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

Abstract

In 1983 Hillert obtained the formula Y η 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.

Low-Temperature Interdiffusion and Ordered Phase Formation in Au/Cu Nanocrystalline Thin Films at the Different Atmospheres

“…It is rather difficult to distinguish DIR and DIGM experimentally (see, for example [24]). It is more and more widely accepted that in both processes the driving forces are related to stress accumulation and relaxation ahead/around the moving boundary [9,25]. In case of low temperature processes (when there is no bulk diffusion), it is most likely to suppose that the migrating GB driving force is originated by the diffusion induced GB stresses created by the differences of the GB atomic fluxes of the two components [26].…”

On the mathematical modelling of cellular (discontinuous) precipitation

“…Now we can derive a transport equation describing how the solute atoms travel along the 'highway'. We start from eqn (15). Integrate from ν = − 1 2 to +∞.…”

“…If Y η 2 f (c eq g ) this reduces to Hillert's [9] formula for the elastic driving force in diffusion-induced grain boundary motion; a less laborious derivation of a formula essentially the same as (47) can be found in ref. [15]. Now consider the alternative case, where the phases on the two sides of the interface are different.…”

Stress- and diffusion-induced interface motion: Modelling and numerical simulations

“…In this paper, we introduce a phase field model for interface motion taking into account driving forces due to interfacial and elastic energies and we allow for diffusion of atoms in the interface. We in particular generalize models that have been studied earlier (we refer to [1,4,6,18,19,22,26,28,30]). Phase field models for stress driven interface motion have been used e.g.…”