It was recalled that the expression, Yη2(c+−c−)2, had been derived for the driving force per unit area of grain boundary, arising from elastic misfit in an isotropic alloy. Here, the mole fractions, c+ and c−, on the 2 sides of the grain boundary were small, η was a measure of the elastic misfit and Y = E/(1−ν) where E was Young's modulus and ν was Poisson's ratio. It was shown here that the formula remained valid (for suitably defined Y and η) when c+ and c− were not small. The formula for Y, in a general anisotropic solid, was given. Eshelby’s energy–momentum tensor was used to quantify the forces on other crystal imperfections, such as dislocations. The theory also predicted the direction of motion of an initially stationary grain boundary.

On the Elastic Driving Force in Diffusion-Induced Grain Boundary Motion. O.Penrose: Acta Materialia, 2004, 52[13], 3901-10