Perturbation Theories for the Thermodynamic Properties of Fluids and Solids

Inhomogeneous Systems 301

density-independent step function, previously introduced by Nordholm et al. (1980),

was used for w(r), namely,

w

(

r

)

=

3

4πσ

3



(

σ −r

)

. (9.82)

The local density of the solid was assumed to be of the form of Equation 9.70 with

the parameter γ determined by minimizing the free energy per particle at a given

density, with densities for which γ = 0 corresponding to the fluid phase and those

with γ = 0 to the solid phase. For certain density range, two solutions appeared: one

with γ = 0 and another with γ = 0, and the coexistence properties were determined

from the usual conditions of equal pressures and chemical potentials in both