Growth of crystals kinetics

The kinetics of crystal growth has been much studied Refs. 98-102 are representative. Often there is a time lag before crystallization starts, whose parametric dependence may be indicative of the nucleation mechanism. The crystal growth that follows may be controlled by diffusion or by surface or solution chemistry (see also Section XVI-2C). 

Nancollas, G.H. and Gardner, G.L., 1974. Kinetics of crystal growth of calcium oxalate monohydrate. Journal of Crystal Growth, 21, 267-276. 

Nielsen, A.E. (1958) The kinetics of crystal growth in barium sulphate precipitation. Acta Chem. Scand., 12, 951-958. 

In this study, D-SCMC seed crystals were put in a racemic SCMC supersaturated solution in a batchwise agitated vessel and growth rates in longitudinal and lateral directions and the optical purity of D-SCMC crystals were measured. The growth rates and optical purity were discussed considering surface states of grown crystal observed by a microscope. The kinetics of crystal growth were measured and a model of inclusion of impurity was proposed. 

The level of impurity uptake can be considered to depend on the thermodynamics of the system as well as on the kinetics of crystal growth and incorporation of units in the growing crystal. The kinetics are mainly affected by the residence time which determines the supersaturation, by the stoichiometry (calcium over sulfate concentration ratio) and by growth retarding impurities. The thermodynamics are related to activity coefficients in the solution and the solid phase, complexation constants, solubility products and dimensions of the foreign ions compared to those of the ions of the host lattice [2,3,4]. 

Kirkpatrick R.J., Robinson G.R., and Hays J.F. (1976) Kinetics of crystal growth from silicate melts. /. Geophys. Res. 81, 5715-5720. 

P. Bennema and G. H. Gilmer, Kinetics of crystal growth, in Crystal Growth, An Introduction, ed. P. Hartman, Amsterdam, North-Holland, 1973, pp. 263-327... 

On the molecular level, hydrate growth can be considered to be a combination of three factors (1) the kinetics of crystal growth at the hydrate surface, (2) mass transfer of components to the growing crystal surface, and (3) heat transfer of the exothermic heat of hydrate formation away from the growing crystal surface (see Section 3.2.3 for heat transfer models). 

At least two resistances contribute to the kinetics of crystal growth. These resistances apply to (1) integration of the crystalline unit (e.g., solute molecules) into the crystal surface (i.e., lattice), and (2) molecular diffusion or bulk transport of the unit from the surrounding solution to the crystal surface. As aspects of molecular diffusion and mass transfer are covered elsewhere, the current discussion will focus only on surface incorporation. 

The topics covered are as follows. The structure of the interfacial region and its experimental investigation are covered in Chapter 1. The following chapter reviews the mechanisms by which heterogeneous catalysis of solution reactions can take place. The third chapter is concerned with the mechanism and kinetics of crystal growth from solution and the final contribution deals with corrosion processes at the metal-solution interface. 

Marshall, R.W. and Nancollas, G.H. The kinetics of crystal growth of dicalcium phosphate dihydrate. J. Phys. Chem. 73, 3838-3844 (1969). 

Armienti P., Pareschi M. T., Innocent I. F., and Pompiho M. (1994) Effects of magma storage and ascent on the kinetics of crystal-growth-the case of the 1991-93 Mt. Etna eruption. Contrib. Mineral. Petrol. 115, 402-414. 

Black, S.N. Davey, R.J. Halcrow, M. The kinetics of crystal growth in the presence of tailor-made additives. J. 

There are four types of coprecipitation surface adsorption, mixed-crystal formation, occlusion, and mechanical entrapment." Surface adsorption and mixed-crystal formation are equilibrium processes, whereas occlusion and mechanical entrapment arise from the kinetics of crystal growth. 

Nielsen, A. (1961) Diffusional controlled growth of a moving sphere. The kinetics of crystal growth in potassium perchlorate precipitation. The Journal of Physical Chemistry, 65, 46-49. 

Bennema, P Glimer, G.H. Kinetics of crystal growth. In Crystal Growth-, Hartmann, P., Ed. North-Holland Amsterdam, 1973 263-327. 

Annealing semicrystalline samples has been found to result in reductions in the tortuosity parameter as much as 50% despite large increases in crystal size (23.,25). Some workers (25.) have suggested, based on the kinetics of crystal growth, that this is the result of the formation of permeable gaps in the crystallite. 

The key reaction of these three is the dimerization (reaction 2) in which the short-lived intermediate monomer radical cation is stabilized. The equilibrium constant (Kx) of this reaction determines not only the stability of the reactive intermediates but also the kinetics of crystal growth and the composition of the crystals. 

The development and operation of industrial crystallization processes can be made significantly easier if some data on the kinetics of crystal growth are available. This information can be incorporated in process models, can be used in process and crystallizer design, and can shed light on the observed behavior of the system. 

Christoffersen MR, Dohrup J, Christoffersen J (1998b) Kinetics of growth and dissolution of calcium hydroxylapatite in suspensions with variable calcium to phosphate ratio. J Ciyst Growth 186 283-290 Davey RJ (1976) The effect of impurity adsorption on the kinetics of crystal growth from solution. J Cryst Growth 34 109-19... 

Apart from the dimensions of critical nuclei under varying conditions, it is also important to consider the kinetics of nucleation, especially relative to the kinetics of crystal growth. The nucleation rate (/) is commonly estimated by means of transition state theory. With the aid of the best available values for transport properties of undercooled water,it has been estimated that in the neighbourhood of —40°C, J increases rapidly with decreasing temperature, by about a factor 20 per degree nucleation is thus a well-defined event that is hardly affected by the rate of cooling. ... 

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