Energetics of heterogeneous Mg [formula omitted] deformation twinning migration using an atomistically informed phase-field model

Abstract

We have constructed an atomistically informed phase-field model for the quantitative energetic analysis of phase transformations. In our model, to describe the general phase transformation with a non-linear correlation between displacive and diffusive modes, we have defined two order parameters, γ and ϕ, which describe the lattice distortion (displacive mode) and shuffling (diffusive mode), respectively. Our method provides a way to introduce the energetics from atomistic simulations to the phase-field model, describes γ and ϕ in an atomic model, and derives phase-field parameters from the free energy calculated by atomistic simulation. As an application of our model, we used the energetics obtained from atomistic simulations using a density functional theory potential, and we calculated the free energy change during the heterogeneous {101¯2} twin migration of hexagonally close-packed (HCP) Mg, which can be considered as a lattice distortion and shuffling mixed phase transformation, by combining our phase-field model with the nudged elastic band method. The activation energy, and the critical nucleus size of the heterogeneous {101¯2} twin migration under a set stress were derived. The critical c-axis tensile stress (athermal stress), at which the activation energy becomes zero, is consistent with the experimental yield stress of {101¯2} for the twinning deformation of HCP Mg nanopillars in tensile tests. The critical nucleus size of the heterogeneous {101¯2} twin migration is on the range of nanometers under several hundred megapascals stress, which is consistent with the experimental observation of nanotwins.