Poole Ch.P., Jr. Handbook of Superconductivity

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x Contributors

Arthur P. Ramirez (96), Lucent Technologies, Bell Laboratories, Murray Hill,

New Jersey

Ctirad Uher (491), Department of Physics, University of Michigan, Ann Arbor,

Michigan

Winnie Wong-Ng (625), Ceramics Division, National Institute of Standards and

Technology, Gaithersburg, Maryland

John E Zasadzinski (445), Physics Department, Illinois Institute of Technology,

Chicago, Illinois

Roberta K. Zasadzinski (445), Physics Department, Illinois Institute of Techno-

logy, Chicago, Illinois

Preface

On April 17, 1986 the brief article "Possible High temperature Superconductivity

in the Ba-La-Cu-O System" by J. G. Bednorz and K. A. Mtiller appeared in the

journal

Zeitschrift f~r Physik,

and the High-Tc era had began. The initial

skepticism about the discovery was soon dispelled when several other research

groups confirmed the findings, and an enormous world wide research effort began

in quest of a room temperature superconductor. Within a year, the critical

temperature was raised to 90-93 K (above liquid nitrogen temperature) with

the discovery of the yttrium compound, and then in 1988 it increased further to

120 K and 125 K with the successive discoveries the bismuth and thallium

cuprates. In 1993, the mercury cuprate went superconducting at 133 K at

atmospheric pressure, and at 155 K when subjected to a pressure of 25 GPa.

We were past the half-way point to room temperature! During this same period,

several new types of compounds were found to exhibit superconductivity, such as

the cubic perovskite BaKBiO, alkali metal doped buckmasterfullerenes, and

borocarbides.

Some of the exciting things about the high Tc cuprates are the ways in

which many of their properties differ from those typical of most classical

materials. For example, their Cooper pair charge carriers are formed from positive

holes rather than negative electrons; they have layered structures with some two

dimensional behaviors; their coherence lengths are approaching interatomic

distances; their pairing mechanism seems to be d-wave rather than s-wave;

their properties are highly anisotropic, fluctuation effects are prominent, and

polycrystalline cuprate materials are composed of micron sized grains. Clarifying

and explaining these properties has been one of the principal concerns of all

workers in the field.

Prior to Bednorz and Mtiller's discovery, the field of superconductivity was

in a steady state of activity, with the number of annual publications on the subject

comprising about 0.6% of the overall physics literature. During the two year

period after the discovery the number of publications underwent a dramatic rise to

about 3.5% of the total, and then two years after that the rate began a gradual

decline, but it is still far above the pre-1986 value. In the early years of the

xii

Preface

high-To era much of the work was carried out with granular samples, and single

crystals were often extensively twinned, especially those of YBaCuO. Most of the

initial important research was reported at meetings, and conference proceedings

became an important vehicle for disseminating information. Many early reports

appeared in letter journals, then longer articles became more frequent, and finally

review articles. The year 1988 saw the appearance of the

Journal of Super-

conductivity,

the review series

Physical Properties of High Temperature Super-

conductors,

and our book

Copper Oxide Superconductors,

signaling that the field

had reached an initial level of maturity. By 1990, several monographs had

appeared, several Institutes of Superconductivity had been established, much

more definitive measurements on well characterized monocrystals and epitaxial

thin films were being reported in the literature, and theoretical explanations were

providing more understanding. Experimental and theoretical progress has con-

tinued to be made until the present time.

During the past decade, an enormous amount of reliable experimental data

have been accumulated on both classical, High To, and other types of super-

conductors. The time is now fight to gather together this information into a

handbook to make it readily available for researchers. This volume represents an

effort to do this for the field of superconductivity as a whole, i.e. for all types of

superconductors. The initial draft for this work was a compilation of handbook

type material made from the 1995 monograph

Superconductivity,

coauthored by

the present editor. This provided definitions, equations, temperature and field

dependencies, and much other information routinely needed by researchers. To

this was added material from other sources, and tabulations of experimentally

determined parameters of various types such as critical temperatures T~, atom

positions, coherence lengths, penetration depths, energy gaps, critical fields B~,

and critical currents Jc, among others. The main conclusions from several models

and theories were summarized for easy comparison with measurements. The goal

is to provide a ready source containing most of the information that a researcher

would be likely to look up during the course of his or her investigations.

