Phase transformation and hysteresis behavior in Cs1 − xRbxH2PO4

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 Cs1 − xRbxH2PO4 solid solution system. Specifically, the correlation between λ2, the middle eigenvalue of the transformation matrix describing the cubic-to-monoclinic superprotonic transition, and the transformation hysteresis was examined. The value of λ2 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 CsH2PO4 end-member. The transformation hysteresis was determined for Cs1 − xRbxH2PO4 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 CsH2PO4 to 256.1 ± 0.3 °C for Cs25Rb75H2PO4, 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, λ2 depends only on the b lattice parameter of the paraelectric phase and the a0 lattice parameter of the cubic phase. The computed values of λ2, 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 λ2 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 λ2 approaches 1, counter to the theoretical expectations, may reflect uncertainties in the method of estimating λ2 for Rb substituted compositions, or the discovery of a system in which hysteresis is not dominated by considerations of crystallographic compatibility.