Facet growth rate

Many compounds have the ability to crystallize with different crystal structures, a phenomenon called polymorphism. Each polymorph is in fact a different thermodynamic solid state and crystal polymorphs of the same compound exhibit different physical properties, such as dissolution rate, shape (angles between facets and facet growth rates), melting point, etc. For this reason, polymorphism is of major importance in industrial manufacture of crystalline products. 

Wang, Z., Li, Y., and Adams, J.B. (2000). Kinetic lattice Monte Carlo simulation of facet growth rate. Surf. Sci. 450, 51-63. 

A pre-factor 1/r contains a time scale r or a frequency which for instance corresponds to the hard phonon or to an atomic frequency. The growth rate of the crystal is proportional to this rate (23). As will be shown later, the nucleus once formed expands in a time scale shorter than the one necessary for nucleation. If the process consists of a series of sequential subprocesses, the global velocity is governed by the slowest one. Therefore, this nucleation process determines the growth rate of a faceted surface. 

Nanoclusters tend to form facets in order to minimize surface energy. Since the surface energy of a face-centered cubic (fee) metal follows the order of (111)<(100) <(1 1 0), most nanoclusters are bounded by (1 1 1) and (1 00) surfaces, Figure 2a and b. In many cases, the ratio of the growth rate along the (100) versus (111)... 

On the other hand, the growth rate of the normal width is different in the two cases. Fig. 3 shows the growth of the facet width versus time in a log-log plot. All data in each case fall into a straight line, indicating that the reconstructed terrace width increases as w af-. For case A, the facet grows as, while it grows as for case B. These results are in complete agreement with the predictions of the classic one-dimensional continuum model of Mullins". 

Fig. 7. 164. Fast- and slow-growing faces as applied to a single crystal sphere. The facets that develop and are observed are those crystal faces with the slowest growth rates.

Consider two faces of a faceted crystal advancing at different velocities during crystal growth as in Fig. 14.17. The growth rates of facets 1 and 2 are V and V2-... 

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