Paracrystalline Structure of Molten Metals

When discussing matter on an atomic level it is often useful to employ the notion of a three-dimensional lattice even if the x-ray diffraction pattern is diffuse and, hence, the long-range order characteristic of a crystalline lattice is absent. Phases in which this notion is particularly helpful are called paracrystalline phases. The theory of paracrystals has been applied to various solids and has recently been employed for analyzing the diffraction pattern from liquid metals. In this paper the theory is used for analyzing the diffraction pattern from liquid Cu at 1100°C, as measured by Ruppersberg. The radial density function out to distance of 25 Å is synthesized extremely well by means of the paracrystalline convolution polynomial made up only of first-neighbor or "coordination" statistics. These statistics are inhomogeneous in the sense that two different first-neighbor distances are employed. Forty percent of the first-neighbor distances are 10% larger than the others and arise from intercrystalline distances measured across the paracrystalline grain boundaries. Since, it is well known from inelastic neutron scattering that the lifetime of the paracrystalline domains is about ${10}^{-11\mathrm{}}$ sec, the intercrystalline distances include diffusive motion. The melt is described in terms of a fcc lattice and consists of microparacrystallites with a mean diameter (for copper of about 5 Å and for alkaline metals up to 100 Å) of about 5 Å. The results of the paracrystalline theory are compared with the model of Kaplow and Averbach which is based on the known structure of the solid. The two approaches agree in the assignment of the same lattice type above and below the melting point.