E-Book, Englisch, 870 Seiten
Poole / Farach / Creswick Superconductivity
3. Auflage 2014
ISBN: 978-0-12-416610-3
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark
E-Book, Englisch, 870 Seiten
ISBN: 978-0-12-416610-3
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark
Charles P. Poole, Jr., professor emeritus in the Department of Physics and Astronomy of the University of South Carolina, Fellow of the American Physical Society and the EPR/ESR Society, Editor of Handbook of Superconductivity and Encyclopedic Dictionary of Condensed Matter Physics. He passed away in 2015.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Superconductivity;4
3;Copyright Page;5
4;Dedication;6
5;Contents;8
6;Preface to the First Edition;20
7;Preface to the Second Edition;24
8;Preface to the Third Edition;28
9;1 Properties of the normal state;30
9.1;I Introduction;30
9.2;II Conducting electron transport;30
9.3;III Chemical potential and screening;34
9.4;IV Electrical conductivity;36
9.5;V Frequency-dependent electrical conductivity;37
9.6;VI Electron–phonon interaction;38
9.7;VII Resistivity;39
9.8;VIII Thermal conductivity;40
9.9;IX Fermi surface;41
9.10;X Energy gap and effective mass;44
9.11;XI Electronic specific heat;46
9.12;XII Phonon specific heat;47
9.13;XIII Electromagnetic fields;51
9.14;XIV Boundary conditions;52
9.15;XV Magnetic susceptibility;53
9.16;XVI Hall effect;56
9.17;Problems;59
9.18;Further Reading;60
9.19;References;60
10;2 Phenomenon of superconductivity;62
10.1;I Introduction;62
10.2;II Brief history;62
10.3;III Resistivity;66
10.3.1;A Resistivity above Tc;66
10.3.2;B Resistivity anisotropy;70
10.3.3;C Anisotropy determination;71
10.3.4;D Sheet resistance of films: resistance quantum;73
10.4;IV Zero resistance;76
10.4.1;A Resistivity drop at Tc;76
10.4.2;B Persistent currents below Tc;77
10.5;V Transition temperature;79
10.6;VI Perfect diamagnetism;84
10.7;VII Magnetic fields inside a superconductor;85
10.8;VIII Shielding current;88
10.9;IX Hole in superconductor;90
10.10;X Perfect conductivity;95
10.11;XI Transport current;96
10.12;XII Critical field and current;100
10.13;XIII Temperature dependences;101
10.14;XIV Two-fluid model;104
10.15;XV Critical magnetic field slope;105
10.16;XVI Critical surface;106
10.17;Problems;111
10.18;References;112
11;3 Transport properties;116
11.1;I Introduction;116
11.2;II Inductive superconducting circuits;116
11.2.1;A Parallel inductances;116
11.2.2;B Inductors;118
11.2.3;C Alternating current impedance;119
11.3;III Current density equilibration;122
11.4;IV Critical current;124
11.4.1;A Anisotropy;124
11.4.2;B Magnetic field dependence;126
11.5;V Magnetoresistance;128
11.5.1;A Fields applied above Tc;128
11.5.2;B Fields applied below Tc;130
11.5.3;C Fluctuation conductivity;132
11.5.4;D Flux flow effects;133
11.6;VI Hall effect;137
11.6.1;A Hall effect above Tc;137
11.6.2;B Hall effect below Tc;139
11.7;VII Thermal conductivity;140
11.7.1;A Heat and entropy transport;141
11.7.2;B Thermal conductivity in the normal state;142
11.7.3;C Thermal conductivity below Tc;145
11.7.4;D Magnetic field effects;147
11.8;VIII Thermoelectric and thermomagnetic effects;147
11.8.1;A Thermal flux of vortices;149
11.8.2;B Seebeck effect;150
11.8.3;C Nernst effect;154
11.8.4;D Peltier effect;157
11.8.5;E Ettingshausen effect;158
11.8.6;F Righi–Leduc effect;160
11.9;IX Photoconductivity;161
11.10;X Transport entropy;165
11.11;Problems;166
11.12;References;167
12;4 Thermodynamic properties;172
12.1;I Introduction;172
12.2;II Specific heat above Tc;172
12.3;III Discontinuity at Tc;179
12.4;IV Specific heat below Tc;181
12.5;V Density of states and Debye temperature;181
