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E-raamat: Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases

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Thermodynamicsandstatisticalphysicsstudythephysicalproperties(mec- nical, thermal, magnetic, optical, electrical, etc.) of the macroscopic system. The tasks and objects of study in thermodynamics and statistical physics are identical. However,the methods of investigationinto macroscopicsystems are di erent. Thermodynamics is a phenomenological theory. It studies the properties of bodies, without going into the mechanism of phenomena, i.e., not taking into consideration the relation between the internal structure of substance and phenomena, it generalizes experimental results. As a result of such a g- eralization, postulates and laws of thermodynamics made their appearance. These laws make it possible to ?nd general relations between the di erent properties of macroscopic systems and the physical events occurring in them. Statisticalphysicsisa microscopic theory.Onthebasisoftheknowledgeof the type of particles a system consists of, the nature of their interaction, and thelawsofmotionoftheseparticlesissuingfromtheconstructionofsubstance, it explains the properties being observedon experiment, and predicts the new properties of systems. Using the laws of classical or quantum mechanics, and alsothe theoryofprobability,itestablishesqualitativelynewstatistical app- priatenesses of the physical properties of macroscopic systems, substantiates the laws of thermodynamics, determines the limits of their applicability, gives the statistical interpretation of thermodynamic parameters, and also works out methods of calculations of their means. The Gibbs method is based on statisticalphysics.Thismethodis themostcanonical.Therefore,inthis book, the exposition of the Gibbs method takes an important place.
Basic Concepts of Thermodynamics and Statistical Physics
1(42)
Macroscopic Description of State of Systems: Postulates of Thermodynamics
1(5)
Mechanical Description of Systems: Microscopic State: Phase Space: Quantum States
6(7)
Statistical Description of Classical Systems: Distribution Function: Liouville Theorem
13(6)
Microcanonical Distribution: Basic Postulate of Statistical Physics
19(3)
Statistical Description of Quantum Systems: Statistical Matrix: Liouville Equation
22(5)
Entropy and Statistical Weight
27(4)
Law of Increasing Entropy: Reversible and Irreversible Processes
31(4)
Absolute Temperature and Pressure: Basic Thermodynamic Relationship
35(8)
Law of Thermodynamics: Thermodynamic Functions
43(50)
First Law of Thermodynamics: Work and Amount of Heat: Heat Capacity
43(7)
Second Law of Thermodynamics: Carnot Cycle
50(6)
Thermodynamic Functions of Closed Systems: Method of Thermodynamic Potentials
56(7)
Thermodynamic Coefficients and General Relationships Between Them
63(6)
Thermodynamic Inequalities: Stability of Equilibrium State of Homogeneous Systems
69(5)
Third Law of Thermodynamics: Nernst Principle
74(5)
Thermodynamic Relationships for Dielectrics and Magnetics
79(4)
Magnetocaloric Effect: Production of Ultra-Low Temperatures
83(3)
Thermodynamics of Systems with Variable Number of Particles: Chemical Potential
86(4)
Conditions of Equilibrium of Open Systems
90(3)
Canonical Distribution: Gibbs Method
93(16)
Gibbs Canonical Distribution for Closed Systems
93(6)
Free Energy: Statistical Sum and Statistical Integral
99(3)
Gibbs Method and Basic Objects of its Application
102(1)
Grand Canonical Distribution for Open Systems
103(6)
Ideal Gas
109(48)
Free Energy, Entropy and Equation of the State of an Ideal Gas
109(3)
Mixture of Ideal Gases: Gibbs Paradox
112(3)
Law About Equal Distribution of Energy Over Degrees of Freedom: Classical Theory of Heat Capacity of an Ideal Gas
115(5)
Classical Theory of Heat Capacity of an Ideal Gas
118(2)
Quantum Theory of Heat Capacity of an Ideal Gas: Quantization of Rotational and Vibrational Motions
120(13)
Translational Motion
122(3)
Rotational Motion
125(3)
Vibrational Motion
128(3)
Total Heat Capacity
