at zero
temperature.
Mohamed et al. [157] also reported the exponential decay of FC
magnetization and ascribed it to flux creep.
They also conclude that
macroscopic persistent current has no effect on the decay because of the
similarity in their results for ring- and out ring-shaped sample, and that
the decay rate is related to the boundary area at which vertices escape.
1.9.2.4
Intergranular and Intragranular Couplings
Usually 2-dimensional XY-spin glass model has been used to describe
the physical properties of high-Tc superconductors [159,160,165,166],
because the only type of disorder resulting in a quasi-de Almeida-Thouless
line is expected to be a weak disorder represented by a random displace­
ment of the cluster center in the range of 0 to 0.2 of the cell parameter
(twinns), and the Josephson coupling is relatively small compared to the
condensation energy of a grain [160,165].
Therefore, the effect of
disorder in the 3-dimensional granular structure, which is the case of
polycrystalline sample, was neglected.
Muller et al. [159] and Blazey et
■i.
al. [166] related the observed
from the deviation point between the
dc and the ac susceptibility and from a point at which a maximum fieldderivative absorption appeared, to the average area of the twins present
in their sample.
Giovannella et al. [160], however, observed the effect of inter­
granular coupling by distinguishing the reversible region from the
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34
irreversible one from the magnetization measurement of La^ 35 Srg 15 CuO^.
From the deviation field of the reversibility at 4.2 K, they identified
that this field (1G) corresponds to the average grain size by the relation
(1.9.2.1.11).
This value was consistent with the field of a influxion
point in the dc susceptibility curves and of the break point of linearity
observed by Senoussi et al. [167].
They also found that the flux
penetration occurred continuously up to 350 G at which was obtained by
linear extrapolation of torques at a high field region to a zero torque
point and also at which indicates the flux penetration into the twin
substrates.
In a region of 10 to 350 G, they found that the flux
penetrates first into intergranular regions, then into the defects in
grains (twin boundaries or zones with different oxygen stoicheometry) from
100 G in La^ 85 Srg.15 CuO^, 100 to 120 G in YBa2Cu307_g polycrystallines,
and 80 to 100 G in YBa2Cu307_g single crystals.
It is expected that
intergrain vortices are in conjunction with intragrain vortices.
They
calculated the average area of the twinns by using the relation
(1.9.2.1.11) and found its consistency with the average value from SEM.
From their study of a phase diagram in a low field region, they found a
order-disorder transition and attributed it to the 3-dimensional disorder
in the intergranular couplings.
From the inflection point of the ZFC
magnetization curves, they found that the critical temperature scales as
H1/^ with 1/V> *=0.55 and concluded that a strong disorder in 3-dimensional
Josephson junction array should be taken into account.
Barbara et al. [168] found two peaks in an imaginary ac suscepti­
bility curves with temperatures, with Hac = 2 G in a polycrystalline
YBa2Cu307_£ and attributed them to intergranular and intragranular
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35
crossover temperatures of supercurrents.
They also suggested that the
process for the screening currents length scale crossover for twin
boundaries is a kink creation associated with a local thermal fluctuation,
through the twin boundaries. The mechanism was explained by a competition
between the superconducting condensation energy and the surface energy
resulting from an increase of the Josephson current path surface due to
the kink creation, on the basis of a 3-dimensional superconductor.
McHenry et al. [46] also suggested two Josephson couplings by
observing two points deviating the linearity in their magnetization curves
measured at different temperatures.
At lower magnetic field, which was
less than 25G at 5 K for their samples made by rapid solidification, the
two couplings were stable and the samples showed a perfect diamagnetism.
Above a certain field,
(25 G at 5 K), the grains were decoupled,
possibly due to the screening current through the grain surface due to
Meissner effect, which is larger than the Josephson current [169,170].
Thus the magnetic field started to penetrate the grain boundaries.
decoupling between grains was irreversible.
This
They showed that the remnant
magnetization, Mr, due to the irreversibility correspond to the Jc in the
bulk polycrystalline YBa2Cu30y_g [14] by the equation [83,169]
Jc - 320 Mr/3irr
(1.9.2.4.1)
for a spherical sample with radius R.
The
was decreased with temperature up to 30 K.
however, find the
at temperatures higher than 80 K.
They could not,
Thus they
interpreted that there exists a temperature between 30 and 80 K, at which
the decoupling occurs at zero field.
At the field above H^, the magnetic response will be that of an
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36
aggregate of noninteracting grains, with the contribution of intragranular
couplings.
They correlated the field deviated from the linearity, Hc^, to
the coherent superconducting loop area projected perpendicular to the
external field by the equation (1.9.2.1.11), and found that the area
corresponded to that of a twin.
They also reported that the irreversibility in the magnetization was
increased with a decreasing temperature and interpreted the observation as
an increase in trapped flux in the twin boundaries with a decreasing
temperature. They showed that the Jc calculated from the Mr due to the
trapped flux in twin boundaries, through the equation (1.9.2.4.1) with R
as the grain dimensions, corresponded to the Jc observed in the single
crystal YBa2Cu30y_5 [152,171].
They observed that although the
was high at low temperatures, it
dropped sharply with a increasing temperature, with a crossover at 30 to
50 K.
They attributed the crossover to the change of pinning strength of
twin boundaries with temperatures.
They inferred that when the tempera­
ture is lower than 40 K, the coherent loop area, S, becomes smaller than
the twin area, A, the twin boundaries act as effective flux pinning sites,
and the observed high critical field for a maximum magnetization and the
high Jc were due to the irreversibility induced by the pinning sites.
On
the other hand, when the temperature is higher than 40 K, S > A, and the
flux is no longer pinned at the sites.
Therefore, the critical field and
the Jc are significantly reduced due to less irreversibility.
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37
1.9.2.5
Anisotropy in Critical Fields
Another resulting feature of superconducting glass state model is
that the magnetization and the magnetic susceptibility are decreased with
increasing field and increasing temperature [10,148,153,172,173,174].
It
can be explained by frustration and phase slip [10,88].
Another important feature in Yl^C^Oy.g is the anisotropy in the
critical magnetic fields.
Worthington et al. [48] observed from the
inductive transition measurement that the ratio of the upper critical
field (Hc2ak) with field parallel to a - b plane to that (Hc2°) with field
perpendicular to the plane is almost 5 by extrapolating dHc2ab/dT = - 2 . 3
Tesla/K, and dHc2c/dT = - 0.46 Tesla/K at T > 78 K and -0.71 Tesla/K at T
< 78 K to zero temperature.
From the relation [175], Hc2 (0) = $0/2?r£
(1.9.2.5.1), where Hc2 (0) is Hc2
at zero temperature and
is quantum
fluxoid, the coherence length in a - b plane, £ab, was estimated 7 A,
which is significantly larger than the spacing between the Cu(II) - 0(4)
layer, 3.9 A.
Therefore they postulated that even though the super­
conductivity is strongly anisotropic, it has 3-dimensional picture down to
very low temperature.
They also reported Hc^c (4.5 K) = 0.5 Tesla and
Hciab (4.5 K) < 0.005 Tesla.
Then they estimated the penetration depths,
Ac = 1250 A and Aab = 260 A by using the equations [176],
ab
Hcl
(1.9.2.5.2)
(4jrAab)2
Hc(0) = H c 2c A/2 Kab, and
(1.9.2.5.3)
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where
— Aa^/^a^, ma^/mc is the constant obtained from the angular
dependence of Hc2 fitting their data.
Moodera et al. [41] measured the
Hc2ak and HC2C in two single crystals - less twinned one and much twinned
one.
For the less twinned one, they found that dHc2a^/dT - - 0.7 Tesla/K
near Tco and -3.6 Tesla/K at about 85 K, and dHc2C — - 0.2 Tesla/K near
Tco. They estimated £ak = 23 A, ?c = 6.3 A and Hc2a^(0)/Hc2 (0) = 3.6.
For a highly twinned one, they found that dHc2C/dT = - 4 Tesla/K and dHc2°
/dT = - 0.96 Tesla/K near Tco, and estimated Hc2a^/Hc2C = 4.1.
The magnetic behavior of the bulk polycrystalline and single crystal
YBa2Cu30y has been discussed mainly in framework of the superconducting
analog of spin glass. The difference between ZFC and FC response, the
existence of (quasi) de Ameida-Thouless Line and, the temperature and
field dependence of magnetization or susceptibility, seem to be well
explained by the superconducting glass model.
However there exist
problems in the decay of remnant magnetization, because of its different
time dependence in different temperature regions and its clear difference
from flux creep model, in the difference in magnetic response between spin
glass and superconducting glass, in how the flux pinning is related to the
superconducting glass, in how one can see the spin glass picture directly
on the high-Tc superconductors, etc.
1.10
Magnetic Structure
The magnetic structure is the way how the material responses to the
magnetic field in terms of an array of quantum fluxoids when the magnetic
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39
field penetrates the material.
It was observed in low-Tc Type II
superconductors that the vortices are ordered and become a regular
structure through the sample.
[164].
A hexagonal vortex array is most stable
For the YBa2Cu30y.^ single crystal, Gammel et al. [177] observed
an hexagonal structure of the vortices at 4.2 K by using Bitter pattern
technique [178,179] and confirmed a quantum fluxoid of hc/2e, not of hc/e
[180], by measuring the local field.
In single-phase polycrystalline YBa2Cu30y samples, Ourmazd et al.
[101] reported a hierarchy of pinning sites, a significant anisotropy in
the characteristics of neighboring twins, and the map of superconducting
regions in the presence of circulating and transport current.
The pinning
hierarchy of decreasing strength was cavities grain boundaries and twin
boundaries from the decoration strength of Bitter patterns. The
anisotropy in the twins was suggested to result from the fact that Cu(I)
-0(1) chains plays a decisive role in the magnetic behavior of YBa2Cu30y.
When the magnetic field was decreased rapidly, it was observed from a
network of undecorated regions surrounding by decorated patches
representing the area swept by vortices during deposition, that vortex
depinning occurred through very wide regions.
They pointed out that the
undecorated networks were not the grain boundaries.
In the presence of
both the magnetic field and electrical current, the decorated patches
appeared along the approximate current direction, and the undecorated
networks were elongated in the direction of
the current.
When the
current was increased, the isolated flux-trapped regions were most
prominent. Thus it was interpreted that high-flux gradients only occurred
over small regions of the sample. From the dynamic experiment in twins,
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AO
they concluded that flux motion begins at pinning site at a grain
boundary, proceeds rapidly along twin boundaries, and terminates at
another pinning site at the opposite-side grain boundary.
Jou et al.
[181] observed that the average spacing between pinning sites was smaller
for the high field than for the low field, which may be a evidence of
Bean's model [83].
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CHAPTER II
IMPORTANT PARAMETERS ON THE PREPARATION OF BULK Y-Ba-Cu-0 SUPERCONDUCTORS
In this chapter, the effect of the parameters on the preparation of
Y-Ba-Cu-0 based superconductors on their physical properties will be
discussed.
Some remarks about special preparation techniques except
coprecipitation method, which have been developed to increase the
superconducting characteristics, the transition temperature, Tc , and the
critical current density, Jc on the bulk superconducting Y-Ba-Cu-0
superconductors are made.
The discussion about the coprecipitation method
is neglected, because it results in smaller grains, and lower Tc , low
magnetization and low critical current due to the bulk nature of the
superconductivity [182,183].
Even though it was found that the phase responsible for the super­
conductivity in the Y-Ba-Cu-0 system is YBa2Cu30y_^ ( 6 < 0.5) [16], the
higher-transition superconductor were reported at off-stoichiometric ratio
from Y:Ba:Cu = 1:2:3 [183,184,185,186,187].
Therefore Y-Ba-Cu-0 super­
conductor instead of YBa2Cu30y.g is termed, as a superconducting system,
to leave more possibility.
The superconducting properties of Y-Ba-Cu-0 based materials were
known to be sensitive to the nominal composition [43,184,188,189,190],
preparation atmosphere [191], heating temperature [188,192], cooling rate
[16,92,193,194], corrosivity with crucible materials and annealing time
[43,191].
Each of these will be discussed, and then our data will be
analyzed in terms of these parameters.
41
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42
2.1
Nominal Composition
Panson et al. [43] reported that according to the 10% change of
stoichiometric ratio of Y and Ba from Y:Ba ■= 1:2, the superconducting
transition onset temperature, Tco, from the magnetic susceptibility
measurement, was varied from 91 K to 71 K, the superconducting volume from
100% to 55%, the transition range, ATC , within which the resistivity is
changed from 95% to 5% of the normal state value, from 5 K
to 21 K, and
the resistivity at 120 K from 730/zft cm to 10,700 f i f l cm.
Hinck et al. [190] also reported the variation of Tc and Jc with
barium concentration in Y^.x^ax<-'u(-)7-5 • ^he best conditions for Tc and ATC
and Jc were X =* 0.65 for Tco = 93K and ATC = 2 K, and X =
168 A/cm2 at 77 K, respectively. The latter value of x
0.67 for Jc =
corresponds to
YBa2Cu307.^. Togano et al. [188] also reported the effect of stoi­
chiometric ratio in nominal composition YxBai_xCu03_y samples sintered at
900°C for 3 hours in air, on the resistively superconducting transition.
