Trends in elastic properties of Ti-Ta alloys from first-principles calculations

Abstract

The martensitic start temperature ($M_{\text{s}}$) is a technologically fundamental characteristic of high-temperature shape memory alloys. We have recently shown [Phys. Rev. B 94, 224104 (2016)] that the two key features in describing the composition dependence of $M_\text{s}$ are the $T=0$ K phase stability and the difference in vibrational entropy which, within the Debye model, is directly linked to the elastic properties. Here, we use density functional theory together with special quasi-random structures to study the elastic properties of disordered martensite and austenite Ti-Ta alloys as a function of composition. We observe a softening in the tetragonal shear elastic constant of the austenite phase at low Ta content and a \emph{non-linear} behavior in the shear elastic constant of the martensite. A minimum of 12.5$\%$ Ta is required to stabilize the austenite phase at $T = 0$ K. Further, the shear elastic constants and Young's modulus of martensite exhibit a maximum for Ta concentrations close to 30$\%$. Phenomenological, elastic-constant-based criteria suggest that the addition of Ta enhances the strength, but reduces the ductile character of the alloys. In addition, the directional elastic stiffness, calculated for both martensite and austenite, becomes more isotropic with increasing Ta content. The reported trends in elastic properties as a function of composition may serve as a guide in the design of alloys with optimized properties in this interesting class of materials.