Kossel crystal

Let us assume that the constituent units of both a crystal and that of growth are simple cubes. This kind of model crystal is called a Kossel crystal, and is shown in Fig. 3.9. The 100 face is completely paved by the unit, and the surface is atomically flat. This face is called the complete plane. The 111 face, however, consists of kinks, as can be seen in Fig. 3.9, and has an uneven surface, and so it is called an incomplete plane. In contrast to [111], [110] corresponds to a face consisting entirely of steps. Kossel did not give a particular name to this t3TJe of crystal face. 

Figure 5.1. Surface microtopographs seen on three types of crystal faces (Kossel crystal), (a) F face (b) S face (c) K face.

To address the problem of faceting of grains, we use a classical atomistic approach by reasoning with a Kossel crystal representation, which is commonly used in crystal growth theories. The main idea is summarized as follows ... 

Figure 2 Simple faceting model based on Kossel crystal explanation. Condensation leads to faceting (a) while sublimation generates a rounding of the grains (b).

In molecular crystals, the binding energies are highly anisotropic due to the complex shape of the molecules in addition to the anisotropy inherent in the crystal packing. Most organic molecules have complex shapes (bucky balls being an exception), so the representation of a molecule as a cube, as in the Kossel crystal, is not a good approximation. A van der Waals box that reflects the shape of the molecule is a better approximation. 

Ter Horst, J.H. and Jansens, P.J. 2005. Nucleus size and Zeldovich factor in two-dimensional nucleation at the Kossel crystal (0 0 1) surface. Surf. Sci. 574 77-88. 

Figure 6.6. Schematic diagram of a Kossel crystal showing F-, S-, and K-faces predicted by the PBC theory along with features predicted by various growth models. Based on Figure 1 in Sleutel ef al. (2012).

Figure 4.4. A Kossel crystal with a screw dislocation creating a growth spiral on the cubic face. The arrows indicate the direction of step advance (a schematic representation).

---