Crystallization nucleation and growth

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

Along with operating variables of the crystallizer, nucleation and growth determine such crystal characteristics as size distribution, purity, and shape or habit. 

A. D. Randolph and D. Etherton, Study of Gypsum Crystal Nucleation and Growth Rates in Simulated Flue Gas Desulfurization Eiquors, EPRI Report CS1885, Electric Power Research Institute, Palo Alto, Calif., 1981. 

Tavare, N.S. and Garside, J., 1986. Simultaneous estimation of crystal nucleation and growth kinetics from batch experiments. Chemical Engineering Research and Design, 64, 109. 

Keywords Induction period Melt and glass crystallization Nucleation and growth Optical microscopy Scattering techniques Spinodal decomposition... 

Crystal nucleation and growth in a crystalliser cannot be considered in isolation because they interact with one another and with other system parameters in a complex manner. For a complete description of the crystal size distribution of the product in a continuously operated crystalliser, both the nucleation and the growth processes must be quantified, and the laws of conservation of mass, energy, and crystal population must be applied. The importance of population balance, in which all particles are accounted for, was first stressed in the pioneering work of Randolph and Larson1371. ... 

Crystal nucleation and growth in hydrolysing iron(III) chloride solutions. Clays Clay Min. 25 49-56... 

Figure 4-7 Comparison of crystal nucleation and growth rate 350...

Ideally, MD or MC gives a complete description of the equilibrium states of liquids and crystals, and a molecular-level picture of any chemical process occurring within the system, including phase transitions. The limitations are obvious. The calculation is heavy, with some 5,000 molecules at most, and times or time-equivalents of the order of at most milliseconds. Force fields are by necessity restricted to atom-atom empirical ones. One gets at best a blurred and very short glimpse of the simulated process. And yet, appropriately designed molecular simulation is, for example, the only access to molecular aspects of chemical evolution involved in crystal nucleation and growth. 

The kinetics of transition from the liquid crystal to the fully ordered crystal of flexible, linear macromolecules was studied by Warner and Jaffe 38) on copolyesters of hydroxybenzoic acid, naphthalene dicarboxylic acid, isophthalic acid, and hydro-quinone. The analytical techniques were optical microscopy, calorimetry and wide angle X-ray diffraction. Despite the fact that massive structural rearrangements did not occur on crystallization, nucleation and growth followed the Avrami expression with an exponent of 2. The authors suggested a rod-like crystal growth. 

In view of the importance of macroscopic structure, further studies of liquid crystal formation seem desirable. Certainly, the rates of liquid crystal nucleation and growth are of interest in some applications—in emulsions and foams, for example, where formation of liquid crystal by nonequilibrium processes is an important stabilizing factor—and in detergency, where liquid crystal formation is one means of dirt removal. As noted previously and as indicated by the work of Tiddy and Wheeler (45), for example, rates of formation and dissolution of liquid crystals can be very slow, with weeks or months required to achieve equilibrium. Work which would clarify when and why phase transformation is fast or slow would be of value. Another topic of possible interest is whether the presence of an interface which orients amphiphilic molecules can affect the rate of liquid crystal formation at, for example, the surfaces of drops in an emulsion. 

Crystal formation depends not only on the interaction energy of a particular synthon but on a wide variety of other factors, particular crystal nucleation and growth kinetics and nucleus-solution interfacial energy. Other important factors are lattice enthalpy and lattice entropy, long range interactions... 

A recurring theme in many studies of nanocrystal doping is the propensity for dopants to be excluded from the internal volumes of the nanocrystals. We therefore begin with a description of crystal nucleation and growth, and of the... 

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