Thermodynamic properties of tungsten

Tungsten has several unusual thermodynamic properties, e.g., very high values of the melting point, the entropy of fusion, the expansion on melting and the lattice anharmonicity. These features are given a semiquantitative explanation, based on the electron density of states N(E). Our treatment includes a numerical calculation of the electronic heat capacity from N(E) and a calculation of the entropy Debye temperature FTHETAS(T) from the vibrational part of the experimental heat capacity. FTHETAS(T) decreases by 36% from 300 K to the melting temperature 3695 K, the largest drop in FTHETAS for elemental metals. Recent quantum-mechanical ab initio calculations of the difference, H^β/α, in Gibbs energy at T=0 K between the metastable fcc tungsten and the stable bcc phase yield H^β/α=50±{}5 kJ/mol, which is much larger than the ``experimental'' values H^β/α=10 and 19 kJ/mol derived from previous semiempirical analyses [the so-called calculation of phase diagrams (``CALPHAD'') method] of binary phase diagrams containing tungsten. We have reanalyzed CALPHAD data, using the results of the first part of this paper. Because of the shapes of N(E) of {α}-W and {β}-W, some usually acceptable CALPHAD procedures give misleading results. We give several estimates of H^β/α, using different assumptions about the hypothetical melting temperature Tf^β of fcc W. The more realistic of our estimates gives H^β/α=30 kJ/mol or larger, thus reducing considerably the previous discrepancy between CALPHAD and ab initio results. The physical picture emerging from this work should be of importance in refinements of the CALPHAD method.