The samples with x < 0.1 or x > 0.7 were not superconducting above 77 K.
The best result was obtained at x = 0.4.
This may be a result of
combination of very small off-stoichiometry with oxygen loss or any other
effects like corrosion of the sample with crucibles.
Bourne et al. [184] reported that the Tco and the superconductingtransition finishing temperature, Tcf, in YBa3Cu40y and YBa^C^Oy were 98
K and 92 K, and 102 K and 97 K, respectively.
They even observed the
temporary zero-resistance state at 230 K under cooling and at 275 K under
warming in YBa^C^Oy, where the zero-resistance means 10"4 ft which is a
maximum resolution of the resistance measurement.
Cai et al. [186]
observed anomalous voltage excursion due to flux jumps, which are
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43
characteristic of granular superconductors, at high temperatures up to 138
K for the concealed formula in Y-Ba-Cu-0 superconducting system, and
concluded that there exist grains with Tc as high as 160 K in this system.
Erbil et al. [187] reported the Tco of about 550 K in the nominal composi­
tion YBayCuOx and YgBagCuOx , which was indicated by the observation of
current-voltage characteristics of a dc Josephson effect up to 390 K.
The above evidence may imply that there exist at least a phase with
much higher Tc . It can be thought that a higher-Tc superconductor is
possible if the structure has multi Cu - 0 pyramidal layers at which Cu(I)
- 0(1) chains are replaced to another Cu - 0 pyramid planes, with proper
combination of Cu^+ and Cu^+ , based on recent understandings in Bi2Sr2Ca2CU3O10 and Tl2Ba2Ca2Cu30^Q [27,28].
2.2
Preparation Atmosphere
In the preparation of the superconducting Y-Ba-Cu-0 materials, the
sintering atmosphere affects the oxygen content of the sintered oxide
materials.
The YBa2Cu3C>7_£ readily takes up or releases oxygen depending
on the kind of the gas [195] and its pressure [191,196,197], and changes
its properties.
Beyers et al. [191] observed that Tc was decreased from 90 K to 20 K
by annealing the YBa2Cu307_£ at 500°C for 6 hours in He gas.
The
resultant sample showed the reduction of orthorhombic distortion and
contained numerous defects.
They also complemented by hot-stage XRD study
in air that all the lattice parameters expanded linearly from 25°C to
550°C, then, the b-parameter contracted and a-parameter expanded at
supralinear rate up to 700°C, and above 700°C, the a- and b-parameters
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44
became equal, which means a tetragonal structure.
Those changes are
believed to be a result of oxygen vacancy disordering on the Cu(I) - 0(1)
basal plane due to oxygen loss at air atmosphere.
sample prepared under highly oxidizing atmosphere.
They also examined the
The sample prepared by
annealing at 670°C for 18 hours in 6 atom oxygen atmosphere and cooling
gradually to 25CC, did not reach zero resistance until it was cooled below
60 K.
However, its crystallography and microstructure were similar to
those of 90 K - Tc YBa2Cu3C>7_g.
This can be interpreted that as the 5
become more negative, the Tc is decreased.
Grader et al. [197] reported the variation of resistivity as a
function of temperature with various oxygen partial pressure which they
related to oxygen content in unit cell, at a temperature range 450°C to
850°C.
Fiory et al. [Ill] also reported the same variation at room
temperature to 900°C as that of Grader et al, with sudden change of the
slope around 550°C to 650°c, depending on the oxygen partial pressure, due
to tetragonal-orthorhombic structural transformation.
The oxygen diffusion study of Tu et al. [195] upon annealing at a
temperature range of 300 to 450°C in He and O2 ambient atmospheres, showed
that the resistivity for the sample annealed in He was increased signifi­
cantly as a function of annealing temperature and time, but immersing the
same sample in precipitously dropping O2 atmosphere resulted in the
recovery of the original low resistivity.
These results show how much
sensitive with atmosphere the YBa2Cu30y.^ is .
Interestingly there was a report [196] that the exposition of
YBa2Cu307_£ to N2 results in the increased Tc according to the exposition
time.
This result, however, was obtained during the cycling at low
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45
temperatures.
2.3
Heating Temperature
Heating in the preparation of Y-Ba-Cu-0 superconductors includes the
calcination process and the sintering process.
The calcination process is
included due to using BaCOj instead of BaO because of its ability to
absorb the moisture in the atmosphere.
Decomposition of BaC03 into BaO
and CO2 occurs at 1360°C in air [198].
This reaction, however, takes
place below 950°C when other oxides are present [199].
However I could
not find any peaks indicating the presence of residual, undecomposed
BaCOj, in XRD analysis of my sample #46 which was calcined at 930°C.
To find the proper sintering temperature, Togano et al. [188]
the variation of Tc with sintering temperature iii Y q ^Bag gCuC^.y,
studied
and
reported that the highest Tc was observed in a sample sintered at around
950°C.
This temperature is in good agreement with the temperature range,
925°C to 1,000°C, indicated for the best result in phase diagram study of
Steinfink et al. [192].
There was a general agreement that 900 - 1000°C
was an appropriate temperature range for oxygen to diffuse inside and
outside the material [200].
As already maintained, the oxygen content is
related to the tetragonal to orthorhombic structural transformation. Above
950°C, Gabelica et al. [199] observed a measurable weight loss by Thermal
Gravity Analysis (TGA), due to oxygen loss from their presumed decomposi­
tion reaction
2YBa2Cu307_£ -> Y2BaCu05 + 3BaCu02 + 2CuO + (l-25)02 ,
which accompanied three endothermic peaks at 945, 980 and 1032°C in
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(2.3.1)
46
Differential Thermal Analysis (DTA). However, this oxygen was absorbed
reversibly at 900 and 915°C on cooling process.
The DTA results of
Holtzberg et al. [201] also indicated that Yl^Ch^Oy.^ decomposes peritectically at about 1020°C.
Grabelica et al. [199] also reported that
repeated long heat treatment in a calcined superconducting precursor
gradually altered its superconducting properties and the sample eventually
became nonsuperconducting.
From the above discussion, 950°C is likely to be a proper sintering
temperature with proper soaking time.
However, the special techniques use
higher sintering temperature to grow single crystals, or to obtain high Jc
or better mechanical property.
Jin et al. used 1200 - 1300°C for the melt
drawing process [202] to obtain good mechanical properties and 1300°C in
the "melt-textured growth" process [50] to obtain a high Jc of 7,400 A/cm2
at 1 Tesla.
Damento et al. [203] used 1150°C to melt the mixture of powder oxides
which had an excess of CuO to lower the melting temperature, and to grow
single crystals with additional heat treatment.
To study the effect of
off-stoichiometry of cation ratio on lowering the melting temperature,
refer to the report of Holtzberg et al. [201].
Haneda et al. [204] heated
the mixture with Ba:Y:Cu — 1.9:1.09:3.0 to 1400°C to grow single crystals.
2.4
Cooling Rate
Grant et al. [193] reported the dependence of the resistance on
cooling rate after final anneal.
The resistance of YBa2Cu307_£ after fast
quench showed the behavior of usual semiconductor until the temperature
was reached at Tco, with much higher resistance than that of slow quenched
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47
one, then showing a wide ATC of approximately 23 K.
On the contrary, the
slow quenched one showed higher Tco and Tcf , after linear decrease in
resistance from room temperature to Tco. The reason for the different
behavior is the oxygen disordering at the basal Cu(I) - 0(1) planes and
0(4) sites through the tetragonal to orthorhombic transition [61,21],
Jorgensen et al. [16] reported the variation of oxygen content, S —
0.3 ~ 0.7, and lattice constants with quenching temperatures 550 to 900°C.
There reported that the best cooling time is 5 6 hours in the furnace
[200].
Gopalakrishnan et al. [193], however, reported that the slow
cooling rate is important on the ATC and Tcf.
Also single crystal growths
uses very slow cooling rates [50,201,204,205] because they give enough
time for shear stress due to tetragonal to orthorhombic transition, to
relax and result in better superconducting properties.
However, this is
not necessarily true because the density of twins may affect the
electrical and magnetic properties on the single crystals [10,41,46,101].
On the effect of the cooling rate on the submicrostructure, Kingon et
al. [206] reported that upon quenching in O2 atmosphere, the size of twins
was considerably reduced, and both (110) and (110) twin with smaller
dimension were observed as going toward the outer boundaries of grains.
They interpreted that upon quenching, the spatial range of ordering of
oxygen vacancies is reduced and it is required a long time for oxygen to
diffuse to the center of grains.
2.5
Reaction With Crucible Materials
Even though all the conditions for the preparation of the best
superconductor keeps properly, the severe reaction of the baked ceramics
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48
with the crusible materials during calcination and sintering causes the
nominal composition to be changed from the desired composition and result
in unfavorable phases.
Gabelica et al. [199] reported that when they used
quartz crusibles, they never could make YBa2Cu307.g , because Si02 itself
acted as reactant at their sintering temperature 950°C.
Holtzberg et al.
[201] also reported that the melted superconducting precursors wetted the
surface of platinum crusible and reacted with the crusible, forming mixed
platinates. We also observed the severe reactivity of Pt with the
precursor at higher temperatures than 950°C.
However, the Pt crusible did
not react with it at temperatures below 900°C.
To avoid the reaction with crusible material, choosing the proper
refractory material as a crusible is very important.
Holtzberg et al.
[201] reported that Au and Cu, single crystal of sapphire, Y-stabilized
zirconia (12% Y), magnetsia and magnesium aluminate (MgA^O^) crusibles
showed little or no visible reaction with the raw oxide powers, Y2O3 , BaO
and CuO.
2.6 Additional annealing
Pension et al. [43] reported the effect of additional annealing time
at 700°C on Tc and ATC (magnetically), Tc (resistively), resistivity at
120 K (pi20 k) > t^ie effective carrier concentration (n ) and the critical
current density (Jc). They found that the best annealing time was 72
hours.
The 72 hour additional annealing caused the lower tail (5% of the
normal state resistance) of the superconducting transition to shift from
90 K to 92 K, P i 2 0 K from 760 to 400 pO cm and n* from 1.4 x 1021 to 4.2 x
1021 cm'3 . The Jc increased significantly both in the presence of and in
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49
the absence of magnetic field.
They reported also that longer annealing
than 72 hours had no effect on the electrical properties.
In magnetic
moment measurements, 36 hours additional annealing increased Tco from 87
to 91 K and decreased ATC (95 to 5%) from 67 to 21 K.
Further cooling
from 36 hours had no effect on the magnetic properties. Upon annealing
longer than 72 hours, the Jc's remained almost unchanged or decreased
slightly.
They interpreted the reason as that a prolonged heat treatment
might reduce the number or the strength of flux pinning sites of a yet
unspecified nature.
Beyers et al. [13] mentioned that the effect of annealing treatment
maximized the perfection of one-dimensional chains of Cu(I) - 0(1) square
planes, which resulted in proper oxygen stoichiometry ( S *= 0 .0) [21] and
oxygen vacancy ordering for a better electronic and phonon structure for
the superconductivity.
However, this is possibly a microstructural (twin
boundaries and grain boundaries) effect through enhanced percalation on
the bulk superconductors [81].
2.7
Experiments
For the preparation of Y-Ba-Cu-0 based superconductors, mainly
YBa2Cu307.^, the powder reagents, Y2O3 (99.999%, CERAC), BaC03 (99.999%,
CERAC) and CuO (99.,999%, CERAC) were used.
All the samples had a nominal
composition YBa2Cu307_£, and were made by the procedure as follows.
The
above reagents were weighed with digital chemical balance (Mettler, 10"6 g
resolution), ground and mixed with mortar and pestal made of agate.
of the powder mixture was pelleted and the rest was not pelleted.
boats (Sargent-Welch S-21845) were used as crucibles.
Some
Zircon
The furnace used
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50
was a single zone tube furnace (Lindberg 54233) with maximum temperature
1500°C and a manual temperature controller.
All the pellets or the powder
mixtures were calcined at temperatures of 750 - 1070°C in air or a flowing
O2 atmosphere, then reground, pelleted except sample nos. 16 and 17, and
sintered at temperatures of 950 - 1030°C in a flowing 0£ atmosphere.
All
the sintered samples were cooled to room temperature at different rates in
a flowing O2 atmosphere.
The resistance and Jc of the samples were measured by a four probe
technique, using silver paint contacts.
An Oxford Instrument CF1200
cryostat, together with the intelligent temperature controller IJC40 was
used to control the sample temperature from 70 K to 300 K.
The resistance
and Jc's were determined by applying constant currents from 1 mA to 100 mA
from a Keithley 224C programmable current source and measuring the voltage
drop in the sample with a Keithley 196 nanovolt meter.
All the measure­
ments were taken during warming after cooling to liquid nitrogen temper­
ature.
In those measurements, special caution was given to distinguish
the thermal effect from the contact junction from the voltage caused by
the destruction of the superconducting state.
The resolution limit was
1 0 ' 6 n.
The microstructures of sample nos. 19, 20, and 21 were studied by
using ISI model 60 scanning electron microscope.
by using acetone.
