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Republic of Iraq Ministry of Higher Education and Scientific Research University of Baghdad College of Education for Pure Science Ibn-AL-Haitham
Synthesis and study structural, electrical and mechanical properties of composite superconductor.
A Thesis Submitted to University of Baghdad \College of Education for Pure Science (Ibn-AL-Haitham) in partial Fulfillment of the Requirements for the Degree of Philosophy Doctorate of Science In Physics
By
Shatha Hashim Mahdi 2015
بسم اهلل الرحمن الرحيم
((وق ل رب أدخلني مدخل صدق وأخرجني مخرج صدق و اجعل لي من لدنك سلطانا نصيرا))
صدق اهلل العظيم سورة اإلسراء اآلية ()08
Content Title
Page
Chapter One( Introduction to Superconductivity) 1.1 Introduction.
1
1.2 Properties of Superconductors.
3
1.2.1Critical Temperature (Tc).
3
1.2.2 Electrical Resistance.
3
1.2.3 Critical Current.
4
1.2.4 Magnetic Field.
5
1.2.5 Effect of Pressure.
6
1.2.6 Isotope Effect.
6
1.3. Meissner effect.
7
1.4 Types of superconductors.
8
1.5 Theories of Low Temperature Superconductor.
9
1.5.1 The London theory.
10
1.5.2 Ginzburg-Landau theory.
11
1.5.3 BCS theory.
13
1.6. Thermodynamics
14
1.6.1 Thermodynamics of Superconducting Transitions
15
1.6.2 Entropy Difference and specific heat. Chapter Two (Superconducting system)
16
2.1 Introduction.
17
2.2 Crystal Structure of Bi-Sr-Ca-Cu-O.
17
2.3 Phase Diagram of Cuprate Superconductors.
19
2.4 Theories of High Temperature Superconductor.
21
2.4.1 Excitons and Plasmons Model.
21
2.4.2 Interlayer Coupling Model.
21
2.4.3 Isotope Model
21
2.4.4 Oxygen Defect Model
22
2.5 Polyaniline.
22
2.5.1 Structure of Polyaniline.
22
2.5 Literature Survey of Bi-Ba-Ca-Cu-O
25
2.6 Aim of the Work
37
Chapter Three (Experimental)
3.1 introduction
38
3.2 Sample Preparation
38
3.3 Devices and measurements.
39
3.3.1 Energy dispersive X-ray spectroscopy EDS.
39
3.3.2 X-Ray Diffraction.
40
3.3.3 Scanning Electron Microscopy (SEM)
42
3. 3. 4 Determination of Oxygen Content (δ).
42
3.3 .5 Electrical measurements
43
3.3.5. 1 Resistivity and Critical Temperature Measurement
43
3.3.5.2 Measurements of dielectric constant with different frequencies.
46
3.3.6 Thermal measurements
47
3.3.6.1 Thermal conductivity
47
3.3.6.2 Differential Scanning Calorimetry (DSC).
49
3.3.7 Mechanical measurements.
49
Vickers hardness.
49
Chapter Four ( Results and Discussion) 4.1 Introduction 50 4.2 The properties of Bi2Ba2Can-1CunO4n+2+δ system. 50 4.2.1 Energy Dispersive X-Ray Spectroscopy (EDS). 50 4.2.2 crystal structures 52 4.2.3 Scanning Electron Microscopy (SEM) 57 4.2.4Electrically properties. 4.2.4.1-Dielectric constant.
61 61
4.2.3.2 Electrical Resistivity (ρ).
63
4.2.4 Thermal properties
65
4.2.4.1 Thermal conductivity
65
4.2.5 Mechanical Properties.
66
4.2.5.1 Vickers Hardness
66
4.3 Effect of Y doped on The properties of Bi2Ba2Can-1CunO4n+2+δ systems.
67
4.3.1 Crystal Structures
67
. 4.3 Results Iodometric Titration
74
4.3.2 Electrical measurements.
77
4.3.2.1 Dielectric constant.
77
4.3.2.2 Electrical Resistivity (ρ).
81
4.3.4 Thermal properties.
89
4.3.4.1 Thermal Conductivity.
86
4.3.4 Mechanical Properties.
91
4.3.4.1 Vickers Hardness
91
4.4 The properties of polymer composite superconductor .
92
4.4.1 The properties of Polyaniline.
92
4.4.1.2 Structural Analysis.
92
a- Energy Dispersive X-Ray Spectroscopy (EDS).
92
b- X-ray structure of Polyaniline.
93
c- Scanning Electron Microscopy (SEM).
94
d- Fourier Transform Infrared (FT-IR).
96
4.4.1.3 Dielectric constant of Polyaniline.
98
4.4.1.4 Electrical Resistivity (ρ)
100
4.4.1.5 Thermal properties.
101
4.4.1.5.1 Thermal conductivity
101
4.4.1.5.2 Differential Scanning Calorimetry (DSC).
101
4.4.1.6 Mechanical Properties.
104
4.4.2 The properties superconductor composite.
104
4.4.2.1 X- ray structure of Composite (Ceramic-polymer).
105
4.4.2.2 Scanning Electron Microscopy (SEM)
110
4.4.2.3 Electrical measurements.
114
4.4.2.3 .1 Dielectric constant.
114
4.4.2.3 .1 Electrical resistivity
119
4.4.2.4 Thermal properties.
123
4.4.2.5 Mechanical properties.
125
4. 4. 3 Describes of the Models in the Search
126
4. 4. 3. 1 Ceramic Superconductor
126
4. 4. 3. 2 Polymer superconductor composite.
127
4. 4. 4 The comparison between ceramic-superconductor and polymersuperconductor composite properties.
128
Chapter Five 5.1 Conclusions
5. 2 Future works
129 131
List of figures Figure
Page
Fig (1.1):Behavior of resistivity
1
Fig (1.2): Electrical resistivity (ρ) vs. temperature (T) for superconductor .The resistivity Vanishes for T ≤ Tc
4
Fig (1.3) variation of the superconducting properties with the external magnetic field
5
Fig (1.4): superconducting phase is stable at low enough temperature, magnetic field, and current
6
Fig.(1.5 ): Normal and superconducting state in the magnetic field
8
Fig (1.6). (a) Type-I superconductor behavior. (b) Type-II superconductor behavior
9
Fig.(1.7):The penetration depth( λ) changes with the temperature.
Fig.(1.8): The boundary between superconducting (green) and normal (white) phases. The dependence of the magnetic field strength H and thc numbcr of superconducting electrons on the distance across the boundary are illustrated in (a) a type I superconductor and (b) a type I1 superconductor
11
12
Fig. (1.9): The formation of a cooper pair: A passing electron attracts the positive charged ions of the lattice, causing a slight ripple in its wake.
13
Another electron passing in the opposite direction is attracted to that displacement Fig. (2.1): Crystal structures of the homologous series of Bi-system superconductors, Bi2Sr2Can-1CunO2n+4+δ (n = 1, 2, 3)
18
Fig (2.2) Phase diagram of cuprate superconductors in the temperaturedoping variables, TN-the Néel temperature, Tc-the critical temperature of
20
the superconducting transition, T∗-the characteristic temperature of a pseudogap, T 0-upper crossover temperature Fig (2.3) Structure of the Polyaniline chain.
23
Figure (2.4): X-ray diffraction of Polyaniline.
25
Fig (2.5): FTIR spectrum of the Polyaniline.
