Antiphase structures of an improper ferroelastic phase transition driven by anM5−zone boundary phonon inRAg1−xInx

Abstract

Rare-earth alloys $R{\mathrm{Ag}}_{1\ensuremath{-}x}{\mathrm{In}}_{x}$ (where $R=\mathrm{La},$ Ce, and Pr) are improper ferroelastic materials with the CsCl structure. A weakly first-order phase transition occurs with the softening of a zone-edge ${\mathrm{M}}_{5}^{\ensuremath{-}}$ mode that drives the material from a cubic phase to a tetragonal phase. Based on Ginzburg-Landau theory, we utilize the complete free-energy density, constructed from a six-dimensional primary order parameter (shuffle) that couples to strain, to study domain formation. The model allows the study of complex antiphase structures that appear in this cubic-to-tetragonal phase transition. With the help of numerical techniques, the order-parameter profiles across antiphase boundaries of different orientations and their temperature dependence are calculated. We find a single set of two coupled dimensionless governing equations, which are applicable to order-parameter profiles across all antiphase boundaries for this transition.