Heat Capacities and Thermodynamic Functions of ZrH2 and ZrD2 from 5 to 350°K and the Hydrogen Vibration Frequency in ZrH2

The heat capacities of ZrH2 and ZrD2 were measured in an adiabatic type calorimeter from 5 to 350°K. X-ray analyses showed the hydrides consist of a single face-centered tetragonal phase. The data for both compounds below 11°K were found to fit the equation Cv=9.8×10—4T+464.6(T/θ)3 cal deg—1 mole—1, where θ=311.4, and this equation was used to extrapolate the heat capacities below 6°K. Between 20 and 100°K the Cp of ZrD2 averages 1% lower than that of ZrH2 but above 110°K the Cp of ZrD2 becomes increasingly greater than that of ZrH2. At 298.15°K the heat capacities and thermodynamic functions calculated from the data are Cp=7.396±0.015 cal deg—1 mole—1, S°=8.374±0.02 cal deg—1 mole—1, H°—H0°=1284.1±2 cal mole—1, and (F°—H0°)/T=—4.067±0.01 cal deg—1 mole—1 for ZrH2, and 9.631±0.019, 9.168±0.02, 1474.4±3, and —4.223±0.01, respectively, for ZrD2. The free energy of formation of ZrH2 at 298.15°K is —30.9±2 kcal mole—1 and that of ZrD2 is —31.2±2. On the assumption that the difference in the heat capacity between the two isotopic compounds arises from a triply degenerate hydrogen vibration, it was found that the difference in the temperature range 100 to 350°K could be satisfactorily fitted by the difference between two Einstein heat capacity functions with a frequency of 1190±30 cm—1 for ZrH2 and 1190/√2 cm—1 for ZrD2. This result is compared with the optical lattice vibration frequency found by neutron scattering experiments.