On kinetics and hydrodynamics related to the growth of faceted crysrals

Abstract

The aim of this study is to propose a generalized model of crystal growth kinetics. This work is conceived to allow a faceted crystal to grow uniformly in a non-uniform fluid environment. Neglecting, fot the time being, the limiting role of the impurities, we construct a macroscopic extension of the classical surface diffusion BCF model. The result appears as a partial differential equation (PDE) whose solution characterizes the surface profile. This PDE is intended to be coupled, through interfacial supersaturation and mass flux, with the PDEs driving transport and dynamics in the fluid phase.The mass flux, feeding the crystal, thus depends not only on the interfacial supersaturation, but also on the instantaneous shape of the growing surface. Furthermore, we verify that this macroscopic approach has the ability to detect the growth instabilities and recovers the microscopic stability criterion by Kuroda, Irisawa and Ookawa [J. Crystal Growth 42 (1977) 41]. This paper also comes back to the origin of the above-mentioned morphological instability of faceted crystals and gives new considerations on this purpose. Especially we study the coupling of an uniform growth with two basic laminar fluid flows: Blasius flow and buoyancy layer flow of natural convection. Results concerning the limit size of the crystal face before appearance of large macrosteps are given in both cases. Some comments are additionally presented for turbulent flows.