Inelastic-neutron-scattering studies on glassy and liquid ${\mathrm{Ca}}_{0.4}$${\mathrm{K}}_{0.6}$${\left(\mathrm{N}{\mathrm{O}}_3\right)}_{1.4}$

Triple-axis inelastic-neutron-scattering measurements have been carried out on the ionic glass material ${\mathrm{Ca}}_{0.4}$ ${\mathrm{K}}_{0.6}$ ${\left(\mathrm{N}{\mathrm{O}}_3\right)}_{1.4}$. Our measurements of the temperature dependence of the position of the main elastic diffraction peak in the liquid give a linear coefficient of thermal expansion of (2.3±0.2)×${10}^{-4\mathrm{}}$, which is markedly greater than the value of 1.2×${10}^{-4\mathrm{}}$ from density measurements. This shows that the expansion is accompanied by structural rearrangements. The Debye-Waller factor, as determined from the temperature dependence of the intensity of the main elastic diffraction peak, shows an anomaly at the calorimetric glass transition temperature, $T_g=335\mathrm{}$ K, but the anomaly at the critical temperature $T_c$ predicted by mode-coupling theory is not seen. In contrast, the change in the effective root-mean-square displacement, ${〈r^2〉}_T^{\mathrm{eff}}-{〈r^2〉}_{300}^{\mathrm{eff}}$ deduced from the $Q$ dependence of the temperature variation of the quasielastic scattering over a wide range of wave vector $Q$ from 2 to 4 ${\mathrm{\AA }}^{-1\mathrm{}}$, shows a break of slope at a temperature that can be identified as $T_c$, but there is no anomaly at $T_g$. Our results give $T_c=368\mathrm{}\pm 5$ K. The inelastic scattering for constant $Q$ scans at frquencies $\nu =\frac{\omega }{2\pi }<~0.5$ THz deviates from harmonic-phonon-like behavior at temperatures above $T_g$. This can be identified as a fast relaxation or $\beta$ process, as predicted by mode-coupling theory. Such a deviation is not observed at higher frequencies. In the present work, we establish the $Q$ and $\nu$ dependences of the $\beta$ process.