Lattice-Dynamical Aspects of the Antiferroelectric Phase Transition in N${\mathrm{D}}_4$${\mathrm{D}}_2$P${\mathrm{O}}_4$

Temperature-dependent quasi-elastic neutron scattering has been observed in the paraelectric tetragonal phase of N${\mathrm{D}}_4$ ${\mathrm{D}}_2$P${\mathrm{O}}_4$ in the vicinity of the $Z$ point of the Brillouin zone, i.e., at ($h,0,l$) where $h+l$ is odd. The data are interpreted in terms of a condensing highly damped optic-phonon mode which initiates the transition to the antiferroelectric state. The intensity contours of the quasi-elastic scattering in the ($a^{*},c^{*}$) plane are roughly elliptical in shape and are centered at the $Z$ points of the extended Brillouin zone. The major axis of the intensity distribution is parallel to the $c^{*}$ direction and is about four times larger than the $a^{*}$-oriented minor axis, thus suggesting a polarization fluctuation perpendicular to $c^{*}$. As the temperature is lowered, the integrated intensities at the $Z$ points increase as $\frac{T}{(T-T_0)}$. The value for $T_0$ of 195°K compares more closely with the actual transition temperature ($T_n=234\mathrm{}$°K) than that obtained by dielectric constant measurements ($T_0\approx 80$°K). The inelasticity of the scattering is 0.7±0.1 meV at 244°K and increases linearly with temperature to 1.8±0.2 meV at 304°K. An interpretation of the scattering at the $Z$ point in terms of an overdamped phonon mode results in a damping constant independent of temperature and a temperature dependence of the frequency of the form $\omega _A^{}{}_{}{}^2\propto K(T-T_0)$. In the antiferroelectric phase, the $Z$ points become permissible Bragg peaks and quasi-elastic scattering is not observed.