The samples were cleaned
The sample no. 21 was grinded, cleaned with acetone,
embedded in berkelite and taken pictures.
For a study of the crystal structure, a Philips type No. 12215/0
diffractometer was used with CuKa , single crystal graphite monochrometer,
H.V. power supply (Canberra Model 3002), x-ray amplifier/pulse height
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51
analyzer (Canberra Model 1718), LIN/LOG parameter (Canberra Model 1481
LA), regulated power supply (NIM STANDARD Model AFC-320-5A) and Honeywell
plotter (Model No. Oil 11).
An x-ray diffractograph was obtained in
sample no. 52 by the powder method.
The magnetization measurements were made in sample no. 22, with an EG
& G Model 155 vibrating sample magnetometer with applied fields from one
to 0.5 Tesla and a temperature range, 1.9 to 300 K, by Rubins et al. [207]
at Montana State University.
To investigate the additional-annealing effect, another 6 samples
were prepared as follows.
After weighing, grinding and mixing, the
mixture was pelleted as circular-disk shapes at 1.96 x 108 N/m2. The
disks were calcined at 930°C for 24 hours in a flowing O2 atmosphere.
Then, after being reground and pelleted as circular disks with diameter
1.905 cm at 2.45 x 108 N/m2, the disks were sintered at 950°C for 12 hours
in flowing O2 atmosphere and cooled to 500°C at a rate of 2°C/min.
the furnace was turned off at 500°C.
furnace after 2 hours.
Then
The disks were removed from the
Then 6 disks were heated at an average rate of
5.8°C/min up to 700°C, hold for 18 hours in flowing O2 atmosphere, cooled
to 497°C at a rate of 1.7°C/min, and then furnace-cooled to room temper­
ature.
The additional annealings were repeated subsequently until the
total annealing time was 72 hours.
Sample nos. 52, 53, 54, 55 and 56
correspond to the samples subsequently -annealed for 0, 18, 36, 54 and 72
hours, respectively. Sample no. 54a was made by pelleting the mixture at
1.96 x 108 N/m2 before sintering, while the Sample no. 54b was pelleted by
the same pressure 2.45 x 108 N/m2 as the rest of the samples.
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52
2.8
Results and Discussion
The preparation history and the values obtained from the electrical
measurements are shown in Table 2 (a) and (b), respectively for compar­
ison.
There Tco and Tcf mean onset and finishing temperatures of the
superconducting transition, respectively.
The samples, nos. 2 to 22, contaminated the zircon crucibles
severely.
As a result of the contamination, their actual compositions
might be changed from YBa2Cu30y.g.
It could be found by the colors which
the samples contained, that they were composed of several phases - mainly
YBa2Cu307_g (black) and Y2BaCu05 (green).
found.
Sometimes a gray color was also
The scanning electron micrographs for the samples, nos. 19 and 20
and 21 are shown in Fig. 2 and 3, respectively.
It could be identified
from the habit of forming the grains that they are composed of three
phases - probably including two phases mentioned above.
From Fig. 2, the spheroidal grains are apparently seen and the
samples have a large porosity.
Sometimes the secondary phases are seen on
the grain-boundaries. This feature is apparent in Fig. 2(b) and 2(c).
From Fig. 3, the twin boundaries are seen.
The details of the twin
boundaries could not be obtained because of low magnification.
The range
of grain sizes in these samples is estimated to be 1 to 100 pm.
To avoid the contamination, it was expected from the thermodynamic
point of view, that pelleting the Y2O3 , BaCC>3 and CuO mixture, reducing
the contact area between the pellet and the crucible, and lowering the
calcination and sintering temperatures, are required.
The samples, nos.
46 and 49, were made by reducing the calcination and sintering to 930°C
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53
Table 2(a).
Sample
Number
2
3
16
17
18
19
20
21
22
44
45
46
49
Preparation history of YBa2Cu307_g samples.
C a lc in a tio n
T em perature
950°C
950°C
1070°C
1000°C
1000°C
1070°C
1000°C
950°C
750°C
950°C
940°C
930°C
930°C
Table 2(b).
Time
24
24
24
21
21
24
21
24
24
24
21
24
24
S in te rin g
Atmoephere
hrs.
hrs.
hrs.
hrs.
hrs.
hrs.
hrs.
hrs.
hrs.
hrs.
hrs.
hrs.
hrs.
air
air
air
q
q
air
Q>
q
q
q
q
q
q
T em perature
Time
1000°C
1000°C
1030°C
16 hrs.
16 hrs.
18 hrs.
------18 hrs.
18 hrs.
18 hrs.
16 hrs.
20 hrs.
20 hrs.
20 hrs.
12 hrs.
12 hrs.
1030°C
1030°C
1030°C
975°C
1000°C
950°C
950°C
950°C
950°C
Coaling
Rate to
500°C
(°C/mln.)
2.0
2.0
1.3
—
1.3
1.3
1.3
1.0
5.0
2.0
2.0
2.0
2.0
A d d itio n a l
A nnealing
T em perature
Time
-------
-------
700°C
24 hrs.
900"C
900°C
24 hrs.
24 hrs.
900°C
30 hrs.
_
"
11
Resistances and superconducting transition
characteristics of the samples with the preparation history described in
Table 2(a).
Sample
Number
2
3
16
17
18
19
20
21
22
44
45
46
49
T
CO
Tc f
(K)
93.5
95.0
99.0
93.0
94.0
92.0
96.0
96.0
98.0
96.0
96.0
96.0
93.0
<K)
90.0
87.0
92.0
91.0
82.0
86.0
86.0
75.0
96.0
92.0
90.0
91.5
88.0
R esistance
at 298 K
(m ill
283.9
79.2
115.3
8.8
15.7
87.3
6.2
325.0
83.2
190.0
160.0
22.0
8.0
R esistance
to
R @ 298 K
(inQ)
R@to
120.0
5.8
63.8
3.1
4.8
55.2
2.8
184.0
32.6
100.0
62.0
7.8
0.51
2.43
3.36
1.81
2.84
3.27
1.58
2.21
1.77
6.99
1.90
2.58
2.82
2.96
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54
/
iO\HTl
i----------- •
(b)
Fig. 2.
SEM micrographs for sample nos. 19 [(a) and (b);
magnifications 370 and 2700, respectively] and 20 [(c) and (d);
magnifications 370 and 390, respectively],
(d) was taken before cleaning
with acetone.
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55
/OO/xm
>?*
!00\m
(d)
Fig. 2.
Continued.
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56
(b)
Fig. 3.
SEM micrographs for sample no. 21.
at magnifications 760 and 240, respectively.
(a) and (b) were taken
The micrographs were taken
after grinding and cleaning with acetone.
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57
and 950°C, respectively, with another condition mentioned above.
They
showed very little contamination on the contact areas and are assumed to
be single phase Yl^CujOy.^.
Table 3.
The
An XRD result for sample no. 46 are shown in
result is almost the sameas that of Beyer et al. [13] and
indicates that the sample contains
lattice constants are a - 3.82 A,
more than 95% of the single phase.
b - 3.89A
The
and c — 11.69A.
Although the data in Table 2 (b) are uncertain because of different
aging times in air, sample uniformity, surface effects, different
dimensions of the samples, etc., the following general trends could be
obtained.
A larger amount of the secondaryphases resulted in a larger
normal state resistance.
Tco was higher in
secondary phases than in single-phase samples.
some samples with much
Whether the cause of the
anomalous enhancement of Tco is the existence of the secondary phases with
high Tc or some kind of cooperation between the superconducting phase and
the secondary
phases, is not clear yet. The slow cooling rate seems to
result in the
small ratio of R298K to ®Tco' Tbis result seems reasonable
because of the slow cooling rate is believed to result in better relax­
ation of shear stresses resulting from tetragonal to orthorhombic
transition outside the grains and better uniformity of oxygen ordering,
and thus better uniformity of the orthorhombic oxygen-deficient structure
through the sample [16,22,23,110].
The samples sintered at temperature higher than 1000°C, were melted
partially, probably due to a low melting temperature of Ba-rich phase
[201], and were denser than those sintered at lower temperatures.
Actually, the sample no. 22 was very dense like glass.
was denser than the sample no. 16.
The sample no. 22
The possible reason seems to be a
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Table 3.
X-ray diffraction data for sample no. 46 (a = 3.280 A, b =
3.893 A and c = 11.688 A).
All peaks are the same as those of Beyer et
al. [13].
2e
hkl
(0 3 0 )^ ^
^
(100)
' / ' m a*(% )
2e
8.4
2.2
32.60
(001)
(021)
(130)
62.5
46.65
47.60
51.50
52.70
32.80
(131____ ^
(101 )
100
53.32
33.70
36.40
38.50
40.37
(111)
(121)
2.0
55.25
55.85
58.20
58.80
22.8
23.25
27.95
_______ -
•^(140)
(131)
4 .4
3.1
18.5 .
20.4
hkl
I !1 m a x (^ )
(060)
(200)
(002)
(151)
(0 6 ,^
(2 7
'
0
„
W
/(1 0 2 )
(221)
(122)
(161)
'"-(231)
(132)
28.9
15.7
6.20
5.60
3.60
3.40
2.20
44.8
18.8
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59
longer holding time in the sintering process.
For the sample sintered at temperatures below 1000°C, as the higher
pelleting pressure was applied, the lower normal state resistance resulted
in, probably due to enhanced contact between grains or less probably due
to larger grain sizes.
Fig. 4 shows the comparison of the resistive superconducting
transition behavior of a single phase YBa2Cu3C>7_5 (no. 46) to that of
multiphase samples (nos. 18 and 20).
Notice the transition characteristic
is much shorter in single-phase material than in multiphase materials.
In
the multiphase samples, the long tail of the transition is observed near
Tcf.
In granular superconductors, it is expected that the presence of
secondary phases makes the coupling probability between grains low and the
randomness of the coupling increase.
As the coupling probability is
temperature-dependent because the Josephson energy depends on the temper­
ature according to equation (1.9.2.1.2), the percolation in the multiphase
sample is expected to be completed at a lower temperature than in the
singlephase sample [81].
The variation of the critical current, Ic , with temperature is shown
in Fig. 5 for samples nos.
18 and 20.
Note that the rate of change of Ic
with temperature became sharper near Tc and was increased after annealing
the sample No. 18 at 900°C for 24 hours, as well as better transition
characteristic and electrical properties.
By comparing the transition
behaviors between the samples nos. 16 and 19, however, it is noted that
the transition temperatures may be lowered by annealing.
This implies
that the critical current is related not to the intrinsic property but to
the microstructure, possibly due to the flux pinning or better aligning of
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60
1
2
3
a
c
(0
in
‘55
o>
4
■o—
5
□
A
•
Sample 18
Sample 20
Sample 46
102
106
Limit of resolution
6
70
74
78
82
86
90
94
98
110
T em perature (K)
Fig. 4.
Comparison of resistive superconducting transition of a
single-phase sample (no. 46) with those of two multiphase samples (nos. 18
and 20).
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61
100
80
60
<
E
20
0
Fig. 5.
-
75
85
95
T(K)
The effect of an additional annealing on the critical
current in the multiphase sample no. 18 (A).
The sample no. 20 (o) was
prepared after annealing the sample no. 18 at 900°C for 24 hours.
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62
the grains or twins. This means that spheroidization of the grains and
removing the residual strain during the annealing may cause the
percolation threshold temperature to decrease due to the increased
junction width in granular superconductors [81], but the critical current
density to increase through the enhanced uniformity.
Fig. 6 shows the effect of an excess of C>2 in a Y-Ba-Cu-0
superconductor (sample No. 21).
The upper curve represents the change of
resistance with temperature, after keeping the sample at room temperature
and 3 atm pressure of oxygen for 3 hours. The excess of oxygen in the
sample hindered the electrical conduction, probably due to the locali­
zation of conduction electrons or holes captured by excessive oxygen (the
metallic conduction behavior in the YBa2Cu3C>7_£ material is believed to be
due to the hole from the positive value of Hall constant [75,208]). The
curve in Fig. 7 corresponds to the upper curve in Fig. 6 in a different
scale.
It shows a similar behavior with that observed by Beyers et al.
[191] for the YBa2Cu307_g sample for annealed at 670°C for 18 hours in 6
atm and slowly cooled.
The sample of Beyers et al. showed Tcf = 60 K, but
our sample did not show its superconducting state near 60 K.
The results about additional annealing effects are tabulated in Table
4.
The low-pressure pelleting in sample no. 54a resulted in a less dense
disk than sample no. 54b, and the degraded electrical properties and
superconducting transition characteristics.
This fact is one of evidence
that this superconductor is granular superconductor. Higher pelleting
pressure is expected to increase percolation probability among the grains
and the contact area.
Our result for the effect of additional annealing is inconsistent
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63
101
10 °
■ Sample 21
♦ #21,3 atm.O
Limitofresolution
60
70
80
90
100
110
120
130
140
150
160
Temperature (K)
Fig. 6. The effect of excessive oxygen on the variation of
resistance with temperature.
The lower curve corresponds to the
resistance variation of sample no. 21 with temperature.