131(2)
Ideal Gas Consisting of Polar Molecules in an External Electric Field
133(8)
Orientational Polarization
133(4)
Entropy: Electrocaloric Effect
137(1)
Mean Value of Energy: Caloric Equation of State
138(1)
Heat Capacity: Determination of Electric Dipole Moment of Molecule
139(2)
Paramagnetic Ideal Gas in External Magnetic Field
141(9)
Classical Case
141(2)
Quantum Case
143(7)
Systems with Negative Absolute Temperature
150(7)
Non-Ideals Gases
157(18)
Equation of State of Rarefied Real Gases
157(7)
Second Virial Coefficient and Thermodynamics of Van Der Waals Gas
164(5)
Neutral Gas Consisting of Charged Particles: Plasma
169(6)
Solids
175(38)
Vibration and Waves in a Simple Crystalline Lattice
175(9)
One-Dimensional Simple Lattice
178(4)
Three-Dimensional Simple Crystalline Lattice
182(2)
Hamilton Function of Vibrating Crystalline Lattice: Normal Coordinates
184(3)
Classical Theory of Thermodynamic Properties of Solids
187(7)
Quantum Theory of Heat Capacity of Solids: Einstein and Debye Models
194(10)
Einstein's Theory
196(1)
Debye's Theory
197(7)
Quantum Theory of Thermodynamic Properties of Solids
204(9)
Quantum Statistics: Equilibrium Electron Gas
213(84)
Boltzmann Distribution: Difficulties of Classical Statistics
214(8)
Principle of Indistinguishability of Particles: Fermions and Bosons
222(7)
Distribution Functions of Quantum Statistics
229(5)
Equations of States of Fermi and Bose Gases
234(3)
Thermodynamic Properties of Weakly Degenerate Fermi and Bose Gases
237(3)
Completely Degenerate Fermi Gas: Electron Gas: Temperature of Degeneracy
240(4)
Thermodynamic Properties of Strongly Degenerate Fermi Gas: Electron Gas
244(5)
General Case: Criteria of Classicity and Degeneracy of Fermi Gas: Electron Gas
249(5)
Low Temperatures
250(1)
High Temperatures
251(1)
Moderate Temperatures: T 'T0
251(3)
Heat Capacity of Metals: First Difficulty of Classical Statistics
254(4)
Low Temperatures
256(1)
Region of Temperatures
256(2)
Pauli Paramagnetism: Second Difficulty of Classical Statistics
258(4)
``Ultra-Relativistic'' Electron Gas in Semiconductors
262(3)
Statistics of Charge Carriers in Semiconductors
265(12)
Degenerate Bose Gas: Bose-Einstein Condensation
277(5)
Photon Gas: Third Difficulty of Classical Statistics
282(7)
Phonon Gas
289(8)
Electron Gas in Quantizing Magnetic Field
297(24)
Motion of Electron in External Uniform Magnetic Field: Quantization of Energy Spectrum
297(5)
Density of Quantum States in Strong Magnetic Field
302(2)
Grand Thermodynamic Potential and Statistics of Electron Gas in Quantizing Magnetic Field
304(6)
Thermodynamic Properties of Electron Gas in Quantizing Magnetic Field
310(4)
Landau Diamagnetism
314(7)
Non-Equilibrium Electron Gas in Solids
321(42)
Boltzmann Equation and Its Applicability Conditions
321(7)
Nonequilibrium Distribution Function
321(2)
Boltzmann Equation
323(2)
Applicability Conditions of the Boltzmann Equation
325(3)
Solution of Boltzmann Equation in Relaxation Time Approximation
328(12)
Relaxation Time
328(2)
Solution of the Boltzmann Equation in the Absence of Magnetic Field
330(6)
Solution of Boltzmann Equation with an Arbitrary Nonquantizing Magnetic Field
336(4)
General Expressions of Main Kinetic Coefficients
340(4)
Current Density and General Form of Conductivity Tensors
340(2)
General Expressions of Main Kinetic Coefficients
342(2)
Main Relaxation Mechanisms
344(15)
Charge Carrier Scattering by Ionized Impurity Atoms
345(3)
Charge Carrier Scattering by Phonons in Conductors with Arbitrary Isotropic Band
348(9)
Generalized Formula for Relaxation Time
357(2)
Boltzmann Equation Solution for Anisotropic Band in Relaxation Time Tensor Approximation
359(4)
Current Density
359(1)
The Boltzmann Equation Solution
360(2)
Current Density
362(1)
Definite Integrals Frequently Met in Statistical Physics
363(6)
Gamma-Function or Euler Integral of Second Kind
363(1)
Integral of Type
364(1)
Integral of Type
365(1)
Integral of Type
366(1)
Integral of Type
367(2)
Jacobian and Its Properties 369(2)
Bibliograpy 371(2)
Index 373
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