12.6;VI Thermodynamic variables;182
12.7;VII Thermodynamics of a normal conductor;184
12.8;VIII Thermodynamics of a superconductor;187
12.9;IX Superconductor in zero field;191
12.10;X Superconductor in a magnetic field;192
12.11;XI Normalized thermodynamic equations;199
12.12;XII Specific heat in a magnetic field;199
12.13;XIII Further discussion of the specific heat;204
12.14;XIV Order of the transition;207
12.15;XV Thermodynamic conventions;207
12.16;XVI Concluding remarks;208
12.17;Problems;209
12.18;References;210
13;5 Magnetic properties;212
13.1;I Introduction;212
13.2;II Susceptibility;212
13.3;III Magnetization and magnetic moment;213
13.4;IV Magnetization hysteresis;216
13.5;V ZFC and FC;217
13.6;VI Granular samples and porosity;221
13.7;VII Magnetization anisotropy;223
13.8;VIII Measurement techniques;224
13.9;IX Comparison of susceptibility and resistivity results;226
13.10;X Ellipsoids in magnetic fields;226
13.11;XI Demagnetization factors;228
13.12;XII Measured susceptibilities;229
13.13;XIII Sphere in a magnetic field;232
13.14;XIV Cylinder in a magnetic field;234
13.15;XV ac susceptibility;237
13.16;XVI Temperature-dependent magnetization;239
13.16.1;A Pauli-paramagnetism;240
13.16.2;B Paramagnetism;240
13.16.3;C Antiferromagnetism;242
13.17;XVII Pauli limit and upper-critical field;244
13.18;XVIII Ideal Type II superconductor;248
13.19;XIX Magnets;249
13.20;Problems;250
13.21;References;251
14;6 Ginzburg–Landau phenomenological theory;254
14.1;I Introduction;254
14.2;II Order parameter;254
14.3;III Ginzburg–Landau equations;255
14.4;IV Zero-field case deep inside superconductor;258
14.5;V Zero-field case near superconductor boundary;260
14.6;VI Fluxoid quantization;263
14.7;VII Penetration depth;264
14.8;VIII Critical current density;268
14.9;IX London equations;271
14.10;X Exponential penetration;272
14.11;XI Normalized Ginzburg–Landau equations;278
14.12;XII Type I and Type II superconductivity;280
14.13;XIII Upper critical field BC2;283
14.14;XIV Structure of a vortex;284
14.14.1;A Differential equations;284
14.14.2;B Solutions for short distances;285
14.14.3;C Solution for large distances;287
14.15;Problems;290
14.16;Further reading;291
14.17;References;292
15;7 Bardeen–Cooper–Schrieffer microscopic theory;294
15.1;I Introduction;294
15.2;II Cooper pairs;294
15.3;III The BCS order parameter;298
15.4;IV The BCS Hamiltonian;301
15.5;V The Bogoliubov transformation and the self-consistent gap equation;302
15.5.1;A Solution of the gap equation near Tc;303
15.5.2;B Solution at T=0;304
15.5.3;C Nodes of the order parameter;304
15.5.4;D Single band singlet pairing;304
15.5.5;E s-Wave pairing;305
15.5.6;F Zero-temperature gap;307
15.5.7;G d-Wave order parameter;309
15.5.8;H Multiband singlet pairing;311
15.6;VI Response of a superconductor to a magnetic field;314
15.7;VII Hubbard models;318
15.8;VIII Electron configurations;319
15.8.1;A Configurations and orbitals;319
15.8.2;B Tight-binding approximation;322
15.9;IX Hubbard model;326
15.9.1;A Wannier functions and electron operators;327
15.9.2;B One-state Hubbard model;328
15.9.3;C Electron-hole symmetry;329
15.9.4;D Half-filling and antiferromagnetic correlations;331
15.9.5;E t-J model;332
15.9.6;F Resonant-valence bonds;333
15.9.7;G Spinons, holons, slave bosons, anyons, and semions;335
15.9.8;H Three-state Hubbard model;335
15.9.9;I Energy bands;336
15.9.10;J Metal–insulator transition;337
15.10;X Band structure of YBa2Cu3O7;339
15.10.1;A Energy bands and DOS;340
15.10.2;B Fermi surface: plane and chain bands;343
15.11;XI Fermi liquids;343
15.12;XII Fermi surface nesting;345
15.13;XIII CDWs, SDWs, and spin bags;346
