Rate Equation for the Transfer of Interstitials across Interfaces between Equilibrated Crystals

This work inspects the thermally activated transfer of solute particles across the interface between two interstitial solid solution phases that equilibrate internally by fast diffusion on conserved arrays of sites. When each phase is considered as an ergodic ensemble of particles, statistical mechanics predicts the occupancy of the transition states at equilibrium to depend on the barrier energy and on the chemical potentials and vacancy fractions in each of the phases. A rate law for the non-equilibrium interfacial transfer, based on a constant transition probability between activated states, naturally satisfies the principle of detailed balance. Contrary to Butler-Volmer-type laws, values of the particle chemical potentials enter explicitly rather than through their difference. This, along with the dependency on the vacancy fractions, implies here an exchange flux density that depends explicitly on the compositions at equilibrium. The results can explain experimental observations of a drastic slow-down in the charging of metal hydrides near phase transformations or miscibility-gap critical points.