PBC theory

Another advantage of the PBC theory is its ability to predict not only the bulk morphology of a polyhedral crystal, but also the morphology of growth layers developing on F faces. When growth layers are polygonal, the step direction is assumed to be defined by the PBC theory. These predictions cannot be made by the BFDH law. 

There are two downsides to the PBC theory the first is that a certain arbitrariness is unavoidable in finding PBCs in real crystal structures, and the second is that PBC analysis is difficult in complicated structures. In answer to the first criticism, Hartman [3] calculated the attachment energy, and correlated this to Jackson s... 

These observations were made and explained by P. Hartman and W.G. Perdok in their periodic bond chain vector (PBC) theory (see the Chapter 1 references), which we introduced in Section 1.2.1. This theory takes into account the fact that 3D crystals are far more complicated structures, which are full of partial bonds and preferred directions. When the PBC vector is parallel with a crystal face, there is maximum growth along that crystal face. 

FIGURE 20.9 Schematic illustrating the PBC theory. In a simple cubic crystal, 100 faces are flat surfaces (denoted as F-faces) with one PBC running through one such surface, 110 are stepped surfaces (S-faces) that have two PBCs, and 111 are kinked surfaces (K-faces) that have three PBCs. (From Hartman, R, and Perdok, W.G., Acta CrystL, 8, 49, 1955.)... 

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 2.11 The way in which a simple two-dimensional morphology can be created using PBC theory.

By means of the approach presented by Liu and Bennema [50,51], the habitcontrolling factors and the relative growth rate are related via the crystal growth mechanism. The PBC theory as well as the interfacial structure analysis forms the... 

PBCs) (2)(3)(91). The deviation in the observed morphology of etch pits from the one predicted by the PBC theory is a consequence of adsorption and diffusion processes. 

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