Diffusion in solids
This chapter starts with a brief history of the science of diffusion. Macroscopically diffusion is characterized by various diffusion coefficients: the self-diffusion coefficient, the tracer diffusion coefficient, the chemical or Fickian diffusion coefficient, and the conductivity diffusion coefficient. Microscopically the gas, liquid-like, and solid state diffusion mechanisms are considered. Solid state diffusion is characterized by the parameters jump rate, jump vector, and coordination number. The stochastic aspects of solid state (jump) diffusion are introduced. Statistical methods (Markov and non-Markov processes) are applied to study the outcome of a sequence of jumps, i.e., the spatial/temporal development of the diffusive process. The nature of the mechanism of a single diffusive event is considered. Topics such as classical jump, phonon-assisted tunnelling, electron-restricted tunnelling, and incoherent tunnelling types, also called hopping, are introduced.
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