NONISOTHERMAL EFFECTIVENESS FACTORS AND THE ROLE OF HEAT-TRANSFER IN CRYSTAL-GROWTH FROM SOLUTIONS AND MELTS

The effect of heat transfer and the role of the surface integration process in crystal growth are analysed quantitatively in terms of a non-isothermal effectiveness factor, defined as the ratio of actual growth rate to the rate that would be obtained if conditions of the supercooled or supersaturated bulk liquid existed at the crystal surface. The expression for simulataneous transfer of mass and heat in the liquid phase in the vicinity of the growing crystal surface is developed. Surface conditions of growing crystals, freely settling in a supercooled or supersaturated liquid, are determined for seven binary systems including organic melts and aqueous solutions of inorganic salts. Organic melt systems and some aqueous systems exhibit effectivenss factors significantly less than unity, indicating that the liquid phase transport phenomena play an important role in crystal growth. As a measure of the contribution of heat transfer, the inorganic systems this ratio increases at high concentrations of the crystallizing component and high heats of crystallization. An empirical criterior for the importance of thermal processes is that the non-dimensional group βd ≡ (k′ ρ{variant}fΔH/h′)(dz*A/dT) should be greater than 0.01. © 1990.