Melt growth of metal crystals

Abstract

In these three kinds of processes, the last one, the melt growth process, is understood most unsatisfactorily in comparison with the other two processes. The crystal growth takes place at the interface between the crystal itself and the environment. So far, three kinds of mechanisms have been accepted; namely, (1) the normal growth on an atomically rough surface, (2) the growth due to two dimensional nucleation on an atomically flat surface, and (3) the growth around a screw dislocation on an otherwise flat surface. Details of these mechanisms should be consulted with books due to Ookawa I and Parker 2 and contributions due to Ovsienko and Alfintsev 3 and Bennema. 4 However, it should be remembered that all of these mechanisms have been originally invented for the growth from gas phase or from solution phase, both of them can be observed as dilute environment, in which the concentration of relevant atoms or molecules is very low in cpmparison with the growing solid phase. I On the other hand, the melt growth must be observed as a dense problem, I since the liquid phase usually has almost the same atomic density with its solid phase, and, in addition, it is generally believed that both phases have very similar short range-order in atomic structure. Therefore, we have to take into account the atomic structure of the environment explicitly for this problem, in contrast to the dilute case. In this respect, the melt growth mechanism should be quite different from the mechanisms of vapour growth and/or solution growth. So far. we have several theories for melt growth mechanism. Of these theories, Jackson ~ introduced the concept of roughness, which depends on materials, from statistical mechanical consideration, and further simulated the growth process therewith by computer. ~ Temkin 7 considered the diffuseness of the interface on the basis of discrete lattice models of solid, and of the liquid adjacent to the solid as well, llke Jackson. 5 Cahn's theory 8,9 contains a phenomenological description of the boundary, applying the conception of diffuseness which is characterized by a number of atomic layers, forming a step-by-step transition from crystal to melt. In the works by Cahn et a~. 8,9 he used a continuous model to describe the boundary layer. According to his theory, the surface energy depends on the position of the boundary relative to the atomic planes in the crystal, i.e. proportionally to its motion the energy of the interface should periodically vary in accordance with the lattice periodicity.