Concentration oscillations at doped crystal growth from solutions
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STRUCTURE OF CRYSTALS
Concentration Oscillations at Doped Crystal Growth from Solutions S. S. Guskov, M. A. Faddeev, and E. V. Chuprunov Nizhni Novgorod State University, Nizhni Novgorod, 603950 Russia email: [email protected] Received April 3, 2009
Abstract—A mathematical model of twocomponent crystal growth from solutions has been developed. The growth rate and component concentration are shown to oscillate near the growth front at certain parameters in the growth system; these oscillations lead to corresponding spatial changes in the grown crystal composi tion: oscillatory zoning. DOI: 10.1134/S1063774510040152
INTRODUCTION Characteristic striations are often observed on the cuts of singlecrystal samples, which are related to the quasiperiodic processes occurring during crystal growth [1, 2]. According to modern concepts, these striations (zoning) are formed either due to changes in the external conditions for crystal growth [1] or as a result of internal growth processes, i.e., via selforga nization [3–6]. Note that the periodic processes that are typical of some chemical reactions are also assigned to selforganization [7]. Twodimensional defects (microzoning) manifest themselves as alternating layers of different qualities oriented parallel to the crystallization front. The char acteristic zoning period is several or several tens of micrometers. The difference in the physical character istics of separate layers is believed to be primarily due to the nonuniform impurity distribution [8, 9]. The nature and mechanisms of nonuniform impu rity distribution have been studied poorly, and no gen eral method for describing zoning has been developed. However, microzoning contains valuable information about the processes occurring during crystal growth and the changes in the crystallization medium. The study of zoning allows one to estimate the quality of many crystals that are widely used in laser production [10] and improve their growth technology. Crystals with microstriations may have new properties [11]. In this paper, we report the results of studying the possible reasons for zoning in the single crystals grown from solutions. The diffusion in a solution that con tains an impurity along with the main material is con sidered. It is found that the solutions to the diffusion equations allow the oscillatory behavior of the growth system under certain conditions. Oscillations of the growth rate and impurity concentration arise in this case and may lead to microzoning. The conditions
leading to a nonuniform impurity distribution are ana lyzed. MASS TRANSFER DURING TWOCOMPONENT CRYSTAL GROWTH FROM A SOLUTION One necessary stage of crystal growth is the supply of the crystallizing components to the solid/liquid interface. During growth from a solution, the crystal lizing material is most often transferred using forced mixing or natural convection. However, due to the finite viscosity of the liquid, a hardtomix boundary layer is formed at the solid crystal surface, where the matter transport is conside
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