The upper curve
was obtained after subjecting the sample no. 21 to 3 atm pressure of
oxygen for 3 hours.
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64
12
o
11
#21,3 atm. O
10
Resistance (£2)
9
8
7
6
5
4
3
2
50
Fig. 7.
70
90
110
130
150 170 190 210
Temperature (K)
230
250
270
290
310
Resistive behavior of sample no. 21 as a function of
temperature, after subjecting it to 3 atm pressure of oxygen for 3 hours.
This is an enlarged figure of the upper curve in Fig. 6 .
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Table 4.
Variation of superconducting properties with respect
additional annealing time at 700°C in flowing oxygen atmosphere.
Annealing
Time
(H ours)
R e sistiv ity
(@275 K) (@100 K)
Jc
(92 K)
(@t =t co)
(m£2-em)
(A-cm 2 )
(K)
(K)
0
96.5
94.5
1.45
0.55
5.1 x 1 0 2
2.39
18
98.5
96.0
0.32
0.11
5.3 x 102
2.04
36a
95.0
92.0
1.27
0.54
0. 29
0.16
36b
95.0
93.5
0.52
0.19
0.12
1.05
54
94.5
93.0
0.60
0.24
0.16
1.09
72
97.0
96.0
0.53
0.21
0.12
2.96
(m£2-cm) (m fl’Cm)
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66
with that of Penson et al. [43].
As many research groups have been
reported that more than 12 to 18 hours of additional annealing was not
recommended for the good superconducting properties (for example, see Ref.
52), our result may be correct.
For the convenience of comparing the change of physical properties
related to additional annealing, the Tco and Tcf versus annealing time are
plotted in Fig. 8, the change of electrical resistivity with annealing
time in Fig. 9, and the change of critical current density with annealing
time in Fig. 10.
Fig.
8 shows that the highest Tco was obtained from the sample No.
53, annealed at 700°C for 18 hours.
The Tco was decreased with increasing
annealing time, but suddenly increased at 72 hours annealing time.
The
transition width, ATC was decreased with increasing additional annealing
time.
It means that oxygen uniformity increases and the defect density
decreases with increasing additional annealing time.
Therefore, the
percolation randomness becomes smaller with increasing annealing time.
The sharpest transition was observed in the sample annealed for 72 hours.
From Fig. 9, it is shown that the lowest normal state resistivity was
observed with the sample annealed for 18 hours.
Fig. 10 shows that the Jc
was decreased with increasing annealing time up to 36 hours, and then
increased with further increase in annealing time.
The maximum Jc was
found in the sample annealed for 72 hours. This critical current density
is expected to be determined by the capability of carrying the super­
current in grain boundaries due to weak superconductivity in grain
boundaries, and by defects and their strain field which play a role of
pinning points against Lorentz force responsible for the motion of the
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67
100
99
98
97
Temperature (K)
□
o Tco (K)
♦ Tcf(K)
l
96
95
94
93
# 5 4 b (M ore D ense)
92
#5 4a (Less Dense)
91
90
10
20
30
_j_
_i_
40
50
60
70
80
Annealing Time (hours)
Fig. 8. Variation of superconducting transition characteristics with
respect to annealing time.
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68
1.4
54a.
Resistivity (mQ-cm)
1.2
Q
•
1.0
Rho (275 K)
Rho (100 K)
Rho (Tco)
a
0.8
54a.
0.6
fi — 54b
0.4
54a —A
0.2
A
A >
J
0.0
0
10
■
♦
A
.
I
i
J
20
30
40
54b
i
♦
A
L
50
60
70
80
Annealing Time (hours)
Fig. 9.
Variation of resistivities at 275 K, 100 K and Tco, as a
function of annealing time.
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69
4.0
3.5
3.0
Critical Current (A/cm
+
•
■
A
H
a
«
A
o
O
Sample 52
Sample 53
Sample 54a
Sample 54b
Sample 55
Sample 56
2.5
©
2.0
1.5
*
1.0
0.5
0.0
84
86
88
90
92
94
96
98
Temperature (K)
Fig. 10.
Variation of critical current density, as a function of
temperature, with annealing time.
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70
damped vortices. As subsequent annealing is expected to reduce the
density of defects and their strain field including shear strain field due
to the tetragonal to orthorhombic transition, it is reasonable that in the
early stage of the subsequent annealing, the critical current density is
reduced with increasing annealing time.
The anomalous increase in Jc ,
however, due to annealing for more than 36 hours is probably due to better
aligning the grains and twins [165].
To investigate the reason for this
anomaly, more detailed microstructural study is required.
It is also
worthwhile to note that the actual measurement of Jc by using the four
probe technique has lots of difficulties such as the surface effect,
junction potential and nonuniformity of the structure through the sample.
From the figures 8 to 10, however, it can be inferred that the
relatively short-time annealing is beneficial for the transition
characteristics, but not beneficial for obtaining a high critical current
density.
The magnetization curves in sample, no. 22, in which it is mainly
composed of Yl^CujOy.^ (black-colored and superconducting) and Y2BaCu05
(green-colored and semiconducting) are shown in Fig. 11 and 12.
measurements were done at 5 K.
Both
The magnetization curve of Fig. 11, in
which the sample was zero-field-cooled and the magnetic fields were
applied up to 1000 G, shows a significant hysteresis and an abrupt change
of slope near 50 G possibly due to decoupling between grains.
Then the
magnetization is increased at different rate, with field up to 1000 G
which is far below Hc^, because this sample was made at high sintering
temperature and some part of the sample was melted. There the super­
conducting grains has relatively low density of twin boundaries [41].
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71
00°OOoo oo0
00 O)
OOo,
°°°o(
°o
Mag.ceTTiu-GxicT')
OoOo
°Oo,OOO
0 OOOoooo<>
.5
-1000
-500 °°0
500°
-5V +
1000
°°°o 0
°°c
000000000°:::^
°8o,
°00oo°8iOOo
Field C G 3
Fig. 11.
The magnetization curve measured by Rubins et al. [207]
after sample no. 22 was zero-field cooled to 5 K.
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72
i>0
.
5-
.
'O
x
0
1
0
Z3
E
CD
+■
1000
500°°,
O'
TD
°o°
°°o°o„
°o
°°*o
-
°®o.
1
FieldCG)
Fig. 12.
The magnetization curve measured by Rubins et al. [207]
after sample no. 22 was zero-field cooled to 5 K and exposed to the field
of 5 KG briefly.
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73
This factor is reflected to the low remnant magnetization, 0.06 emu,
because the remnant magnetization consists of the trapped flux at grain
boundaries plus the trapped flux in twin boundaries. Therefore the sample
with higher density of twin will have higher remnant field and higher
critical current density.
The magnetization measurement of Fig. 12 was
done at 5 K after the field applied to the same sample had been raised to
5000 G.
The curve shows positive magnetization at initial weak fields,
due to the trapped flux. Notice that the decoupling field is shifted to
high value, indicating the remnant magnetization due to 5000 G has the
direction opposite to the field direction.
This was also confirmed by our
experiments on the microwave response at low fields [207].
Notice also
that the resultant remnant is almost same as that in Fig. 12.
This
implies that the remnant flux was cancelled with the applied field during
the field sweep to 1000 G.
In an effort to increase Tc, YF3 was substituted for Y2O3, to obtain
the nominal composition YBa2Cu3F30x . Two samples were made with 900°C
calcining temperature and 1000°C sintering temperature.
The difference in
the preparation procedure between the two samples was the calcination
atmospheres-air and flowing O2 . Both were sintered at flowing O2
atmosphere.
The sample calcined at air showed almost same transition
behavior shown in Fig. 13, as usual YBa2Cu30y, with Tc ~ 90 K.
However,
the sample calcined at flowing O2 atmosphere was found to be a semi­
conductor.
Both samples annealed at 900°C for 18 hours in flowing N2
atmosphere, were insulators.
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74
I O'
0
0
»o
0 0
©
• •
-I
S I01
to
’00
s
-2
o
10
©
I03
o
o4
o
00
lo 5
50
100
150
200
250
300
T ( K)
Fig. 13.
The resistance vs. temperature curve showing an resistive
transition characteristic in YBa2Cu3F30x calcined at air and sintered in
flowing oxygen atmosphere.
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CHAPTER III
MICROWAVE SPECTROSCOPY IN Y-Ba-Cu-0 BASED SUPERCONDUCTING MATERIALS
Microwave spectroscopy has proved to be a useful technique for
characterizing and studying the high-Tc superconductors [49,166,207,209,
210,211,212,213,214,215,216,217,218,219,220,221].
While characterizing
the superconducting transition via resistivity measurement requires a
continuous sample and good electrical contacts, the microwave technique
does not.
Even powdered samples can be used in the microwave technique.
The microwave spectrograms in the high-Tc superconductors are composed of
two distinct spectra - the conventional Cu^+ electron paramagnetic
resonance (EPR) spectrum and the low-field signal.
While the Cu^+ EPR
spectrum is observed both above and below Tc , the low-field signal begins
to appear through the transition, indicative of the superconducting state.
The Cu
EPR system has been used to study the crucial role played by
9+
Cu^T in the occurrence of high-Tc superconductivity through the experi­
mental parameters which are g-values, linewidth, line-shape and signal
intensity [207,209,210,211,212,213,214].
While the low-field signal has
been used to study the magnetic and thermal responses of the super­
conductors, through the dependence of the signal on the preparation
history, the surface dimensions and the magnetic history of the sample,
and on the other experimental parameters such as the frequency and power
of the microwave, the amplitude and the frequency of the ac modulation
field, the range of the dc field sweep [166,214,215,216,217,218,219,220,
221,222,223,224,225] .
75
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76
Much more attention has been paid to the low-field signal due to its
unusual occurrence, regarding its origin and its dependence on the
experimental parameters mentioned above.
3.1
Experimental Set-Up for the Microwave Response of the Y-Ba-Cu-0
Superconductors
For the experiment on the microwave spectroscopy of Y-Ba-Cu-0 based
superconductors, we used Helmholtz coils made of copper wires with a HP
6427 B dc power supply to obtain a zero-field, low fields and negative
fields in a directional sense with respect to swept dc fields, in addition
to the conventional Ku-band spectrometer including a Varian type 12-inch
electromagnet for dc magnetic fields for sweep with a Field Dial V-Fr 2501
power supply. Modulation of the dc magnetic field was provided by a Kepco
75-5(M) bipolar power supply with the reference provided by PAR 121
lock-in amplifier phase detector.
The whole of the spectrometer is
schematically shown in Fig. 14.
A Varian type X-12 reflex klystron, which has a frequency range 12.4
to 18 GHz, was employed to generate 15.0853 GHz frequency microwave with a
maximum output 430 mW.
A HP 716B power supply was used to heat the
filament of the klystron and supply power to reflector, resonator and
cathode electrodes.
The microwaves were guided to an isolator to permit
the transmission of microwaves in the forward direction.
A part of the
microwave was coupled to a FXR type Y410 A wavemeter with frequency range
12.5 to 18 GHz by a directional coupler, and to a CRO.
The rest of the
microwave was divided into an HP 5246 L electronic counter and an HP P382
A variable attenuator.
The counter with HP 5256 A frequency converter
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77
Isolator
Klystron
Wave Meter
Electronic Counter
with Frequency
C onverter
DC
Power Supply
Variable
A ttenuator
Magnets
Magnet Power
Supply
3-Port Melabs
C irculator
Jjrost^Sam pleJ’
Bi-poiar Power
Supply / Amp
Magnets
D etector
A m plifier
R e-transm ltting
Potentiom eter
X-Y Recorder
Fig. 14.
Lock-In Amplifier
Phase Detector
T ransform er
Current Meter
Schematic diagram of I^-band spectrometer.
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78
allowed direct measurement of the microwave frequency.
The microwave
passed through the attenuator, was coupled to a 3-port Melabs circulator.
The circulator was employed to divert the
microwave energy to the sample
and to direct that coming back from the sample to the detector mount which
housed a Microwave Associate MA 4325 A Schottky barrier diode.
This diode
was coupled by a transformer to a PAR CM 113 low-noise preamplifier.
The
preamplifier was operated in the Hi-Z mode in order to obtain the proper
impedance matching with the transformer.
The signal from the preamplifier
was demodulated by the PAR 121 lock-in amplifier/phase detector.
spectra were recorded by a HP Moseley 7005B x-y recorder.
The
The x-drive was
obtained from a retransmitting potentiometer coupled to the magnetic field
sweep and the y-drive from the output signal of the lock-in amplifier/
phase detector.
The signal obtained on the x-y recorder is usually the
field-derivative of the absorption of microwave energy by the sample.
To control the temperature of the sample, two coils made of
constantan were employed.
Each coil has 10 fi.
Power was supplied by a
Calrad variable transistorized dc power supply.
The temperature of the sample was measured by 3 thermometers.
One
was a constantan - copper thermocoupler connected to a Newport type E
digital thermocouple indicator.
Another was an Omega 2 PA 100 RR663
platinum resistor connected to a Keithley 196 system DMM by 4 probe
measurement.
