Elastic energy anisotropy effects on antiphase boundaries

Abstract

The effect of elastic energy on the anisotropy of antiphase boundary (APB) interfacial energy has been studied theoretically. The model used, a generalization of one developed by Kikuchi and Cahn, treats composition and atomic ordering as local variables defined on each of the atomic planes parallel to the APB. The equilibrium APB structure is found as the set of planar variables that minimizes the free energy. A strain energy term involving an orientation-dependent stiffness parameter and a phenomenological law giving lattice constant as a function of local composition and order parameter is included in the definition of the free energy. Elastic effects in APBs in B2 ordered FeAl alloys with 0.2 – 0.3 atomic fraction Al were investigated. It was found that, despite the high elastic anisotropy of FeAl alloys, elastic effects would not result in any substantial anisotropy in APB interfacial energy. This is because in FeAl alloys the variation in lattice constant due to order parameter variation at the APB is almost completely cancelled out by the variation in lattice constant due to compositional variation. In a hypothetical model with physically reasonable parameters, APB energies were found to vary by up to 9% with orientation, purely as a result of elastic effects. It was concluded that elastically induced APB anisotropy would be observable in alloys such as FeSi in which lattice constant variations due to order parameter variation are cooperative with those due to compositional variation.