The Electrical Resistivity of Metals and AlloysNow in paperback, this comprehensive book is the first text devoted to the problem of understanding the electrical properties of metals and alloys. Dr Rossiter, well-known for his work on the electrical resistivity of alloys, has written a book which blends results and theory, but does not rely on a strong grounding in quantum mechanics. After an introduction to the basic ideas, the concepts of atomic and magnetic correlations and their microstructural consequences are explained. Later chapters then deal with the effects of such correlations on electrical resistivity. Examples and applications of the concepts derived are given in discrete sections, allowing the uninterrupted development of theory for each specific problem, and enhancing the value of the book for a wide range of readers from theoretical and experimental solid state physicists to metallurgists and materials scientists. Anyone with an interest in the electrical conduction process or in the application of resistivity measurements to the study of alloy configuration will find this essential reading. |
Contents
13 Scattering anisotropy | 7 |
15 Matthiessens rule | 9 |
16 Simple and nonsimple metals | 10 |
17 Elastic and inelastic scattering | 15 |
173 Magnetic scattering | 16 |
18 The Boltzmann equation and relaxation time | 17 |
182 The linearised Boltzmann equation | 21 |
183 The relaxation time approximation | 22 |
551 Scale of phase separation | 170 |
552 Scale of phase separation A | 184 |
56 Atomic displacement effects | 195 |
b Substitutions impurity | 197 |
d Impurity interstitial | 198 |
563 Static atomic displacements in a concentrated alloy | 203 |
564 Displactive transitions | 207 |
565 Combined effects | 208 |
185 Other solutions of the Boltzmann equation anisotropic relaxation times | 24 |
186 Other formalisms | 28 |
Atomic configuration of an alloy | 30 |
23 Composition waves | 39 |
24 Reciprocal space representation | 40 |
25 Short range atomic configurations | 41 |
252 Phase separation | 43 |
b Precipitation | 45 |
c Spinodal decomposition | 46 |
253 Atomic ordering | 49 |
bType 11a heterogeneous SROmicrodomain model | 50 |
261 Long range ordering | 51 |
262 Twophase mixtures | 54 |
27 Atomic displacement effects | 57 |
271 Atomic size effects | 58 |
272 Dynamic atomic displacements | 61 |
b Debye model | 63 |
273 Displacive phase transitions | 67 |
28 Amorphous alloys | 69 |
281 Static atomic structure | 71 |
282 Dynamic fluctuations | 75 |
The structure of magnetic materials | 76 |
32 Magnetic configuration | 80 |
322 Spin glasses | 84 |
323 Magnetic clusters | 87 |
324 Long range magnetic order TTc | 89 |
325 Short range magnetic order TTc | 94 |
326 Macignons | 95 |
33 Nearly magnetic metals spin fluctuations | 98 |
34 Effects of atomic rearrangements | 102 |
341 Long range effects | 103 |
342 Short range effects | 104 |
Electrons in simple metals and alloys | 107 |
42 Pseudo and model potentials | 115 |
43 Electronelectron interactions | 119 |
431 Screening in metals | 120 |
432 Exchange and correlation | 122 |
44 Nearly free electron theory | 124 |
45 The scattering matrix | 127 |
451 The first and second Born approximations | 128 |
452 Factorisation of the matrix elements | 129 |
453 The pseudopotential in alloys | 130 |
454 The pseudopotential in a deformed lattice | 134 |
Electrical resistivity of simple metals and alloys | 137 |
51 A general resistivity expression | 138 |
52 The resistivity of alloys with short range atomic correlations | 139 |
52 1 Homogeneous atomic correlations | 141 |
522 Inhomogeneous atomic correlations | 143 |
a Small zone limit | 145 |
b Intermediate zone size | 147 |
c Large zone limit | 150 |
53 Homogeneous long range atomic ordering | 160 |
a BraggWilliams model | 162 |
532 Electron band structure effects | 164 |
54 Inhomogeneous long range ordering | 167 |
55 Long range phase separation | 169 |
57 Some applications | 212 |
a Alkali metals | 213 |
b Noble metals | 218 |
572 Residual resistivity of disordered random solid solutions | 220 |
a Dilute alloys | 221 |
b Concentrated alloys | 236 |
573 Homogeneous short range atomic correlations | 237 |
574 Long range ordering | 253 |
575 Precipitation | 257 |
576 Long range phase separation | 261 |
b Scale of phase separationᐸᐱ | 264 |
577 Displacive transitions | 271 |
Nonsimple nonmagnetic metals and alloys | 272 |
61 Band structure and the electrical resistivity | 273 |
62 Model and pseudopotentials in nonsimple metals | 274 |
63 The phase shift method | 279 |
64 The Tmatrix | 284 |
the KKRGreens function method | 287 |
66 Some applications | 289 |
bound and virtual bound states | 291 |
67 Concentrated alloys | 300 |
the average tmatrix approximation ATA and coherent potential approximation CPA | 306 |
Magnetic and nearly magnetic alloys | 318 |
712 Twosubband model | 323 |
72 Local environment effects and magnetic clusters | 334 |
local spin fluctuations | 339 |
732 Exchangeenhanced alloys | 341 |
733 Composition dependence | 345 |
734 Nearly magnetic pure metals and concentrated alloys | 348 |
74 Spin glasses | 351 |
8 Other phenomena | 356 |
812 The electrical resistivity near Tc | 358 |
a Ferromagnets | 363 |
b Antiferromagnets | 365 |
c Atomic orderdisorder | 366 |
d Miscibility gap | 368 |
813 Related phenomena | 370 |
82 Highly resistive materials | 372 |
822 Aao | 375 |
b CPA interband and other bandbased calculations | 377 |
823 Aao | 378 |
824 Some general comments | 379 |
83 Amorphous metals | 380 |
832 Resistivity in nonmagnetic glasses | 382 |
b 0DT0 | 386 |
833 Resistivity of metallic glasses containing magnetic components | 388 |
b Spin glasses | 389 |
834 Resistivity minima | 391 |
Appendices | 393 |
B Integrations over dk dS dE and dO | 394 |
C The average expix | 396 |
D High and low temperature limits of pT | 397 |
E Determination of 2kfR ? in a nearly free electron solid | 398 |
| 399 | |
| 421 | |
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Common terms and phrases
alloys anisotropy antiferromagnetic antiphase approximation assumed atomic correlations atomic displacements average band structure behaviour Boltzmann equation boundary Brillouin zone calculation Chapter cluster coefficient composition concentrated alloys conduction electrons considered contribution correlation parameters curve d-band Debye-Waller Debye-Waller factor density determined deviation diffraction diffuse scattering discussed in Section disordered distribution dp/dT effects electrical resistivity electron scattering empty-core energy Fermi surface ferromagnetic form factors function give given impurity increase interaction lattice Lett localised long range order low temperatures magnetic magnetic moment mean free path obtained phase shifts phonon Phys plane wave point-ion pseudopotential R₁ range atomic region relaxation residual resistivity Rossiter scattering potential shown in Figure simple metals Solid St spin fluctuation spin glass Stat static structure factor Table temperature dependence theory thermal transition metal values variation wavefunction Ziman μΩ