Kinetics and Thermodynamics of Fast Particles in Solids

Preface

1. THEORETICAL BACKGROUND AND MODEL PRESENTATION  •  Two theoretical disciplines: non-equilibrium statistical mechanics and non-equilibrium statistical thermodynamics  •  Short description of the non-equilibrium system  •  Channeling effect of charged particles  •  A brief overview  •  Some assumptions of the classical theory of channeling

2. CHANNELING OF CHARGED HIGH-ENERGY PARTICLES AS A STOCHASTIC PROCESS  •  Markov process with a normal (Gaussian) distribution  •  Transport coefficients of channeled particles in electron scattering (non-local theory)   •  Fokker–Planck equation with fluctuations. The diffusion function and the friction coefficient  •  Stochastic theory for the thermodynamic level of description  •  Kinetic features of channeled particles in the presence of thermal lattice vibrations (local theory)   •  Local matrix of random effects  •  Diagonal element of the local matrix. Correlation of random effects  •  The system of stochastic equations and Fokker–Planck equation. Kinetic features of the local theory  •  Dechanneling  •  The average lifetime of a dynamic system under random effects  •  Eigenvalues of the kinetic Fokker–Planck equation and the main functions of the theory of dechanneling  •  Three modes of motion of fast particles  •  The angular distribution of backscattered particles incident on thin crystals in the direction of chains or planes. Elastic collisions with atoms of the ‘frozen chain’  •  The energy distribution of backscattered particles. Elastic electron scattering  •  Singularities of the energy losses in the local theory

3. LOCAL BOLTZMANN KINETIC EQUATION AS APPLIED TO PLANE AND AXIAL CHANNELING  •  The distribution function for the complex of a fast particle and r atoms in the crystal  •  The chain of BBGKY equations in channeling theory  •  Local linearized Boltzmann equation  •  Planar channeling  •  Axial channeling. The limiting case of a spatially homogeneous environment  •  The equation of local balance of the number of particles in the channeling problem  •  Diagonal element of the matrix of effects in electron scattering  •  Features of the kinetic functions as a consequence of locality of the theory  •  Transition to the kinetic Boltzmann equation in the theory of rarefied gases

4. TWO CLASSES OF IRREVERSIBLE PROCESSES IN STATISTICAL THEORY OF CHANNELING  •  Phase mixing and dissipative processes  •  Phase mixing at shallow depths of penetration (S-contributions)   •  Phase shifts of the trajectories. The role of anharmonicity of the particles in the process of approach to quasi-equilibrium  •  Evolution of the depth of distribution of channeled particles on the transverse coordinates  •  Local and non-local theory of the state density of fast particles  •  The linear theory of reaction  •  Symptoms of a mechanical disturbance  •  Dissipative process (V-contributions) at low velocities of channeled particles

5. NON-EQUILIBRIUM STATISTICAL THERMO- DYNAMICS AS APPLIED TO CHANNELING  •  General view of the statistical operator for non-equilibrium systems  •  Non-equilibrium statistical operator in quantum theory of channeling  •  Model representations. Thermodynamic parameters  •  Invariant part of the quasi-equilibrium statistical operator. The particle number flux  •  Definitions of the quantum theory of dechanneling  •  Expressing the rate constant by means of spectral intensity  •  The total Hamiltonian of the system which includes electrons and fast particles  •  Fokker–Planck–Kolmogorov finite difference equation  •  The statistical coefficient of dechanneling rate  •  The kinetic coefficient in quantum theory  •  Semi-classical approximation  •  The rate of release of particles from the channeling regime, taking into account the spatial separation of directional beam  •  Resonant transition of particles to the quasi-channeled fraction. Relaxation frequency  •  Dechanneling due to the resonance transitions

6. NON-EQUILIBRIUM STATISTICAL THERMODYNAMICS OF DIRECTIONAL PARTICLE BEAMS CONCEPT OF TRANSVERSE QUASI-TEMPERATURE  •  Formulation of the theory based on expansion of the non-equilibrium statistical operator  •  The energy–momentum balance equation in the comoving coordinate system  •  Linearization of the balance equation  •  The solution of the balance equation  •  The dependence of equilibrium distributions on transverse quasi-temperature (axial channel)   •  The angular distribution of channeled particles after passing through a thin crystal  •  Determination of transverse quasi-temperature based on experimental data  •  Distribution of particles over exit angles in backscattering  •  Quasi-temperature of strongly non-equilibrium systems  •  Dependence of the coefficient of the dechannelling rate and dissociation of molecules in plasma on quasi-temperature  •  Quasi-temperature as quasi-equilibrium distribution modulus  •  Comparative analysis: channeled particles and the spin gas  •  Spin temperature in a strong magnetic field  •  Statistical characteristics of channeled particles and the spin gas

7. NON-EQUILIBRIUM THERMODYNAMICS OF CHAOTIC PARTICLES  •  Relaxation kinetics and quasi-temperature of positronium atoms  •  Ore model. The energy balance equation  •  Phonon and electron scattering on positronium atoms  •  Eigenvalue of the relaxation matrix and quasi-temperature of positronium  •  Thermalization of positronium atoms  •  Thermodynamics of hot charge carriers in semiconductors  •  Separation of subsystems into fractions and thermodynamic parameters of fractions  •  Kinetic equations for carriers and quasi-temperature of carriers and quasitemperature of optical phonons  •  Evolution of quasi-temperature of carriers during thermalization  •  Displacement cascade and thermodynamics of knocked-on atoms  •  Cascade function. Geometric parameters of the cascade  •  Transition to the thermodynamic description level  •  The energy balance equation of knocked-on atoms  •  Quasi-temperature of the subsystem of knocked-on atoms and thermodynamic stability of states  •  Discussion of the concept of the quasi-temperature of knocked-on atoms  •  Kinetics of thermal sputtering

8. STATISTICAL THERMODYNAMICS OF LIGHT ATOMS MOVING WITH THERMAL VELOCITY  •  Coefficient (constant) of the exit velocity of particles from the potential minimum  •  Tunneling transitions of hydrogen atoms due to the collapse of local deformation in the bcc lattice  •  Thermally activated tunneling in bcc metals  •  Concluding remarks on the migration of hydrogen atoms  •  Thermal fracture of activation energy near Debye temperature θ_D  •  Classical and anomalous isotope effects  •  Departure from the concept of hopping conduction of small radius polarons

CONCLUSION

REFERENCES

INDEX