The structural-mapping approximation introduced by Lutsko and Baus [Phys. Rev. A 41, 6647 (1990)] in the generalized effective-liquid approximation is extended to include a local thermodynamic mapping based on a spatially dependent effective density for approximating the solid phase in terms of the uniform liquid. This latter approximation, called the local generalized effective-liquid approximation (LGELA) yields excellent predictions for the free energy of hard-sphere solids and for the conditions of coexistence of a hard-sphere fcc solid with a liquid. Moreover, the predicted free energy remains single valued for calculations with more loosely packed crystalline structures, such as the diamond lattice. The spatial dependence of the weighted density makes the LGELA useful in the study of inhomogeneous solids.

• Received 15 November 1991

DOI:https://doi.org/10.1103/PhysRevA.45.5654