Crystal growth evolution

Based on this mechanism. Wild et al.l l developed a two-dimensional computer program to simulate the crystal growth evolution and the surface morphology of polyerystalline films grown from square nuclei with random orientations and random positions on a substrate. The calculated - - and experimentalP lP l results show that, for the diamond films (150-400 pm in thickness) investigated under the experimental conditions, (110) is the direction of fastest growth with the film surfaee eonsisting of 111 planes. 

Monitoring of reaction kinetics and crystal growth evolution. 

The reaction engineering model links the penetration theory to a population balance that includes particle formation and growth with the aim of predicting the average particle size. The model was then applied to the precipitation of CaC03 via CO2 absorption into Ca(OH)2aq in a draft tube bubble column and draws insight into the phenomena underlying the crystal size evolution. 

The relaxation of a thermodynamic system to an equilibrium configuration can be conveniently described by a master equation [47]. The probability of finding a system in a specific state increases by the incoming jump from adjacent states, and decreases by the outgoing jump from this state to the others. From now on we shall be specific for the lattice-gas model of crystal growth, described in the previous section. At the time t the system will be found in the state. S/ with a probability density t), and its evolution... 

This equation describes not only the crystal growth, but with an additional noise term it also describes the evolution of the surface width and is called the Edward-Wilkinson model. An even better treatment has been performed by renormalization methods and other techniques [44,51-53]. 

Figure 5.9. Time evolution of the radii of selected 2D spherulites from Fig. 5.8. The curves correspond to R t) obtained by integration of Eq. (5.9). Reprinted from Journal of Crystal Growth, Vol. 209, J. Caro, J. Fraxedas and A. Figueras, Thickness-dependent spherulitic growth observed in thin films of the molecular organic radical p-nitrophenyl nitronyl nitroxide, 146-158, Copyright (2000), with permission from Elsevier.

The concentration profiles for crystal growth under different controls and their evolution with time are shown in Figure 1-11. Whether crystal growth (or dissolution) is controlled by interface reaction or mass transfer can be determined experimentally using these criteria. Theoretically, when departure from equilibrium (i.e., degree of oversaturation or undercooling) is small (e.g., undercooling... 

Figure 14.19 Stepped-surface evolution during crystal growth.

Both the evolution of the atomic fractions in the solution and of the chemical shift of all species (Fig. 9(b)-(e)) allow four steps in the formation of A1P04—CJ2 induction, dissolution, nucleation and crystal growth. During the induction period, a constant amount of A1 atoms in the solution is observed during the set up of the pH synthesis. The dissolution step, which is quasi simultaneous with the induction period, is characterized by an increase of the amount of A1 species in the solution (Fig. 9(b)-(c)). During this period, the different NMR results show the development of the right solution composition for the formation of soluble reactive species, the development of supersaturation conditions (with an increase of the soluble species concentration) and the formation of the solution species involved in the crystallization. 

Figure 11. Evolution of A—ip trajectory for deposited Si film. (Reproduced with permission from Ref. 2. Copyright 1980 Journal of Crystal Growth.)...

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