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Computation of surface energies in an electrostatic point charge model: II. Application to zircon (ZrSiO4)
Authors:C F Woensdregt
Institution:1. Department of Geochemistry, Section of Crystallography, Institute of Earth Sciences, Utrecht University, P.O. Box 80.021, 3508, TA Utrecht, The Netherlands
Abstract:The attachment energies, the slice energies and the specific surface energies can be calculated in an electrostatic point charge model using the formula derived by Madelung for the potential introduced by an infinite row of equally spaced point charges. Power series are given for the Hankel function iH (0) (1) (iy) and PSgr(x)=d ln x!/dx. The logarithmic expression in the Madelung formula converges rapidly when applying a power series, which combines equally charged cations and anions. Besides the specific surface energy (gamma hkl), the slice energy (E s hkl ) and the attachment energy (E a hkl ) can be considered as special categories of surface energies as they depend on surface configurations as well. The specific surface energy gamma is the energy per unit area of surface needed to split the crystal parallel to a face (hkl). The attachment energy (E a) is the energy released per mole, when a new slice of thickness d hkl crystallizes on an already existing crystal face (hkl). The growth rate of the crystal face (hkl) is a function of its attachment energy. The slice energy (E s) is the energy released per mole, when a new slice d hkl is formed from the vapour neglecting the influence of edge energies. The lattice energy (E c) which is the energy released per mole of a crystal crystallizing from the vapour, is given by the following relation: E c=E a+E s.
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