Specific-Heat Anomaly and Calculation of the Configurational Entropy Change at the Phase Transition in Copper Formate Tetrahydrate

Abstract

Specific-heat anomalies of copper formate tetrahydrate, Cu${(\mathrm{HCOO})}_{2}$4${\mathrm{H}}_{2}$O, and its deuterium substitute Cu${(\mathrm{HCOO})}_{2}$4${\mathrm{D}}_{2}$O were found at respective antiferroelectric transition points. It has a typical $\ensuremath{\lambda}$ shape, sharply peaked at the transition. The transition point was shifted from -37.7 to -27.5\ifmmode^\circ\else\textdegree\fi{}C by deuterium substitution. The transition entropies were measured as 0.78 and 0.90 cal/mole deg in hydrated and deutrated crystals, respectively. The transition was considered to be due to an order-disorder phenomenon arising from the hydrogens in the water of crystallization. The number of configurations of hydrogens in the water layer of the structure, the positions of which have been determined by a previous neutron-diffraction study at room temperature, was calculated taking account of the full correlation through oxygens by the use of a simple equivalent model. A different value was obtained from that obtained by Pauling's method; the latter does not agree with experiment in this layer-structured crystal. The configurational entropy change between the disordered and the antiferroelectric states was calculated as $R\mathrm{ln}\frac{1}{2}(2+\sqrt{2})\ensuremath{\simeq}1.06$ cal/mole deg. The theoretical value agrees well with the experimental values obtained from thermal measurements on both crystals.