25
Fig.(3.1) shows X-Ray diffraction pattern Bi2O3 (pure)
40
Fig.(3.2) shows X-Ray diffraction pattern CaO (pure).
40
Fig.(3.3) shows X-Ray diffraction pattern CuO (pure).
41
Fig.(3.4) shows X-Ray diffraction pattern BaO (pure).
41
Figure (3.5) Scanning electron microscope (InspectTM S50- SEM).
42
Fig.(3.6) Circuit diagram of the sample of resistivity measurement
44
Fig. (3.7): Liquid nitrogen cryostat instrument
45
Fig.(3.8): Calculation of Tc from the resistivity curve
46
Fig (3 .9): LRC meter .
47
Figure (3.10) Lees’ Disk Apparatus (schematic)
48
Fig (4.1) EDXimage for Bi2 Ba2Ca1 Cu2 O6+δ sample.
51
Fig (4.2) EDX image for Bi2 Ba2Ca1 Cu2 O8+δ sample.
51
Fig (4.3) EDX image for Bi2 Ba2Ca2 Cu3 O10+δ sample.
52
Fig (4.4): X – ray diffraction pattern of Bi2 Ba2 Cu1 O6+δ .
53
Fig (4.5): X – ray diffraction pattern of Bi2 Ba2Ca1 Cu2 O8+δ
53
Fig (4.6): X – ray diffraction pattern of Bi2 Ba2Ca2 Cu3 O10+δ
54
Fig .(4 .7) : c/a ratio Density (dm ) as a function of n for superconducting system Bi2Ba2CanCun-1O2n+2+δ Figs. (4.8): SEM micrographs of the fracture surface of Bi2 Ba2 Cu1 O6+δ samples with (n=1) sintered at 750oC for 120h Figs. (4.9): SEM micrographs of the fracture surface of Bi2 Ba2 Ca1 Cu2 O8+δ samples with (n=2) sintered at 750oC for 120h Figs. (4.10): SEM micrographs of the fracture surface of Bi2 Ba2 Ca2 Cu3 O10+δ samples with (n=3) sintered at 750oC for 120h Fig (4.11
r)
with frequency for Bi2 Ba2Can-
1CunO2n+4+δ.
55
58
59
60
62
Fig (4. 12): Dielectric constant ( r) with ( n ) Cu-O Layer for Bismuth system
63
Fig (4.13). Resistivity versus temperature for Bi2 Ba2Can-1CunO2n+4+δ, with n = 1–3 phases
64
Fig (4.14). Thermal Conductivity for Bi2 Ba2Can-1CunO2n+4+δ.
66
Fig (4.15). Vickers Hardness for Bi2 Ba2Can-1CunO2n+4+δ.
67
Fig (4.16): X – ray diffraction pattern of Bi2 Ba2-XYX Cu1 O6+δ at X=0.05
69
Fig (4.17): X – ray diffraction pattern of Bi2 Ba2-XYX Ca Cu2 O8+δ at X=0.15
69
Fig (4.18): X – ray diffraction pattern of Bi2 Ba2-XYX Ca Cu2 O8+δ at X=0.2.
70
Fig (4.19): X – ray diffraction pattern of Bi2 Ba2-XYX Ca2 Cu3 O10+δ at X=0.05.
71
Fig (4..20): X – ray diffraction pattern of Bi2 Ba2-XYX Ca2 Cu3 O10+δ at X=0.1.
72
Fig (4..21): X – ray diffraction pattern of Bi2 Ba2-XYX Ca2 Cu3 O10+δ at X=0.15.
72
Fig (4..22): X – ray diffraction pattern of Bi2 Ba2-XYX Ca2 Cu3 O10+δ at X=0.2.
73
Fig. (4.23 ) :Critical temperature (Tc), oxygen content (δ) function of Y content for Bi2 Ba2-x YXCan-1CunO2n+4+δ .
75
Fig (4.24) Dielectric constant ( ) with frequency for Bi2 Ba2-x YXCan1CunO2n+4+δ,where
n=1,X=0.0 to X=0.2 .
78
Fig (4.25) Dielectric constant ( ) with frequency for Bi2 Ba2-x YXCan1CunO2n+4+δ,where
n=2,X=0.0 to X=0.2.
79
Fig (4.26) Dielectric constant ( ) with frequency for Bi2 Ba2-x YXCan1CunO2n+4+δ,where
n=3,X=0.0 to X=0.2.
80
Fig(4.27) Temperature dependence of resistivity for Bi2Ba2-x YXCu1O6+δ with different Y content
82
Fig(4.28) Temperature dependence of resistivity for Bi2 Ba2-x YX Ca1Cu2O8+δ with different Y content. Fig(4.29) Temperature dependence of resistivity for Bi2 Ba2-x YX Ca2Cu3O10+δ with different Y content
83 83
Fig (4.30): Critical temperature (Tc) with Volume fraction for Bi2 Ba2-x YXCan1CunO2n+4+δ
,(a) Bi-2201, (b) Bi-2212 ,(c) Bi-2223
84
Fig. (4.31): Critical temperature (Tc), density (ρ) as a function of Y content for Bi2 Ba2-x YXCan-1CunO2n+4+δ a) Bi-2201, (b) Bi-2212 ,(c) Bi-2223
85
Fig. (4.32) :Relation of transition temperature (Tc) and c-axis lattice constant with the values of effective cationic size for Bi2 Ba2-x YXCan-1CunO2n+4+δ a) Bi-2201, (b) Bi-2212 ,(c) Bi-2223
87
Fig (4.33 ): Thermal conductivity (K) (W/m.K.) with Y content for three phase
90
Fig (4.34 ): Vickers Hardness Number (VHN) for specimens with with Y content for three phase [Bi-2201], [Bi-2212] ,[ Bi-2223] .
91
Fig (4.35) EDX image for Polyaniline (PANI) composition
93
Fig (4.36) X-ray diffraction ofr Polyaniline .
94
Figs (4.37): The SEM image of pure Polyaniline sample .
95
Fig (4.38): FTIR spectrum of the Polyaniline .
96
Fig (4.39) Dielectric constant at (room temperature) versus frequency for PANI.
99
Fig (4.40). Resistivity versus temperature for PANI
100
Fig (4.41):DSC for tested powder polyaniline sample
103
Fig.(4.42) XRD pattern of composites of BSCCO(Bi2Ba2Can-1CunO4n+2+δ) 25% Polyaniline after of annealing at 80C for 2h.
106
Fig (4.43): X – ray diffraction pattern of composites of BSCCO ( Bi2 Ba2-XYX Cu1 O6+δ at X=0.05), 25% Polyaniline after of annealing at 80C for 2h. .
