Figarova Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases

1. Auflage 2009
ISBN: 978-3-642-03171-7
Verlag: Springer
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 374 Seiten

This book deals with theoretical thermodynamics and the statistical physics of electron and particle gases. It treats the laws of thermodynamics from a classical and a quantum theoretical view point. The free energy is calculated with a Gibbs formalism.

After graduating in Physics from Baku State University, Azerbaijan, Bahram Askerov received his Ph.D. from Institute of Semiconductors, St.Petersburg, Russia, in 1962 (principal supervisor Professor A. I. Anselm). Since 1971 he is Chair of Solid State Physics, Department of Physics, Baku State University, Azerbaijan. S.Figarova received her Ph.D. in 1981 (her principal supervisor was professor B.M.Askerov), and her DSc in 2008. She is the author of a manual and numerous research articles in the field of condensed matter physics. At present her research efforts center around studies of transport properties in low-dimensional systems. She is an associate professor of the Chair of Solid State Physics, Department of Physics, Baku State Univers

Autoren/Hrsg.

Figarova, Sophia

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;1 Basic Concepts of Thermodynamicsand Statistical Physics;13
3.1;1.1 Macroscopic Description of State of Systems: Postulates of Thermodynamics;13
3.2;1.2 Mechanical Description of Systems: Microscopic State:Phase Space: Quantum States;18
3.3;1.3 Statistical Description of Classical Systems: Distribution Function: Liouville Theorem;25
3.4;1.4 Microcanonical Distribution: Basic Postulate of Statistical Physics;31
3.5;1.5 Statistical Description of Quantum Systems: Statistical Matrix: Liouville Equation;34
3.6;1.6 Entropy and Statistical Weight;39
3.7;1.7 Law of Increasing Entropy:Reversible and Irreversible Processes;43
3.8;1.8 Absolute Temperature and Pressure: Basic Thermodynamic Relationship;47
4;2 Law of Thermodynamics: Thermodynamic Functions;54
4.1;2.1 First Law of Thermodynamics:Work and Amount of Heat: Heat Capacity;54
4.2;2.2 Second Law of Thermodynamics: Carnot Cycle;61
4.3;2.3 Thermodynamic Functions of Closed Systems: Method of Thermodynamic Potentials;67
4.4;2.4 Thermodynamic Coefficients and General Relationships Between Them;74
4.5;2.5 Thermodynamic Inequalities: Stability of Equilibrium State of Homogeneous Systems;80
4.6;2.6 Third Law of Thermodynamics: Nernst Principle;85
4.7;2.7 Thermodynamic Relationships for Dielectrics and Magnetics;90
4.8;2.8 Magnetocaloric Effect:Production of Ultra-Low Temperatures;94
4.9;2.9 Thermodynamics of Systems with Variable Number of Particles: Chemical Potential;97
4.10;2.10 Conditions of Equilibrium of Open Systems;101
5;3 Canonical Distribution: Gibbs Method;104
5.1;3.1 Gibbs Canonical Distribution for Closed Systems;104
5.2;3.2 Free Energy: Statistical Sum and Statistical Integral;110
5.3;3.3 Gibbs Method and Basic Objects of its Application;113
5.4;3.4 Grand Canonical Distribution for Open Systems;114
6;4 Ideal Gas;120
6.1;4.1 Free Energy, Entropy and Equationof the State of an Ideal Gas;120
6.2;4.2 Mixture of Ideal Gases: Gibbs Paradox;123
6.3;4.3 Law About Equal Distribution of Energy Over Degrees of Freedom: Classical Theory of Heat Capacityof an Ideal Gas;126
6.3.1;4.3.1 Classical Theory of Heat Capacity of an Ideal Gas;129
6.4;4.4 Quantum Theory of Heat Capacity of an Ideal Gas: Quantization of Rotational and Vibrational Motions;131
6.4.1;4.4.1 Translational Motion;133
6.4.2;4.4.2 Rotational Motion;136
6.4.3;4.4.3 Vibrational Motion;139
6.4.4;4.4.4 Total Heat Capacity;142
6.5;4.5 Ideal Gas Consisting of Polar Molecules in an External Electric Field;144
6.5.1;4.5.1 Orientational Polarization;144
6.5.2;4.5.2 Entropy: Electrocaloric Effect;148
6.5.3;4.5.3 Mean Value of Energy: Caloric Equation of State;149
6.5.4;4.5.4 Heat Capacity: Determination of Electric Dipole Moment of Molecule;150
6.6;4.6 Paramagnetic Ideal Gas in External Magnetic Field;152
6.6.1;4.6.1 Classical Case;152
6.6.2;4.6.2 Quantum Case;154
6.6.2.1;Magnetization;156
6.6.2.2;Entropy, Mean Energy and Heat Capacity;158
6.7;4.7 Systems with Negative Absolute Temperature;161
7;5 Non-Ideals Gases;167
