  Kinetic Monte Carlo models parameterized by first principles calculations are
widely used to simulate atomic diffusion. However, accurately predicting the
activation energies for diffusion in substitutional alloys remains challenging
due to the wide variety of local environments that may exist around the
diffusing atom. We address this challenge using a cluster expansion model that
explicitly includes a sublattice of sites representing transition states and
assess its accuracy in comparison with other models, such as the broken bond
model and a model related to Marcus theory, by modeling vacancy-mediated
diffusion in Pt-Ni nanoparticles. We find that the prediction error of the
cluster expansion is similar to that of other models for small training sets,
but with larger training sets the cluster expansion has a significantly lower
prediction error than the other models with comparable execution speed. Of the
simpler models, the model related to Marcus theory yields predictions of
nanoparticle evolution that are most similar to those of the cluster expansion,
and a weighted average of the two approaches has the lowest prediction error
for activation energies across all training set sizes.
