Liquid Metals: Concepts and Theory

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ISBN: 9780521019613 | 0521019613
Cover: Paperback
Copyright: 9/15/2005

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Liquid metals remain of both fundamental and technological interest and the concepts needed to understand their properties are set out in this book, starting from a survey of the basic experimental facts to be explained. The quantitative theory of liquid pair correlation functions, effective ion-ion interactions, thermodynamic properties and electronic and atomic transport is then developed. The book goes on to discuss inelastic neutron scattering, critical behaviour, magnetism, the liquid/metal surface, binary liquid metal alloys, the two component theory of pure liquid metals, shock wave studies, liquid hydrogen plasmas and the constitution of giant planets.

Preface

1 Outline

(2)

2 Pair correlation function and structure factor of ions

(5)

2.1 Liquid structure factor

(2)

2.2 Ornstein-Zernike direct correlation function

(3)

3 Thermodynamics

(18)

3.1 Simple monatomic fluids

(3)

3.2 Approximate methods

(4)

3.3 Simple liquid metals

(3)

3.4 Specifics

(7)

3.5 One-component plasma as reference liquid

(1)

4 Electron screening and effective ion-ion interactions

(9)

4.1 Screening of impurity centre in electron liquid

(2)

4.2 Lindhard dielectric function

(1)

4.3 Introduction of exchange and correlation

(2)

4.4 Effective ion-ion interactions in simple (s-p) metals

(1)

4.5 Structure factor of alkali metals modelled in terms of one-component plasma

(3)

5 Interionic forces and structural theories

(8)

5.1 Force equation

(2)

5.2 Simple structural theories

(1)

5.3 Refined structural theories: factorization of triplet correlations

(1)

5.4 Inversion of structure factor to yield effective interionic pair potentials

(4)

6 Statistical mechanics of inhomogeneous systems and freezing theory

(19)

6.1 Single-particle density related to direct correlation function

(1)

6.2 Free-energy difference between homogeneous and periodic phases

(2)

6.3 Relation to the hypernetted-chain method

(1)

6.4 Verlet's rule related to Lindemann's law of melting

(3)

6.5 Cluster expansion and density functional theory

(1)

6.6 Other approximations

(1)

6.7 Applications

(2)

6.8 Correlation of melting temperature and vacancy formation energy

(4)

6.9 Supercooling of liquid Rb

(4)

7 Electronic and atomic transport

(15)

7.1 Wiedemann-Franz law and Lorenz number

(1)

7.2 Exact resistivity formula for finite-range spherical potential

(4)

7.3 Weak scattering theory of electrical resistivity

(4)

7.4 Hall coefficient

(2)

7.5 Atomic transport; generalized Stokes-Einstein relation

(2)

7.6 Self-diffusion related to shear viscosity at the melting temperature

(2)

8 Hydrodynamic limits of correlation functions and neutron scattering

(26)

8.1 Self-motion in liquids and incoherent neutron scattering

(1)

8.2 Frequency spectrum (or spectral function) g(ω)

(2)

8.3 Van Hove dynamical structure factor S(k, ω)

(2)

8.4 Friction constant theory of transport

(4)

8.5 Observation of collective modes

(2)

8.6 Hubbard-Beeby theory

(9)

8.7 Generalized shear viscosity in liquid Rb

(4)

8.8 Transport in supercooled liquid Rb

101

(2)

9 Critical behaviour

103

(18)

9.1 Concept of order parameter

103

(1)

9.2 Liquid-vapour critical point: a second-order phase transition

104

(3)

9.3 Ornstein-Zernike theory of static structure

107

(1)

9.4 Predictions from more general equation of state

108

(3)

9.5 Critical constants of fluid alkali metals

111

(3)

9.6 Spinodal curves

114

(2)

9.7 Dynamics of critical behaviour

116

(5)

10 Electron states, including critical region

121

(26)

10.1 Electron states in simple s-p metals

121

(3)

10.2 Electronic structure of nonsimple liquid metals

124

(5)

10.3 Partition function of a liquid metal

129

(2)

10.4 Electron states in expanded liquid Hg

131

(3)

10.5 Band model for electronic structure of expanded liquid caesium

134

(4)

10.6 Optical properties

138

(9)

11 Magnetism of normal and especially of expanded liquid metals

147

(33)

11.1 Spin susceptibility of normal liquid metals

147

(1)

11.2 Relation between spin and orbital magnetism of simple liquid metals

148

(3)

11.3 Effects of electron-ion interaction

151

(1)

11.4 Nuclear magnetic resonance: normal conditions

151

(1)

11.5 NMR study of expanded liquid caesium

152

(3)

11.6 Experimental results: Knight shift for Cs

155

(4)

11.7 Theory for NMR shifts and relaxation in fluid metals

159

(2)

11.8 Interactions between electrons

161

(3)

11.9 Characteristics of high-density liquid Cs

164

(5)

11.10 Dynamic nonuniform susceptibility in expanded Cs

169

(3)

11.11 Evolution of electronic structure of expanded liquid Cs

172

(2)

11.12 Phenomenology and heavy Fermion theory of magnetic susceptibility of expanded fluid alkali metals

174

(6)

12 Liquid-vapour surface

180

(22)

12.1 Thermodynamics of liquid surfaces

180

(2)

12.2 Model using theory of inhomogeneous electron gas

182

(2)

12.3 Formally exact pair potential theory

184

(2)

12.4 Triezenberg-Zwanzig formula for surface tension: direct correlation function

186

(2)

12.5 Microscopic foundation of Cahn-Hilliard phenomenology

188

(4)

12.6 Nonequilibrium problems: condensation and evaporation

192

(10)

13 Binary liquid-metal alloys

202

(58)

