Crystal growth attachment energy

Crystals grow by addition of molecules from the surroundings to the exposed faces of the crystal. When there are present in the surroundings not only substrate molecules but also impurity molecules that are stereochemically similar to the substrate, these latter molecules may also add to the surfaces. The result will be a retardation of crystal growth (267). Furthermore, since the energy of the attachment of the impurity will differ from face to face, a modification of the crystal morphology may also result (268,269). 

Hartman and Bennema (19) found that relative growth rate always increases with At low supersaturation, they were able to show that the growth rate of a given crystal face, hkl is direcdy proportional to the attachment energy ... 

Hartman, P., and P. Bennema, The Attachment Energy as a Habit-Controlling Factor, J. Crystal Growth 49 145 (1980). 

The clusters transform into the crystal nuclei having ability for the growth under certain conditions. Only clusters with some critical size r = 2 Oct/Ap can become potential centers of crystallization (here Cl is the specific volume of an atom or molecule involved into the cluster, a is the specific surface energy of interphase boundary and Ap is the difference in chemical potentials for the phases) [10]. There are two main possible ways to transform the clusters into the critical crystal nuclei as a result of fluctuations [1] (1) attachment of individual atoms (molecules) to the cluster and (2) coalescence of clusters with each other. It should be noted that in principle the critical nuclei formation as a result of coalescence of individual atoms (molecules) with each other is possible too. In all these cases the clusters must grow to the size r > r, in order the start a crystal growth process. 

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