Measuring simulated hydrogen diffusion in symmetric tilt nickel grain boundaries and examining the relevance of the Borisov relationship for individual boundary diffusion

Grain boundaries are known to act as important diffusion pathways in metals. Here we examine how hydrogen diffusion in nickel grain boundaries is affected by different grain boundary types. We simulate 26 [ 1 0 0 ] symmetric tilt grain boundaries at several temperatures and develop a modified mean squared displacement method for isolating the grain boundary diffusivity from the bulk diffusivity. We analyze the diffusivity data for the different boundaries and find the grain boundary diffusivity to be higher than the bulk diffusivity up to a temperature where the two converge. We test a model developed by Borisov et al. (Phys. Met. Metallogr. 17, 1964, 80-84) that relates grain boundary diffusion to grain boundary interfacial energy. Despite the fact that the Borisov relationship has never been used to examine solute interstitial diffusion before, it fits the simulated diffusion data well for temperatures where the grain boundary diffusivity is higher than the bulk diffusivity. Some parameters in the Borisov relationship, related to the geometry of the grain boundary and its activated states, have always taken on assumed values because they are hard to measure or acquire. The fit of the simulated data provides estimates for these values that are physically realistic and provides evidence that the use of the traditionally assumed values should be reconsidered. This work also demonstrates that while there is a need for further validation, the Borisov relationship can reasonably relate solute interstitial diffusivity of hydrogen to the interfacial energy of individual [ 1 0 0 ] symmetric tilt nickel grain boundaries, whereas in the past it has been used to relate self diffusion and interfacial energy of a grain boundary network as a whole.