Theoretical modeling of molar volume and thermal expansion

The molar volumes and thermal expansions of transition cubic metals were studied by means of the Calphad approach and the Debye–Grüneisen model. Experimental data were collected and assessed using Calphad procedures, and consistent results were obtained which give the best description of all experimental data. In order to put the prediction of the thermodynamic properties of metastable phases on a sound physical basis, the Debye–Grüneisen model was chosen to account for the vibrational contribution and calculate the coefficients of linear thermal expansion (CLEs) of stable cubic metals. Two approximations for Grüneisen parameter γ, i.e. Slater’s and Dugdale and MacDonald’s expressions were adopted. A modified calculation scheme, first proposed by Wang et al., was derived in a straightforward way and used to evaluate the Debye temperature from ab initio electronic total-energy calculations at T = 0 K. The thermal electronic contribution to CLE was also evaluated from the electronic density of states. The calculated total CLEs were compared with those from the Calphad assessments. A satisfactory agreement is reached.