The third was a standard 100 ft resistor made of carbon and
connected to a HP 3440 A digital voltmeter with a HP 3444 A dc multifunction-unit.
The non-resonant cavity was made of MACOR™ machinable glass-ceramic
and coated with silver paint, to obtain better sensitivity.
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For the zero-field and the low fields less than 100 G, a F.W. Bell
STB 1-0404 gaussmeter probe was used with a Bell 610 gaussmeter.
The
gaussmeter was calibrated by using a RFL 1890 gaussmeter.
For almost all of our microwave experiment, a conventional EPR
geometry was used, in which the magnetic field of the microwave was
perpendicular to the dc sweep fields.
The microwave field parallel to the
dc field was also employed by rotating the dc field by 90°.
No difference
between the spectra in the perpendicular and parallel geometries were
found.
When the term, zero-field cooling (ZFC), is used, it means that the
sample was quenched to a certain temperature below Tc from a temperature
higher than Tc at zero dc field and a certain ac field used to obtain the
spectrum, except for Figs. 17 and 18.
For this microwave response, sample nos. 2, 21, 22, 52 and 56 were
used. Some of the data were taken by Rubins et al. [207] at Montana State
University. The sign of their spectra is conventional and opposite to that
of our spectra.
3.2
Results
The whole spectra near Tc in sample no. 2 are shown in Fig. 15 for
fields between zero and 8 KG.
It shows the appearance of the low-field
signal through the normal - to superconducting - state transition.
Therefore the existence of the low-field signal at a certain temperature
means that the sample is in the superconducting state at that temperature.
Note that at the temperatures below Tc , the intensity of the low-field
signal is significantly increased with decreasing temperatures near Tc ,
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80
84 K
88K
94K
0
Fig. 15.
5 KG
8 KG
The whole of spectra in sample no. 2 near Tc (= 92 K) . The
low-field signal appeared through the superconducting transition.
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81
while the high-field Cu^+ signal intensity is changed slightly.
3.2.1
Low-Field Signals
Figure 16 shows spectra in low fields for sample no. 22, which is a
multiphase material, near zero-field after zero-field cooling (ZFC) to 77
K.
1.18 G of the modulation amplitude (Hm) was used.
Each spectrum was
obtained by raising subsequently the upper or lower limit of the sweep
field range by 10 G.
Through all spectra, the positive and negative
signal peaks appeared at the positive magnetic field side.
The appearance
of positive and negative signal peaks at the positive field side, was due
to nonlinear response of the Hall probe to the ac modulation field present
when the field was measured.
the center of the signal.
The actual zero-field is expected to be at
Among all spectra, the maximum signal intensity
appeared for the sweeping from 20 to -30 G, which is (E). After (E), the
signal intensity was gradually decreased by repetition of the sweep with
the increasing field range.
The signal peak field was increased by
repetition of the sweep with the increasing field range, indicating that
the response of the sample to the low and high limits of the sweep fields
became important. Khachaturyan et al. [218] reported that the signal peak
is dependent on temperature, modulation amplitude and prior magnetic
history. Glarum et al. [219] also reported that the peak-to-peak height
and width are dependent on temperature.
In our case, the field at which
the positive signal peak was observed varied from 6.4 to 11.5, which is
consistent with the value observed by Khachaturyan et al. [218] - 8 G for
YBa2Cu30y . The field at which the signal peak was observed, depended on
the maximum field intensity in the field sweep prior to the sweep.
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As
82
-30G
Fig. 16.
0G
30G
The spectra near zero-field for sample no. 22 after ZFC to
77 K with Hm ■= 1.18 G.
Each spectrum was obtained by raising the upper
and lower limits of the sweep field range by 10 G.
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OG
-IOOG
Fig. 16.
IOOG
Continued.
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84
continually increasing sweep ranges were applied, the negative peak in the
forward sweep and the positive peak in the reverse sweep become flat, and
the spectrum from the forward sweep became asymmetric to that from the
reverse sweep.
The flattening of the signal peaks as well as their shift
is expected to be due to the trapped fluxes during the forward and reverse
field sweeps.
Note that the signal intensity was suddenly increased at
the spectrum (C'), and it was returned to its earlier value at (E').
Figure 17 shows the variation of the peak-to-peak signal height
(Ap.p) and width (Hp.p) with modulation field, in sample no. 52, ZFC to 77
K from 110 K without an ac field.
ing modulation amplitude.
Both parameters increase with increas­
Blazey et al. [216], however, reported that in
YBa2Cu307_£, the signal intensity first decreased with increasing modu­
lation amplitude and then increased linearly with the amplitude.
turn-over amplitude was near 0.9 G.
The
As our result was obtained in the
modulation amplitude range 0.95 to 23.69 G, it can be said that our result
is consistent with theirs.
Blazey et al. [223] also reported that in
Lai.85 Bap,15 CuO^, the field at the signal in forward and reverse sweeps
merge decreased with increasing modulation amplitude in a modulation
amplitude range 1.25 to 10 mG.
Our result, however, showed that the field
seemed to respond nonlinearly to the modulation amplitude.
The noise
intensity was increased with decreasing Hm .
Figure 18 shows the variation of the peak-to-peak signal height
(Ap.p) and the dc component of the absorption with the microwave power.
All points were obtained at 77 K after the sweeps for Fig. 17.
The dc
components of the absorption were measured with a current gauge coupled to
the transformer.
The Ap.p and the dc component increased almost linearly
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85
180
160 *
140
V)
120
S3
fe.
100
<
Q.
CL
<
•a
c
cu
O
£
40
X
p-p
p-p
0
2
4
6
8
10
12
14
16
18
20
22
24
H m (G)
Fig. 17.
Variation of the peak-to-peak signal height (Ap.p) and
width (Hp.p) with Hm , in sample no. 52, ZFC to 77 K without ac field.
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86
250
ra 100
9-
Fig. 18.
50
Variation of the peak-to-peak signal height (Ap.p) and the
dc component (Idc) of the absorption with microwave power in sample no.
52, ZFC to 77 K without ac field.
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87
with increasing power level.
spectra became significant.
As the power was increased, the noise in the
This fact may be related to the appearance
and widening of the second series with increasing microwave power,
observed by Blazey et al. [221].
Figure 19 shows the time dependence of the low-field signal.
The
spectrum (A) was obtained after the sample had been at -100 G for 3
minutes after (N') in Fig. 16.
The spectra (B) and (C) were obtained
successively following a 10 minute wait after (A). The signal intensities
were reduced, relative to that of (N') in Fig. 16.
These features tell
that the low-field absorption may be related to the superconducting glass
state through the time dependence of the magnetization.
It may mean that
as the sample becomes stabilized by approaching an equilibrium, the
absorption signal becomes small.
Figure 20 shows spectra for sample no. 22 swept at the exactly same
conditions as that for Fig. 16, except that the first sweep was done from
0 to positive 10 G.
The sample was heated to around 200 K after the
sweeps for Fig. 19, and then ZFC to 77 K.
The signs of the spectra were
totally reversed with respect to those for Fig. 16 and 19.
shift was observed.
No base line
Blazey et al. [166] reported the sign change between
forward and reverse sweep at 0.005 G modulation amplitude and that the
sign change was independent of microwave power and modulation frequency.
They explained this sign change by the change of the free fluxon density
through the critical state theory [83, 87].
Glarum et al. [219] also
observed the sign change due to the change of sweep direction at 0.006 G
of modulation amplitude.
Both of the groups did not observe the sign
change at modulation amplitude as high as 1.7 G.
The spectra in Fig. 20
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88
-IOOG
Fig. 19.
OG
The time dependence of the low-field signal.
IOOG
The spectrum
(A) was taken after holding the external field of -100 G for 3 minutes
after (N') in Fig. 16.
The spectra (B) and (C) were obtained successively
after holding the external field of 100 G for 10 minutes after (A).
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89
i____________________I__________________ I
-30G
Fig. 20.
0G
30G
The different sign of the spectra from that in Fig. 16.
The spectra were obtained in sample no. 22 after heating up to 200 K and
ZFC to 77 K.
All the conditions were kept same as those in Fig. 16.
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90
K ->
-IOOG
Fig. 20.
OG
IOOG
Continued.
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91
do not change sign through changing of the sweep direction.
The same sign
change was also observed in sample no. 52 which is a single phase YBa2Cu3*
C>7_£ specimen.
The spectra shown in Fig. 21, when the sample was ZFC to
77 K from 168 K and held for 51 minutes at that temperature, had the same
sign as that in Fig. 16.
When the same sample was ZFC to 77 K from 137 K
and held for 8 minutes at that temperature, the resulting spectra are
shown in Fig. 22, in which the signal sign is the same as that in Fig. 20.
The experimental condition for Figs. 21 and 22 is the same as that for
Figs. 16, 19 and 20, except that the modulation amplitude increased by a
factor of two.
To see if the sign change is due to the presence of the ac
modulation when the sample was zero-field cooled to 77 K, the sample No.
52 was zero-field quenched to 77 K from 300 K in the absence of the
modulation field.
The resulting spectra also had two different signs.
Therefore, it was identified that the different signs of the signals did
not arise from the effect of the presence of ac field when the sample was
zero-field cooled.
16 and 21.
The sign of the spectra was the same as those in Fig.
Because a nonresonant cavity was used and our spectrometer is
sensitive only to the absorption, not the dispersion signal, it is not
expected that the signal sign change would arise from the instrument.
Comparison of the spectra in Figs. 16 and 20 shows that in very low
fields, the signal intensity in Fig. 16 became larger up to the sweep field
range 20 to -30 G, while that in Fig. 20 became smaller up to the sweep
field range -20 to 30 G.
Up to those ranges, the peak-to-peak field width
(Hp.p) was increased with increasing field sweep range.
At the larger
field ranges than those, the signal was roughly stabilized in both cases.
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92
OG
-IOOG
Fig. 21.
IOOG
The spectra obtained from sample no. 52 ZFC to 77 K.
The
spectra were obtained by lowering the zero-field to -100 G and sweeping
subsequently, with Hm - 2.37 G.
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93
-IOOG
Fig. 22.
OG
IOOG
The spectra obtained from sample no. 52 ZFC. to 77 K
the conditions were kept same as those in Fig. 21.
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All
94
To investigate the contribution of the negative field on the spectra,
sample no. 22 was scanned from zero to only positive fields increased by
20 G each cycle, after ZFC to 77 K from the normal state.
All the
conditions for the scanning were the same as those for Fig. 16, 19 and 20.
The resulting spectra are shown in Fig. 23.
By comparing these spectra
with those in Fig. 20, it is noted that the prominence of the positive
peaks still remain in forward-swept spectra in Fig. 23 in contrast to
their flattening in Fig. 20.
Therefore, it is inferred again that the
flattening of the negative signal peak in Fig. 20 is related to the
trapped flux due to the previous forward field sweep.
As the magnitude of
the applied field increases, the magnitude of the trapped flux increases
and hence the negative peak becomes more flat.
As the signal intensity in
Fig. 23 is much less than that in Fig. 20, it can be inferred that the
signal intensity is related to interaction between the trapped flux due to
the negative sweep-field and that due to the positive sweep-field.
Figure 24 shows the effect of the upper field in the sweep field
range on the peak-to-peak field (Hp.p) and the effect of successively
sweeping the field from -200 to 200 G on the signal intensity.
The
spectra were obtained by lowering the field to zero-field after (N') in
Fig. 20 and sweeping first the magnetic field from zero to 100 G.
Increasing the upper field to 150 G resulted in a shift of the positive
peak to negative field and the decrease in the signal intensity.
Khachaturyan et al. [218] reported that at 15 K, applying a magnetic field
greater than 100 G began to reduce the signal intensity and the decrease
in the signal intensity was saturated by applying 600 G.
In our case, the
signal intensity was also decreased by applying fields higher than 30 G.
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95
I-------------------------------------------------------- 1
OG
Fig. 23.
Hm = 1.18 G.
IOOG
The spectra obtained from sample no. 22 ZFC to 77 K , with
The sweep fields have only one sign.
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96
200G
Fig. 24.
200G
The spectra A, B, C, D, E and F were obtained by raising
the upper and lower limits of the sweep fields by 50 G, after (N') in Fig.
20.
The spectra F to N are ones which showed the anomalous increase or
decrease in the signal intensity through 41 continuous cycles in a sweep
range of -200 to 200 G after (E) .
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97
As the sweeps proceeded successively in the sweep range of -200 to 200 G,
the signal intensity continued to decrease.
However, the sudden increase
in the intensity in both sweep directions, as in spectra (I), (M) and (N),
was observed by carrying out 41 sweeps for 3 hours after (N). In those
spectra in which the signal intensity increased anomalously, the signal
peak field seemed to move to a higher field.
This could possibly be due
to the interaction between the trapped fluxons (the mixing of the vortex
states) or the interaction between the applied field and the mixed vortex
states during the reconfiguration process of the trapped flux.
Figures 25, 26 and 27 show hysteresis due to flux trapping caused by
the upper field of the field sweep.
The upper field was increased to 200,
800 and 2300 G, successively, after the successive 41 sweeps in Fig. 23,
while the lower field was held at -200 G.
