Diffusivity and derivatives for interstitial solutes: Activation energy, volume, and elastodiffusion tensors

TL;DR

This paper derives a comprehensive framework for calculating the diffusivity tensor and its derivatives for interstitial solutes in crystalline lattices using atomic-scale computational methods, with open-source implementation and applications to various crystal structures.

Contribution

It introduces a general expression for the anisotropic diffusivity tensor and its derivatives, integrating site and transition state energies with symmetry considerations, and provides open-source tools for these calculations.

Findings

Analytic expressions for octahedral-tetrahedral networks in FCC, BCC, HCP lattices

Numerical results for carbon diffusion in iron

Open-source implementation of the computational algorithm

Abstract

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.