First-principles characterization of reversible martensitic transformations

Reversible martensitic transformations (MTs) are the origin of many fascinating phenomena, including the famous shape memory effect. In this work, we present a fully ab initio procedure to characterize MTs in alloys and to assess their reversibility. Specifically, we employ ab initio molecular dynamics data to parametrize a Landau expansion for the free energy of the MT. This analytical expansion makes it possible to determine the stability of the high- and low-temperature phases, to obtain the Ehrenfest order of the MT, and to quantify its free energy barrier and latent heat. We apply our model to the high-temperature shape memory alloy Ti-Ta, for which we observe remarkably small values for the metastability region (the interval of temperatures in which the high- and low-temperature phases are metastable) and for the barrier: these small values are necessary conditions for the reversibility of MTs and distinguish shape memory alloys from other materials.

Figure 1

The MT in Ti-Ta. The austenitic phase (left) is a bcc structure. The martensitic phase (right) is orthorhombic, and it is obtained from the austenitic phase by cell distortion and gliding of alternating $\left\{110\right\}$ planes (in brown) along the $〈-110〉$ direction, described by the parameter $\mathrm{\Delta }y$.

Figure 2

Lattice parameters of Ti-25Ta (red) and Ti-31.25Ta (blue) as a function of temperature. Circles are experimental data on bulk samples and thin films at room temperature. Empty squares are DFT calculations from Ref. [20]. Broken lines are guides to the eye.

Figure 3

(a) Spontaneous lattice strain of ${\alpha }^{″}$ for Ti-25Ta (red) and Ti-31.25Ta (blue) as a function of temperature. (b) The time- and atom-averaged $\mathrm{\Delta }y$ parameter as a function of temperature for Ti-25Ta (red) and Ti-31.25Ta (blue). The inset shows the directions of the average atomic displacements observed in the aiMD simulations. For both order parameters, squares are extracted from the aiMD simulations, circles are experimental data for bulk and thin film samples at room temperature, and solid lines are predictions from the Landau-Falk expansion (no fit).

Figure 4

The free energy profiles as a function of the order parameter for Ti-25Ta (left) and Ti-31.25Ta (right) for different temperatures. The inset shows the same profiles for an interval of temperatures around the transition temperature $T_0$.

Figure 5

Entropy as a function of the order parameter for Ti-25Ta (red) and Ti-31.25Ta (blue) obtained from the Landau-Falk expansion.