Grain shape, grain boundary mobility and the Herring relation Original Research Article

Motivated by recent experiments on grain boundary migration in Al, we examine the question: does interface mobility depend on the nature of the driving force? We investigate this question in the Ising model and conclude that the answer is “no.” This conclusion highlights the importance of including the second derivative of the interface energy with respect to inclination γ′′ in the Herring relation in order to correctly describe the motion of grain boundaries driven by capillarity. The importance of this term can be traced to the entropic part of γ′′, which can be highly anisotropic, such that the reduced mobility (i.e., the product of interface stiffness γ+γ′′ and mobility) can be nearly isotropic even though the mobility itself is highly anisotropic. The cancellation of these two anisotropies (associated with stiffness and mobility) originates in the Ising model from the fact that the number of geometrically necessary kinks, and hence the kink configurational entropy, varies rapidly with inclination near low-energy/low mobility, but slowly near high-energy/high-mobility interfaces, where the kink density is high. This implies that the stiffness is high where the mobility is low and vice versa. Consequently, the grain shape can appear isotropic or highly anisotropic depending on whether its motion is driven by curvature or an external field, respectively, but the mobility itself is independent of driving force. We discuss the implications of these results for interpreting experimental observations and computer simulations of microstructural evolution, where γ′′ is routinely neglected.