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

In 1983 Hillert obtained the formula Y?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, ? is a measure of the elastic misfit and Y=E/(1-?) where E is Young's modulus and ? is Poisson's ratio. It is shown here that the formula is still valid (with suitably defined Y,?) 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. © 2004 Acta Materialia Inc.published by Elsevier Ltd. All rights reserved.