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)E^hkl_a, is the energy released per mole, when a new elementary growth layer, called a slice, with a thickness of d_hkl crystallizes on an existing crystal face. Theoretical growth forms can be constructed by making use of the supposition that E^hkl_a 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 d_hkl, e.g. zircon (011), garnets (110) and (112), which may lead to growth via slices of thickness ½d_hkl, 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 YBa₂Cu₃O_{7 –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.