Modeling martensitic phase transformations in shape memory alloys with the self-consistent lattice dynamics approach

The unusual properties of shape memory alloys (SMAs) are due to solid-to-solid martensitic transformations (MTs) which correspond to a lattice level instability of the crystal structure. Currently, there exists a shortage of material models of MTs based on the material's atomic composition and crystal structure. The present work develops a model using first-order self-consistent lattice dynamics (SCLD) that captures the qualitative behavior of MTs. The effects of atomic vibrations on the material properties are captured by renormalizing the frequencies of atomic vibration using self-consistent equations. These renormalized frequencies are dependent on both configuration and temperature. The model is easily extended to three-dimensional problems. The model is illustrated for the case of a one dimensional bi-atomic chain. The constant Morse pair potential parameters are chosen to demonstrate the usefulness of the SCLD model. The resulting model is evaluated by generating equilibrium paths with temperature and mechanical load as the loading parameters. In both types of loading, a first-order entropically stabilized MT is predicted indicating that the current model is able to capture the first-order MTs that occur in SMAs. This qualitative prediction of a first-order MT indicates the likely-hood that the SCLD model can be used for the computational design and discovery of SMAs with better properties. Such an undertaking would involve, first, determining the potential parameters of new alloys from first-principles calculations and, second, using these parameter values with the SCLD to evaluate the shape memory behavior of the new previously unstudied materials.