Theory of the Ferroelectric Phase Transition in Cs(H_1−xD_x)₂PO₄

Abstract

To understand the role of hydrogens in the ferroelectricity of hydrogen-bonded crystals, the effect of deuteration in the mixed crystal Cs(H_1−xD_x)₂PO₄ is studied on the basis of the coupled proton-dipole model presented by the present authors (J. Phys. Soc. Jpn. 57 (1988) 4391) for pure CsH₂PO₄ and CsD₂PO₄. The model is essentially reduced to a one-dimensional Ising system with random bonds, and the static dielectric constant is analytically obtained in the paraelectric phase. Variation of the ferroelectric phase transition temperature with deuteration, T_C(x), is calculated. The result predicts that the T_C(x) curve of Cs(H_1−xD_x)₂PO₄, which has not yet been determined by experiments, should have a large bowing because of the quasi-one-dimensionality of the system.