Unraveling the composition dependence of the martensitic transformation temperature: A first-principles study of Ti-Ta alloys

The martensitic start temperature ${M}_{\text{s}}$ is one of the key characteristics of shape memory materials. High-temperature shape memory alloys are a special class of materials where transformation temperatures between the martensite and austenite phase above 373 K are desirable. For the design of new high-temperature shape memory alloys it is therefore important to understand and predict the dependence of ${M}_{\text{s}}$ on the composition of the material. Using density functional theory in combination with the quasiharmonic Debye model, we evaluate the different contributions to the free energy to determine the transition temperature ${T}_{0}$ over a wide range of compositions in Ti-Ta alloys. Our approach provides physical insight into the various contributions that explain the strong composition dependence of ${M}_{\text{s}}$ that is observed experimentally. Based on our calculations, we identify the relative phase stability at $T=0$ K and the vibrational entropy difference between the involved phases as critical parameters to predict changes in ${T}_{0}$. We propose a simple, one-dimensional descriptor to estimate the transition temperature that can be used in the identification of new alloys suitable for high-temperature shape memory applications.