13.1 Simple binary fluid mixtures

203

(3)

13.2 Thermodynamics in terms of number-concentration correlation functions

206

(2)

13.3 Number-concentration structure factors as response functions

208

(2)

13.4 Structure and forces in liquid-metal alloys

210

(2)

13.5 Chemical approaches

212

(1)

13.6 Concentration fluctuations Scc(0)

213

(2)

13.7 Short-range-order parameter

215

(1)

13.8 Regular and conformal solutions

216

(3)

13.9 Activity, free energy of mixing, and concentration fluctuations

219

(6)

13.10 Complex formation as model for Scc(0)

225

(2)

13.11 Phase diagrams

227

(6)

13.12 Vacancies and melting curve in binary alloys

233

(4)

13.13 Theory of freezing

237

(2)

13.14 Surface segregation

239

(8)

13.15 Metal-insulator transitions

247

(2)

13.16 Magnetic properties of alloys

249

(11)

14 Two-component theory of pure liquid metals

260

(43)

14.1 Electron-ion Hamiltonian and density fluctuation operators

260

(3)

14.2 Wigner distribution functions

263

(5)

14.3 Electronic effects in dynamical structure

268

(1)

14.4 Longitudinal response of a two-component pure liquid metal

269

(6)

14.5 Random phase approximation (RPA) for response functions

275

(2)

14.6 Thermodynamics

277

(6)

14.7 Hydrodynamics in two-component theory

283

(8)

14.8 Electrical resistivity

291

(4)

14.9 Elastic scattering of neutrons by liquid metals

295

(2)

14.10 Single-particle motion from two-component theory

297

(5)

14.11 Diffraction evidence on pair correlation functions in two-component theory

302

(1)

15 Shock-wave studies

303

(6)

15.1 Shock compression

303

(1)

15.2 Dynamics of shock waves

304

(2)

15.3 Some results on hot expanded metals

306

(3)

16 Liquid hydrogen plasmas and constitution of Jupiter

309

(23)

16.1 Bijl-Jastrow variational theory of liquid metal hydrogen

310

(10)

16.2 Inverse problem: proton-proton interaction in hydrogen plasmas

320

(5)

16.3 Hydrogen-helium mixtures and constitution of giant planets

325

(7)

Appendices

332

(139)

2.1 Fluctuation theory derivation of S(0) in terms of compressibility

332

(3)

3.1 Percus-Yevick hard sphere solution for direct correlation function

335

(3)

3.2 Weeks-Chandler-Andersen (WCA) approximation to structure factor

338

(2)

5.1 Pressure dependence of pair function related to three-particle correlations

340

(2)

5.2 Conditions to be satisfied by thermodynamically consistent structural theories

342

(3)

5.3 Gaussian core model and Kirkwood decoupling of triplet correlations

345

(3)

5.4 Specific heats of liquids in terms of higher-order correlation functions

348

(2)

5.5 Inversion of measured structure, constrained by pseudopotential theory, to extract ion-ion interaction

350

(3)

6.1 Vacancy formation energy evaluated in a hot (model) crystal

353

(2)

6.2 Vacancy formation energy related to Debye temperature

355

(6)

7.1 Inverse transport theory for noninteracting electrons

361

(4)

8.1 Method of fluctuating hydrodynamics

365

(3)

8.2 Asymptotic behaviour of other Green-Kubo time correlation functions

368

(2)

8.3 Dynamics of S(k, ω) included through self-function Ss(k, ω)

370

(3)

8.4 Fourth moment theorem for dynamical structure factor

373

(2)

8.5 One-dimensional barrier crossing: Kramers' theory

375

(7)

8.6 Mode-coupling and velocity field methods

382

(3)

9.1 Ornstein-Zernike treatment of critical correlations

385

(2)

9.2 Homogeneity, scaling, and an introduction to renormalization group method

387

(5)

9.3 Compressibility ratios and thermal pressure coefficients of simple monatomic liquids from model equations of state

392

(1)

9.4 Mode coupling applied to critical behaviour

393

(5)

9.5 Proof of Wiedemann-Franz law up to metal-insulator transition for Fermi liquid model

398

(3)

10.1 Plasmon properties as function of phenomenological relaxation time

401

(4)

11.1 Heavy Fermion theory

405

(3)

13.1 Conformal solution theory: thermodynamics and structure

408

(2)

13.2 Results for concentration fluctuations from quasi-chemical approximation

410

(3)

13.3 Density profiles, direct correlation functions, and surface tension of liquid mixtures

413

(4)

13.4 Relation of surface segregation phenomenology to first-principles statistical mechanics

417

(3)

13.5 Long-time behaviour of correlation functions in binary alloys

420

(2)

13.6 Hydrodynamic correlation functions in a binary alloy

422

(4)

13.7 Metallic binary liquid-glass transition

426

(8)

13.8 Haeffner effect, electromigration, and thermal transport

434

(10)

13.9 Theory of disorder localization of noninteracting electrons

444

(3)

14.1 Phonon-plasmon model

447

(2)

14.2 Response functions for mass densities

449

(2)

14.3 Quantum hydrodynamic limit of two-component theory

451

(3)

14.4 Evaluation of transport coefficients

454

(2)

14.5 Electron-ion structure factor in a nonequilibrium situation

456

(1)

14.6 Relations between long-wavelength limit structure factors in binary metallic alloys

457

(3)

16.1 Integral equations for correlations in liquid metals, specially hydrogen

460

(7)

16.2 Quantum Monte Carlo calculations of ground state of solid hydrogen

467

(4)

References

471

(14)

Notes added in proof

485

(2)

Index

487

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Liquid Metals: Concepts and Theory

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