15.14;XIV Mott insulator transition;347
15.15;Problems;348
15.16;Further Reading;349
15.17;References;349
16;8 Type I superconductivity and the intermediate state;352
16.1;I Introduction;352
16.2;II Intermediate state;352
16.3;III Surface fields and intermediate-state configurations;353
16.4;IV Type I ellipsoid;357
16.5;V Susceptibility;359
16.6;VI Gibbs free energy for the intermediate state;360
16.7;VII Boundary-wall energy and domains;363
16.8;VIII Current-induced intermediate state;365
16.9;IX Recent developments in Type I superconductivity;371
16.9.1;A History and general remarks;371
16.9.2;B The intermediate state;375
16.9.3;C Magneto-optics with in-plane magnetization—a tool to study flux patterns;376
16.9.4;D AC response in the intermediate state of Type I superconductors;379
16.10;Problems;380
16.11;References;382
17;9 Type II superconductivity;384
17.1;I Introduction;384
17.2;II Internal and critical fields;384
17.2.1;A Magnetic field penetration;384
17.2.2;B Ginzburg–Landau parameter;388
17.2.3;C Critical fields;390
17.3;III Vortices;393
17.3.1;A Magnetic fields;396
17.3.2;B High-kappa approximation;398
17.3.3;C Average internal field and vortex separation;402
17.3.4;D Vortices near lower critical field;404
17.3.5;E Vortices near upper critical field;406
17.3.6;F Contour plots of field and current density;406
17.3.7;G Closed vortices;408
17.4;IV Vortex anisotropies;410
17.4.1;A Core region and current flow;410
17.4.2;B Critical fields;412
17.4.3;C High-kappa approximation;414
17.4.4;D Pancake vortices;417
17.4.5;E Oblique alignment;418
17.5;V Individual vortex motion;418
17.5.1;A Vortex repulsion;419
17.5.2;B Pinning;423
17.5.3;C Equation of motion;424
17.5.4;D Onset of motion;425
17.5.5;E Magnus force;426
17.5.6;F Steady-state motion;427
17.5.7;G Intrinsic pinning;428
17.5.8;H Vortex entanglement;428
17.6;VI Flux motion;429
17.6.1;A Flux continuum;429
17.6.2;B Entry and exit;430
17.6.3;C 2D fluid;430
17.6.4;D Dimensionality;431
17.6.5;E Solid and glass phases;432
17.6.6;F Flux in motion;432
17.6.7;G Transport current in a magnetic field;433
17.6.8;H Dissipation;435
17.6.9;I Magnetic phase diagram;435
17.7;VII Fluctuations;437
17.7.1;A Thermal fluctuations;437
17.7.2;B Characteristic length;438
17.7.3;C Entanglement of flux lines;438
17.7.4;D Irreversibility line;438
17.7.5;E Kosterlitz–Thouless transition;441
17.8;Problems;442
17.9;References;443
18;10 Irreversible magnetic properties;454
18.1;I Introduction;454
18.2;II Critical states;454
18.3;III Current–field relationships;455
18.3.1;A Transport and shielding current;455
18.3.2;B Maxwell curl equation and pinning force;456
18.3.3;C Determination of current–field relationships;457
18.4;IV Critical-state models;458
18.4.1;A Requirements of a critical-state model;458
18.4.2;B Model characteristics;458
18.5;V Reversed critical states and hysteresis;459
18.5.1;A Reversing field;460
18.5.2;B Magnetization;462
18.5.3;C Hysteresis loops;464
18.5.4;D Magnetization current;466
18.6;VI Perfect Type I superconductor;468
18.7;VII Concluding remarks;471
18.8;References;471
19;11 Magnetic penetration depth;474
19.1;I Isotropic London electrodynamics;474
19.2;II Penetration depth in anisotropic samples;476
19.3;III Experimental methods;479
19.4;IV Absolute value of the penetration depth;480
19.5;V Penetration depth and the superconducting gap;483
19.5.1;A Semiclassical model for superfluid density;483
19.5.1.1;a Isotropic Fermi surface;485
19.5.1.2;b Anisotropic Fermi surface, isotropic gap function;486
19.5.2;B Superconducting gap;486
19.5.3;C Mixed gaps;488
19.5.4;D Low temperatures;489
19.5.4.1;a s-wave pairing;489
19.5.4.2;b d-wave pairing;489
19.5.4.3;c p-wave pairing;490
