By Ichiro Sunagawa
A readable and informative assessment of the technology of crystal development for complex scholars and researchers.
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Extra resources for Crystals: Growth, Morphology, and Perfection
5). In equilibrium thermodynamics, the ﬁnal stable phases are determined by a given temperature–pressure range. However, it is not always possible to achieve nucleation and growth of the stable phase from the very beginning when the system is kept under this condition. In many cases, the earliest phase that appears by nucleation is a metastable phase, which is different from the stable phase. This phenomenon is called Ostwald’s step rule . This can be understood as a result of the competition between the driving force and the interface free energy terms.
In the case of crystal growth from the vapor phase, this value is estimated to be around 25–50% in terms of supersaturation. In real cases, we observe crystals growing under supersaturation as low as 1%. This large discrepancy between the theoretical and experimental values originates from the fact that Kossel and Stranski assumed the crystal to be perfect. Real crystals, however, are imperfect, containing impurities and dislocations. Frank’s spiral growth model has been proposed to account for the growth mechanism of real crystals.
Kϭ kink; SD ϭ surface diffusion; DEADS ϭ desolvation; DBL ϭ diffusion boundary layer. equilibrium concentration. In the days before we could measure the surface concentration directly, the driving force of a bulk phase was evaluated for simplicity assuming the equilibrium concentration, but now it is assumed that the surface concentration is slightly higher than this value. Therefore, the driving force for crystal growth is now considered to be the difference and its gradient between the concentration at the outermost region of the diffusion boundary layer and the concentration at the surface (surface supersaturation).