Phase transformation and hysteresis behavior in Cs_(1-x)Rb_xH_2PO_4

Abstract

A new theory on the origin of hysteresis in first order phase transformations was evaluated for its applicability to the phase transformation behavior in the Cs_(1 − x)Rb_xH_2PO_4 solid solution system. Specifically, the correlation between λ_2, the middle eigenvalue of the transformation matrix describing the cubic-to-monoclinic superprotonic transition, and the transformation hysteresis was examined. The value of λ_2 was estimated from a combination of room temperature diffraction data obtained for compositions in the solid solution system and high temperature diffraction data obtained for the CsH_2PO_4 end-member. The transformation hysteresis was determined for Cs_(1 − x)Rb_xH_2PO_4 compositions (x = 0, 0.25, 0.50 and 0.75) by single-frequency electrical impedance measurements. It was found that the transition temperature increases monotonically with increasing Rb content, from 227.6 ± 0.4 °C for the end-member CsH_2PO_4 to 256.1 ± 0.3 °C for Cs_(25)Rb_(75)H_2PO_4, as does the hysteresis in the phase transition, from 13.4 °C to 17.4 °C. Analysis of the transformation matrix reveals that, for this system, λ_2 depends only on the b lattice parameter of the paraelectric phase and the α_0 lattice parameter of the cubic phase. The computed values of λ_2, based on extrapolations accounting for chemical contraction with increasing Rb substitution and thermal expansion on heating, were far from 1, ranging from 0.9318 to 0.9354. The observation of λ_2 increasing with Rb content is attributed to the relatively large thermal expansion in the b-axis of the low temperature monoclinic phase in combination with an increase in transition temperature with increasing x. That the hysteresis does not decrease as λ_2 approaches 1, counter to the theoretical expectations, may reflect uncertainties in the method of estimating λ_2 for Rb substituted compositions, or the discovery of a system in which hysteresis is not dominated by considerations of crystallographic compatibility.

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