Ferroelectric Transition in KD2PO4

The ferroelectric transition in K${\mathrm{D}}_2$P${\mathrm{O}}_4$ has been investigated both experimentally and theoretically. Coherent neutron scattering by fluctuations associated with the transition was studied both above and below the transition temperature. None of the optic-phonon modes was found to change in frequency near the Curie temperature, in contrast with materials such as SrTi${\mathrm{O}}_3$. The ferroelectric fluctuations gave rise to quasi-elastic scattering, increasing in intensity as the transition was approached. The intensity distribution showed that the pattern of displacement of the atoms in these fluctuations was similar to that which relates the crystal structures of K${\mathrm{H}}_2$P${\mathrm{O}}_4$ above and below the transition temperature. It was found that the macroscopic electric field plays a large part in determining the probability distribution of the fluctuations. The results have been analysed in terms of an Ising model with one "spin" per unit cell. The intensity of the scattering is shown to be consistent with a relation connecting the dielectric and scattering properties. The implications of these results for the theory of ferroelectricity in K${\mathrm{H}}_2$P${\mathrm{O}}_4$ and K${\mathrm{D}}_2$P${\mathrm{O}}_4$ are discussed.