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

Frank C Hawthorne

doi:10.1007/s00269-012-0538-4

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 [4] Si n O(m+2n) and MgSO4(H2O) n .

Highlights

The last 50 years have seen an explosion in analytical mineralogy as experimental techniques have allowed more and more detailed characterization of smaller and smaller samples
What kind of theoretical framework have we been using to interpret the data that we have accumulated over the past 50 years? We have been using crystal chemistry to systematize mineral properties and behaviour, classical thermodynamics to examine processes involving minerals, and more recently, computational mineralogy to derive properties of minerals the stabilities of which are beyond the reach of current experimental techniques
Why do minerals have the chemical formulae that they do? Why do they have their specific structural arrangements? Why are minerals stable over specific ranges of pH, Eh, temperature, pressure and activities of their various constituents? What are the relations between crystal structure and both enthalpy and Gibbs free energy of formation? Many of these questions are fundamental to Mineralogy itself and yet have tended to be ignored in the past

Summary

Introduction

The last 50 years have seen an explosion in analytical mineralogy as experimental techniques have allowed more and more detailed characterization of smaller and smaller samples. There is little intuitive connection between the essential features of a crystal structure, the relative positions of the atoms and the disposition of the chemical bonds, and the usual methods for deriving the electronic energy densityof-states.

Results

Conclusion