Accurate calculation of isotropic-plastic and isotropic-nematic transitions in the hard-ellipsoid fluid

A density-functional theory for the transitions from isotropic to plastic crystal and to nematic fluid in a fluid of prolate hard ellipsoids is presented. Direct correlations are computed with a variational technique based on the Percus-Yevick equation for the correlation functions. As anisotropy is increased from the case of hard spheres, the isotropic-plastic transition density increases, as seen in computer simulations. For large anisotropies, the direct correlations are modified from previously assumed forms, bringing the isotropic-nematic transition density into agreement with simulations.