Correlation of Successive Atomic Steps in Crystals by Relaxation Mode Analysis

The relaxation mode analysis is used to compute the average value of the cosine of the angle between successive steps of an ion diffusing by a vacancy mechanism on a lattice. The technique is applicable to tracers (self-diffusion) or impurities, on any lattice. The result, given in terms of the eigenvalues and eigenvectors of a secular equation, is suitable for machine computation. Sample computations for self-diffusion on an fcc lattice illustrate the method. It is necessary, in order to do the calculations, to have a lattice of finite size, the boundary of which is chosen either totally reflecting or completely transparent to vacancies. For self-diffusion, the boundary can be centered on the vacancy, and convergence of the computed value with boundary radius is rapid. For impurity diffusion, the boundary must be centered on the impurity, and convergence is much slower.