Hartman-Perdok theory

The result of Hartman Perdok theory is to allow prediction of the growth shape of crystals from the slice energy of different F faces. 

Bennema, P. Growth and morphology of crystals integration of theories of roughening and Hartman-Perdok theory. In Growth Mechanisms Handbook of Crystal Growth la Thermodynamics and Kinetics, Hurle, D.T.J., Ed. North-Holland Amsterdam, 1993 477-581. 

Bennema, P. On the Crystallographic and Statistical Mechanical Foundation of the Hartman Perdok Theory. In Crystal Growth of Organic Materials. Conference Series, USA. 1996 15-21. 

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 ... 

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.)... 

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... 

Terpstra RA, Bermema P, Hartman P, Woensdregt CF, Perdok WG, Senechal ML (1986) F faces of apatite and its morphology Theory and observation. J Cryst Growth 78 468-78 Thirioux L, Baillif P, Ildefonse JP, Touray JC (1990) Surface reactions during fluorapatite dissolution-recrystallization in acid media (hydrochloric and citric acids). Geochim Cosmochim Acta 54 1969-1977... 

The morphological theory of Hartman and Perdok (1955) considers the bond energies involved in the integration of growth units into the lattice. In this... 

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