The kinetics of hopping motion of interstitials with chemical reactions in arbitrary time dependent inhomogeneous interactive fields

Atomic hopping motions of interstitial species with chemical reactions in an arbitrary time- and space-dependent field have been formulated in terms of a linear but coupled set of differential equations for a general lattice structure. The decoupled form of these equations has been solved exactly using the discrete Fourier k-space transformation supplemented by a Laplace transformation with respect to time. An explicit and compact expression for the Fourier transform of the partial concentration of interstitials is obtained for interactive fields which have absolutely convergent norms in the time domain. Some special cases of general interest such as the simple harmonic, almost periodic, or static inhomogeneous fields are also treated extensively. The power dissipation and the storage terms associated with interstitial hopping motion in harmonic or almost periodic fields are formulated rigorously. The effect of static inhomogeneous bias field due to other imperfections on the relaxation time spectrum is considered in terms of the first-order perturbation theory.