Power terms in the construction of thermodynamic functions for melting description

A linear combination of power terms considered as an effective form of the Gibbs free energy for a homogeneous system is constructed in order to describe its behavior in the neighborhood of the melting temperature. The construction is based on a common solution of the equation of state, which is determined by the thermodynamic functions for solid and liquid phases, treated separately. The exact, ab initio Gibbs free energy given by the Los Alamos National Laboratory group is taken, as an example, into account. One of the conclusions seems to be that the relation between volume and the crystallinity order parameter is now generalized and, first of all, very well established due to the self-consistent character of the presented construction. In this case, the construction needs the effective form extended to a linear combination of power terms with respect to the crystallinity order parameter representation. Moreover, two examples of the considered construction are reported for the generic forms of the van der Waals model. The examples correspond then to the polynomial form of the constructed potential which belongs then to a narrower class of functions.