On the elastic driving force in diffusion-induced grain boundary motion

Abstract In 1983 Hillert obtained the formula Yη 2 ( c + − c − ) 2 for the driving force per unit area of grain boundary arising from elastic misfit in an isotropic alloy, where the mole fractions c + and c − on the two sides of the grain boundary are small, η is a measure of the elastic misfit and Y = E /(1− ν ) where E is Young's modulus and ν is Poisson's ratio. It is shown here that the formula is still valid (with suitably defined Y , η ) when c + , c − are not small. The formula for Y in a general anisotropic solid is given. The physical origin of the elastic force on the grain boundary is considered, with help from the `energy–momentum tensor' devised by Eshelby to quantify the forces on other crystal imperfections such as dislocations. The theory also makes a prediction about the direction of motion of an initially stationary grain boundary.