Hartman–Perdok theory: influence of crystal structure and crystalline interface on crystal growth

Abstract

Hartman–Perdok theory enables classification of crystal faces as F, S or K faces. Only F faces should be present on growth forms as they grow slowly according to a layer mechanism. Such a classification can be quantified for ionic crystals by the calculation of attachment energies in electrostatic point-charge models. The attachment energy of a crystal face (hkl)Ehkla, is the energy released per mole, when a new elementary growth layer, called a slice, with a thickness of dhkl crystallizes on an existing crystal face. Theoretical growth forms can be constructed by making use of the supposition that Ehkla is directly proportional to the growth rate. Often these growth forms are very similar to the morphologies of crystals grown in nature or in laboratory experiments {zircon (ZrSiO4), alkali feldspars ((K,Na)AlSi3O8), natural silicate garnets [A2+3 B3+2(SiO4)3]}. The structure of the crystalline interface is very important for the crystal growth processes. The derivation of F faces provides the atomic topology of the crystalline interface as well. Sometimes there is more than one possible surface of a slice with a thickness of dhkl, e.g. zircon (011), garnets (110) and (112), which may lead to growth via slices of thickness ½dhkl, causing a significant increase of the growth rate. Ordering of the ions which are situated on the slice boundaries may reduce the growth rate (alkali feldspars and YBa2Cu3O7 –x). Experimental crystal growth of PbCl2 shows that adsorption of OH– and H3O+ ions on special sites of the crystalline interfaces may cause habit modifications. This effect can be explained for PbCl2 in terms of adsorption of Pb(OH)Cl on {211}. The influence of the solvent on the growth can also be explained in terms of impurity adsorption on the crystalline interface. The growth of flattened PbCl2 crystals from HCl due to the reduction of the growth rates of {010} and {121} is such an example.