Diffusional decay of striations

During crystal growth from melts and solutions, compositional striations in the bulk crystal parallel to the growth surface usually result from fluctuations in the growth rate and/or the flow of the growth fluid. This paper presents a one-dimensional analysis of the effect of solid-state diffusion on growth striations. A sinusoidal variation in the solid composition at the interface of a semi-infinite ingot growing at constant velocity is assumed and the damping behavior of this compositional fluctuation is followed as it moves away from the solid-liquid interface. Numerical results that include the effect of a temperature gradient in the solid are presented as well as an analytical solution that assumes that the solid is isothermal. The only parameter in the analytical solution is the dimensionless frequency ω= {D}/{V ²t _c}. The dimensionless distance overlinex_d for 99.9% decay decreases with increasing ω. The relationship between overlinex_d and ω has two distinct regions. For ω < 0.01, the dimensional distance x_d for 99.9% decay is proportional to {V ³t ²_c}/{D}. In this region, the striations are carried into the solid by crystal growth and damping is achieved by solid-state diffusion. For ω > 200, x_d is proportional to √ Dt_c. The rate of crystal growth is negligible over this range of ω and the striations are spread into the solid by diffusion. An increase in the diffusivity causes the striations to penetrate deeper into the solid and, consequently, x_d to increase. In general, the application of the ACRT to the vertical Bridgman-Stockbarger growth of concentrated solid solutions is not likely to lead to striations being frozen into the grown ingot. Analytical results are also given for the decay of striations in an isothermal ingot induced by a sinusoidal fluctuation in crystal growth rate. These striations decay by the same mechanisms as the sinusoidal striations discussed above. With the proper choice of dimensionless concentration, they decay in a dimensionless distance which is a maximum of 5% less than sinusoidal striations for the same value of ω.