Kinetics of hopping of octahedral interstitials in arbitrary time dependent and inhomogeneous field: body-centered cubic lattice

Atomic movements of interstitials (octahedral sites) species in an arbitrary time and space dependent field have been formulated in terms of a set of coupled linear differential equations for a body-centered cubic (bcc) lattice. The decoupled form of these equations has been solved exactly using the discrete Fourier k space transformation supplemented by a Laplace transform with respect to time. An explicit and compact expression for the Fourier transform of the partial concentration of interstitials is obtained for fields which have absolutely convergent norms in the time domain. Some special cases of general physical interest such as simple harmonic or static inhomogeneous fields are also treated. For the latter situations, a steady-state power dissipation and the thermodynamic equilibrium partition of defects over energetically distinguishable sites are uniquely determined, respectively. The inverse relaxation time spectrum of octahedral-interstitials which has three distinct branches, one acoustic and two optical in the first Brillouin zone, is also computed and presented along the [100], [110], and [111] directions of the cubic cell of a bcc structure.