7.1;5.1 Equation of State of Rarefied Real Gases;167
7.2;5.2 Second Virial Coefficient and Thermodynamics of Van Der Waals Gas;174
7.3;5.3 Neutral Gas Consisting of Charged Particles: Plasma;179
8;6 Solids;185
8.1;6.1 Vibration and Waves in a Simple Crystalline Lattice;185
8.1.1;6.1.1 One-Dimensional Simple Lattice;188
8.1.2;6.1.2 Three-Dimensional Simple Crystalline Lattice;192
8.2;6.2 Hamilton Function of Vibrating Crystalline Lattice: Normal Coordinates;194
8.3;6.3 Classical Theory of Thermodynamic Properties of Solids;197
8.4;6.4 Quantum Theory of Heat Capacity of Solids: Einstein and Debye Models;204
8.4.1;6.4.1 Einstein's Theory;206
8.4.2;6.4.2 Debye's Theory;207
8.5;6.5 Quantum Theory of Thermodynamic Properties of Solids;214
9;7 Quantum Statistics: Equilibrium Electron Gas;223
9.1;7.1 Boltzmann Distribution: Difficulties of Classical Statistics;224
9.2;7.2 Principle of Indistinguishability of Particles: Fermions and Bosons;232
9.3;7.3 Distribution Functions of Quantum Statistics;239
9.4;7.4 Equations of States of Fermi and Bose Gases;244
9.5;7.5 Thermodynamic Properties of Weakly Degenerate Fermi and Bose Gases;247
9.6;7.6 Completely Degenerate Fermi Gas: Electron Gas: Temperature of Degeneracy;250
9.7;7.7 Thermodynamic Properties of Strongly Degenerate Fermi Gas: Electron Gas;254
9.8;7.8 General Case: Criteria of Classicity and Degeneracy of Fermi Gas: Electron Gas;259
9.8.1;7.8.1 Low Temperatures;260
9.8.2;7.8.2 High Temperatures;261
9.8.3;7.8.3 Moderate Temperatures: TT0 ;261
9.9;7.9 Heat Capacity of Metals:First Difficulty of Classical Statistics;264
9.9.1;7.9.1 Low Temperatures;266
9.9.2;7.9.2 Region of Temperatures;266
9.10;7.10 Pauli Paramagnetism: Second Difficulty of Classical Statistics;268
9.11;7.11 ``Ultra-Relativistic'' Electron Gas in Semiconductors;272
9.12;7.12 Statistics of Charge Carriers in Semiconductors;275
9.13;7.13 Degenerate Bose Gas: Bose–Einstein Condensation;287
9.14;7.14 Photon Gas: Third Difficulty of Classical Statistics;292
9.15;7.15 Phonon Gas;299
10;8 Electron Gas in Quantizing Magnetic Field;307
10.1;8.1 Motion of Electron in External Uniform Magnetic Field: Quantization of Energy Spectrum;307
10.2;8.2 Density of Quantum States in Strong Magnetic Field;312
10.3;8.3 Grand Thermodynamic Potential and Statistics of Electron Gas in Quantizing Magnetic Field;314
10.4;8.4 Thermodynamic Properties of Electron Gas in Quantizing Magnetic Field;320
10.5;8.5 Landau Diamagnetism;324
11;9 Non-Equilibrium Electron Gas in Solids;330
11.1;9.1 Boltzmann Equation and Its Applicability Conditions;330
11.1.1;9.1.1 Nonequilibrium Distribution Function;330
11.1.2;9.1.2 Boltzmann Equation;332
11.1.3;9.1.3 Applicability Conditions of the Boltzmann Equation;334
11.2;9.2 Solution of Boltzmann Equation in Relaxation Time Approximation;337
11.2.1;9.2.1 Relaxation Time;337
11.2.2;9.2.2 Solution of the Boltzmann Equation in the Absence of Magnetic Field;339
11.2.3;9.2.3 Solution of Boltzmann Equation with an Arbitrary Nonquantizing Magnetic Field;345
11.3;9.3 General Expressions of Main Kinetic Coefficients;349
11.3.1;9.3.1 Current Density and General Formof Conductivity Tensors;349
11.3.2;9.3.2 General Expressions of Main Kinetic Coefficients;351
11.3.2.1;Galvanomagnetic Effects;351
11.3.2.2;Thermomagnetic Effects;351
11.4;9.4 Main Relaxation Mechanisms;353
11.4.1;9.4.1 Charge Carrier Scattering by Ionized Impurity Atoms;354
11.4.2;9.4.2 Charge Carrier Scattering by Phonons in Conductorswith Arbitrary Isotropic Band;357
11.4.2.1;Scattering by Acoustic Phonons, Deformation Potential Method;357
11.4.2.2;Scattering by Nonpolar Optical Phonons, Deformation Potential Method;360
11.4.2.3;Scattering by Polar Optical Phonons;363
11.4.3;9.4.3 Generalized Formula for Relaxation Time;366
11.5;9.5 Boltzmann Equation Solution for Anisotropic Band in Relaxation Time Tensor Approximation;368
11.5.1;9.5.1 Current Density;368
11.5.2;9.5.2 The Boltzmann Equation Solution;369
11.5.3;9.5.3 Current Density;371
12;Definite Integrals Frequently Met in Statistical Physics;372
12.1;A.1 Gamma-Function or Euler Integral of Second Kind;372
12.2;A.2 Integral of Type;373
12.3;A.3 Integral of Type;374
12.4;A.4 Integral of Type;375
12.5;A.5 Integral of Type;376
13;Jacobian and Its Properties;378
14;Bibliograpy;379
15;Index;381