This handbook is not just about the copper oxide superconductors, but

about all superconductors. The first chapter provides an overview, units and

conversion factors, and a lengthy glossary of terms. Chapter 2 summarizes the

properties of the normal state, and Chapter 3 does the same for the super-

conducting state. The fourth chapter presents the results of the main models and

theories that are routinely used to explain experimental data. Chapter 5

summarizes the properties of the various types of classical materials as well as

those of more recently discovered superconducting systems, and provides an

extensive tabulation of their transition temperatures. The crystal structures of

these compounds are presented in the sixth chapter. The general features of the

atom arrangements in high Tc cuprates are reviewed in Chapter 7, and the details

of their individual structures are provided in Chapter 8. The ninth chapter

furnishes long tabulations of the various parameters such as B~ and J~ that

were mentioned above. The next chapter covers thermal properties such as the

Preface xiii

specific heat, thermal conductivity, and entropy transport, as well as thermo-

electric and thermomagnetic effects. Chapter 11 surveys electrical properties such

as the Hall effect, tunneling, Josephson junctions, and superconducting quantum

interference devices (SQUIDS). Chapter 12 covers magnetic properties such as

susceptibility, magnetization, critical fields, vortices including their anisotropies

and their motion, transport current in a magnetic field, and intermediate states.

Chapter 13 examines various mechanical properties like elastic, shear, and bulk

moduli, Poisson's ratio, flexural and tensile strength, hardness, and fracture

toughness. Finally, the last chapter on compositional phase diagrams presents

many ternary and a few quaternary (tetrahedral) phase diagrams for all the basic

cuprate systems. Included are several liquidus surface, subsolidus equilibrium,

primary crystallization field, and temperature/composition plots.

It is hoped that, Deo volente, the data tabulations, and other information

gathered together in this volume will have a significant influence on expediting

the progress of future research.

Charles P. Poole, Jr.

Columbia, South Carolina

This Page Intentionally Left Blank

Chapter I

Introduction

Charles

Poole, ]r.

Department of Physics and Institute of Superconductivityr

University of South Carolina, Columbia, South Carolina

A. Introduction 1

B. Definition of a Superconductor 2

C. Form and Content of Handbook 3

D. Several Miscellaneous Tables 3

E. Glossary of Terms 11

References 27

Introduction

This handbook is concerned with superconductors, materials characterized by

certain electrical, magnetic, and other properties, many of which will be

explained in the third chapter. In this chapter we will define the two types of

superconductors, describe the format and content of the Handbook, make some

suggestions for how to use it, and provide the basic units and conversion factors

that are commonly used in the field. Much of the material in this handbook has

been elaborated upon in greater detail in the 1995 monograph

Superconductivity

[Poole

et al.],

and for many topics that volume will provide more details. The

present book, of course, is much more complete in areas such as tabulations of

data and descriptions of crystallographic structures. Some topics found here,

such as mechanical properties and phase diagrams, were not covered in the earlier

work.

ISBN: 0-12-561460-8 HANDBOOK OF SUPERCONDUCTIVITY

$30.00 Copyright 9 2000 by Academic Press.

All fights of reproduction in any form reserved.

Chapter 1: Introduction

Definition of a Superconductor

A Type I superconductor exhibits two characteristic properties, namely zero dc

electrical resistance and perfect diamagnetism, when it is cooled below its critical

temperature To. Above Tc it is a normal metal, but ordinarily not a very good

conductor. The second property of perfect diamagnetism, also called the Meiss-

ner effect, means that the magnetic susceptibility has the value g = -1 in mks

or SI units, so a magnetic field (i.e., magnetic flux) cannot exist inside the

material. There is a critical magnetic field Bc with the property that at the

temperature 0 K applied fields

Bap p >_

B c drive the material normal. The tempera-

ture dependence of the critical field

B~(T)

can often be approximated by the

expression, where we use the notation B~(0) = Be,

Bc(T ) -- Bc[1

- (T/Tc)2].

(1)

The Type I superconductors are elements, whereas alloys and compounds are

Type II.