19.6;VI Effect of disorder and impurities on the penetration depth;491
19.6.1;A Nonmagnetic impurities;491
19.6.2;B Magnetic impurities;493
19.7;VII Surface ABS;494
19.8;VIII Nonlocal electrodynamics of nodal superconductors;497
19.9;IX Nonlinear Meissner effect;498
19.10;X AC penetration depth in the mixed state (small amplitude linear response);501
19.11;XI The proximity effect and its identification by using AC penetration depth measurements;504
19.12;XII Eilenberger two-gap scheme: the .-model;505
19.12.1;A Superfluid density;507
19.13;References;511
20;12 Upper critical field with magnetic and non-magnetic scattering;514
20.1;I Introduction;514
20.2;II The Bc2 Problem;515
20.2.1;A T?Tc;518
20.2.2;B Strong pair breaking at Tc?0;519
20.2.3;C Numerical results;520
20.3;III Field-dependent spin-flip scattering;521
20.4;IV The d-wave case;524
20.5;V Discussion;526
20.6;References;527
21;13 Energy gap and tunneling;530
21.1;I Introduction;530
21.2;II Phenomenon of tunneling;530
21.2.1;A Conduction-electron energies;530
21.2.2;B Types of tunneling;532
21.3;III Energy-level schemes;533
21.3.1;A Semiconductor representation;533
21.3.2;B Boson condensation representation;533
21.4;IV Tunneling processes;534
21.4.1;A Conditions for tunneling;534
21.4.2;B Normal metal tunneling;535
21.4.3;C Normal metal–superconductor tunneling;535
21.4.4;D Superconductor–superconductor tunneling;538
21.5;V Quantitative treatment of tunneling;540
21.5.1;A Distribution function;540
21.5.2;B Density of states;541
21.5.3;C Tunneling current;542
21.5.4;D N–I–N tunneling current;545
21.5.5;E N–I–S tunneling current;545
21.5.6;F S–I–S tunneling current;546
21.5.7;G Nonequilibrium quasiparticle tunneling;551
21.5.8;H Tunneling in unconventional superconductors;552
21.5.8.1;a Introduction;552
21.5.8.2;b Zero-bias conductance peak;553
21.5.8.3;c c-Axis tunneling;554
21.6;VI Tunneling measurements;554
21.6.1;A Weak links;554
21.6.2;B Experimental arrangements for measuring tunneling;555
21.6.3;C N–I–S tunneling measurements;558
21.6.4;D S–I–S tunneling measurements;559
21.6.5;E Energy gap;560
21.6.6;F Proximity effect;561
21.6.7;G Even–odd electron effect;564
21.7;VII Josephson effect;565
21.7.1;A Cooper-pair tunneling;565
21.7.2;B dc Josephson effect;566
21.7.3;C ac Josephson effect;569
21.7.4;D Driven junctions;570
21.7.5;E Inverse ac Josephson effect;573
21.7.6;F Analogues of Josephson junctions;578
21.8;VIII Magnetic field and size effects;582
21.8.1;A Short Josephson junction;582
21.8.2;B Long Josephson junction;588
21.8.3;C Josephson penetration depth;590
21.8.4;D Two-junction loop;591
21.8.5;E Self-induced flux;593
21.8.6;F Junction loop of finite size;595
21.8.7;G Ultrasmall Josephson junction;597
21.8.8;H Arrays and models for granular superconductors;598
21.8.9;I Superconducting quantum interference device;599
21.9;Problems;600
21.10;References;601
22;14 Spectroscopic properties;606
22.1;I Introduction;606
22.2;II Vibrational spectroscopy;607
22.2.1;A Vibrational transitions;607
22.2.2;B Normal modes;608
22.2.3;C Soft modes;610
22.2.4;D IR and Raman active modes;610
22.2.5;E Kramers–Kronig analysis;611
22.2.6;F IR spectra;613
22.2.7;G Light-beam polarization;616
22.2.8;H Raman spectra;618
22.2.9;I Energy gap;620
22.3;III Optical spectroscopy;624
22.4;IV Photoemission;629
22.4.1;A Measurement technique;629
22.4.2;B Energy levels;630
22.4.3;C Core-level spectra;631
22.4.4;D Valence band spectra;637
22.4.5;E Energy bands and density of states;640
22.5;V X-ray absorption edges;641
22.5.1;A X-ray absorption;641
22.5.2;B Electron-energy loss;643
22.6;VI Inelastic neutron scattering;644
22.7;VII Positron annihilation;649
