Modeling of molar volume of the sigma phase involving transition elements

The molar volume of the sigma phase has been modeled and evaluated at room temperature and atmospheric pressure for binary systems concerning 19 transition elements Au, Co, Cr, Fe, Ir, Mo, Nb, Ni, Os, Pd, Pt, Re, Rh, Ru, Ta, Tc, V, W and Zr by using the CALPHAD approach. The volume model proposed in this work expresses the molar volume of a non-stoichiometric sigma phase as a linear average of volumes of the constituting elements in their hypothetic sigma structure, which can be assessed as model parameters based on experimental data from the literature. Reasonable model parameters have been obtained giving a best description of most experimental data. For comparison, volumes of the 19 transition elements in the sigma structure have been calculated by first-principles calculations. The results are compatible with the assessed values.