Paracrystalline microdomains in monatomic liquids. II. Three-dimensional structure of microdomains in liquid lead

The radial density function of liquid observed at 350, 450, and 550°C can be synthesized by a three-dimensional convolution polynomial. In constrast to other averaging methods ours enables one to obtain direct information about the three-dimensional structure of the paracrystalline microdomains. These microdomains can be quantitatively described by a face-centered arrangement of bimodal coordination statistics. Their centers of gravity are at the same distance from the reference atom as when below the melting point. The weight of the coordination statistics gives the coordination number. We find that this diminishes at the melting point from 12 to $K=11.6\mathrm{}\pm 0.2$. We can explain this decrease by Schottky and Frenkel defects. In addition to this decrease we observed that the volume of fluctuation of the coordination statistics is six times larger. From these two observations and from a consideration of the shape of the coordination statistics one obtains some information concerning the diffusion of the vacancies and the one- and two-dimensional collective motions of the atoms to interstitial sites. Furthermore, the statistics were found to be bimodal. One component corresponds to intraparticle distances which are smaller than in the solid state. The other component corresponds to interparticle distances, which can be attributed to semidislocations and other distortions as, for example, grain boundaries. In the conventional theories of liquids only spherically symmetric (one-dimensional) functions are applied to average the microdomains. Here we point out that such one-dimensionally defined "direct correlation functions" and pair potentials hide the real nature of the short-range order.