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

Abstract

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 CPwere 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 CPto obtain the heat capacity at constant volume CV. This heat capacity was taken to consist only of independent contributions from electron excitations (CVE), harmonic lattice vibrations (CVH), anharmonic lattice vibrations (CVA), and the formation of vacancies (CVV). Three models of CVE(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. CVHis assumed to be given by the Debye model, with a single Debye temperature. Thus, the excess heat capacity CVEX= CV-CVE-CVHis taken as equal to (CVA+CVV), where CVAis linear with temperature (CVA=A T), and we have fitted the values of CVEXto 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 CPdata. 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%.