107
Fig (4.44): X – ray diffraction pattern of composites of BSCCO ( Bi2 Ba2Cu2 O8+δ at X=0.15, 0.2), 25% Polyaniline after of annealing at 800C for 2h. Fig (4.45): X – ray diffraction pattern of composites of BSCCO(Bi2 Ba2-XYX Ca2 Cu3 O10+δ at X= 0-0.2), 25% Polyaniline after of annealing at 800C for 2h
XYX Ca
108
109
Figs. (4.46): SEM micrographs of the fracture surface of composites of BSCCO (Bi2 Ba2 Cu1 O6+δ samples with (n=1), 25% Polyaniline after of annealing at 80°C for 2h
111
Figs. (4.47): SEM micrographs of the fracture surface of composites of BSCCO (Bi2 Ba2Ca1 Cu2 O8+δ samples with (n=2), 25% Polyaniline after of annealing at 80°C for 2h
112
Figs. (4.48): SEM micrographs of the fracture surface of composites of BSCCO (Bi2 Ba2Ca2 Cu3 O10+δ samples with (n=3), 25% Polyaniline after of annealing at 80°C for 2h. Figs (4.49) Dielectric constant ( ) with frequency for composites of BSCCO Bi2 Ba2-x YXCu1O6+δ ),where n=1,X=0 , 0.15) , 25% Polyaniline after of annealing at 80°C for 2h. (4.50) Dielectric constant ( ) with frequency for composites of BSCCO Bi2 Ba2-x YXCa1Cu2O8+δ ),where n=2,X=0 , 0.15 .0.2) , 25% Polyaniline after of annealing at 80°C for 2h. Figs (4.51) Dielectric constant ( ) with frequency for composites of BSCCO Bi2 Ba2-x YXCa2Cu3O10+δ ),where n=3,X=0 to 0.2) , 25% Polyaniline after of annealing at 80°C for 2h. Fig.(4.52) Resistivity versus temperature for composites of BSCCO(Bi2Ba2Can-1CunO2n+4+δ) 25% Polyaniline after of heat treating (or annealing) at 80C for 2h .
113
116
117
118 120
Fig(4.53): Resistivity versus temperature for composites of BSCCO ( Bi2 Ba2-XYX Cu1 O6+δ at X=0.05), 25% Polyaniline after of heating at 80C for 2h
120
Fig (4.54) Resistivity versus temperature for composites of BSCCO Bi2 Ba2-x YXCa1Cu2O8+δ ),where n=2,X=0 , 0.15 .0.2) , 25% Polyaniline after of heating at 80C for 2h
121
Fig (4.55) Resistivity versus temperature for composites of BSCCO Bi2 Ba2-x YXCa2Cu3O10+δ ),where n=3,X=0 to 0.2) , 25% Polyaniline after of heat treating (or annealing) at 80C for 2h.
121
Fig. (4.56): Crystal structures of Bi-system superconductors, Bi2Ba2-x YX Can-1CunO2 +4+δ (n = 1, 2, 3),and (x=0,0.05,0.1,0.15and 0.2)
127
List of Tables Tables
Page
Table(4.1): Lattice parameters of the superconducting system Bi2Ba2CanCun-1O2n+4+δ
55
Table(4.2): Indices of the superconducting system Bi2Ba2CanCun1O2n+4+δ
56
Table (4.3): Tc(Offset), Tc(onset),transition width ΔT(K), Tcmid(K), for Bi2Ba2Can-1CunO2n+4+δ, with n = 1, 2, and 3
65
Table(4.4): Lattice parameters of the superconducting system Bi2Ba2CanCun-1O2n+4+δ Table (4.5 ):- oxygen content(δ) and the average Cu valence for different composition of Bi2 Ba2-x YXCan-1CunO2n+4+δ . Table (4.6 ): The dielectric constant values measured at 1MHz in room temperature for Bi2 Ba2-x YXCan-1CunO2n+4+δ.
73 76 81
Tables(4.7 ):- Tconset, Tczero,transition width ΔT(K), Tcmid(K), for different composition of Bi2 Ba2-x YxCan-1CunO2n+4+δ .
88
Table( 4 .8 ) Thermal conductivity (K) *10-4 (W/m.K.) at room temperature for [Bi-2201], [Bi-2212] ,[ Bi-2223]
90
Table( 4 .9 )EDS image for Polyaniline (PANI) composition.
93
Table (4.10): The list of the observed peaks for the prepared Polyaniline at room temperature Table (4.11):the exothermic transition of Polyaniline specimen under a nitrogen atmosphere.
97 103
Table(4.12): Indices of composites of BSCCO ( Bi2 Ba2-XYX Cu1 O6+δ ) 25% Polyaniline after of annealing at 805C for 2h.
Appendix
Table(4.13): Indices of composites of BSCCO ( Bi2 Ba2-XYX Ca1Cu2O8+δ ), 25% Polyaniline after of annealing at 805C for 2h.
Appendix
Table(4.14): Indices of composites of BSCCO ( Bi2 Ba2-XYX Ca2Cu3O10+δ ), 25% Polyaniline after of annealing at 805C for 2h.
Appendix
Table(4.15): The dielectric constant values measured at 1MHz in room temperature for composites of BSCCO ( Bi2Ba2-x YxCanCun-1O2n+4+δ),25% Polyaniline after of heat treating (or annealing) at 80C for 2h Table(4.16): Thermal conductivity K (W/m.k) values measured at room temperature for composites of BSCCO ( Bi2Ba2-x YxCanCun-1O2n+4+δ) with 25% Polyaniline after of heat treating (or annealing) at 80C for 2h Table(4.17): Thermal conductivity K (W/m.k) values measured at room temperature for composites of BSCCO ( Bi2Ba2-x YxCanCun-1O2n+4+δ) with 25% Polyaniline after of heat treating (or annealing) at 80C for 2h
115
122
124
Table(4.18): Vickers Hardness Number (VHN) for composites of BSCCO ( Bi2Ba2-x YxCanCun-1O2n+4+δ) with 25% Polyaniline after of heat treating (or annealing) at 80C for 2h
125
The following list includes definitions of most of the symbols used: n
number of CuO2 layers
Tc
Critical temperature
Hc
Critical magnetic field
r
radius of the wire
IC
Critical Current
S
Entropy
μo
Permeability of free space
Bc
magnetic flux density
λ
penetration depth
H
External magnetic field
m
Mass of electron
ns
The local density of superconducting curriers
ξ
The coherence length
Eg
Superconducting energy gap
Δ
Energy gap
K
Boltzmann constant
M
Isotopic masses Debye temperature.
G M U
The Gibbs free energy Magnetization internal energy
P
Pressure
v
Volume
Q
latent heat
C (Cel)S
specific heats electronic specific heat of superconductor
a
Constant
μ
Chemical potential
HTCS
High Temperature Superconductor
LTP
Low – Tc phase
HTP
High – Tc phase
CN
Coordination number
BCCO
Bi2Sr2Can-1CunO2n+4+δ
CRB
Charge reservoir block
a, b, c
Lattice parameters constant
NA
Avogadro's number
Vph
volume fraction of the phases
δ
Excess of oxygen content
W
Atomic Weight
MA
molar mass of the sample HBCCO or BCCO
mA
weight of the sample
dm
Density
ρ
Electrical resistivity
Mo
atomic weight of oxygen
C
the concentration of theNa2S2O3x=0.015gm/ml
MB
the molar mass of Na2S2O3.5H2O =248.18
I
the current passing through the sample
v
is the voltage drop across the electrodes
t
thickness of the pellet
L
length of the sample
w
width of the sample
Tc1
onset of the transition temperature
Tc2
offset of the transition temperature at the zero resistivity point
r
TA, TB and Tc
dielectric constant temperature of discs A, B and C respectively in (k).
dA,dB and dc
diameter of disks A,B and C respectively in (m)
rd
sample radius (m)
ds
sample thickness (m)
e
the emitted energy (heat) per unit area per unit time in (W/m2).