A Type II superconductor is also a perfect conductor of electricity, with zero

dc resistance, but its magnetic properties are more complex. It totally excludes

magnetic flux in the Meissner state when the applied magnetic field is below the

lower critical field Bcl, as indicated in Fig. 1.1. Flux is only partially excluded

when the applied field is in the range from Bcl to Bc2 , and the material becomes

normal for applied fields above the upper critical field Bc2. Thus, in the region of

Fig. 1.1.

BC2

Be,

MELTING LINE

......--

oo,o

MEISSNER

~----

TEMPERATURE (T)

NORMAL STATE

-- -Bc2(T) CURVe

- - B:,(T) CURVE

Simplified magnetic phase diagram of a Type II superconductor showing the Meissner region

of excluded magnetic flux below the lower critical curve Bcl(T), the flux solid and flux liquid

phases separated by the melting

curve Tm,

and the normal state region that lies outside the

upper critical field

curve Bcz(T).

[From Owens and Poole (1996), Fig. 3.12.]

D. Several Miscellaneous Tables 3

higher magnetic fields the diamagnetism is not perfect, but rather of a mixed type

that exhibits solid-like properties at lower temperatures and liquid-like properties

at higher temperatures, as indicated in the figure. The melting line separates these

two regions of magnetic behavior.

These definitions of superconductors have been expressed in terms of

properties. In addition, they do not take into account demagnetization effects that

cause the diagmagnetism to depend on the shape of the sample and its orientation

in an applied field. More fundamentally, a superconductor can be defined as a

conductor that has undergone a phase transition to a lower energy state below a

transition temperature T c in which conduction electrons form pairs called Cooper

pairs, which carry electrical current without any resistance to the flow, and which

are responsible for the perfect diamagnetism and other properties.

Form and Content of Handbook

The various chapters of this Handbook cover different aspects of the field of

superconductivity. The present chapter provides the units and conversion factors

that will be widely referred to throughout the remainder of the text, as well as a

glossary of terms. This is followed by chapters that describe the normal state

above T c and the superconducting state below T c. Then comes a chapter that

summarizes the important theories and models that are employed to understand

the nature and explain the properties of superconductors. Next we present, in

succession, the classical superconductors, the superconducting materials that

were discovered during the past decade and a half, and most importantly, the

cuprates. The remaining seven chapters present data on the various properties of

superconductors. The chapters are self-contained, so any one of them can be

referred to without previously reading earlier ones. It is anticipated that the main

use of the Handbook will be its consultation by researchers who need information

on particular topics or data on particular compounds, although many sections can

be read to refresh one's memory about particular aspects of the subject. Of

especial interest are the tabulations of critical temperatures in Chapter 5 and the

tabulations of data on critical magnetic fields, critical currents, and other

properties found in Chapter 9. The glossary in Section E of this chapter contains

many definitions of terms.

Several Miscellaneous Tables

Table 1.1 provides some of the physical constants and key equations that are

commonly encountered in superconductivity research, and lists some conventions

4 Chapter 1: Introduction

Table 1.1.

List of physical constants and important equations.

Fundamental constants

Avogadro's number

Boltzmann constant

Dieletric constant of vacuum

Electron charge

Fine structure constant

Gas constant

Gravitation constant

Light speed in vacuo

Permeability of vacuum

Planck constant

Planck reduced constant

Quantum of circulation

Rydberg (H-atom) energy

Stefan Boltzmann constant

Wien displacement law

N A = 6.0221 x 1023 mo1-1

k B = R/N A = 1.3807 x 10 -23 J/K

e 0 = 8.8542 x 10 -12 F/m

e = 1.6022 x 10 -19 C

~= e2/4~zeohc=7.2974x 10-3(! ,~ 137)

R = NAk B = 8.3145 J/mol K

G = 6.6726 x 10 -11 m3/kgs 2

c = 2.9979 x 108 m/s

#0 = 4re x 10 -7 N/A 2 = 1.2566 x 10 -6 N/A 2

h =6.6261 x 10

Js (4.1357 x 10 -15 eVs)

h = h/2~z = 1.0546 x 10

h/m e = 7.2739 x 10-4m2/s

e2/81teoao = 2.1799 x 10 -18 J (13.606eV)

a = 5.6705 x 10 -8 W/m2K 4

2ma x T = 2.8978 x 10 -3 mK

Electromagnetic constants

Bohr magneton

Nuclear magneton

Faraday constant

Flux quantum, magnetic

g-factor, electron

Hall resistance

Resistance quantum

Josephson frequency

tl B

e'h/2m e = 9.2740 x 10

-24

J/T

]2 N -- 5.0508 X 10 -27

J/T

F = NAe = 96485 C/mol

% = h/2e = 2.0678 x 10 -15 Wb

ge = 2.0023

R H = h/e 2 -- 25,813 f~

RQ = RH/4 = 6453.2 f~

ooj = 2rc(2 eV/h) [ 1 ktV = 483.60 MHz]

