Anomalous phonon behavior in the high-temperature shape-memory alloy ${\mathrm{Ti}}_{50}{\mathrm{Pd}}_{50-x}{\mathrm{Cr}}_x$

${\mathrm{Ti}}_{50}{\mathrm{Pd}}_{50-x}{\mathrm{Cr}}_x$ is a high-temperature shape-memory alloy with a martensitic transformation temperature strongly dependent on the Cr composition. Prior to the transformation, a premartensitic phase is present with an incommensurate modulated cubic lattice with wave vector of $q_0=(0.22,0.22,0)$. The temperature dependence of the diffuse scattering in the cubic phase is measured as a function temperature for $x=6.5$, 8.5, and $10\mathrm{at.}\%$. The lattice dynamics has been studied and reveals anomalous temperature and $q$ dependences of the $\left[110\right]\text{−}{\mathrm{TA}}_2$ transverse phonon branch. The phonon linewidth is broad over the entire Brillouin zone and increases with decreasing temperature, contrary to the behavior expected for anharmonicity. No anomaly is observed at $q_0$. The results are compared with first principles calculation of the phonon structure.

Figure 1

(Color online) Phase diagram of ${\mathrm{Ti}}_{50}{\mathrm{Pd}}_{50-x}{\mathrm{Cr}}_x$ reproduced from (Ref. 4).

Figure 2

Rocking curve of (1,0,0) Bragg peak above and below the martensitic transformation.

Figure 3

(Color online) Intensity contour measured around the (1,2,0) Bragg peak showing the satellite peak at $q=(0.22,0.22,0)$ and diffuse scattering near the Bragg peak. The intensity scale bar on the right is logarithmic. $x=6.5\mathrm{at.}\%$.

Figure 4

Elastic diffuse scattering measured from the (0,3,0) (BZ) center to the (1,2,0) BZ center.

Figure 5

Temperature dependence of the satellite intensity for ${\mathrm{Ti}}_{50}{\mathrm{Pd}}_{50-x}{\mathrm{Cr}}_x$ for $x=6.5\mathrm{at.}\%$ (top) and $x=10\mathrm{at.}\%$ (bottom).

Figure 6

Temperature dependence of the inverse correlation length determined from the linewidth of the satellite peak for ${\mathrm{Ti}}_{50}{\mathrm{Pd}}_{50-x}{\mathrm{Cr}}_x$ for $x=10\mathrm{at.}\%$ (top) and $x=6.5\mathrm{at.}\%$ (bottom).

Figure 7

Temperature dependence of the diffuse scattering measured near the (1,2,0) Bragg peak for ${\mathrm{Ti}}_{50}{\mathrm{Pd}}_{50-x}{\mathrm{Cr}}_x$, $x=10\mathrm{at.}\%$. Note that $800\mathrm{K}$ is the martensitic transformation temperature of ${\mathrm{Ti}}_{50}{\mathrm{Pd}}_{50}$.

Figure 8

Partial phonon dispersion curves measured along the $\left[00q\right]$ and $\left[qq0\right]$ directions. The direction of the error bars indicate the direction of the scans. The bars for the $\left[qq0\right]$-${\mathrm{TA}}_2$ branch indicate the phonon linewidths measured at $873\mathrm{K}$.

Figure 9

$x=10$ alloy. Observed spectra at $T=500$ and $1273\mathrm{K}$ for $\left[qq0\right]$-${\mathrm{TA}}_2$ branch for (a) $q=0.1$ and (b) $q=0.2$. The curves at $1273\mathrm{K}$ are displaced in (a) and (b) by 500 and 200 cts, respectively.

Figure 10

Temperature dependence of the phonon energy (top) and linewidth (bottom) for two phonons measured at $q=0.075$ and $q=0.2$.

Figure 11

The phonon dispersion of the $\left[qq0\right]$-${\mathrm{TA}}_2$ measured at $T=673\mathrm{K}$ (top) and $T=1273\mathrm{K}$ (bottom). The bars and the shading indicate the linewidths determined from a Gaussian fit to the spectra.