K
The thermal conductivity
F
force
VHN
Vickers hardness Number
Acknowledgments At first, I thank my God for helping me to complete this thesis. Then, I would like to express my sincere appreciation and deep gratitude to Ministry of Higher Education& Scientific Research /Research & Development Directorate / Pioneer Projects Department for providing the facilities and devices necessary for this work. I'm grateful to the University of Baghdad, College of Education for Pure Science (Ibn-AL-Haitham), and of the Department of Physics. I would like to express my sincere appreciation and deep gratitude to my supervisors for their suggestion of the topic of this thesis and their encouragement throughout all the stages of this work . Last, I offer my deep gratitude to my family for their patience throughout this work.
Dedication To My
Parents with my great love, Brother and sisters with my respect, Ahmad Al-Taee with respect and thankfulness.
Shatha
Abstract
Multilayered cuprates of Bi2Ba2-xYx Can-1CunO4n+2+δ superconductors for (n= 1, 2 and 3, x=0,0.05,0.1,0.15, and 0.2 ) and superconductor
composites
Bi2Ba2Ca2Cu3O10+δ
samples
(Bi2Ba2CuO6+δ, with
25%
polymer-
Bi2Ba2Ca1Cu2O8+δ
Polyaniline),
have
and been
synthesized by using solid state reaction method in order to investigate the variation of crystal
structural, dielectric constant, hardness and
transition temperature. The structural was studied by using X-ray powder diffraction (XRD) and scanning electron microscope (SEM). X-ray diffraction analysis showed that all samples have orthorhombic structures correspond to the high and low- phase with changing of the lattice parameters, , the ratio c/a, the mass density and volume fraction VPh by increasing the Cu-O layer and Y concentration. Scanning electron microscope pictures show the various of Cu-O layer and Y concentration due to various grain sizes and formation many phases. Energy dispersive X-ray spectroscopy (EDX) analysis was used to test the composition for bulk of the compounds, and show there was no unwanted elements in the samples. Dielectric constant was measured at room temperature as a function of frequency in the range 50-1MHz. It was found that Increasing of Cu-O layer and Y concentration leads to change the dielectric constant Increasing of Cu-O layer and Y concentration leads to increasing thermal conductivity, but they lead to decrease hardness. It was found that the mechanical property for ceramics-superconductors samples higher
than
polymer-superconductor
composites,
but
thermal
conductivity for polymer-composites are higher than for ceramicssuperconductors. Electrical resistivity, using the four-probe technique, were used to find the critical temperature, With an increase in Cu-O layers and Y concentration , the superconducting transition temperature is determined by electrical resistivity-temperature dependency and rises reaching a maximum value (TC=118,3K) for Bi2Ba2Ca2Cu3O10+δ sample, besides the resistivity for polymer-composite decreases nearly linearly with decreasing temperature, samples may be having low Tc , but we can’t get the critical temperature Tc(off) for being under a temperature of liquefied hydrogen
الخالصة
انًشكثاخ انًرعذدِ انطثقاخ Bi2Ba2-xYx Can-1CunO4n+2+δانفائق انرٕصٛم عُذيا ٔ ٔ n=1, 2 ,3نقٛى x=0,0.05,0.1,0.15
ٔ,انًرشاكة تٕنًٛش-فائق انرٕصٛم
( ٔ Bi2Ba2Ca2Cu3O10+δ ٔ Bi2Ba2Ca1Cu2O8+δ ٔ Bi2Ba2CuO6+δتٕن ٙاَٛهٍٛ تُسثّ )25%ذى ذحضٛش اانًُارج تاسرخذيد طشٚقح ذفاعم انحانح انصهثح يٍ أجم دساسّ انرغٛشاخ ف ٙانرشكة أنثهٕس٘ ،ثاتد انعضل انكٓشتائٔ، ٙانصالتح ٔدسجح حشاسج انرحٕلٔ .قذ دسط انرشكة انثهٕس٘ تاسرخذاو حٕٛد األشعح انسُٛٛح (ٔ )XRDانًجٓش اإلنكرشَٔ ٙانًاسح (ٔ .)SEMأظٓش ذحهٛم حٕٛد األشعح انسُٛٛح أٌ جًٛع انعُٛاخ نذٓٚا ْٛاكم يع ُٙٛيرعايذ انًحأس ذحٕ٘ عهٗ اطٕاس ذشكٛثّ يُخفضح ٔعانٛح يع ذغٛٛش ثٕاتد انشثٛكّ َٔسثّ ٔ c/aانكثافح انكرهٔ ّٛانُسة انطٕسَ( ّٚسثّ انطٕس انعه ٙانٗ االطٕس االخشٖ) َرٛجّ نضٚادج طثقاخ ٔ Cu-O ذشكٛض . Yذظٓش صٕس انًجٓش اإلنكرشَٔ ٙانًاسح انضٚادِ ف ٙطثقاخ ٔ Cu-Oذشكٛضٕٚ Yد٘ انٗ ذغٛٛش ف ٙاألحجاو انحثٕتٔ ّٛذشكٛم اطٕاس ذشكٛث ّٛيرعذدِ .تاسرخذاو انرحهٛم انطٛف ٙنألشعح انسُٛٛح ( )EDXنهراكذ انعُاصش انًكَّٕ نههًشكثاخ قٛذ انذساسّ ،ذث ٍٛاٌ ْزِ انعُاصش يٕجٕدِ ٔتانُسة انًقثٕنّ عذو ٔجٕد عُاصش غٛش يشغٕب فٓٛا ف ٙانعُٛاخ. ذى قٛاط ثاتد انعضل انكٓشتائ ٙف ٙدسجح حشاسج انغشفح كذانّ نهرشدد ضًٍ انًذٖ (-05 ٔ .)1MHzقذ ٔجذ أٌ صٚادج طثقاخ ٔ Cu-Oذشكٛضٚ Yؤد٘ إنٗ ذغٛٛش ف ٙثاتد انعضل انكٓشتائ.ٙ اٌ صٚادج صٚادج طثقاخ ٔ Cu-Oذشكٛضٚ Yؤد٘ إنٗ صٚادج انرٕصٛم انحشاس٘ ،نكُٓا اٚضا ذؤد٘ إنٗ ذقهٛم صالتح انًُٕرج .ذث ٍٛأٌ انخاصٛح انًٛكاَٛكٛح نعُٛاخ انسٛشايٛك ّٛانفائقّ انًٕصٛم انفائقح أعهٗ يٍ نعُٛاخ انًرشاكثاخ انثٕنًٛش-سٛشايٛك فائقّ انرٕصٛمٔ ،نكٍ انًٕصهٛح انحشاسٚح نهًرشاكثاخ أعهٗ يٍ عُٛاخ انسٛشايٛك ّٛانفائقّ انًٕصٛم. انًقأيٛح انكٓشتائٛح ،ذًد دساسرٓا ٔرنك تاسرخذاو ذقُٛح انقطاب األستعح انرحقٛق ٔحساب دسجح انحشاسج انحشجح ،يع صٚادج طثقاخ ٔ Cu-Oذشكٛض ، Yذى احرساب دسجح انحشاسج انحشجح نهًشكثاخ ٔانًرشاكثاخ انفائقح انرٕصٛم تٕاسطح اعرًاد ّٚانًقأيٛح انكٓشتائٛح عهٗ دسجّ انحشاسج ،قذ ٔجذ اٌ اعهٗ دسجح انحشاسج حشجح نهرٕصٛم انفائق ْ)TC(off) = 118. 3K( ٙ
نهًشكة Bi2Ba2Ca2Cu3O10 + δاضافّ انٗ رنهك اٌ انًقأيٛح انكٓشتائٛح نهًرشاكثاخ انثٕنًٛش- سٛشايٛك ذقم خطٛا ذقشٚثا يع اَخفاض دسجح انحشاسجٔ ،نكٍ نى َرًكٍ يٍ انحصٕل عهٗ دسجّ انحشاسِ انحشجّ نكَٕٓا ذحد دسجّ حشاسِ انٓاٚذسٔج ٍٛانًسال.
