Nature of the many-particle potential in the monatomic liquid state: Radial and angular structure

Abstract

The atomic configurational order of random, symmetric, and crystalline states of sodium is investigated using molecular-dynamics simulations. Pair distribution functions are calculated for these states. Consistent with the liquid- and random-state energetics, we find that, by cooling, the liquid configurations evolve continuously to random-state structures. For sodium, the random pair distribution function has a split second peak characteristic of many amorphous materials and has the first subpeak exceeding the second subpeak. Experiments have shown this to be the case for amorphous Ni, Co, Cr, Fe, and Mn. A universal pair distribution function is identified for all random structures, as was hypothesized by liquid-dynamics theory. The peak widths of the random pair distribution function are considerably broader, even at very low temperatures, than those of the bcc and symmetric structures. No universal pair distribution function exists for symmetric structures. For low-temperature random, symmetric, and crystalline structures we determine average Voronoi coordination numbers, angular distributions between neighboring atomic triplets, and the number of Voronoi edges per face. Without exception the random and symmetric structures show very different trends for each of these properties. The universal nature of the random structures is also apparent in each property exhibited in the Voronoi polyhedra, unlike for the symmetric structures. Angles between neighboring Voronoi triplets common to random close-packing structures are favored by the random structures whereas those hinting at microcrystalline order are found for the symmetric structures. The distribution of Voronoi coordination numbers for both random and symmetric structures are peaked at 14 neighbors, but while the symmetric structures are essentially all 14, the random structures have nearly as many 13 and 15 neighbor polyhedra. The number of edges per face also shows a stark difference between the random and symmetric structures; the number is broadly distributed about the peak value 5 for the random structures, but contains many more four- and six-edged faces (and very few five-edged faces) for the symmetric structures.