Extended least-squares analysis of heat capacities incorporating the effect of phase transitions and its application to the deuteration-induced phase transition in Rb 3D(SO 4) 2

Abstract

A non-linear least-squares method of analysis has been developed for the heat capacities of solids undergoing phase transitions. It utilizes harmonic heat capacity functions corrected for thermal expansion. The unique feature of the method is that it incorporates the effect of a gradual phase transition in the fitting function for the low temperature phase. Compact expressions approximating the Debye function and the Ising model heat capacity function have been derived and presented in practical forms for use in the Kaleidagraph software. The method has been tested on the heat capacity of sodium chloride (which lacks a phase transition) and tri-rubidium deuterium disulfate (Rb 3D(SO 4) 2, TRDS) which undergoes a phase transition at 78.5 K in the deuterated form but not in the normal hydrogenous form. The excess entropy based on the fitting was 5.27 J K −1 mol −1, close enough to R ln 2=5.76 J K −1 mol −1 to suggest an order–disorder mechanism for the phase transition.