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

In 1983 Hillert obtained the formula Yη2(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 Youngʹs modulus and ν is Poissonʹs 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 tensorʹ 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.