Molecular field study of the isotopic effect in KH2x D2(1−x)PO4 mixed crystals

Abstract

Theory of KDP and isomorphous crystals is developed, which takes into consideration possible difference in ferroelectric interactions between pairs of H-bonds with deuteration. It is shown, why the interaction should differ for pairs of H-H, D-D, and H-D isotopes. Expressions for the transition temperature and static susceptibility above it are derived by approximating the molecular field acting on a proton (deuteron) by the field of the average surrounding. The theory results in a linear dependence of the asymptotical transition temperature and the Curie-Weiss constant on concentration. For the actualT c(x) also a linear dependence was found under the condition that tunneling is small, the distribution of H, D isotopes over H-bonds is quite random, and that the interaction between isotopes is of purely dipolar character. Modifications of the linear dependence due to ordering and deviations of the interaction from dipolar are found. It is further suggested, as a result of comparison with recently performed measurements of pressure dependence of the transition point, that the main part of the isotopic shift of the transition point is due to the difference in H-H and D-D coupling, whereas the tunneling contributes by a relatively small amount.