Proton-glass dielectric behavior of a ${\mathrm{Rb}}_{0.52}$${\left({\mathrm{ND}}_4\right)}_{0.48}$${\mathrm{D}}_2$${\mathrm{PO}}_4$ crystal

The $c$ axis dielectric permittivity at 1 kHz was measured for a 71.4 at.% deuterated crystal of ${\mathrm{Rb}}_{0.52}$ ${\left({\mathrm{ND}}_4\right)}_{0.48}$ ${\mathrm{D}}_2$ ${\mathrm{PO}}_4$ from 4 to 300 K. The permittivity follows, down to 150 K, a Curie-Weiss law with a Curie temperature of 0 K. Below this temperature the susceptibility rounds off to a broad maximum at 80 K, and below 50 K, starts decreasing rapidly. Between 25 and 40 K, the inverse susceptibility obeys a Curie-Weiss law which extrapolates to zero at 43 K. At 4 K, the relative permittivity flattens out to a value of 11.5. The results show general agreement with predictions of a Landau model giving a second-order transition to an antiferroelectric state at 43 K, but the rounding of the susceptibility peak over a very wide temperature range agrees better with predictions of a model which considers the asymmetry of the typical hydrogen bond caused by the crystal being only partly ammoniated. Permittivity results of Courtens and of Iida and Terauchi for undeuterated crystals with 35% and 60% ammonium, respectively, are also compared with predictions of this second model.