Temperature Dependence of the Lattice Vibrations in ND4Cl

Translational and librational modes in N${\mathrm{D}}_4$Cl at the high-symmetry points $\Gamma$, $X$, $M$, $R$ in the Brillouin zone were studied over a temperature range from 82 to 300 °K by coherent inelastic scattering of thermal neutrons utilizing the McMaster triple-axis crystal spectrometer at Chalk River. The temperature dependence of the frequencies and widths were obtained from the measurements. Several modes were found to undergo an abrupt decrease in frequency in the vicinity of the order-disorder transition ($T_{\lambda }=249.5\mathrm{}$ °K), while others are insensitive to the transition. The widths of the neutron groups for some of the modes increased rapidly at temperatures beyond 200 °K. The dynamics of those lattice modes associated with the phase transition is briefly discussed. In addition some acoustic modes at small waves vectors were measured, and the associated elastic constants ($c_{11}$ and $c_{44}$) calculated, as functions of temperature. An interesting effect was noted. The constant $c_{11}$ as measured for N${\mathrm{D}}_4$Cl with neutrons (and thus appropriate to very high frequencies) shows much less effect of the transition than does $c_{11}$ measured for N${\mathrm{H}}_4$Cl at ultrasonic frequencies. The effect is believed to arise from the kinetics of the ordering process.