March / Ter Haar Liquid Metals

International Series of Monographs In: Natural Philosophy
1. Auflage 2017
ISBN: 978-1-4831-5479-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 142 Seiten, Web PDF

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.

Autoren/Hrsg.

March, N. H.

Ter Haar, D.

Inhaltsverzeichnis

1;Front Cover;1
2;Liquid Metals;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;8
6;CHAPTER 1. Outline;10
6.1;Liquid Metals;11
7;CHAPTER 2. Liquid structure;12
7.1;2.1 Debye's formula;12
7.2;2.2 Monatomic liquids;14
7.3;2.3 Radial distribution function and structure factor;15
7.4;2.4 Forces and structure;16
7.5;2.5 Ornstein-Zernike direct correlation function;17
7.6;2.6 Localization of direct correlation function in . space for

metals;19
8;CHAPTER 3. Electron theory;25
8.1;3.1 Pair potential for insulating fluid argon;25
8.2;3.2 Fermi momentum distribution;26
8.3;3.3 Ionic shielding;28
8.4;3.4 Dielectric constant;34
8.5;3.5 Electrostatic ion-ion interaction;36
9;CHAPTER 4. Statistical theory;39
9.1;4.1 Born-Green theory;40
9.2;4.2 Hyperchain and Percus-Yevick theories;41
9.3;4.3 Force correlation function and thermodynamic consistency;43
10;CHAPTER 5. Pair potentials;45
10.1;5.1 Direct correlation function and pair potential;46
10.2;5.2 Potentials for AI, Pb and Ga;50
10.3;5.3 Molecular dynamics and pair potential for Na;53
10.4;5.4 Asymptotic form of radial distribution function;56
11;CHAPTER 6. Melting;59
11.1;6.1 Mukherjee's relation;59
11.2;6.2 Order-disorder theory of melting;63
11.3;6.3 Comparison with experiment;64
12;CHAPTER 7. Electrical transport;67
12.1;7.1 Probability of scattering by a single ion;68
12.2;7.2 Distribution function in electric field;70
12.3;7.3 Relaxation time;72
12.4;7.4 Calculation of current;73
12.5;7.5 Ion-ion correlations and electron scattering;74
12.6;7.6 Choice of scattering potential U(K);75
12.7;7.7 Thermoelectric power;80
12.8;7.8 Hall coefficient;81
12.9;7.9 Blurring of Fermi surface;82
12.10;7.10 Optical properties;84
12.11;7.11 Alloys;85
13;CHAPTER 8. Liquid dynamics;88
13.1;8.1 Definition of van Hove correlation function;88
13.2;8.2 Models of self-correlation function;92
13.3;8.3 Neutron scattering law;94
13.4;8.4 Small time expansion of intermediate scattering function;95
13.5;8.5 Expansion of velocity correlation function;96
13.6;8.6 Large . expansion of self-correlation function;97
13.7;8.7 Comparison with machine calculations and with experiment;98
13.8;8.8 Coherent scattering function;101
13.9;8.9 Sum rules;104
14;CHAPTER 9. Electron states;106
14.1;9.1 Green function calculation;108
14.2;9.2 Perturbation theory;109
14.3;9.3 Partial summation of Green function series;110
14.4;9.4 Results;111
15;APPENDIX 1: Long-wavelength limit of structure factor;116
16;APPENDIX 2: Dielectric function of high density Fermi gas;118
17;APPENDIX 3:

Electrostatic model of i.n-i.n

interaction in Fermi gas;120
18;APPENDIX 4: Structure factor and direct correlation function for hard spheres;124
19;APPENDIX 5: Asymptotic relation between total and direct correlation functions for van der Waals fluids;128
19.1;A5.1 Diagrammatic methods;128
19.2;AS.2 Born-Green theory;129
20;APPENDIX 6: Conductivity and van Hove correlation function;132
21;Notes added in proof;134
22;References;135
23;Index;140