One-dimensional ordering in ferroelectric Cs${\mathrm{D}}_2$P${\mathrm{O}}_4$ and Cs${\mathrm{H}}_2$P${\mathrm{O}}_4$ as studied with neutron scattering

The triple-axis neutron technique has been used in a detailed study of the intensity distribution and temperature dependence of the diffuse quasielastic scattering associated with the ferroelectric transitions in monoclinic Cs${\mathrm{D}}_2$P${\mathrm{O}}_4$ and Cs${\mathrm{H}}_2$P${\mathrm{O}}_4$. The diffuse scattering differs greatly from that observed previously in tetragonal K${\mathrm{D}}_2$P${\mathrm{O}}_4$, in which case the intensity distribution clearly exhibits characteristics of three-dimensional dipolar interactions. In the present study, the nature and extent of the diffuse scattering can be explained quantitatively on the basis of chainlike ordering with temperature-dependent interchain correlations. The variation in intensity measured perpendicular to the chains (which are parallel to the ferroelectric $\overrightarrow{\mathrm{b}}$ axis) is mostly due to variations in the dynamical structure factor of a hydrogen-bonded chain of phosphate groups, and approaches a purely-one-dimensional form at temperatures well above $T_c$. The width of the scattering along the chain direction has been measured accurately for Cs${\mathrm{D}}_2$P${\mathrm{O}}_4$ and yields an intrachain correlation of about 600 Å near $T_c$ (264 K), decreasing to about 140 Å at 315 K. Near $T_c$, the cross section develops short-range three-dimensional interchain correlations with no appreciable change in linewidth. Very near $T_c$, the range of the latter is only about 30 Å.