Molecular dynamics simulations were performed to study the effect of the composition of the intergranular film (IGF) on anisotropic and isotropic grain growth in alpha-Al2O3. In the simulations, the IGF is formed while in contact with two differently oriented alumina crystals, with the alumina (0001) basal plane on one side and the (11 (2) over bar0) prism plane on the other. Five different compositions in the IGFs were studied. Results show preferential growth along the [11 (2) over bar0] of the (11 (2) over bar0) surface in comparison to growth along the [0001] direction on the (0001) surface for compositions near a Ca/Al ratio of 0.5. Such preferential growth is consistent with anisotropic grain growth in alumina, where platelets form because of faster growth of the prism orientations than the basal orientation. The simulations also show the mechanism by which Ca ions in the IGF inhibit growth on the basal surface. At compositions with high or low Ca/Al ratios, growth along each surface normal is equivalent, indicating isotropic grain growth, although the attachment rates are quite different, which may indicate differences between normal grain growth and abnormal, but isotropic, grain growth. The simulations provide an atomistic view of attachment onto crystal surfaces, affecting grain growth in alumina.