, Volume 39, Issue 10, pp 841-874,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 27 Sep 2012

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 (H2O) 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 density-of-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]Mg m [4] Si n O(m+2n) and MgSO4(H2O) n .

Article based on the IMA Medal Lecture given at the International Mineralogical Association meeting in Budapest (2010).