Brillouin-scattering study of the elastic anomaly in ferroelectric KH2PO4

Abstract

Brillouin-scattering measurements have been performed on potassium dihydrogen phosphate (KDP) in the temperature range $113<T<\mathrm{}291\mathrm{}$ °K with electric fields between 0 and 3937 V/cm. Values of the adiabatic $x-y$ shear elastic constant $c_{66}^{E,S}$ deduced from the experiment are presented in tabular form. The data are compared with the predictions of several free-energy expressions. The Slater-SUS (Silsbee, Uehling, and Schmidt) theory is shown to predict values of the elastic constant in reasonable agreement with the experimental values, but the SUS parameters which provide the best fit to the elastic-constant data are somewhat different from those which give a best fit to spontaneous-polarization data. The data are also compared to the predictions of three phenomenological free-energy expressions which are all variants of the Landau-Devonshire power-series expansion. The simple molecular-field expression is shown to give poor agreement with the $c_{66}^{E,S}$ data, and to require parameter values for even a poor fit which then predict unreasonably large values for the spontaneous polarization. Two other phenomenological free energies are considered, one having a tenth-power nonlinear polarization term and predicting a second-order transition, and another, proposed by Benepe and Reese, having fourth-and eighth-power nonlinear polarization terms and predicting a slightly first-order transition. These two phenomenological free energies have previously been utilized in the analysis of various thermodynamic properties of KDP, and it is found that both are able to predict values for the elastic constant $c_{66}^{E,S}$ in reasonable agreement with experiment while providing adequate predictions for the spontaneous polarization with the same parameters. The behavior of $c_{66}^{E,S}$ within 0.1 °K of the transition, however, favors the Benepe-Reese free energy.