The 1960 Wagner-Hamilton-Seidensticker theory of crystal growth phenomena in Ge was critically reviewed and was shown to be able to explain the preservation of an ABC stacking order in 2 dimensions in face-centered cubic crystals of effectively spherical closed-shell molecules. In order to preserve this stacking order in all directions (and explain isotropic 3-dimensional face-centered cubic crystal growth) the Wagner-Hamilton-Seidensticker model was extended so as to contain at least 2 (crossing) twin lamellae rather than one. The main result was that local 5-fold symmetry was to be expected. This was related to the frequent observation of multiply twinned particles which exhibited 5-fold symmetry, in the case of materials whose preference for the face-centered cubic structure (rather than the hexagonal close-packed one) could not be explained satisfactorily. It was suggested that the atomic arrangement in the crossing region should not be regarded as being the result of cross-twinning, but rather as its cause. That is, face-centered cubic crystal growth was a process which started with the coalescence or inter-growth of decahedra with 5-fold symmetry. One implication of this proposed growth model was that the observed crystal structure of a substance was not necessarily that with lowest free energy for an infinite crystal, but could instead correspond to a local minimum that was made accessible by the kinetics of a particular growth process.

B.W.Van de Waal: Journal of Crystal Growth, 1996, 158[1-2], 153-65