Chapter One
Introduction to Superconductivity
1.1 Introduction. The phenomenon of superconductivity has not lost its fascination ever since its discovery in 1911[1]. Dutch physicist H. Kamerlingh Onnes discovered that for some materials a certain temperature exists, called the critical temperature Tc, below which the resistivity is zero and the conductivity Helium called this phenomenon superconductivity[2]. The result of this investigation was unexpected at a temperature below 4.15 K, the resistance disappeared almost instantaneously.[1-2] The behavior of resistance as a function of temperature is shown schematically in Fig.(1.1) [ 3].
Fig (1.1):Behavior of resistivity [3].
in 1933 by W. Meissner and colleagues[4], who determined that a superconducting metal expels any magnetic field when it is cooled below the critical transition temperature, Tc, and becomes superconducting. By expelling the field and thus distorting nearby magnetic field lines, a superconductor will create a strong enough force field to overcome gravity. In 1934, Gorter and Casimir(GC) [5] introduced the two fluid model of superconductivity, in order to explain thermodynamic properties of superconductors. In this model, Analysis of the specific heat and critical field data, prompted GC to suggest an empirical form for the 1
Chapter One
Introduction to Superconductivity
temperature dependence of the density of superconducting electrons, ns = n(1 −t4), where t = T/Tc and n is the total density of conduction electrons. In 1935, F. and H. London[5] introduced a phenomenological model of superconductivity in which the magnetic field inside a superconductor B. In
1950
Maxwell
and
Reynolds[6]
discovered
that
the
superconducting transition temperature of lead depends on its isotopic mass (M), and inversely proportional to M-1/2. The understanding of superconductivity has been advanced in 1957 by three American physicists Bardeen, Cooper and Schrieffer[6], through their theories of superconductivity, known as the BCS theory. It predicts that under certain conditions, the attraction between two conduction electrons due to a succession of phonon interactions can slightly exceed the repulsion that they exert directly on one another due to the Coulomb interaction of their like charges. The two electrons are thus weakly bound together forming a so-called Cooper pair. They attributed the responsibility of the superconductivity to these Cooper pairs. In 1962 Josephson made a prediction
[7]
that a finite supercurrent
should exist between two superconducting electrodes separated by very thin insulating layer. The Josephson effect is not just relevant to artificial devices; imperfect superconductors naturally contain Josephson junctions. In particular, granular superconductors (as in thin deposited metal films) can be modeled as a random array of superconducting islands connected by Josephson links[7-11]. Up to 1973 the highest transition temperature found for the onset of superconductivity was 23.3K[11]. This was for a compound of niobium and germanium, Nb3Ge and here it stayed until 1986 when Bednorz and Muller[13]reported a significant increase in Tc to 34K in a (La-Ba-Cu-O) ceramic material.
2
Chapter One
Introduction to Superconductivity
In early 1987[14], groups at the University of Alabama at Huntsville and the University of Houston announced superconductivity at about 92 K in an oxide of yttrium, barium, and copper (YBa2Cu3O7). Later that year, teams of scientists from Japan and the United States reported superconductivity at 105 K in an oxide of bismuth, strontium, calcium, and copper. Bismuth and thallium based superconductors were discovered in 1988
[15]
which became superconducting at 110K and 125K,
respectively. Superconductivity of mercury-based compounds were discovered in 1993[15], with a transition temperature claimed to be up to 164K under high pressure . In 2008, a new fascinating family of superconductors came into focus containing an iron layer of anti-PbO structure as the superconducting component[15].
1.2 Properties of Superconductors. Superconductors have three important critical parameters that each of them is very dependent on the other. These critical parameters are:
1.2.1Critical Temperature (Tc). As most high-purity metals are cooled down to temperatures nearing 0 K, the electrical resistivity decreases gradually, approaching some small yet finite value that is characteristic of the particular metal. There are a few materials, however, for which the resistivity, at a very low temperature, abruptly plunges from a finite value to one that is virtually zero and remains there upon further cooling[16]. Materials that display this latter behavior are called superconductors ,and the temperature at which they attain superconductivity is called the critical temperature Tc as shown in Fig. (1.2). [16]
1.2.2 Electrical Resistance(ρ). The electrical resistance of Superconductors drops to zero at the transition temperature. Superconductors have almost zero resistance and 3
Chapter One
Introduction to Superconductivity
infinite conductivity at below critical temperature. The resistivity of Superconductors can be measured by causing a current to flow in a ring shaped sample and observing the current as a function of time. If the sample ring is in the normal state, the current damps out quickly because of its resistance but if the ring has zero resistance, the current once set up flows without any decrease in its value. Such circuits are called persistent circuit.[16].The critical temperature (Tc) for superconductors is the temperature at which the electrical resistivity of a material drops to zero as shown in Fig. (1.2).
Fig (1.2): Electrical resistivity (ρ) vs. temperature (T) for superconductor .The resistivity Vanishes for T ≤ Tc [16]
1.2.3 Critical Current (Ic). The superconducting properties of the superconducting materials disappear when sufficiently heavy current is passed through them. Since, when current flows through a superconductor it will set up the magnetic field which can destroy the superconducting state. According to Silsbee’s rule, for a current carrying superconductor [17]. ………………………………………………………(1) Where, IC is Critical Current, HC is Critical field , r is radius of the wire 4
Chapter One
Introduction to Superconductivity
In superconductors, not only the motion of Cooper pairs, but also the motion of magnetic flux tubes determines the temperature behaviour. Especially in superconductors systems[17] .
1.2.4 Magnetic Field (Hc). In superconductors, their normal resistance may be restored if the applied magnetic field is greater than the critical field (Hc) of them .The value of critical field (Hc) depends both on the material properties and the temperature. Critical field is zero at superconducting transition temperature and as the temperature is reduced, the critical field (H c), increases as shown in Fig (1.3). The relation between critical field and critical temperature is given by [17] HC
2 T ………………(2) H 0 1 TC
where H0 – Critical field at 0K T - Temperature below TC TC - Transition Temperature
Fig (1.3) variation of the superconducting properties with the external magnetic field[18]
5
Chapter One
Introduction to Superconductivity
The balance between superconducting and normal states is usually described by three critical parameters: critical temperature, critical magnetic field and critical current density. A schematic phase diagram is shown in Figure (1.4).[19]
Fig (1.4): superconducting phase is stable at low enough temperature, magnetic field, and current [19].