As the signal sizes were
reduced by the previous cycles, the modulation amplitude was increased to
4.7 G and the sensitivity increased by a factor of 10 from that for Figs.
16, 19, 20 and 21 to obtain a comparable signal size to that obtained
originally.
The hysteresis and the flattening of the negative signal peak
became significant with increasing upper field, suggesting that the
trapped flux is dependent on the magnitude of the upper field.
To investigate the effect of trapped flux due to suddenly applied
magnetic fields on the signal, 1, 5 and 10 KG fields were applied to the
sample No.
22 for 30 seconds successively after ZFC to 77 K.
Because
of the slow response of our electromagnet, it actually took around 10
seconds to raise the field to 10
KG
and to lower it to zero field,
respectively. The corresponding spectra are shown in Figs. 28 and 29.
modulation amplitude was held at 4.7 G, the same value as that in Figs.
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The
98
OG
-200G
Fig. 25.
200G
The spectra in sample no. 22 when the sensitivity and the
modulation amplitude were increased by a factor of 10 and 4, respectively,
from those in Fig. 24.
The spectra were obtained after 41 continuous
cycles shown in Fig. 24.
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99
L
-200G
Fig. 26.
_L
OG
200G
400G
600G
800G
The spectra obtained by raising the upper limit of the
sweep field to 800 G after sweeps in Fig. 25.
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100
-200G 0G
Fig. 27.
1KG
2KG 23KG
The spectra obtained by raising the upper limit of the
sweep field to 2.3 KG after sweeps in Fig. 26.
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101
L
I
---------------------------- 1--------------------------- _j
0G
Fig. 28.
I75G
350G
The spectra obtained after sample no. 22 was ZFC to 77 K
and the external fields of 1 (A, B) and 5 KG (C, D) were suddenly applied
for 30 seconds, respectively.
Hm = 4.7 G.
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102
OG
Fig. 29.
350G
The spectra (A) and (B) show an anomalous sign change when
a field of 10 KG was suddenly applied after (D) in Fig. 28.
The spectra
(C) and (D) were obtained by repetitive sweeps after (B).
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103
25, 26 and 27.
However, the sensitivity was reduced by a factor of 5 for
the spectra (A) and (B) in Fig. 28 and by a factor of 10 for the spectra
(C) and (D) in Fig. 28, and (A), (B), (C) and (D) in Fig. 29.
(A) and (B), and (C) and (D) in Fig. 28 are the spectra for 1 and
5 KG applied fields, respectively.
When 10 KG was applied suddenly and
removed, the sign of the spectrum was changed as shown in (A) and (B) in
Fig. 29.
When the field was swept from 0 to 350 G again to identify the signal
sign change of (A) and (B) in Fig. 29, however, the spectra (C) and (D) in
Fig. 29 appeared with noticable noise.
The spectra (A) and (B) were the
characteristic spectra, which appeared when sample no. 22 was field cooled
to 77 K at higher fields than 1 KG and the field was removed.
Note also
that the signal sign is the same as that of the spectra in Fig. 22
obtained from the single-phase sample no. 52, ZFC to 77 K from 137 K. This
signal was also broadened by trapped flux.
Therefore, the sign difference
possibly can be related to the interaction of the trapped flux due to the
suddenly applied magnetic field with the trapped flux due to the previous
magnetic history.
In Fig. 28, the hysteresis due to trapped flux became greater, as the
suddenly applied field was increased to 5 KG.
The shift of the remnant
signal at zero field due to the suddenly applied fields appeared to be
significant.
The shift for the 10 KG
applied field became less signif­
icant as shown in (C) and (D) of Fig. 29, probably due to the anomalous
sign change shown in (A) and (B) of Fig. 29.
To identify whether the appearance of (A) and (B) in Fig. 29 was
real, the same experiment was repeated by heating the sample to 200 K and
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104
ZFC to 77 K.
The resulting spectra are shown in Fig. 30.
Every experi­
mental setting was the exactly same as that for Fig. 29, except that the
sweep field range was reduced to the range zero to 100 G.
Sweeping the
magnetic field from zero to 100 G to see the line-shape induced by the
ZFC, resulted in (A) and (B) which are the same as those in Fig. 20.
The
spectra after applying 1 and 5 KG for 30 seconds are shown in (C) and (D),
and (E) and (F), respectively.
The signal shape was almost flat. In (D),
the spectrum was shifted to right side from (C), due to additionally
trapped flux by the sweep to 100 G, while there was no difference between
(E) and (F). By comparing all the spectra in Fig. 28 and the spectra (C)
and (D) in Fig. 29 with the spectra in Fig. 30, it can be inferred that a
state in which the signal has a negative sign on the positive field side
is more sensitive to the suddenly applied field than that with a positive
signal sign on the positive field side.
Fig. 31 shows the temperature dependence of the flux trapping at
sample no. 22.
The spectra were obtained by Rubins et al. [207] at
temperatures between 76 and 4 K, with 20 G modulation amplitude.
spectra were obtained by applying 9 KG
spectrum was run.
The
for a short time before each
Note that as their sign convention is opposite to ours,
the signal shape is basically same as that in Fig. 20 and 22.
As the
temperature decreases, the signal peak becomes flat and is shifted to the
positive field side.
Therefore, it can be concluded that maximum trapped
flux increases with decreasing temperature.
Fig. 32 shows the effect of decay of the remnant magnetization in the
sample no. 22 FC at 10 KG to 77 K.
The spectra (A) and (B), (C) and (D),
and (E) and (F) were obtained by sweeping successively from zero to
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105
I_______________________________________ I
OG
Fig. 30.
to 77 K.
IOOG
The spectra (A) and (B) were obtained in sample no. ;
The spectra (C) and (D), and (E) and (F) were obtained by
applying suddenly the fields of 1 and 5 KG after (B) , respectively.
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ZFC
106
76K
48K
28K
4K
0
Fig. 31.
500G
I000G
The spectra obtained in sample no. 22 ZFC to different
temperatures and briefly exposed to 9 KG each time.
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107
— $>
0G
Fig. 32.
to 77 K.
The spectra obtained in sample no. 22 field-cooled at 10 KG
The spectra were obtained successively at times 2 min. (A, B),
11 min. (C, D) and 30 min. (E, F) after removing the field of 10 KG.
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108
500 G at 2, 11 and 30 minutes, respectively, after removing the field of
10 KG.
The modulation amplitude and the sensitivity were kept at the same
values as those for Fig. 28.
As the remnant magnetization of the FC
sample has the opposite direction to the magnetization induced by the
forward field sweep [10], the spectra shown in Fig. 32 are believed to
involve the interaction between the different magnetizations.
The remnant
magnetization decays as the time after removing the field of 10 KG
passes.
The decay is the stabilization process to an equilibrium.
The
result of Fig. 32 indicates that as the sample becomes more stable, the
signal intensity becomes weaker. Therefore it can be inferred that the
remnant magnetization decays with time in the manner of making the sample
becomes insensitive to the microwave.
In the spectrum (B), the trapped
flux due to the field sweep up to 500 G in the sweep (A) caused the
spectrum to be shifted to the right.
As the time passes, the shift seemed
to remain constant, but the intensity was reduced.
To eliminate the effect of the trapped flux due to the previous
sweep-fields, the sample was each time heated up to the normal state,
field-cooled at 10 KG to 77 K and scanned at 11 and 30 minutes after the
field of 10 KG was removed.
The resulting spectra are shown in Fig. 33.
Evidently, as the time passes, the signal intensity and the effect of
trapped flux due to the forward field sweep on the intensity in the
reverse sweep were reduced.
It means that as the sample becomes stabi­
lized due to the decay of remnant magnetization, the effect of addi­
tionally applied field on the magnetization state of the sample becomes
smaller.
Therefore, the rate of change in flux density with the sweep
field becomes smaller.
As it is believed [216] that the absorption
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109
Fig. 33.
to 77 K.
The spectra obtained in sample no. 22 field-cooled at 10 KG
The spectra were obtained at times 11 min. (A, B) and 30 min.
(C, D) after heating up the sample to its normal state, FC and removing
the field of 10 KG, after each cycle.
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110
is proportional to the free fluxon density, the rate of change in the
microwave conductive loss with sweep-field becomes smaller [220].
Fig. 34 shows the anomalous behavior in the microwave absorption in
the sample no. 22.
The spectra were obtained at the same condition as
that for Fig. 32 and 33, at 19 min. (A, B), 29 min. (C, D) and 42 min. (E,
F) successively, after taking the spectra (A) and (B) in Fig. 33 without
additional thermal-eyeling.
The sign change in spectrum (A) can possibly
be related to the interaction of the remnant magnetization due to FC with
the trapped flux due to the previous magnetic history.
Furthermore, the
sudden sign change in the spectrum A seems to have the same nature as that
for the spectra A and B in Fig. 20 or (and) that for the sign change
between Fig. 21 and Fig. 22.
The implication of these anomalies is that
there exists a critical state in which the absorption changes. It is
expected that this critical state has a different origin from that
suggested by Bean [83] and Kim et al. [87]. It is possibly associated with
the existence of great effective capacitance in the intra-granular
Josephson junctions through twin boundaries [139].
The important aspect
of the sign change is that it occurs frequently and easily.
This fact
could be related to the magnetic chaos reported by Datta et al. [156].
Note that although much noise was observed in the spectra (A) and (B),
it disappeared in spectrum (C). This noise could probably be due to the
trapped flux in the junction area or in the nonsuperconducting area
surrounded by the superconducting current loop.
Fig. 35 shows the spectra for the field-cooled sample no. 52 at
1 KG to 77 K from 168 K.
Then the spectra were obtained at 2 minutes
after lowering the field of 1 KG to -100 G, with a modulation amplitude
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Ill
— s>
< .■■■
I__________________ :
____________________________________I
OG
Fig. 34.
to 77 K.
500G
The spectra obtained in sample no. 22 field-cooled at 10 KG
The spectra were successively obtained at 19 min. (A, B), 29
min. (C, D) and 42 min. (E, F) after taking the spectra (A) and (B) in
Fig. 32.
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112
I_____
-IOOG
Fig. 35.
to 77 K.
0
IOOG
The spectra obtained in sample no. 52 field-cooled at 1 KG
The signals were locally modulated by the decay of the remnant
magnetization.
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113
2.4 G.
The signal sign was the same as those typically obtained from the
field-cooled sample no. 22.
In the spectra for the field-cooled sample
no. 52, however, the signal appeared to be modulated by local peaks with
rounded saw-tooth shape.
For the field-cooled sample at 1 KG, the local
peaks had a periodicity, 7.3 G.
When the same sample was field-cooled at
5 KG to 77 K from 138 K, the periodicity was approximately 9.3 G, as can
be seen in Fig. 36.
Note the shape difference in local peaks between in
the increasing field-magnitude (neglecting the sign of the field) sweep
and in the decreasing field-magnitude sweep, and between in the 1 KG
field-cooled and the 5 KG one.
As the field used in the field-cooling
increased, the shape during the increasing field-magnitude sweep became
sharp and the shape during the decreasing field-magnitude sweep became
flat.
From the difference in the shape and the periodicity of the local
peaks between in Fig. 35 and in Fig. 36, it can be inferred as follows.
This field-cooled sample is in the superconducting glass state, which
is composed of many clusters of superconducting current loops with
different coupling strength in the junctions, different loop size and
random distribution.
As the sample is field-cooled at a field larger than
Hci, weakly-coupled junctions are decoupled, and relatively stronglycoupled junctions remain coupled with a reduced coupling strength due to
trapped flux.
In this case, as the field used in the field-cooling
increase, the stronger loops will trap greater number of fluxons. There­
fore, relatively large field-gradient in the strongly-coupled junction is
necessary for a flux jump to occur through the junction during the
increasing field-magnitude sweep. Remember that the flux quantum is
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-IOOG
Fig. 36.
to 77 K.
0
IOOG
The spectra obtained in sample no. 52 field-cooled at 5 KG
The signals were locally modulated with longer periodicity and
step-like shape due to the decay of the larger remnant magnetization than
that in Fig. 35.
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115
the product of the magnetic field and the phase-coherent area and the area
will increase with the magnitude of the cooling field.
Therefore, the
shape will become steeper and the periodicity will relatively increase
with the cooling-field magnitude.
During the decreasing field-magnitude,
releasing the trapped flux occurs relatively easily.
Fig. 37 shows the enlarged picture of the local peaks of the spectra
in Fig. 36 during the decreasing (A) and the increasing (B) fieldmagnitude sweep, by increasing the sensitivity by a factor of 5.
two-basic signals.
It shows
One is due to flux jump mentioned above. Another is
ambiguous in this case, whether it is instrumental noise or noise due to
the damped motion of fluxon in the superconducting matrix [220] or in the
Josephson junction area, because of high modulation field amplitude (2.4
G). Recently, Tyagi et al. [226] reported two noise structures observed
in the single phase YBa2Cu30y, with a modulation field of 0.05 G. They
interpreted that the latter would arise from the flux reconfiguration in a
magnetically viscous medium.
Stankowski et al. [227] attributed the
absorption to the Josephson oscillation.
Therefore there remains two
possibilities for the latter noise.
