This book provides the fundamental statistical theory of atomic transport in crystalline solids, that is the means by which processes occurring at the atomic level are related to macroscopic transport coefficients and other observable quantities. The cornerstones of the authors' treatment are (i) the physical concepts of lattice defects, (ii) the phenomenological description provided by non-equilibrium thermodynamics and (iii) the various methods of statistical mechanics used to link these (kinetic theory, random-walk theory, linear response theory etc.). The book is primarily concerned with transport in the body of crystal lattices and not with transport on surfaces, within grain boundaries or along dislocations, although much of the theory here presented can be applied to these low-dimensional structures when they are atomically well ordered and regular.
A new integro-differential equation for the singlet distribution function in a model dense fluid is derived and solved. In the model considered, the pair interaction potential is represented as a rigid core plus a soft attraction. Interactions between two rigid cores are handled as in the theory of the dense rigid-sphere fluid, while interactions between the soft attractions are handled, following Kirkwood, in the Fokker-Planck approximation. The use of coarse graining in time to provide a time scale permitting the above separation, the relaxation in momentum space, the kinetic flux vectors, and the physical basis of the analysis are all discussed.
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