A bond-topological approach to theoretical mineralogy: crystal structure, chemical composition and chemical reactions

Abstract

Here, I describe a theoretical approach to the structure and chemical composition of minerals based on their bond topology. This approach allows consideration of many aspects of minerals and mineral behaviour that cannot be addressed by current theoretical methods. It consists of combining the bond topology of the structure with aspects of graph theory and bond-valence theory (both long range and short range), and using the moments approach to the electronic energy density-of-states to interpret topological aspects of crystal structures. The structure hierarchy hypothesis states that higher bond-valence polyhedra polymerize to form the (usually anionic) structural unit, the excess charge of which is balanced by the interstitial complex (usually consisting of large low-valence cations and (H 2 O) groups). This hypothesis may be justified within the framework of bond topology and bond-valence theory, and may be used to hierarchically classify oxysalt minerals. It is the weak interaction between the structural unit and the interstitial complex that controls the stability of the structural arrangement. The principle of correspondence of Lewis acidity-basicity states that stable structures will form when the Lewis-acid strength of the interstitial complex closely matches the Lewis-base strength of the structural unit, and allows us to examine the factors that control the chemical composition and aspects of the structural arrangements of minerals. It also provides a connection between a structure, the speciation of its constituents in aqueous solution and its mechanism of crystallization. The moments approach to the electronic energy densityof-states provides a link between the bond topology of a structure and its thermodynamic properties, as indicated by correlations between average anion coordination number and reduced enthalpy of formation from the oxides for [6]

High-temperature order–disorder phase transition in nacaphite, Na2CaPO4F

“…(valence units)] compared to the O atoms of the PO 4 tetrahedra that have the Lewis base strengths equal to 0.25 v.u. (Hawthorne 2013). The effect of temperature upon the structural complexity of nacaphite polymorphs can be estimated using Shannon information content per atom (I G ) and per unit cell (I G,total ) calculated according to the following formulae (Krivovichev 2012(Krivovichev , 2013(Krivovichev , 2014: where k is the number of different crystallographic orbits and p i is the random choice probability for an atom from the ith crystallographic orbit, that is:…”

Oxidation-hydration weathering of uraninite: the current state-of-knowledge

“…SO 4 2-, PO 4 3-, AsO 4 3-, SiO 4 4-). In order to simplify and classify the crystal structures of uranyl minerals, the structural hierarchy of the structures was developed based on the topologies of the basic structure units -uranyl anion topologies Burns 1999bBurns , 2005 following the general idea of Hawthorne (1983Hawthorne ( , 1994 and in accord with the bond-valence theory (Brown 1981(Brown , 2002(Brown , 2009. The topologies of the structural units (Fig.…”

Fontarnauite, (Na,K)2(Sr,Ca)(SO4)[B5O8(OH)](H2O)2, A New Sulfate-Borate Mineral From Doğanlar (Emet), Kütahya Province, Western Anatolia, Turkey

“…This correlation suggests a mechanism for the crystallization of minerals from aqueous solutions, whereby crystallization proceeds by condensation of complex oxyanions in solution (Hawthorne 1979, 1983, Schindler & Hawthorne 2001a. In turn, this suggests a strong relationship between the pH of the environment of crystallization and the identity and proportions of borate clusters constituting the structures of specific minerals (Hawthorne 2012(Hawthorne , 2014.…”