1.2.5 Effect of Pressure. By applying very high pressure , it is possible to reach superconducting transition temperature(Tc) of a material near room temperature, i.e , by increase pressure on the superconducting material superconducting transition temperature(Tc) also increases , Tc depended of pressure (high values).[17]
1.2.6 Isotope Effect. Experimental study of superconducting materials shows that the transition temperature varies with the average isotopic mass, M, of their constituents. In particular[17], TC M-1/2
TcM1/2=constant………………..(3)
For example, in mercury Tc was found vary from 4.185K to 4.146K with the variation of its average isotopic mass from 199.5 to 203.4 atomic 6
Chapter One
Introduction to Superconductivity
mass units [20] .More recent experiments suggest the above variation in the following general form TC M-α……………… (4) Where α is called the isotope effect coefficient and is defined as
……………… (5) On the other hand, according to recent theories α is given by α =0.5 [1-0.01(N (0) V)-2] ……………….. (6) Where N(0) is the density of single particle states for one spin at the Fermi level and Vis the potential between the electrons[20].
1.3. Meissner effect. This effect was reported in 1933 by two German physicists, W. Meissner and R. Ochsenfeld. Superconductivity had hitherto been thought of as merely a disappearance of electric resistance. But it is a more sophisticated phenomenon than simply the absence of resistance. Superconductivity is, in addition, a certain reaction to an external magnetic field. The Meissner effect consists of forcing a constant, but not very strong, magnetic field out of a superconducting sample. The magnetic field in a superconductor is weakened to zero, superconductivity and magnetism being, so to speak, “opposing” properties. When seeking new superconductors, one has to test a material for both these principal properties: whether the resistance vanishes and whether the magnetic field is forced out. In “dirty” superconductors, the fall of resistance with temperature may sometimes be much more extended than is shown in Fig. (1.5)[21, 17]: ……………………..(7) = μo H+ μo M = μo H (1+χm) …………………… (8) Where 7
Chapter One
Introduction to Superconductivity
μo: permeability of free space M : magnetization χm: the magnetic susceptibility H : external magnetic field Since B = 0 in the superconducting state, it follows that: M=-H χm = - 1
Fig.(1.5 ): Normal and superconducting state in the magnetic field[22].
1.4 Types of superconductors. On the basis of magnetic response, superconducting materials may be divided into two classifications designated as type I and type II. Type I materials, while in the superconducting state, are completely diamagnetic; that is, all of an applied magnetic field will be excluded from the body of material As H is increased, the material remains diamagnetic until the critical magnetic field Hc is reached. At this point, conduction becomes normal, and complete magnetic flux penetration takes place[23]. Several metallic elements including aluminum, lead, tin, and mercury belong to the type I group. Type II superconductors are completely diamagnetic at low applied fields, and field exclusion is total. However, the transition 8
Chapter One
Introduction to Superconductivity
from the superconducting state to the normal state is gradual and occurs between lower critical and upper critical fields, designated Hc1 and Hc2, respectively. The magnetic flux lines begin to penetrate into the body of material at Hc1, and with increasing applied magnetic field, this penetration continues; at Hc2, field penetration is complete. For fields between Hc1 and Hc2, the material exists in what is termed a mixed state both normal and superconducting regions are present.
as shown in
Fig.(1.6) .[23]
Fig (1.6). (a) Type-I superconductor behavior. (b) Type-II superconductor behavior[6]
1.5 Theories of Low Temperature Superconductor. During the first half of the century after the discovery of superconductivity
the
problem
of
fluctuation
smearing
of
the
superconducting transition was not even considered. In bulk samples of traditional superconductors the critical temperature Tc sharply divides the superconducting and the normal phases. It is worth mentioning that such behavior of the physical characteristics of superconductors is in perfect agreement
both
with
the
Landau-
Ginzburg-
Landau
(GL)
phenomenological theory (1950) and the BCS microscopic theory of superconductivity (1957) [6] . 9
Chapter One
Introduction to Superconductivity
1.5.1 The London theory Electron conduction in the normal state of a metal is described by .
Ohm's law j=
We modifies this to describe and the Meissner effect in
the superconducting state. We assume that in the superconducting state the current density is directly proportional to the vector potential A of the local magnetic field .Here, [ 24]
. The constant of proportionality is
. ………………………...(9)
Here, λL is a constant with the dimensions of length. This is the London equation. Taking the curl of both sides, we get ……………………… (10) Now, consider the Maxwell equation ……………………………..…(11) ………………………….(12) Now, (div B=0) - 2B= μ0
*
………………………....(13)
J +
………...(14)
……………………(15) Where λ: is the London penetration depth (this term relates to how deeply a magnetic field will penetrate the surface of a superconductor). Combining this definition with the GC form for the density of superconducting electrons results in a temperature dependent penetration depth,
[25]
√
…………………….….(16)
10
Chapter One
Introduction to Superconductivity
Although Eq.(16) has no microscopic justification, at low ,(
temperatures it takes the form nearly
indistinguishable
from
the
) exponential
- which is behavior
predicted by BCS theory[25]. …………… (17) where λ(0)is the penetration depth at T=0K. Fig.(1.7)shows the variation of penetration depth with temperature[14].
Fig.(1.7): penetration depth( λ) changes with the temperature
[25]
.
1.5.2 Ginzburg-Landau theory. Ginzburg-Landau theory macroscopically describes the behavior of superconductors, including quantum effects. It assumes a second order phase transition, which is correct for ZFC. It also assumes that the conduction electrons in a superconductor behave in a coherent manner,allowing them to be described by a single wave function with a possible phase difference[26] 11
Chapter One
Introduction to Superconductivity
ψ(r) = |ψ(r)|eiφ ………………………..(19) We must now define two characteristic lengths for a superconductor. The first is the coherence length(ζ) .One victory of Ginzburg-Landau theory is the prediction of type-II superconductivity.Defining ( κ = λ/ ξ ), we can make a statement about the sign of the interface energy σ ns[26] . The interface between two such domains is shown in Fig. (1.8). The ratio of penetration depth ( L ) to coherence length (ζ) is known as GinzburgLandau parameter (k) this parameter leads to a classification of superconductors into two types (Type I and Type II) as shown in Fig. (1.8).
Fig.(1.8): The boundary between superconducting (green) and normal (white) phases. The dependence of the magnetic field strength H and thc numbcr of superconducting electrons on the distance across the boundary are illustrated in (a) a type I superconductor and (b) a type I1 superconductor [27].
12
Chapter One
Introduction to Superconductivity
1.5.3 BCS theory. The first microscopic theory of superconductivity was proposed by John Bardeen, Leon Cooper, and Robert Schrieffer in 1957, now known as the BCS theory. A key conceptual element in this theory is the pairing of electrons close to the Fermi level into Cooper pairs through interaction with the crystal lattice. Roughly speaking the picture is the following as shown in Fig( 1.9)[28].
Fig. (1.9): The formation of a cooper pair: A passing electron attracts the positive charged ions of the lattice, causing a slight ripple in its wake. Another electron passing in the opposite direction is attracted to that displacement[28,29].
An electron moving through a conductor will attract nearby positive charges in the lattice. This deformation of the lattice causes another electron, with opposite momentum and spin, to move into the region of higher positive charge density. This looks like one electron attracts another electron through the lattice vibration, which can overcome the Coulomb repulsion, then two electrons become correlated. Individual pairs are not stuck together forever. They are constantly breaking and reforming. Individual electrons cannot be identified, so rather than consider them to be
13
Chapter One
Introduction to Superconductivity
dynamically changing pairs, they may be considered as permanently paired[28]. The BCS superconducting state arises as the consequence of (retarded) electron–phonon interaction and the cutoff is associated with the energy of the relevant phonons ћωP. In case of density wave states such retardation does not play a role, and the cutoff energy is the bandwidth of the metallic state. As this is usually significantly larger than the phonon energies, the transition temperatures for density waves are, in general, also larger than the superconducting transition temperatures. Another difference lies in the character of the state: if we calculate the electronic density for superconductors, we find it constant and independent on position, this is due to the observation that the total momentum of the Cooper pairs is zero – the superconducting gap opens at zero wave vector[30]. Coherence can be observed easily in system , such as electron pairs in superconductors. However, in case a decoherence time can be defined. In cases coherence in many particles systems is best observed if all particles are in the same state (superconductivity)and in both cases the transition from coherent to incoherent is due to the interaction with a bath[31].