22.8;VIII Magnetic resonance;653
22.8.1;A Nuclear magnetic resonance;653
22.8.2;B Quadrupole resonance;660
22.8.3;C Electron spin resonance;662
22.8.4;D Nonresonant microwave absorption;664
22.8.5;E Microwave energy gap;668
22.8.6;F Muon spin relaxation;668
22.8.7;G Mössbauer resonance;670
22.9;Problems;674
22.10;References;675
23;15 Classical superconductors;680
23.1;I Introduction;680
23.2;II Elements;680
23.3;III Physical properties of superconducting elements;683
23.4;IV Compounds;688
23.5;V Alloys;690
23.6;VI Miedema’s empirical rules;693
23.7;VII Compounds with the NaCl structure;695
23.8;VIII Type A15 compounds;697
23.9;IX Laves phases;700
23.10;X Chevrel phases;701
23.11;XI Chalcogenides and oxides;703
23.12;Problems;704
23.13;References;704
24;16 Cuprate high-Tc superconductors;706
24.1;I Introduction;706
24.2;II Perovskites;707
24.2.1;A Cubic form;707
24.2.2;B Tetragonal form;709
24.2.3;C Orthorhombic form;710
24.2.4;D Planar representation;712
24.3;III Perovskite-type superconducting structures;713
24.4;IV Aligned YBa2Cu3O7;716
24.4.1;A Copper oxide planes;718
24.4.2;B Copper coordination;718
24.4.3;C Stacking rules;719
24.4.4;D Crystallographic phases;720
24.4.5;E Charge distribution;720
24.4.6;F YBaCuO formula;721
24.4.7;G YBa2Cu4O8 and Y2Ba4Cu7O15;723
24.5;V Aligned HgBaCaCuO;724
24.6;VI Body centering;727
24.7;VII Body-centered La2CuO4, Nd2CuO4, and Sr2RuO4;729
24.7.1;A Unit cell of La2CuO4 compound (T phase);730
24.7.2;B Layering scheme;730
24.7.3;C Charge distribution;731
24.7.4;D Superconducting structures;734
24.7.5;E Nd2CuO4 compound (T' phase);735
24.7.6;F La2-x-y RxSryCuO4 compounds (T* phase);736
24.7.7;G Sr2RuO4 compound (T phase);737
24.8;VIII Body-centered BiSrCaCuO and TlBaCaCuO;738
24.8.1;A Layering scheme;738
24.8.2;B Nomenclature;738
24.8.3;C Bi–Sr compounds;739
24.8.4;D Tl–Ba compounds;741
24.8.5;E Modulated structures;742
24.8.6;F Aligned TI–Ba compounds;742
24.8.7;G Lead doping;742
24.9;IX Symmetries;743
24.10;X Layered structure of the cuprates;744
24.11;XI Infinite layer phases;747
24.12;XII Conclusion;749
24.13;Problems;750
24.14;Further reading;751
24.15;References;751
25;17 Noncuprate superconductors;756
25.1;I Introduction;756
25.2;II Heavy-electron systems;756
25.3;III Magnesium diboride;762
25.3.1;A Structure;762
25.3.2;B Physical properties;763
25.3.3;C Anisotropies;766
25.3.4;D Fermi surfaces;767
25.3.5;E Energy gaps;769
25.4;IV Borocarbides and boronitrides;770
25.4.1;A Crystal structure;771
25.4.2;B Correlations of superconducting properties with structure parameters;772
25.4.3;C Density of states;775
25.4.4;D Thermodynamic and electronic properties;777
25.4.5;E Magnetic interactions;780
25.4.6;F Magnetism of HoNi2B2C;783
25.5;V Perovskites;787
25.5.1;A Barium–potassium–bismuth cubic perovskite;788
25.5.2;B Magnesium–carbon–nickel cubic perovskite;788
25.5.3;C Barium–lead–bismuth lower symmetry perovskite;790
25.6;VI Charge-transfer organics;791
25.7;VII Buckminsterfullerenes;793
25.8;VIII Symmetry of the order parameter in unconventional superconductors;795
25.8.1;A Symmetry of the order parameter in cuprates;795
25.8.1.1;a Hole-doped high-Tc cuprates;795
25.8.1.2;b Electron-doped cuprates;796
25.8.2;B Organic superconductors;798
25.8.3;C Influence of band structure on superconductivity;801
25.8.3.1;a MgB2;802
25.8.3.2;b NbSe2;803
25.8.3.3;c CaAlSi;804
25.8.4;D Some other superconductors;804
25.8.4.1;a Heavy fermion superconductors;804
25.8.4.2;b Borocarbides;805
25.8.4.3;c Sr2RuO4;806
25.8.4.4;d MgCNi3;806
25.9;IX Magnetic superconductors;807
25.9.1;A Coexistence of superconductivity and magnetism;807
25.9.2;B Antiferromagnetic superconductors;809