Length constants

Classical electron radius

Thomson cross section

Compton wavelength (electron)

Bohr radius

r e = ~2a 0 = e2/4Tceome c2 = 2.8179 x 10 -15 m

a = (8n/3)~ = 6.6525 x 10 -29 m 2

'~c -- h/meC -- 2.4263 x 10 -12 m

a o = re/~ 2 = 4neoh2/me 2 = 5.2918 x 10 -11 m

Temperature expressions

Debye temperature

Fermi temperature

Supercond. trans. Temp.

Specific heat (T << |

Critical current

Critical field

Critical field slope

Energy gap

Penetration depth

Superelectron density

(~D = h(-OD/kB

T F =EF/kB =h2k2/2mkB

T~ =

o.e834E~/k~

C = 7T + AT e

tic(T) -- ffc(0)[1 - (T/Tc)2][1 -

(Z/Tc)4] 1/2

Bc(T ) = Be(0)[1 - (T/Tc) 2]

dBc2/dT = - 1.83 T/K

~g(T) = Eg(0)[1 -

(7/rc)] ~/2

)~T = )],(0)[1 --

(T/Tc)4] -1/2

ns(T ) = ns(0)[1

(T/Tc) 4]

(continued)

D. Several Miscellaneous Tables 5

Table 1.1.

(continued)

Temperature expressions (0~ = 273.15K)

He 4 lambda point T~ = 2.174 K

He 3 boiling point T m, = 3.20 K

He 4 boiling point TBp = 4.216 K

H 2 boiling point T m, = 20.28 K

N2 boiling point TBp = 77.35 K

02 boiling point TBp = 90.18 K

Conversion factors

Energy:

Length:

Magnetic field:

Pressure:

Temperature:

Multiples:

Submultiples:

1 eV = 1.6022 x 10 -19 J -- 1.7827 x 10 .36 kg

-- 2.4180 x 10

Hz -- 806554 m -1

-- 1.0735 x 10 -9 u -- 1.1604 x 104 K

1 m -- 100 cm -- 101~ 1 marathon=42.352km

1 T= 1Wb/m2= 104G

GPa -- 10 kBar = 7.5 x 106 torr -- 0.987 x 104 atm

1 K = 1.3807 x 10 -23 J -- 1.5362 x 10 -4~ kg -- 2.0837 x 101~ Hz

--69.504 m -1 = 9.251 x 10-14 u---8.6174 x 10 -5 eV

k (kilo, 103); M (mega, 106); G (giga, 109); T (tera, 1012); P (peta, 1015);

E (exa, 1018); Z (zetta, 1021); Y (yotta, 1024)

m (milli, 10-3); I.t (micro, 10-6); n (nano, 10-9); p (pico, 10-12);

f (femto, 10-15); a (atto, 10-18); z (zepto, 10-21); y (yocto, 10 -24)

Particle properties

Particle Mass Rest energy Rest energy Magnetic moment

(xl0

kg) (xl0 -19 J) (MeV) (xl0 -26 J/T)

Electron 9.10939 0.81871 0.51100 928.48

Muon 1883.53 169.29 105.66 4.4905

Proton 16726.2 1503.3 938.27 1.4106

Neutron 16749.3 1505.4 939.57 - 0.99624

Atomic 16605.4 1492.4 931.494

constant

(1/12 of 12C)

Normal state expressions

Density of states

Electrical conductivity

Hall effect

Magnetic field

Plasma frequency

Electronic specific heat

D(EF)

= (1/2rc2)(2m*/hZ)3/ZE~/2

o- 0 --

ne2z/m

R n = +l/ne

B = ~0(H + M) = mH(1 + Z) = ~H

COp -- (neZ /%m) 1/2

(continued)