Development of Burton–Cabrera–Frank Theory for the Growth of a Non-Kossel Crystal via Chemical Reaction
A. V. Redkov, С. А. Кукушкін
Abstract
The growth of an arbitrary multicomponent crystal via the Burton–Cabrera–Frank mechanism due to chemical reaction is studied. The rates of advancement of a single step, a group of equidistant steps, and a step formed by a screw dislocation on a surface are analyzed for three cases: growth of a single-component crystal via chemical reaction; growth of a multicomponent crystal from its vapors; growth of a multicomponent crystal due to chemical reaction. It is shown that the cases are very similar to the single-component case of crystal growth from its vapor and can be described by the same formulas as derived in classical paper of Burton–Cabrera–Frank, while in the multicomponent case the diffusion coefficient and incorporation rate are dependent on properties of individual components of the crystal, and mean free paths of adatoms are dependent on the rate of reverse chemical reaction. Some effects taking place in multicomponent systems with chemical reactions, such as dependence of the growth rate at given supersaturation on the reaction rate and nucleation of pure components at terraces, are discussed.