Thermodynamic properties of bcc crystals at high temperatures: The transition metals

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Abstract
The second-neighbor central-force model of a bcc crystal, previously used in lowest-order anharmonic perturbation theory to calculate the thermodynamic properties of the alkali metals, is here applied to the transition metals V, Nb, Ta, Mo, and W. The limitations of the model are apparent in the thermal-expansion results, which fall away from the experimental trend above about 1800 K. The specific heat similarly fails to exhibit the sharp rise that is observed at higher temperatures. A static treatment of vacancies cannot account for the difference between theory and experiment. The electrons have been taken into account by using a model that specifically includes d-band effects in the electron ground-state energy. The results thus obtained for the bulk moduli are quite satisfactory. In the light of these results, we discuss the prerequisites for a better treatment of metals when the electrons play an important role in determining the thermodynamic properties.