  Computational atomic-scale methods continue to provide new information about
geometry, energetics, and transition states for interstitial elements in
crystalline lattices. This data can be used to determine the diffusivity of
interstitials by finding steady-state solutions to the master equation. In
addition, atomic-scale computations can provide not just the site energy, but
also the stress in the cell due to the introduction of the defect to compute
the elastic dipole. We derive a general expression for the fully anistropic
diffusivity tensor from site and transition state energies, and three
derivatives of the diffusivity: the elastodiffusion tensor (derivative of
diffusivity with respect to strain), the activation barrier tensor (logarithmic
derivative of diffusivity with respect to inverse temperature) and activation
volume tensor (logarithmic derivative of diffusivity with respect to pressure).
Computation of these quantities takes advantage of crystalline symmetry, and we
provide an open-source implementation of the algorithm. We provide analytic
results for octahedral-tetrahedral networks in face-centered cubic,
body-centered cubic, and hexagonal closed-packed lattices, and conclude with
numerical results for C in Fe.
