Ab initio study of interacting lattice vibrations and stabilization of the $\beta$ phase in Ni-Ti shape-memory alloy

Lattice dynamical methods used to predict phase transformations in crystals typically evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the $\beta$ structure when it appears as a high-temperature phase of the shape memory alloy Ni-Ti. Here it is shown by self-consistent ab initio lattice dynamical calculations that the critical temperature for the premartensitic $R$-to-$\beta$ phase transformation in Ni-Ti can be effectively calculated with good accuracy, and that the $\beta$ phase is a result primarily of the stabilizing interaction between different lattice vibrations.

Figure 1

(Color online) The phonon dispersions of $\beta \text{-NiTi}$ calculated at different temperatures together with experimental data measured at 400 K (black circles), at 338 K (empty circles), and at 423 K (crosses) (Ref. 10). Solid, dashed, dotted, and dashed-dotted lines are the first-principles self-consistent phonon calculations.

Figure 2

(Color online) The calculated temperature dependence of the ${\text{T}}_2\text{A}$ phonon frequency at $q=\left[\frac{1}{3}\frac{1}{3}0\right]$ (red squares) and at $q=\left[\frac{1}{2}\frac{1}{2}0\right]$ (black circles) in $\beta \text{-NiTi}$, here displayed together with experimental data for $q=\left(\frac{1}{3},\frac{1}{3},0\right)$ (empty blue circles) (Ref. 10). The width of the error bars are the square root of the mean-square deviation of the last 10 SCAILD iterations relative to the frequency of the 150th SCAILD iteration.

Figure 3

(Color online) Fermi surface of the $\beta \text{-NiTi}$. In (a) the Fermi surface in the $T=0$ case (i.e., no phonon-induced disorder). In (b) we show the cut through the Fermi surface displayed in (a). The leftmost panel in (b) shows a cut through the red bowl-shaped surface sheets in (a). The rightmost panel in (b) shows a cut through the turquoise sheets in (a). In (b) the nesting vector $q_n=\left(\frac{1}{3},\frac{1}{3},0\right)$ interconnecting the nested parts of the Fermi surface is also shown. In (c) we show a cut through of the Fermi surface in (a) down folded to the first Brillouin zone of the undistorted $3\times 3\times 3$ super cell. In (d) we show a cut through the Fermi surface calculated from four of the $T=300\text{K}$ atomic configurations produced by the SCAILD scheme.

Figure 4

(Color online) The calculated susceptibility as a function of $q=\left(\xi ,\xi ,0\right)$ in $\beta \text{-NiTi}$. The full black curve is the susceptibility for the $T=0\text{K}$ case (i.e., no phonon-induced disorder). The dashed red curve is the mean-susceptibility calculated from four of the $T=300\text{K}$ atomic configurations produced by the SCAILD scheme. Here the width of the error bars correspond to the standard deviation of the $T=300\text{K}$ susceptibility distribution. The susceptibilities are calculated within a $3\times 3\times 3$ supercell, resulting in a shift of the susceptibility peaks from $\xi =\frac{1}{3}$ to $\xi \approx 0.177$, due to the down folding of the bands into the first Brillouin zone of the $3\times 3\times 3$ cell.