Instability of the fluid pair structure and the freezing density of liquids

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Abstract
An instability of the pair-distribution function of the fluid with respect to the diagrammatic iteration loop has been discovered recently [Phys. Rev. A 43, 6526 (1991)], which correlates well with the freezing density of the soft inverse-power potentials. The present work extends that study to a large variety of pair interactions and establishes the general validity and accuracy of this instability as a semiempirical freezing indicator. Preliminary results for the instability lines for mixtures are also presented that are in qualitative agreement with freezing densities from thermodynamic calculations and from recent experiments on the phase behavior of mixtures of colloids. The stability analysis of the iteration loop is complicated by the need to go beyond linear order.