Convection effects, crystal growth

J. Holuigue, O. Bertrand, E. Arquis. Solutal convection in crystal growth effect of interface curvature on flow structuration in a three-dimensional cylindrical configuration. J Cryst Growth 180 591, 1997. 

Supersaturation has been observed to affect contact nucleation, but the mechanism by which this occurs is not clear. There are data (19) that infer a direct relationship between contact nucleation and crystal growth. This relationship has been explained by showing that the effect of supersaturation on contact nucleation must consider the reduction in interfacial supersaturation due to the resistance to diffusion or convective mass transfer (20). 

Figure 3.3. Various features of diffusion and convection associated with crystal growth in solution (a) in a beaker and (b) around a crystal. The crystal is denoted by the shaded area. Shown are the diffusion boundary layer (db) the bulk diffusion (D) the convection due to thermal or gravity difference (T) Marangoni convection (M) buoyancy-driven convection (B) laminar flow, turbulent flow (F) Berg effect (be) smooth interface (S) rough interface (R) growth unit (g). The attachment and detachment of the solute (solid line) and the solvent (open line) are illustrated in (b).

K. Onuma, K. Tsukamoto, and I. Sunagawa, Effect of buoyancy driven convection upon the surface microtopographs of BalNOjjj and Cdl crystalsJ. Crystal Growth, 98,1989, 384-90... 

The solubility concentration is c which is smaller than the bulk concentration c. The total concentration drop Ac = c - c is split up into two contributions. The first part (c - Cj) within the concentration boundary layer is the driving force for diSusion and convection whereas the second part (cj - c ) in the very thin layer where the integration step takes place is effective for this step. The index I means Interface. In the case of growth completely controlled by diffusion and convection, (cj - c ) (c - Cj) or (Cj - c )/(c - Cj) l is valid. Contrary to this with the ratio (c - Cj)/ cj - c ) l crystal growth is controlled by the integration step. The molar flux density h directed toward the crystal srrrface is... 

Fluid flow within the melt has a crucial effect on crystal quality. If the crystal is stationary, the dominant convection pattern is upward flow of material at the crucible walls and radial flow inward at the surface (type I). Rapid rotation of crystal causes material to be thrown radially outward at the surface, and opposes the thermal convective flow (type III). These flow patterns are shown in Figure 3. In the intermediate regime, where the two flows are of comparable rates, a more complex surface pattern is observed, labeled type II. The crystal-liquid interface is convex toward the melt in type I flow and planar in type II, a condition that is used for the growth of large crystals of gadolinium gallium garnet ... 

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