Crystal growth periodic bond chains

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. 

Early work by Hartman and Perdok described crystal growth in terms of the formation of strong bonds between neighboring crystallizing units. Uninterrupted straight chains of these bonds were classified as Periodic Bond Chains (PBC). This theory led to the classification of three types of crystal faces F-faces (flat), S-faces (stepped), and K-faces (kinked) based on the number of PBCs in a slice thickness, dhki- K-faces, which had no PBCs present in a slice, were shown to be... 

Periodic bond-chains are strongly related to the occurrence of faces on a crystal (and, in turn, the major growth directions of a crystal) [21-23]. We refer to periodic bond-chains as polyhedron chains. 

As is obvious in Fig. 10, there are common features of molecular packing in photo-reactive crystals. In all the photopolymerizable crystals in Table 4, nearly planar molecules are piled up and displaced in the direction of the molecular longitudinal axis by about half a molecule to form a parallel plane-to-plane stack. The periodicity in the stack is about 7 A. The shortest intermolecular distance between the double bonds in photopolymerizable crystals is about 3.9 A (Table 4) and it is found between molecules related to the center of symmetry in the stack. The second shortest distance between molecules in different stacks is more than 5 A. Therefore, the double bonds in the stack react to form a cyclobutane ring consequently, polymer chains should grow in the direction of the stack. The crystal axis along the stack in each photopolymerizable crystal, i.e. the presumed chain-growth direction, is indicated by c) in Table 4. 

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