The role of defects on thermophysical properties: Thermal expansion of V, Nb, Ta, Mo and W

Thermophysical properties at high temperatures and pressures are difficult to measure. Many reviews have approximated experimental data with empirical polynomial functions. In the case of thermal expansion and molar volume, extensive results for refractory body centered cubic (BCC) metals have been published. A critical evaluation of these experimental data is essential for many other studies. We provide this evaluation in terms of models that interrelate the thermophysical properties, self diffusion, and high temperature thermal defects. Experimental and theoretical methods for measuring and representing thermal expansion and the limitations of such methods are also briefly reviewed. Results for V, Nb, Ta, Mo, and W fall into two distinct subgroups relating to their elemental positions in the periodic table. The thermal expansions for these elements are analyzed within the constraints of a simple vibrational model and its equation of state. This approach represented the thermal expansion as the contributions from a perfect crystal and the crystalʹs high temperature anharmonicity as well as its thermal defects. Quantitative expressions, neglecting electronic contributions, are provided for the coefficient of thermal expansion and the expansivities for these five BCC metals from near 20°K to their melting temperatures. Vacancy formation enthalpies and entropies are also estimated. Our vacancy thermodynamic results are compared with earlier predictions and results from positron annihilation, thermal expansion, and specific heat measurements.