Periodic bond chains

Hartman and Perdok f6Q-62 > in 1955 developed a theory which related crystal morphology to its internal structure on an energy basis. They concluded that the morphology of a crystal is governed tty a chain of strong bonds (called periodic bond chains (PBC)), which run through the structure. The period of these strong bond chains is called the PBC veaor. In addition, Hartman and Perdok divided the crystal face into three types. These types are ... 

Figure 4.3 Three-dimensional crystal with three periodic bond chain vectors. The figure shows F-faces (100), (010), and (001) S-faces (110), (101), and (Oil) and the K-face (111).

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... 

In 1955, Hartman and Perdok (18) refined the BFDH model by relating the crystal morphology to its internal structure on an energy basis. They identified that chains of strong intermolecular bonds known as periodic bond chains (PBC) govern the crystal morphology. According to the number of PBC inside a slice of thickness, they classified the crystal faces as (i) F-faces (flat), two or more PBC, (ii) S-faces (stepped), one PBC, or (iii) K-faces (kinked), zero PBC. 

In summary, for a crystal to grow in the direction of a strong bond the chain must be uninterrupted throughout the structure, and if a bond chain contains more than one type of bond it is the weakest bond present that determines the development of that orientation. Faces of a crystal can subsequently be classed into three types of faces according to periodic bond chains F faces that have at least two PBC vectors parallel, S faces which are parallel to at least one PBC and K faces which have no PBC parallel. 

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