One is due to the damped oscillation
of fluxons for the reconfiguration.
Another is due to incoherent
Josephson absorption.
However these two may be related to each other,
because it is largely possible for the reconfiguration of flux to occur at
the site where the incoherent coupling can be established.
This may be
related to the structure of the critical state driven by the modulation
field [228].
The locally modulated signals shown in Figs. 35, 36 and 37
can possibly be due to bubbling of liquid nitrogen present inside the
dewar used for these experiments.
This effect, however, is expected to be
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116
CB>
JOG
Fig. 37.
in Fig. 36.
The enlarged feature of the locally modulated signal shown
These were obtained during a forward sweep with the increased
sensitivity by a factor of 5 from that in Fig. 36.
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117
very small.
The spectra obtained with a modulation amplitude 2.36 G when the
sample No. 52 was zero-field cooled to 4.2 K, are shown in Fig. 38.
The
peak-to-peak height of the spectra is much decreased due to the low
temperature.
This is attributed to the reduced ratio of the microwave
penetration depth to the induced current relaxation length (static
penetration depth) with decreasing temperature [228,229].
The peak-
to-peak width becomes much broader compared to that at 77 K.
This means
that the critical current density increased greatly with the decreased
temperature through the increase in Josephson energy, resulting in the
much stronger screening strength.
Thus, higher magnetic pressure at 4.2 K
is required for the magnetic field to penetrate up to the same position
inside the sample than at 77 K.
Khachaturyan et al. [218], however,
reported the temperature independence of the signal peak position and
ascribed it to the grain size dependence and relatively temperature
independence of A^ and the penetration depth, Aj, into the junction area
for the case R < Aj or R < A^ where R is the grain size.
However, their
argument is successful only when one is concerned about the intergranular
junction [230].
In their magnetic field region, almost all of inter­
granular junctions are decoupled [160] and intragranular effects dominate.
In this case, the penetration depth into intragranular junction is less
then the twin size.
The signal peaks become more flat with decreasing
temperature, suggestive of the temperature dependence of the maximum
trapped flux due to the prior magnetic field and of the screening strength.
The spectra at 4.2 K shows another signal peak near zero-field. This is
expected to be due to the cancellation of the trapped flux by the applied
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118
'\VJS
-306
Fig. 38.
0
-- ,J
30G
The spectra obtained with a modulation amplitude 2.36 G in
sample no. 52 ZFC to 4.2 K.
The lower and upper limits of the sweep
fields were first increased gradually by 10 G each time, then by 30 and 20
G.
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119
-IOOG
Fig. 38.
0
IOOG
Continued.
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120
I________________________________________ I____________________________________ i
-1006
Fig. 38.
0
100G
Continued.
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121
field, which was also observed in the spectra obtained without modulation
by Pakulis and Osada [47].
Note that the remnant magnetization is oppo­
site in sign to the diamagnetic response of the sample to the external
field.
Note also that the signal is almost noiseless following ZFC, while
the noise starts to appear when there is trapped flux inside the sample.
This is a strong evidence of reconfiguration of the flux.
Fig. 39 shows spectra when the sample was exposed to 1 KG for 30
seconds after the run for Fig. 38.
The whole spectrum becomes almost flat
after the brief exposure to 1 KG, suggesting that the flux trapping at low
temperatures is significant.
When the static magnetic field was scanned up to 6.5 KG, the spectra
became totally chaotic, on repitition of the field sweep, suggesting that
the interaction between the trapped fluxes and between the trapped flux
and the induced supercurrent, is significant at low temperatures.
3.2.2
High-Field EPR Signals
Conventional EPR signals were studied in sample nos. 2, 21, 22, 52
and 56 in the temperature region from room temperature to lower
temperature below Tc . All the samples studied showed different lineshapes at room temperature and different temperature dependences of the
line-shape and signal intensity.
Common features of the line-shapes in
all the samples were axial symmetry at room temperature, and the axial
symmetry is reduced or becomes isotropic near Tc . When the sample No. 52
was investigated, no signal could be found with our non-resonant cavity
system, while the sample was put in the spectrometer more sensitive by an
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6
•1006
Fig. 39.
0
1006
The spectra obtained after sweeping (Q) in Fig. 39 and
applying the field of 1 KG for 30 seconds.
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123
order of 3 than ours, it also showed an axial symmetry from room temper­
ature to 107 K.
The spectrum becomes isotropic at 107 K and disappeared
on passage through Tc . However, the samples nos. 52 and 56 showed a
different axial symmetry down to 109 K and became isotropic below 101 K.
It may be believed that this high-field signal is due to Cu ion (Cu+ ,
Cu^+ or Cu^+) contained in the impurity phases usually present in the
ceramic Y-Ba-Cu-0 compound.
The different shape and the different
temperature dependence of the signal are believed to depend on the
relative amount and the type of the impurity phases, such as Y2BaCu05
[211,231,232], Y2Cu205 [211] and BaCu02 [211].
3.3
Discussion
Up to now, on the basis of the experimental results which includes
the dependence of the signal on preparation history [49,139,166,225],
magnetic history [49,139,166,207,218], surface dimensions [220], oxygen
content [217], temperature [49,139,166,207,217,218,222,227,228,229],
microwave power [221,225,228] and amplitude of the modulation field
[216,218,219,223,228,229], and its independence on rate of the field sweep
and frequency of the modulation field [216], several theories for lowfield microwave absorption were suggested such as Josephson oscillation
[214,222,227], decoupling of the Josephson junction [218], microwave
conductive loss [47,220], field-dependent flux relaxation [219], the
critical state [216,233] and mixing of macroscopic flux states [221].
Among the theories, it is believed that the observed microwave
absorption arises from microwave conductivity loss brought about by the
interaction between the superconducting carriers and damped fluxons [220],
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124
and the field dependence of the modulated absorption arises from the
existence of a critical state [216,233].
Also the magnetic properties of
the high-Tc superconductors are believed to be related to those of
superconducting glass [10,100].
Therefore the observed absorption
behavior seems to be related to the properties of the superconducting
glass.
For the occurrence of the glass state in the high-Tc super­
conductions, Deutscher and Muller [234] attributed it to considerable
weakening of the pair potential at surfaces and interfaces (grain
boundaries and twin boundaries) due to the short coherence length of the
superconductors. They showed that the change of the pair potential near
the boundary, as a function of temperature.
This lowered pair potential
leads to the network of intergranular and intragranular Josephson junction
array responsible for the glassy behaviors discussed in Sec. 1.9.2.1.
For the microwave absorption, Portis et al. [220] suggested that the
microwave absorption is due to the microwave conductivity loss limited by
the motion of damped fluxons driven by microwave supercurrent.
The motion
can be described by
dV
1
mf — + jjV + Kx - — JM$0 ,
dt
c
(3.3.1)
where mj is the fluxon mass per unit length, r) the flux viscous damping
constant, K the restraining force constant, and
the microwave super­
current density (because this microwave supercurrent is a source due to
its nonequilibrium nature, for the fluxons to move, while the screening
supercurrent induced by external magnetic field creates a equilibrium
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125
distribution of the fluxons).
By taking
to have a time dependence
exp[-iwt],
V - Jp$0/(-iwmf + fj + iK/w)c
(3.3.2)
The moving flux produces an electric field that opposes the current
1
E ± - - — VfB - - J$0fB/(-iwmf + tj + iK/w)c2
(3.3.3)
C
where fB/$c is the density of free or weakly pinned fluxons due to the
fact that only this portion of the fluxons participates the motion, with
f = 0 .1 .
From the London equation,
-»
c
-+
A,
(3.3.4)
4?ruA2
L
me2
| 1/2
where Al
4jrne2/x J
the microwave supercurrent is obtained from the derivative of the London
equation
dJp
c2
dt
4iruA2
L
(E+E^),
(3.3.5)
where E is the microwave electric field.
- E/{ [$0fB/(-iwmf + n + iK/w)c2] - 4jriw/iA2/c2}
(3.3.6)
L
Neglecting restraining force and fluxon inertia, which are comparatively
small at microwave frequencies, complex resistivity is
p ■» e/J = ($QfB/f?c2) - 47riw^iA2/c2
L
(3.3.7)
Therefore the microwave absorption is proportional to n$Q2, where n is the
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126
free fluxon density, which is
n -
fB /$ 0 .
(3.3.8)
On the basis of Portis model which states that the microwave
absorption arises from the motion of the damped fluxons driven by the
microwave supercurrent, and that the absorption is proportional to n$02,
the field dependence of the absorption is believed to be governed by the
field dependence of the free fluxon density weighed by the microwave
penetration portion exp[-2z/XL].
Blazey et al. [216] assumed the free
fluxon density, n, is proportional to the gradient of the flux intensity
inside the sample by
XL
. ®o .
dB
dz
where a = 10 from the fact that n is at most 20% of B/$0 [220].
From the observation that the absorption signal and the magnetization
change sign due to reversal of the sweep field, Blazey et al. [216]
noticed that there exist the critical state [83] in the high-Tc super­
conductors.
Oussena et al. [235] and Senoussi et al. [167] attributed
their observed magnetic hysteresis in La^ 35 SrQ 15 CUO4 to the presence
of the critical state.
Thus, |dB/dz| in equation (3.3.9) is expected to
be governed by the critical state.
According to the Bean's model, for an applied field, Hext, parallel
to the sample surface, the flux intensity is governed by
47T
B(z) = Hext ±
Jcz
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(3.3.10)
127
where z is directed into the superconductor and Jc is the critical current
independent of B at low fields.
The negative sign is for increasing
fields and the positive for decreasing fields.
Blazey et al. [216], however, assumed that when Hext < H* -
(47t/ c )
AJC , the flux intensity inside the superconductors is given by
B(z) - Hext exp[-z/A],
(3.3.11)
where A is the induced screening length, typically a fraction of a
millimeter, and when H > H*, it follows the equation (3.3.10). Therefore,
for Hext > H , the flux intensity decreases linearly for z < zc = A(Hext
-H )/H
and exponentially for z > zc .
The mean flux density weighed by the microwave is
CO
2 '
<B> - —
B(z) exp{-2z/AL)dz
aL
0
(3.3.12)
<n) - «(AL/A)(Hext/*0)/(l + Al /2A)
(3.3.13)
Thus, for Hext < H*,
and for Hext > H* with neglecting the flux intensity at z > zc ,
(n) - a(AL/A)H*/#0
If the field sweep
HextHujax,
(3.3.14)
direction is reversed at Hmax,forHmax - 2H*
<
at z < zc,
B(z)
= Hmax - (Hjj,ax - Hex^.)e Z/A - (z/A)H,
(3.3.15)
because the flux decreases exponentially from the surface into the
r
a
t-*
J
superconductor and
\
<n>
v$
wo J W A
J
I
fl
Hmax'Hext
1 - 2exp{-zx
2
_ + —
1 + Xj_/2X
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128
1
H
[1 - 2exp{-2zx /Xl )
(3.3.16)
where zx - A ln[(Hmax - Hext)/H*] > 0 is the position at which the field
gradient changes sign.
During this stage, the free fluxon density first
decreases because of reduction of flux gradient and flux pinning by
reducing the external field, and then increases because further reduction
of external field creates a reversed flux gradient that depins fluxons.
For this decreasing Hext, (n) initially drops as
1
*
'
a
'
al
.
A
<n> «
[H* - (Hmax - Hext)/(1 + Aj_/2A) ]
$
*o J
(3.3.17)
.
At the limit of Hext = Hmax - 2H*,
/■
a
'
$
*o J
.x
2H*
XL
(1 - 2’2a A l ) - H*[ 1 - 21_2a /aL]|
<n>
.
. 1
+ Al/2A
.
(3.3.18)
Al gives
■*
which for A »
■ H* '
<n) ~
VA
J
. ^o .
indicating nearly full recovery to equation (3.3.14).
For Hext <
-2H*, a reverse critical state is developed for z < A/H*)(Hmax - Hext
-2H*)
H
B(x) — Hext + —
A
z
(3.3.19)
Here, another factor affecting the field dependence of the free
fluxon density arises from the field dependence of the macroscopic
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129
screening length A.
Blazey et al. [223] and Portis et al. [236] pointed
out that the A for the superconducting glass is expected to be of the
order of the distance between fluxons
A « (Sq /B)1/^,
(3.3.20)
while the A in a simple granular superconductor such as PbMogSg, is
relatively independent of the field.
The existence of the critical state in high-Tc superconductors was
experimentally identified by Warden et al. [228] and Stalder et al. [229],
with dynamic pinning and depinning of the fluxons during a modulation
cycle by recording directly from the preamplifier the nonlinear absorption
synchronized with the modulation cycle.
Their result showed that the
modulation amplitude, Hm , less than the critical field, H*, found
experimentally, did not cause any hysteresis which occurred for Hm > H*.
As Hm increased, the peak-to-peak absorption, Ap.p, during the modulation
cycle increased according to a power law Ap.p = (Hm)^ with d » 0.77 ± 0.04
in the modulation amplitude range of 1 mG to 10 G.
As the temperature was
increased, the butterfly-shape absorption became more asymmetric and the
depth of the trough became smaller, according to the increase in the
ration rp ■= A^/A, where A^ is the microwave penetration depth and A is the
macroscopic screening length.
