Mean-field potential approach to thermodynamic properties of metal: Al as a prototype

We propose a classical mean-field potential (MFP) model for evaluating the vibrational contribution of the lattice ion to the total free-energy, where the mean-field potential $g(r,V)$ seen by the lattice ion is entirely and yet simply derived from the 0-K total-energy volume curve. The physical basis of the MFP is supported by the fact that, as a second-order approximation of the MFP, the three commonly used expressions for the Gr\"uneisen parameter, i.e., that due to Slater, that due to Dugdale and MacDonald, and that for the free-volume theory, can be explicitly deduced. Furthermore, a first-principles scheme for calculating thermodynamic properties of a metal is developed. The present scheme permits efficient computation and allows us to investigate almost all kinds of thermodynamic parameters, since it only needs the 0-K total-energy curve and electronic density of states as the inputs. Taking aluminum (Al) as a prototype, we demonstrate that our scheme correctly describes most of the thermodynamic properties, such as static compression, shockwave compression, thermal expansion, bulk modulus, and anharmonic effect.