Some variables affecting the rate of crystal growth in aqueous solutions

Abstract

A large amount of work, both theoretical and experimental, has been done on studies of crystal form and crystallography, the structure of crystals, crystal habits, and some phases of crystal growth and dissolution. However, relatively few researches have been reported which furnish equations relating the various variables affecting growth such as the specific crystallization velocity coefficient, rate of growth, supersaturation, and temperature or which furnish equations which are useful for the practical design of industrial crystallizers.The theoretical work of Volmer, Stanski, Becker, and others (1) has provided a semiquantitative basis for understanding the factors that control the rate of nucleation and growth. Miers and his co-workers (2), following an earlier suggestion by Ostwald, postulated the existance of a supersolubility curve approximately parallel to the usual saturation curve dividing the supersaturated region into a metastable (low supersaturation) region and a labile (high supersaturation) region. In accordance with Miers' theory crystal growth occurs in both regions, while nucleation can occur only in the labile region.Modern diffusion theories may be said to date from the publication of a work, dealing principally with the dissolution of crystals, by Noyes and Whitney ( 3 ) in 1897. . Nernst concluded that in dissolution, diffusion is entirely controlling and that by intense agitation the film thickness can be made to assume very small values. In applications to crystal growth he also found the diffusion gradient to be equal to the degree of supersaturation.Berthoud (6) was the first to investigate crystal growth on the basis that there is not, as assumed in the pure diffusion theories, an infinitely rapid reaction at the crystal surface. He postulated a theory on the assumptions that the diffusional process is followed in series by a first-order interfacial reaction, the net rate of crystallization depends C . S. Grove, ] I . , is at Syracuse University, Syracuse. New York.on both the rate of dlffusion and on the rate of interfacial reaction, and the concentration of solution at the crystal surface is not, as assumed by Nernst, the saturation concentration but some higher value which is less than the supersaturation concentration in the bulk of the solution. He proposed for the diffusion process the equation and for the interfacial reaction process the equationA combination of these two equations and the elimination of Ci, a quantity which cannot be measured directly, results in the (4) dw a ( C -C s )This equation, first derived by Berthoud, is essentially the same as that obtained by Valeton (7,8) and by Friedel { 9, 1 0 ) . This theory has become known as the BerthoudValeton theory.McCabe (11 ) from theoretical considerations derived the equation ( 5 )This equation is the basis of the AL law which McCabe postulated. In accordance with this law all geometrically similar crystals of the same material suspended in the same solution grow at the same rate, if the growth is measured as the incre...

Mathematical Modeling of Transport Phenomena During Alloy Solidification

“…Nonetheless, convective heat and mass transfer coefficients have rarely been measured. Some data is available for equiaxed crystals grown from aqueous solutions (e.g., Palermo and Grove, 1964;Hayakawa and Matsuoka, 1973), which is relevant to industrial crystallizers used in the chemical industry (these crystals are not dendritic). While generalized correlations for heat and mass transfer coefficients that cover the entire liquid fraction range exist (Agarwal, 1988), they need to be adapted to the microstructures present in alloy solidification.…”