Phase transformation and hysteresis behavior in Cs sub(1 - x)Rb sub(x)H sub(2)PO sub(4)

• Published in: Solid state ionics Vol. 181; no. 3-4; pp. 173 - 179
• Main Authors: Louie, Mary W, Kislitsyn, Mikhail, Bhattacharya, Kaushik, Haile, Sossina M
• Format: Journal Article
• Language: English
• Published: 24.02.2010
• Subjects: Diffraction; Eigenvalues; Hysteresis; Lattice parameters; Phase transformations; Solid solutions; Thermal expansion; Transformations; Transition temperature
• ISSN: 0167-2738
• DOI: 10.1016/j.ssi.2008.11.014

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 sub(1 - x)Rb sub(x)H sub(2)PO sub(4) solid solution system. Specifically, the correlation between lambda sub(2), the middle eigenvalue of the transformation matrix describing the cubic-to-monoclinic superprotonic transition, and the transformation hysteresis was examined. The value of lambda sub(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 sub(2)PO sub(4) end-member. The transformation hysteresis was determined for Cs sub(1 - x)Rb sub(x)H sub(2)PO sub(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 degree C for the end-member CsH sub(2)PO sub(4) to 256.1 +/- 0.3 degree C for Cs sub(25)Rb sub(75)H sub(2)PO sub(4), as does the hysteresis in the phase transition, from 13.4 degree C to 17.4 degree C. Analysis of the transformation matrix reveals that, for this system, lambda sub(2) depends only on the b lattice parameter of the paraelectric phase and the a sub(0) lattice parameter of the cubic phase. The computed values of lambda sub(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 lambda sub(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 lambda sub(2) approaches 1, counter to the theoretical expectations, may reflect uncertainties in the method of estimating lambda sub(2) for Rb substituted compositions, or the discovery of a system in which hysteresis is not dominated by considerations of crystallographic compatibility.