Ferroelectric-Mode Motion in KD2PO4

The atomic motions of the ferroelectric soft mode in K${\mathrm{D}}_2$P${\mathrm{O}}_4$ have been determined by neutron tripleaxis spectrometry. Kaminow and Damen have investigated the ferroelectric mode in K${\mathrm{H}}_2$P${\mathrm{O}}_4$ and find it is overdamped, and Buyers et al. find the mode in K${\mathrm{D}}_2$P${\mathrm{O}}_4$ to be extremely overdamped. We have carried out an extensive study of this mode throughout both the [010] and [001] zones of the reciprocal lattice, and an energy analysis has indicated an inelasticity of less than 0.2 meV. The mode is not directly observable, as it superposes the Bragg peak, but a careful study of the temperature dependence of the compatible over-damped ${\Sigma }_2$ optic branch permitted an accurate determination of the ferroelectric mode intensity at the $\Gamma$ points of 60 Brillouin zones. A least-squares calculation of the inelastic structure factors fits the intensities well, and this permitted an evaluation of the relative atomic movements. The model fit consisted of a linear combination of the seven modes spanning the ${\Gamma }_3$ representation as determined by Shur. The movement consists of K, P, and D atomic motions as proposed by Cochran from the structural studies of Bacon and Pease. In addition, a large $z$ motion for the deuterium atoms and a large distortional motion in the $x-y$ plane of the oxygen tetrahedra are observed.