25.9.3;C Magnetic cuprate superconductor (SmCeCuO);809
25.10;References;811
26;18 London penetration depth in iron base superconductors;818
26.1;I Introduction;818
26.1.1;A Measurements of the London penetration depth;819
26.2;II TDR measurements;819
26.2.1;A Frequency-domain measurements;819
26.2.2;B Measurements of the absolute value of .(T);821
26.2.3;C Out-of-plane penetration depth;821
26.3;III London penetration depth and superconducting gap;822
26.3.1;A London penetration depth;824
26.3.2;B Isotropy on a general Fermi surface;825
26.3.3;C 2D d-wave;825
26.3.4;D Eilenberger two-gap scheme: the weak-coupling model;826
26.3.5;E Superfluid density;827
26.4;IV Effects of scattering;831
26.4.1;A Gapless limit;831
26.5;V Experimental results;832
26.5.1;A In-plane london penetration depth;835
26.5.2;B Absolute value of the penetration depth;839
26.5.3;C Anisotropy of London penetration depths;845
26.5.4;D Pair-breaking;849
26.6;Conclusion;852
26.7;References;852
Properties of the normal state
The normal state is the state of a metallic material that either does not superconduct or is a superconductor at a temperature below its transition temperature c. This chapter emphasizes their electrical properties such as the electrical conductivity and its reciprocal the resistivity. Their temperature and frequency dependencies are given. Other properties and phenomena are explained such as the chemical potential, the electron–phonon interaction, thermal conductivity, energy gaps and effective masses, electronic and phonon specific heats, electromagnetic fields, magnetic susceptibilities, and the Hall effect. The Fermi–Dirac distribution function is emphasized. The physical properties of 14 metallic elements are tabulated.
Keywords
Electrical conduction; magnetic properties; relaxation time; Fermi–Dirac statistics; electron collisions; influence of impurities; temperature dependencies
I Introduction
This text is concerned with superconductivity, a phenomenon characterized by certain electrical, magnetic, and other properties, many of which will be introduced in the following chapter. A material becomes superconducting below a characteristic temperature, called the c, which varies from very small values (millidegrees or microdegrees) to values above 100 K. The material is called normal above c, which merely means that it is not superconducting. Elements and compounds that become superconductors are, generally, conductors—but not good conductors—in their normal state. The good conductors, such as copper, silver, and gold, do not superconduct.
It is helpful to survey some properties of normal conductors before discussing the superconductors, so that we can review some background material and define some of the terms that will be used throughout the text. Many of the normal state properties that will be discussed here are modified in the superconducting state. Much of the material in this introductory chapter will be referred to later in the text.
II Conducting electron transport
The electrical conductivity of a metal may be described most simply in terms of the constituent atoms of the metal. In this representation, the atoms lose their valence electrons, causing a background lattice of positive ions, called , to form, and the now delocalized conduction electrons move between these ions. The number density (electrons/cm3) of conduction electrons in a metallic element of density m (g/cm3), atomic mass number (g/mole), and valence is given by
=NAZ?mA, (1.1)
where A is Avogadro’s number. The typical values listed in Table 1.1 are a thousand times greater than those of a gas at room temperature and atmospheric pressure.
