A Hard-Sphere Model of Crystal Growth

Abstract

A hard-sphere model analogue of undirectional crystal growth has been devised and used to measure quantitatively the rates of growth normal to (111) and (100) planes in a face-centred cubic crystal structure. It has been found that 〈111〉 growth is much faster than 〈100〉 growth, and the result is interpreted in terms of the atomic-packing arrangements in the “solid” and “liquid” phases at their common interface. The phenomena of planar, cellular, and dendritic growth are reanalysed in terms of atomic-packing arrangements at the solid/liquid interfaces, and it is shown that a consistent interpretation of the development of the characteristic preferred orientations can be obtained. It is argued that the specific crystallographic orientations that arise under the different conditions of growth are due both to the variation of interface structure with orientation and to the generation of free volume at the solid/liquid interface during freezing.