1.6 Thermodynamics. The thermodynamic properties provide us with a great deal of important information on a material in particular on the energetics. Clearly, we learn something about the bulk while many spectroscopies suffer from surface sensitivities. However, it is not always trivial to isolate the desired quantity out of a large variety of contributions. In addition, in the presence of magnetism the thermodynamic potentials are not uniquely defined and the energy of the field B itself needs to be included in a way appropriate for the experimental circumstances. For a superconductor in the Meissner state, for instance, the field energy stored in the sample volume equals the 14
Chapter One
Introduction to Superconductivity
condensation energy. For simplicity we use the magnitudes of B, H, and M rather than the vectorial quantities. This corresponds to a specialization to cylindrical symmetry and homogeneous media[32].
1.6.1 Thermodynamics of Superconducting Transitions . The Gibbs free energy per unit volume in the magnetic field is give [20] …………………………….(20) Where M is the Magnetization, S is the entropy and PV is neglected Also , from second law of the thermodynamics, the internal energy given by …………………………..(21) At comparing this value with the standard expression for internal energy for a gas, we find that H plays a role of P and M for –V .Now differentiating eq. 20, we obtain …(22) Further, at constant temperature, d T= 0, so that eq.22 reduces to …………………….(23) Integrating eq.(23) for the superconducting state ,we get ∫
∫
…………………(24) ∫
………..
…..(25)
On other hand, if the sample is in the normal state ,it is a paramagnet and therefore M
0 or X 0,so that from eq.25,we can write ………………..(26)
or
Implying that in normal state the Gibbs function remains invariant under the application of the magnetic field. Now ,if we see the curve HC versus T (Fig .1.4) ,we find that the normal state and the superconducting state are in equilibrium and therefore the free energies of the two state at boundary must be equal .this gives ………………….(27) 15
Chapter One
Introduction to Superconductivity
Combing eqs.25 and 27 ,we obtain ……………..(28)
∫
= And eqs. 26 ,28 give ∫ ΔG
∫
or
or
…………………….(29)
∫
Now , from Meissner effect we know that M= -H (B=0) ,so that ∫
∫
……………..(30)
1.6.2.Entropy Difference and specific heat. Transition between the normal and superconducting states is thermodynamically reversible . The entropy difference between the two states is given by[20] …………….(31) The latent heat of the system is related to the entropy difference as …………….(32) The difference in the specific heats of the two state is given as (
) ……………….(33)
The electronic specific heat of superconductor is given by ⁄
……………..(34)
Where a is constant and
is the energy is the energy gap
16
Chapter Two
Superconducting system
2.1 Introduction. The major breakthrough came in 1986 when J.G. Bednorz and K.A. Muller discovered superconductivity with a TC (onset) of 35 K a new record in a mixed phase copper-oxide ceramic containing La2–xBaxCuO4. The end of 1986 and the beginning of 1987 was marked by synthesis of rare-earth metal oxides with the discovery of Yttrium barium copper oxide (YBa2Cu3O7) , which has a critical temperature of about 92 K. This was a significant breakthrough as it meant that for the first time the world has witnessed the existence of a superconductor with a Tc above that of liquid nitrogen (boiling point 77 K).[33]
2.2 Crystal Structure of Bi-Sr-Ca-Cu-O. Since the discovery of a High Tc superconducting phase in the Bi-SrCa-Cu-O(BSCCO) system by Maeda and his coworkers in January 1988 , extensive research has gone into the areas of processing, characterization, phase equilibria, physical property measurement, and device fabrication of these materials[34]. Of the material systems that superconductor above liquid nitrogen temperature (77.3K). The BSCCO compound consists of anoxygen deficient perovskite layer containing Copper oxide planes sandwiched between bismuth oxide layers .The number of copper oxide planes corresponds to the n in the chemical formula Bi 2Sr2Ca(n.1)CunO
x
where n = 1, 2, or 3. As the number of copper oxide planes increases, so does the critical temperature[34].Bi-2223 has a tetragonal, layered, orthorhombic perovskite structure composed of two charge-reservoir layers (Bi-O , Sr-O) sandwiching three CuO2 planes of strong superconductivity. This picture of a block-layer structure is shown schematically in Fig.(2-1)[35], . The lattice parameters of the fundamental unit cells, determined by X-ray diffraction, are as follows: a= 5.49Å , b=5.46Å and c=39.3
for 2212-phase. The substitution of cations
frequently occurs in these phases. The values of these parameters changes 17
Chapter Two
Superconducting system
slightly depending on the cationic substitution [36]. Partial substitution for Bi+3 by ions of various radii and valance such as Pb+2 in Bi2Sr2Ca2Cu3O10+δ compound may be affect the HTSC phase formation, chemical stability and the superconducting properties [36], and a= 5.4082 Å, b= 5.4082Å and c= 34.1315Å for 2223-phase .The formation of Bi-2223 phase by quenching the samples in air gave Tc 110K[37], which is higher than the Tc. The perovskite structure are known to be stable when the tolerance factor tf is the range of (0.8 tf 0.9)[36,37],tf in the Bi2Sr2Can-1CunO2n+4+δ superconductors which can be expressed as follows [38]; tf
⁄
……………………. (35)
Fig. (2.1): Crystal structures of the homologous series of Bi-system superconductors, Bi2Sr2Can-1CunO2n+4+δ (n = 1, 2, 3)[35]
18
Chapter Two
Superconducting system
2.3 Phase Diagram of Cuprate Superconductors. All electron properties of high temperature superconductors depend strongly on the doping. High temperature superconductors without doping are dielectrics and antiferromagnetics. As the concentration x increases, these materials become metals. Superconductivity arises at large x, behind the limits of the magnetically ordered phase. The experiments showed that the charge carriers have the hole character for all classes of hightemperature superconductors. It becomes clear recently that the hightemperature superconductivity is related to peculiarities of the behavior of these compounds in the normal phase. As seen from phase diagram (Fig. 2.2), the superconducting states arise near the antiferromagnetic phase. In yttrium containing systems, the antiferromagnetic and superconducting regions adjoin one another. The experiments on the inelastic magnetic scattering of neutrons indicate the existence of strong magnetic fluctuations in the doped region, even beyond the limits of the antiferromagnetic phase. In high temperature superconductors, the gap is present in the absence of the phase coherence, i.e., in nonsuperconducting specimens. This gap is called a pseudogap. A pseudogap is shown in (Fig. 2.2). It appears at temperatures less than some characteristic temperature T∗ which depends on the doping. Its nature is not completely explained else. The study of a pseudogap in the electron spectrum of hightemperature superconductors was carried out in many works.13 Metals become superconductors, if their free electrons are bound in Cooper‟s pairs. Moreover, the pairs are formed in such a way that their wave functions have the same phase. The phase coherence is responsible for the change of the resistance on the cooling below the critical temperature Tc. The presence of coupled pairs in a superconductor causes the appearance of a gap in the spectrum of excitations. In the standard superconductors, the phase coherence of pairs appears simultaneously with the appearance 19
Chapter Two
Superconducting system
of pairs. From one viewpoint, a pseudogap is related to the appearance of coupled pairs, which is not related to the phase coherence. Another viewpoint consists in the following. The pseudogap arises in HTSC in connection with the formation of magnetic states which compete with superconducting states. The efforts of experimenters aimed at the solution of this dilemma are complicated by a strong anisotropy of the superconductor gap. Some physicists believe that the most probable situation is related to the creation of the superconducting state with paired electrons at a certain doping which coexists with antiferromagnetism. It is possible that just it is the “new state of matter” which has been widely discussed for the last years in connection with HTSC[39].
