Theories of crystallization

Born M and Huang K 1954 Dynamical Theory of Crystal Lattices (Oxford Clarendon)... 

M. Born and K. Huang, Dyncunical Theory of Crystal Lattices, Oxford University Press, New York, 1954. 

The theory of crystal growth accordingly starts usually with the assumption that the atoms in the gaseous, diluted, or hquid mother phase will have a tendency to arrange themselves in a regular lattice structure. We ignore here for the moment the formation of poly crystalhne solids. In principle we should start with the quantum-mechanical basis of the formation of such lattice structures. Unfortunately, however, even with the computational effort of present computers with a performance of about 100 megaflops... 

The theoretical treatment of the properties of ionic crystals and molecules has been carried farther than that of other types of atomic aggregates. The Bom theory of crystal energy permits the calculation to within... 

The most developed and widely used approach to electroporation and membrane rupture views pore formation as a result of large nonlinear fluctuations, rather than loss of stability for small (linear) fluctuations. This theory of electroporation has been intensively reviewed [68-70], and we will discuss it only briefly. The approach is similar to the theory of crystal defect formation or to the phenomenology of nucleation in first-order phase transitions. The idea of applying this approach to pore formation in bimolecular free films can be traced back to the work of Deryagin and Gutop [71]. 

M. Bom and K. Huang, Dynamical Theory of Crystal Lattices, Clarendon Press, Oxford, UK, 1951, Appendix VII. 

As with nucleation, classical theories of crystal growth 3 20 2135 40-421 have not led to working relationships, and rates of crystallisation are usually expressed in terms of the supersaturation by empirical relationships. In essence, overall mass deposition rates, which can be measured in laboratory fluidised beds or agitated vessels, are needed for crystalliser design, and growth rates of individual crystal faces under different conditions are required for the specification of operating conditions. 

Comprehensive reviews of theories of crystal growth have been presented by Garside(43), Nielsen(44), Pamplin145 and Kaldis and Scheei/46 . 

All real crystals deviate more or less from their equilibrium habits since all grow at finite velocities Rj. Hartman and Betmema (4) and Hartman (5.61 showed how the empirical law of Dotmay-Harker can be explained on the basis of current molecular theories of crystal growth. The energy required to split a crystal along the plane A--B parallel to the plane (hkl) is the sum... 

Born, M. and Huang, K., Dynamical Theory of Crystal Lattices, International Series of Monographs on Physics, Clarendon Press Oxford (1954), p. 25. 

Granasy L. and James P.F. (1999) Non-classical theory of crystal nucleation application to oxide glasses review. J. Non-Cryst. Solids 253, 210-230. 

Bom M, Huang K (1954) Dynamical theory of crystal lattices. Clarendon Press, Oxford... 

The dependence of the elastic pressure on the density can be expressed approximately by a power function p = Bpn, usually called polytropic. It could alternatively be considered that the force centers are repelled according to the relationship F = a/(3n-2) as assumed in the Bohr theory of crystal lattices. The thermal motion, at this degree of compression, consists of small oscillations. To each vibrational degree of freedom there corresponds an energy RT (per mole). The total oscillatory energy equals cvT, where cv is independent of the volume in this approximation... 

F. C. Frank, On the kinetic theory of crystal growth and dissolution process, in Growth and Perfection ofGrystals, eds. R. H. Doremus, B. W. Roberts, and V. Turnbull, New York, John Wiley Sons, 1958... 

Cations are found with a range of coordination numbers. For some, such as the range is narrow, essentially only one coordination number being known (Fig. 6.1(a)). For others, such as Cs, the range is broad covering coordination numbers from 3 to 14 (Fig. 6.1(c)). Most cations, for example whose distribution is shown in Fig. 6.1(b), lie between these two extremes, but in each case there is a tendency for the distribution to peak near the middle. Any theory of crystal chemistry must be able to explain this variation and provide a reliable estimate for the coordination number found in a particular compound. 

The kinetics of the transition from Graham s glass to trimetaphosphate crystals follow Stranski and Kaischew s theory of crystallization (157, 277) and yield an activation energy of 62.9 kcal/mole (124). Trimetaphosphate occurs as the equilibrium phase in the system NaP03—H20 at between 450° and 620°C (199). 

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