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

Abstract

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 C_v=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 C_p of ZrD₂ averages 1% lower than that of ZrH₂ but above 110°K the C_p of ZrD₂ becomes increasingly greater than that of ZrH₂. At 298.15°K the heat capacities and thermodynamic functions calculated from the data are C_p=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.