Observation of a Continuous Phase Transition in a Shape-Memory Alloy

Elastic neutron-scattering, inelastic x-ray scattering, specific-heat, and pressure-dependent electrical transport measurements have been made on single crystals of AuZn and ${\mathrm{Au}}_{0.52}{\mathrm{Zn}}_{0.48}$. Elastic neutron scattering detects new commensurate Bragg peaks (modulation) appearing at $Q=(1.33,0.67,0)$ at temperatures corresponding to each sample’s transition temperature ($T_M=64$ and 45 K, respectively). Although the new Bragg peaks appear in a discontinuous manner in the ${\mathrm{Au}}_{0.52}{\mathrm{Zn}}_{0.48}$ sample, they appear in a continuous manner in AuZn. Surprising us, the temperature dependence of the AuZn Bragg peak intensity and the specific-heat jump near $T_M$ are in favorable accord with a continuous transition. A fit to the pressure dependence of $T_M$ suggests the presence of a critical end point in the AuZn phase diagram located at $T_M^{*}=2.7\mathrm{K}$ and $p^{*}=3.1\mathrm{GPa}$.

Figure 1

(a) The excess specific heat divided by temperature versus temperature in the vicinity of the martensitic transitions for ${\mathrm{Au}}_{0.52}{\mathrm{Zn}}_{0.48}$ and AuZn. (b) Temperature dependence of the satellite-peak intensity along $Q=(1.33,0.67,0)$. The satellite-peak intensity is proportional to the square of the order parameter.

Figure 2

Temperature dependence of the satellite-peak intensity on heating along $Q=(1.33,0.67,0)$ in AuZn, near the transition temperature. A fit to mean-field theory for $T\le T_c$. The points above 64 K are background.

Figure 3

Temperature dependence of the phonon dispersion in AuZn along the ${\mathrm{TA}}_2$ branch. At 300 K one notices considerable phonon softening at $q=(0.33,0.33,0)$ (vertical line). The dashed lines between points are provided as guides to the eye.

Figure 4

Inelastic x-ray scattering data showing the temperature dependence near the soft mode, $q=(0.35,0.35,0)$. The 300 and 200 K data are offset by 0.004 and 0.0005, respectively, on the $y$ axis for clarity. The energy positions are fit to a double Lorentzian (solid curve) at 300 K to determine the phonon energy. The intrinsic resolution for inelastic x-ray scattering is 2 meV.

Figure 5

(a) The electrical-resistivity data taken on cooling and warming is shown in the vicinity of $T_M$. (b) Plot of $\ln p$ versus $1/T$ to test the applicability Clausius-Clapeyron equation.

Figure 6

Pressure dependence of the transition temperature up to pressures of nearly 3 GPa, together with a fit to Salje’s model [30] which accounts for quantum saturation effects close to zero absolute temperature. We find that quantum effects become important for temperatures lower than ${\theta }_s=48.3\pm 3.7\mathrm{K}$, and a critical end point is predicted at $T_M^{*}=2.7\mathrm{K}$ and $p^{*}=3.1\mathrm{GPa}$.