Fig:( 2.2) Phase diagram of cuprate superconductors in the temperature- doping variables, TN-the Néel temperature, Tc-the critical temperature of the superconducting transition, T∗-the characteristic temperature of a pseudogap, T 0upper crossover temperature[39].
2.4 Theories of High Temperature Superconductor.
20
Chapter Two
Superconducting system
The discovery of superconductivity in ceramic marked the beginning of high temperature superconductor (HTSc). Many theoretical models have been proposed to explain the pairing mechanisms in HTS [40].
2.4.1 Excitons and Plasmons Model. Allender et al[40] proposed a metal into such intimate contact with analogue to a polarizable narrow gap semiconductor that the metallic electrons would be able to interact strongly with interband excitations of the semiconductor. Pairing would then occur by the exchange of these virtual excitations. The Plasmon mechanism, looks like the exciton mechanism. Eliashbreg[40] assumes that electronic polarization serves only to cancel part of the direct coulomb repulsion, and that only phonon polarization is sufficiently strong and retarded to contribute to pair binding. Thus, a reasonable question is whether, in the absence of phonons, the other polarization mechanisms can cause superconductivity
2.4.2 Interlayer Coupling Model. In this model, the superconductivity occurs in the two-dimensional Cu-O2 layers, and interlayer tunneling is essential because the coherence length normal to the Cu-O2 layer is so short[40]. So the supercurrent could then flow between Cu-O2 layers by taking the advantage of the metallic states on the intervening layers ,essentially hopping from copper-oxygen layer to another copper-oxygen layer by tunneling through the metallic interlayer[38,40].
2.4.3 Isotope Model. The important point to be noted is that an isotope effect strongly indicates that phonons are involved in the pairing and that the lack of an isotope effect cannot be interpreted as a conclusive evidence of the absence of phonon mediated pairing [38,40].
2.4.4 Oxygen Defect Model. 21
Chapter Two
Superconducting system
This model depends on the fact that the structural analysis of the unit cell shows that there are oxygen defects (vacancies)in the Cu-O2 layers, and suggests that the special structure of the oxygen defects together with the electronic filling of Copper pairs in particular are combined to enhance the pairing interaction significantly in HTS materials[28]. The vacancies are assumed to be randomly distributed in the copper oxide planes. One-electron energetically attract electrons to the pairs of copper ions next to vacancies. Electrons at these sites have an enhanced probability to be found between the two ions with singlet spin correlation. Similarly, there are many reported experimental phenomena including spin glass-like behavior emphasize the dependence of the superconducting properties on the oxygen content of the oxide and this leads to shortening of positron lifetimes in the superconductors [38,40].
2.5 Polyaniline. Polyaniline is one such polymer whose synthesis does not require any special equipment or precaution. Among the PANI has become one of the most technologically important one due to its unique process ability, together with relatively inexpensive monomer and high yield of polymerization . PANI is fast replacing the conventional materials because of its fascinating electrical properties. This interest is caused by diverse, but also unique ,properties of PANI allowing its potential applications in various fields, such as energy storage and transformation (alternative energy sources, erasable information storage, non-linear optics, shielding of electromagnetic interference), as well as catalysts, indicators, sensors, membranes of precisely controllable morphology, etc[41].
2.5.1 Structure of Polyaniline . The molecular structures were characterized by FTIR, UV-Vis absorption and X-ray diffraction, showing that, the main chain and electronic structure are identical to the doped polyaniline, but exhibit 22
Chapter Two
Superconducting system
partial crystallinity.18 Ab initio calculations give an accurate description for the structure and vibrational spectra for huge number of molecules[42] . There are 36 calculated genuine vibrations corresponding to this molecule. The general formual for aniline beside its calculated structure is mentioned in Figure (2.3a). Aniline has an empirical formula C6H7N4 and its molecular point group Cs is equal to 1. The general formula and structure of polyaniline is described in Figure (2.3b)[42,43].
Fig (2.3) Structure of the Polyaniline chain[42,43]
Oxidative Polymerization of Aniline: Passage of current through a solution results in oxidation (electron loss) at the anode and reduction (electron gain) at the cathode. This process is referred to as electrochemical polymerization when polymer is formed. Polyaniline [IUPAC: poly(imino-1,4-phenylene)] is obtained by the oxidative polymerization of aniline in aqueous HCl solution, either by electrochemical polymerization or by using a chemical oxidant such as ammonium persulfate, (NH4)2S2O8 . Polymerization proceeds by a chain polymerization mechanism, but is included in this section on conjugated polymers for convenience. Initiation involves a loss of two electrons and one proton from aniline to form a nitrenium ion (Eq. 36), which subsequently attacks aniline by electrophilic substitution (Eq. 37). 23
Chapter Two
Superconducting system
Propagation proceeds in a similar manner by oxidation of the primary amine end of a growing polymer chain (Eq. 38) followed by electrophilic substitution (Eq. 39). The process has been referred to as reactivation chain polymerization to highlight the fact that the chain end formed after each addition of aniline must be reactivated to the nitrenium ion by oxidation and proton loss. The product formed directly from oxidative polymerization is not the neutral structure shown in Eq. 39. The polymer has the positively charged structure LVI, which is referred to as emeraldine salt, and it is the conducting form of polyaniline. Other forms of polyaniline can be obtained after synthesis by varying the applied voltage and pH . Polyaniline offers considerable promise for commercialization. There have been extensive studies using substituted anilines alone or in copolymerization with aniline to alter the conducting and optoelectronic properties of the polymer as well as their solubility characteristics[44].
24
Chapter Two
Superconducting system
Fig (2.4): X-ray diffraction of Polyaniline[45] .
Fig (2.5): FTIR spectrum of the Polyaniline[46].
2.5 Literature Survey of Bi-Ba-Ca-Cu-O Dawud. [2000] [47]. Studied the effect of n variation on the HTSC behavior and the addition of Pb of the Bi2Sr2Can-1CunO2n+4 system. Two types of samples have been prepared by solid state reaction method, the first type without addition of PbO and the second type with PbO doped by 5% wt. of the calcined powder. She found that the highest Tc obtained for the Pb-free samples was about 105K,while that of the Pb contained samples was about 130K by sintering temperature (845-848)oC under low flow rate of oxygen, and she observed that Tc increase with increasing n up 25
Chapter Two
Superconducting system
to n=3.5, further increasing of n to values greater than 4 has negative effect on the value of Tc. Hermiz. [2001] composition
[48]
. Studied prepared was HSC with a nominal
(Bi1-xPbx)2(Sr1-yBay)2Ca2Cu3O10+δ
for
(0>x>0.5)
and
(0