Table 1.1
Characteristics of selected metallic elements
| 11 Na | 1 | 0.97 | bcc | 4.23 | 2.65 | 2.08 | 0.8 | 4.2 | 170 | 32 | 1.38 |
| 19 K | 1 | 1.33 | bcc | 5.23 | 1.40 | 2.57 | 1.38 | 6.1 | 180 | 41 | 1.0 |
| 29 Cu | 1 | 0.96 | fcc | 3.61 | 8.47 | 1.41 | 0.2 | 1.56 | 210 | 27 | 4.01 |
| 47 Ag | 1 | 1.26 | fcc | 4.09 | 5.86 | 1.60 | 0.3 | 1.51 | 200 | 40 | 4.28 |
| 41 Nb | 1 | 1.0 | bcc | 3.30 | 5.56 | 1.63 | 3.0 | 15.2 | 21 | 4.2 | 0.52 |
| 20 Ca | 2 | 0.99 | fcc | 5.58 | 4.61 | 1.73 | 3.43 | 22 | 2.06 |
| 38 Sr | 2 | 1.12 | fcc | 6.08 | 3.55 | 1.89 | 7 | 23 | 14 | 4.4 | ˜0.36 |
| 56 Ba | 2 | 1.34 | bcc | 5.02 | 3.51 | 1.96 | 17 | 60 | 6.6 | 1.9 | ˜0.19 |
| 13 Al | 3 | 0.51 | fcc | 4.05 | 18.1 | 1.10 | 0.3 | 2.45 | 65 | 8.0 | 2.36 |
| 81 Tl | 3 | 0.95 | bcc | 3.88 | 10.5 | 1.31 | 3.7 | 15 | 9.1 | 2.2 | 0.5 |
| 50 Sn (W) | 4 | 0.71 | Tetragonal | =5.82 | 14.8 | 1.17 | 2.1 | 10.6 | 11 | 2.3 | 0.64 |
| =3.17 |
| 82 Pb | 4 | 0.84 | fcc | 4.95 | 13.2 | 1.22 | 4.7 | 19.0 | 5.7 | 1.4 | 0.38 |
| 51 Sb | 5 | 0.62 | Rhombic | 4.51 | 16.5 | 1.19 | 8 | 39 | 2.7 | 0.55 | 0.18 |
| 83 Bi | 5 | 0.74 | Rhombic | 4.75 | 14.1 | 1.13 | 35 | 107 | 0.72 | 0.23 | 0.09 |
Notation: , lattice constant; e, conduction electron density; s=(3/4e)1/3; , resistivity; , Drude relaxation time; th, thermal conductivity; =th/T is the Lorentz number; , electronic specific heat parameter; *, effective mass; H, Hall constant; TD, Debye temperature; p, plasma frequency in radians per femtosecond (10-15 s); IP, first ionization potential; WF, work function; F, Fermi energy; F, Fermi temperature in kilokelvins; F, Fermi wavenumber in mega reciprocal centimeters; and ?F, Fermi velocity in centimeters per microsecond.
The simplest approximation that we can adopt as a way of explaining conductivity is the Drude model. In this model, it is assumed that the conduction electrons
• do not interact with the cations (“free electron approximation”) except when one of them collides elastically with a cation, which happens, on average, 1/ times per second, with the result that the velocity of the electron abruptly and randomly changes its direction (“relaxation time approximation”);
• maintain thermal equilibrium through collisions, in accordance with Maxwell–Boltzmann statistics (“classical statistics approximation”);
• do not interact with each other (“independent-electron approximation”).
This model predicts many of the general features of electrical conduction phenomena, as we shall see later in the chapter, but it fails to account for many others, such as tunneling, band gaps, and the Bloch 5 law. More satisfactory explanations of electron transport relax or discard one or more of these approximations.
Ordinarily, we abandon the free electron approximation by having the electrons move in a periodic potential arising from the background lattice of positive ions. Figure 1.1 shows an example of a simple potential that is negative near the positive ions and zero between them. An electron moving through the lattice interacts with the surrounding positive ions, which are oscillating about their equilibrium positions, and the charge distortions resulting from this interaction propagate along the lattice, causing distortions in the periodic potential. These distortions can influence the motion of yet another electron some distance away that is also interacting with the oscillating...
