Liquid Metals

International Series of Monographs In: Natural Philosophy

1st Edition - January 1, 1968
Author: N. H. March
Editor: D. Ter Haar
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 5 4 7 9 - 4

Liquid Metals covers topics about the properties of liquid metals, with emphasis on the microscopic description of the electron states. The book discusses radial distribution… Read more

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Liquid Metals covers topics about the properties of liquid metals, with emphasis on the microscopic description of the electron states. The book discusses radial distribution function, which is the quantitative way by which the structure of a monatomic fluid may be described, and the scattering of X-rays (or neutrons) from the fluid. The text describes the way by which the forces operating in liquid metals may be qualitatively described; the theory of electron screening in metals; the shielding of a structureless ion core in the Born approximation; and ways by which the structure of the ion core can profoundly influence the shielding. The forces operating between ions in liquid metals; the properties of solid metals; the time-dependent generalization of the structure factor; the dynamics of fluids from inelastic neutron scattering; and the nature of the energy level spectrum of the electrons in a liquid metal are also considered. Students of elementary quantum mechanics and statistical thermodynamics and physicists will find the book invaluable.

Preface

Chapter 1. Outline

Chapter 2. Liquid Structure

2.1 Debye’s Formula

2.2 Monatomic Liquids

2.3 Radial Distribution Function and Structure Factor

2.4 Forces and Structure

2.5 Ornstein-Zernike Direct Correlation Function

2.6 Localization of Direct Correlation Function in Κ Space for Metals

Chapter 3. Electron Theory

3.1 Pair Potential for Insulating Fluid Argon

3.2 Fermi Momentum Distribution

3.3 Ionic Shielding

3.4 Dielectric Constant

3.5 Electrostatic Ion-Ion Interaction

Chapter 4. Statistical Theory

4.1 Born-Green Theory

4.2 Hyperchain and Percus-Yevick Theories

4.3 Force Correlation Function and Thermodynamic Consistency

Chapter 5. Pair Potentials

5.1 Direct Correlation Function and Pair Potential

5.2 Potentials for Al, Pb and Ga

5.3 Molecular Dynamics and Pair Potential for Na

5.4 Asymptotic Form of Radial Distribution Function

Chapter 6. Melting

6.1 Mukherjee's Relation

6.2 Order-Disorder Theory of Melting

6.3 Comparison with Experiment

Chapter 7. Electrical Transport

7.1 Probability of Scattering by a Single Ion

7.2 Distribution Function in Electric Field

7.3 Relaxation Time

7.4 Calculation of Current

7.5 Ion-Ion Correlations and Electron Scattering

7.6 Choice of Scattering Potential U(K)

7.7 Thermoelectric Power

7.8 Hall Coefficient

7.9 Blurring of Fermi Surface

7.10 Optical Properties

7.11 Alloys

Chapter 8. Liquid Dynamics

8.1 Definition of van Hove Correlation Function

8.2 Models of Self-Correlation Function

8.3 Neutron Scattering Law

8.4 Small Time Expansion of Intermediate Scattering Function

8.5 Expansion of Velocity Correlation Function

8.6 Large Κ Expansion of Self-Correlation Function

8.7 Comparison with Machine Calculations and with Experiment

8.8 Coherent Scattering Function

8.9 Sum Rules

Chapter 9. Electron States

9.1 Green Function Calculation

9.2 Perturbation Theory

9.3 Partial Summation of Green Function Series

9.4 Results

Appendix 1. Long-Wavelength Limit of Structure Factor

Appendix 2. Dielectric Function of High Density Fermi Gas

Appendix 3. Electrostatic Model of Ion-Ion Interaction in Fermi Gas

Appendix 4 . Structure Factor and Direct Correlation Function for Hard Spheres

Appendix 5. Asymptotic Relation between Total and Direct Correlation Functions for Van Der Waals Fluids

Appendix 6. Conductivity and Van Hove Correlation Function

Notes Added in Proof

References

Index