The effect of the sweep field direction was
that the strongest absorption occurred at the end point of the modulation
corresponding to the sweep direction.
Applying the previously mentioned argument to our results, the
following may be inferred.
As the conventional EPR spectrometer registers only the first
harmonic of its response, the spectrum obtained from our spectrometer is
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130
expected to be the rate of change in the total absorption in one cycle of
the modulation with the changing sweep field, if high-order harmonic terms
are negligible.
The reduced signal peak intensity of the spectra at 4.2 K
compared to that at 77 K in our results, corresponds to the increased
depth and symmetry of the trough due to the decreased rp.
The increase in
the signal intensity in our spectra with increasing Hm corresponds to the
increase in Ap.p and increased hysteresis in the modulation absorption.
It is expected that the rate of change of Ap.p with sweep fields becomes
more prominent in high Hm than low Hm . The smoother change near the
signal peaks at 4.2 K than at 77 K may be attributed to the increased
value of rj in equations (3.3.1) and (3.3.7) which results from the
increased superconducting electron density with a decreasing temperature,
resulting in the slower rate of change of the resistive energy loss with
increasing applied fields.
Due to the increased superconducting electron
density with the decreased temperature, it is harder for the magnetic flux
to penetrate inside the sample.
Therefore the field at which the first
fluxon enters the intragranular junction, will be much increased.
This
explains the shift of the signal peak field to a higher field.
The flattening and shift of the spectra due to trapped flux may be
attributed to the fact that
<n> a (B + E ^ 1 / 2
(3.3.21)
where Bt is the trapped magnetic induction and the magnetization due to Bt
has an opposite direction to that due to B, from equations (3.3.14) and
(3.3.20).
As the Bt increases, the rate of the change of (n) decreases,
explaining the smoother signal with larger trapped flux and the shift of
the spectrum to a higher field, observed in Fig. 22, 27 and 29 (neglecting
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131
the different signal signs). The flattening of the signal peak can be
explained by the superconducting glass model, which indicates that the
magnetization increases steeply to a maximum and then decreases slowly
with increasing fields [46,155,166].
The equation (3.3.21) also explains
the shift of the field at which the signal changes its sign, with the fact
that the absorption derivative is an odd function of field [212].
The change of the spectrum with temperatures shown in Fig. 31 can be
also explained with the temperature dependence of the magnitude of trapped
flux and the rp.
It is expected that as the temperature decreases, the superconducting
electron density increases and the increased density plays a role of
stronger barriers to the depinning of flux, resulting in a larger trapped
flux inside the superconductor at a lower temperature, when the applied
field is removed.
Another way to look at the increase in trapped flux
with a decreasing temperature is through the superconducting cluster
model, that the increased current density in the superconducting cluster
loops via Josephson links governed by equation (1.2.1), with a decreased
temperature, can traps larger magnetic flux inside the loop.
Blazey et
al. [216] attributed the pinning and depinning of magnetic flux to the
nucleation and denucleation of fluxons [237] with the supercurrent as a
driving force, while Portis et al. [233] attributed it to a nucleation of
a reverse wall behind which a reverse flux bundle moves into the super­
conductor.
It may be thought, however, from the extremely small value of
H* (0.05 G) [228] and the prediction of non-quantization of flux by
observing the periodicity in the signal noises [226] , that the critical
state may arise at the entering edges of the Josephson junctions.
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The
132
reason for this is that near the entering edges, a series of incoherent
Josephson links dominates with small currents, and the incoherent links
can not make loops with coherent-phases and not quantize the flux.
In interpreting the physical meaning of the field, H^, at which the
field-derivative absorption signal reaches a maximum, Blazey et al. [166]
related the
to appear.
to the field at which a superconducting glass state begins
Warden et al. [228] and Stalder et al. [229] related the H,^
to the threshold field for the establishment of a critical state with a
critical current density and a screening length A.
Khachaturyan et al.
[218] related it to the field at which the current through Josephson
junctions present in granular superconductors, reaches a maximum, which is
that at which the first fluxon is trapped in the junction area,
*o
Hjnx = --2dAL
(3.3.22)
in the relation with equation (1.8.4).
Blazey et al. [216,223] and Portis et al. [236] correlated the origin
of the critical state to disorder in the superconducting glass state, and
suggested that the H,^ is the threshold field for the establishment of the
critical state, as well as the critical field of the superconducting glass
state, that is H* - H^*,
With the relation (3.3.20), they obtained the
relation
4tt
rwo
$ i 1/2
Jc
HC1*
.
c .
(3.3.22)
I B J
Blazey et al. [223] suggested as evidence for equation (3.3.22), their
experimental observation that the field at which the signals in increasing
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133
and decreasing fields merge, increased with decreasing modulation
amplitude Hm in a range of 1.25 to 10 mG, with Hm = Hqp *.
Our result,
however, showed nonlinear dependence of the field on the Hjj,, probably due
to different mixing states of the trapped flux.
Rather, the hystersis
interval, as an interval of two fields at which the field-derivative
signals are zero in forward and reverse sweeps, was roughly increased with
decreasing Hm , with a local maximum value at Hjjj — 9.48 G.
Returning to the physical meaning of H^, as the modulation amplitude
increases, Hp.p increases, as shown in Fig. 17.
with the result of Glarum et al. [219],
This is in an agreement
It was reported [166,216,219]
that the Hmx varies from 0.5 G to 100 G, depending upon the nominal
composition, cluster size, temperature and modulation amplitude.
Blazey
et al. [166] reported that as the oxygen content through the sample became
more uniform, the
shifted to a lower value, and inferred that it
happened due to the increase in the uniform phase area.
The temperature
dependence of H,^ can be described in terms of B and Jc. As B decreases
and Jc increases with decreasing temperature, H q ]^* in equation (3.3.22)
will increase.
The
increased with increasing Hm as shown in Fig. 17.
This means that the effect of hysteresis due to the modulation field on
the signal is increased with increasing Hm . The hysteresis, however,
begins to smear out gradually with increasing sweep field.
Therefore, if
there exist a certain critical state, the effect of the modulation field
in combination with the sweep field will be to shift it to a higher field
if Hm is increased.
As mentioned early in the previous section, the microstructure mainly
responsible for the microwave absorption is expected to be junction areas
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134
in Josephson junctions.
The magnetic flux penetrates easier into the
junction area than into the crystallites, because the superconducting
electron density in the junctions is much smaller than that in the
crystallites and the screening strength in the crystallites is much larger
than that in the junctions.
Between the two-kind junction areas, the
intragranular ones are expected to play stronger barriers to limit the
flux penetration, because the intergranular link is decoupled at much
lower temperature [160].
The Hj decreases with increasing temperature
because Josephson coupling energy is reduced with increasing temperature
as can be seen in equation (1.9.2.1.2).
Therefore, it is expected that
relatively high modulation field affects flux densities only in the
intragranular junction areas.
This is the crossover in screening length
scale observed by Raboutou et al. [238] and Barbara et al. [168].
Comparison of the field (50 G) deviating from a linearity in the
magnetization curve shown in Fig. 11 to the observed
[207] in the same
sample, no. 22, and at the same temperature, 5 K, gives an insight that
the Hmx is related to intergranular decoupling.
As the sample no. 22 had
a glassy surface due to partial melting of the sample when it was
sintered, it is expected that the inter- and intra- granular decoupling
fields are enhanced to much higher fields.
Therefore, the
is expected
to be related to the field at which the intergranular junction is decou­
pled and the first fluxoid enters the intragranular junction.
the
However, as
changes with Hjjp it is also expected that there exists a certain
magnetic structure in the response of the material to the modulation
field.
As the flux in the intragranular junction is in conjunction with that
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135
in the intergranular junction [101,238] and there exist a hysteresis
effect due to the intergranular junction [46,169], even though it is
negligible at high temperature, this hysteresis also may be one of
possible cause of low H
such as 0.05 G [228,229], as well as the cause of
the noise mentioned in the previous section.
In our experiment, anomalous sharp peaks in the spectra, even though
they are not shown in this dissertation, were observed, similar to the
result of Kuznik et al. [139].
It may be related to the break-down due to
piling up of capacitance in the junctions, as discussed by Kuznik et al.
The reason for the existence of different signal signs still can not
be elucidated.
The possible reasons are expected to be the change in
absorption state due to the large capacitance in the junction [139] and
the effect of the quenched structure from its normal state.
As it is expected that the high-field signal arises only from the
secondary phases present in the sample, the high-field signal may be a
powerful method to detect the kinds and amounts of the secondary phases.
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CHAPTER IV
CONCLUSIONS
The physical properties of Y-Ba-Cu-0 superconducting materials are
very sensitive to the preparation parameters such as nominal composition,
preparation atmosphere, heating temperature, cooling rate, corrosivity
with crucible material, pelleting pressure, and additional annealing time.
In this dissertation, the variation of the physical properties with the
preparation parameter was investigated in terms of superconducting
characteristics by the 4-probe electrical measurement.
To overcome the
low critical current density in high-Tc superconducting ceramics,
intensive microstructural studies are suggested in conjunction with their
magnetic properties, to enhance 3-dimensional intergranular coupling,
aligning of the crystallites and flux-pinning strength.
The following is a summary of the findings about the effect of the
preparation parameters on the superconducting characteristics:
1.
The presence of secondary phases resulted in degradation of the
superconducting characteristic of YBa2Cu30y.g ceramics.
2.
Corrosion of zircon crucibles with the mixture of Y2O3, BaO and
CuO powders changed the nominal composition and resulted in
occurrence of secondary phases.
3.
To avoid the corrosion in the zircon crucible, 930° C was proper
as the sintering temperature.
4.
The slow cooling rate resulted in the small ratio of resistance at
room temperature to that at onset temperature of the transition.
136
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137
5.
Higher sintering temperature resulted in higher density of the
sample.
6.
Higher pelleting pressure resulted in lower normal-state
resistance and enhanced superconducting properties.
7.
High oxygen content in the material degraded its superconducting
property.
8.
Around 18 hour-annealing resulted in the highest onset temperature
of the superconducting transition and the lowest normal-state
resistivity.
9.
The superconducting transition width decreased with annealing
time.
10.
The critical current density initially decreased with increasing
annealing time up to 36 hr, and then increased.
11.
The variation of electrical properties in the normal and
superconducting states with the preparation parameters, including
the variation of the superconducting transition properties, can be
explained in terms of pinning strength and inter- and intra­
granular coupling.
12.
The resistive superconducting-transition characteristic in
YBa2Cu3F30x was almost the same as that in YBa2Cu307.g.
The microwave spectroscopy has been a powerful technique to charac­
terize the superconducting transition, and study the magnetic property of
the superconducting state and the magnetic impurities present in high-Tc
superconductors.
In this dissertation, the variation of the field-
derivative absorption signals were studied mainly in low-field regions,
with different preparation history, temperature and magnetic history.
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The
138
interpretation of our data was restricted due to the absence of the
magnetization measurement at 77 K in our sample.
The magnetization curves
obtained from the glassy sample no. 22 was much different from those
[10,46,167,169,235] reported up to now.
However, its absorption behaviors
were almost similar with those reported [166,216,217,218,219], Therefore,
the thought that the
seems to be too early.
is equal to decoupling field of the junction
Rather, it is inferred that the nature of the
modulated absorption signal is related to the response of the magnetic
structure of the sample to the modulation field.
Further research is
suggested for elucidating the cause of the response . The following is a
summary of the findings from the microwave spectroscopy experiments:
1.
The low-field signal appeared below the superconducting transition
temperature.
2.
Two different signs of the modulated absorption signal were
observed in zero-field cooled samples.
3.
The signal intensity was dependent on the duration time of the
sweep field.
4.
The magnitude of trapped flux was dependent on the magnitude of
the previous field applied to the sample.
5.
The signal intensity was decreased by repeating sweeps in the same
field range.
6.
The interaction between trapped fluxes seems to be related to the
low-field signal intensity.
7.
Sudden changes in the sign of the signal were observed during
field sweeps after brief exposures to high fields in zero-field
cooled samples, and in field-cooled samples.
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139
8.
The absorption signal may be related to interaction between the
magnetization due to trapped flux and that due to applied field.
9.
The signal with minus sign at positive field side was more
sensitive to brief exposure to high field, than that with plus
sign at positive field side.
10.
The magnitude of trapped flux increased with decreasing
temperature.
11.
Noises in the low-field signal may be related to the interaction
between trapped flux and applied field.
12.
Decay of the remnant magnetization in single-phase Yl^C^Oy.g
may modulate the microwave absorption.
13.
The peak-to-peak signal height decreased with decreasing
temperature, decreasing modulation amplitude and decreasing
microwave power.
14.
The peak-to-peak signal width increased with decreasing
temperature and increasing modulation amplitude.
15.
The dc component of the absorption increased with increasing
microwave power.
16.
The microwave absorption and its noise seem to be related to
inter- and intra- granular junction area.
17.
The field at which the signal peak appears, seems to be related to
the field at which the intergranular junction is decoupled and the
first fluxon enters the intragranular junction.
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