Contributions to the heat capacity of solid molybdenum in the range 300–2890 K

An analysis has been made of contributions to the heat capacity of Mo, with a special examination of the effect of the formation of vacancies near the melting point. Literature values of the heat capacity at constant pressure C_Pwere fitted to a polynomial. Using recent measurements of the velocity of sound at high temperature and literature data of the coefficient of expansion, the dilation correction was made to C_Pto obtain the heat capacity at constant volume C_V. This heat capacity was taken to consist only of independent contributions from electron excitations (C_VE), harmonic lattice vibrations (C_VH), anharmonic lattice vibrations (C_VA), and the formation of vacancies (C_VV). Three models of C_VE(free electron, band theory, and electron-photon) have been used to calculate the electronic contribution, and an examination of the results indicates that the electron-phonon model is the best. C_VHis assumed to be given by the Debye model, with a single Debye temperature. Thus, the excess heat capacity C_VEX= C_V-C_VE-C_VHis taken as equal to (C_VA+C_VV), where C_VAis linear with temperature (C_VA=A T), and we have fitted the values of C_VEXto determine the values of A and the energy and entropy of formation of vacancies which give the best fit. The anharmonic contribution is positive. The energy of vacancy formation is 100,000 J · mol^–1, in agreement with estimates by Kraftmakher from C_Pdata. The entropy of formation is 11.6 J · mol^–1 · K^–1. The concentration of vacancies at the melting point (2890 K) is calculated to be 6.3%.