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Published February 24, 2010 | public
Journal Article

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


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.

Additional Information

© 2008 Elsevier B.V. Received 27 August 2008; accepted 18 November 2008. Available online 8 January 2009. The authors gratefully acknowledge Ayako Ikeda for providing selected samples and valuable discussions. This work has been funded by a Department of Defense MURI award administered by the Army Research Office (W911NF-07-1-0410). Additional funding has been provided by the National Science Foundation through the Graduate Research Fellowship Program and through NSF support of the Caltech Center for the Science and Engineering of Materials (DMR-0520565).

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