Energy minimum criteria in modeling structures and properties of minerals

Abstract

Abstract. The leading principle in modeling procedures is the minimization of structural energy. It is assumed that the calculated minimal energy has to be compared with the experimental estimate of cohesion energy of a crystal. The reference state for structure energy depends on bonding type: the lattice energy for purely ionic crystals consisting of cations and anions, the atomization energy for covalent and metallic crystals consisting of atoms, the sublimation energy for molecular crystals consisting of molecules etc.As is well-known, a majority of minerals can not be correctly described as purely ionic crystals. Moreover, for these crystals lattice energy cannot be determined empirically because free anions, such as 0 2-, S 2-, As 3 -, etc., do not exist. In order to describe crystal structures and properties in a better approximation it is usually proposed that the bonding character of such crystals is intermediate between ionic and covalent, so that effective charges instead of formal ones, and an appropriate covalent contribution, are involved in energy calculations. However, the corresponding calculated structure energies are not comparable to any experimental values. Moreover, they decrease with increasing effective charges and a purely ionic structure seems, as before, to be most stable from energetic point of view.To avoid this "energetic catastrophe" the so-called "charge-transfer energy" has to be taken into account. Estimations of charge-transfer energies were sometimes faced with difficulties because of limitation of knowledge about valence-state energies of atoms. Now it is possible to refine this approach using new data on the average one-electron energies of the valenceshell electrons in ground-state free atoms. It is demonstrated for the examples of Si and O atoms. The successive ionization of mixed s, p valence-shell of silicon atom from Si ~ to Si 4+ states is reconstructed and a new extrapolation procedure to obtain the electron affinity of 0 2-is applied.Correspondence to: V.S. Urusov The structure energy of stishovite SiO 2 as a function of the ionicity degree parameterfis calculated with the aid of pair potential consisting of the effective ionic, the covalent Morse type contributions and the charge transfer correction. The structure energies change from -6.32 eV for the ionic structure (f= 1) to -11.91 eV for the covalent structure (f=0) with minimum value of -15.41 eV for f= 0.49. The latter can be compared to the experimental value of atomization energy (-18.9 eV). The corresponding oxygen atomic coordinate x varies from 0.310 0c= 1) to 0.300 (f=0) being equal to the true value of 0.306 at f=0.75. Atfless than 0.7 the improvement of the simulated elastic and dielectric constants, when compared to the ionic model, is sufficient.

On the structure and compressibility of CaSiO3 perovskite

“…It is possible to significantly improve VIB's treatment of Si-O interactions by simply reducing the ionicities of Si and O [Bukowinski and Downs, 2000], consistent with Pauling's claim that the Si-O bond is as much as 50% covalent [Pauling, 1980]. To preserve VIB's efficiency, we model this covalency by adding a parametric potential, È covalent , to the Si-O interaction, which is weighted by a function of the ionicity of Si and O, as suggested by [Urusov and Eremin, 1995]:…”

“…It is possible to significantly improve VIB's treatment of Si‐O interactions by simply reducing the ionicities of Si and O [ Bukowinski and Downs , 2000], consistent with Pauling's claim that the Si‐O bond is as much as 50% covalent [ Pauling , 1980]. To preserve VIB's efficiency, we model this covalency by adding a parametric potential, Φ covalent , to the Si‐O interaction, which is weighted by a function of the ionicity of Si and O, as suggested by [ Urusov and Eremin , 1995]: where Φ long is the simple point‐Coulomb interaction for fully charged ions, and the short‐range interactions, Φ short ′, are calculated from the new resulting electronic charge densities. It should be noted that the new electronic charge densities affect the interactions and self energies of all the ions.…”

Importance of open-shell effects in adhesion at metal-ceramic interfaces

“…SiO 2 is a more covalently bonded crystal than either Al 2 O 3 or ZrO 2 , 37 with an estimated covalent character of ϳ50%. 38 The key feature distinguishing this case from that of Al 2 O 3 or ZrO 2 on Ni is that the trend of increasing preference for intraceramic ionic bonding at the expense of interface adhesion is not observed. In fact, the adhesion of silica films to nickel remains relatively constant even for films several times thicker than the trilayer alumina coating.…”

On the mechanism of impurity influence on growth kinetics and surface morphology of KDP crystals—I: defect centres formed by bivalent and trivalent impurity ions incorporated in KDP structure—theoretical study

“…(2), B ij and D ij denote the parameters characteristic for Buckingham and Morse potentials, respectively. The repulsion parameter s ij in the Morse potential and parameter r ij in the Buckingham potential are specific to the interactions between the bonding atoms, and can be estimated using the fitting procedure [21].…”