On the basis of experiments on grain-boundary migration in Al, it was questioned whether interface mobility depended upon the nature of the driving force. This was investigated in terms of the Ising model, and it was concluded that it did not. This highlighted the importance of including the second derivative of the interface energy with respect to the inclination, γ′′, in the Herring relation; in order to describe correctly the motion of grain boundaries as driven by capillarity. The importance of this term could be traced to the entropic part of γ′′, which could be highly anisotropic, so that the reduced mobility (product of interface stiffness, γ+γ′′, and mobility) could be almost isotropic; even though the mobility itself was highly anisotropic. The cancellation of these 2 anisotropies (associated with stiffness and mobility) originated, in the Ising model, from the fact that the number of geometrically necessary kinks (and hence the kink configurational entropy) varied rapidly with inclination near to low-energy low-mobility interfaces, but slowly near to high-energy high-mobility interfaces, where the kink density was high. This implied that the stiffness was high where the mobility was low, and vice versa. The grain shape could thus appear to be isotropic or highly anisotropic, depending upon whether its motion was driven by curvature or an external field, respectively. However, the mobility itself was independent of the driving force.

Grain Shape, Grain Boundary Mobility and the Herring Relation. A.E.Lobkovsky, A.Karma, M.I.Mendelev, M.Haataja, D.J.Srolovitz: Acta Materialia, 2004, 52[2], 285-92