A Theoretical Basis for Mineralogy and the Behaviour of Minerals in Earth Processes

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Minerals are the fundamental materials of the Earth, and if we wish to understand the processes which formed the Earth, and which continue to modify its landscape and the human environment, we need to understand the behaviour of minerals under the full spectrum of conditions experienced on Earth. This proposal focuses on a wide variety of minerals in an attempt to understand the atomic-scale factors affecting their constitution and behaviour, and to use this understanding to rationalize and predict their behaviour at the macroscopic scale. I use various forms of radiation (X-rays, neutrons) to 'see' into a mineral at the atomic scale via diffraction, and to derive the arrangement of atoms from which it is built. Details concerning atomic disorder can be seen with spectroscopy using other forms of radiation (e.g. infrared, gamma rays). The resulting atomic-scale details of the mineral give us the information from which we can understand aspects of how and at what conditions the mineral formed, and under what conditions it is stable. 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 constituent activities? What are the relations between crystal structure and enthalpy, entropy and Gibbs free energy of formation? How can we derive the atomic-scale mechanisms of geological processes? What is the relation of mathematical complexity to mineral structures and the behaviour of minerals in equilibrium and non-equilibrium processes? These questions are fundamental to Mineralogy itself and yet have been ignored in the past because they are not susceptible to established theoretical techniques in Physics and Chemistry. The work proposed here addresses several of these problems from a fundamental perspective, and will further our understanding of different Earth materials and the way that they respond to changes in their environment. A major part of this proposal involves the further development of a theoretical approach to answering these questions, an approach based on the topology (connectivity) of chemical bonds in space. I will use various aspects of Mathematics (Graph Theory, Combinatorial Topology, Complexity Theory) and Chemistry (the moments approach to the energy density-of-states of solids) to [1] develop connections between patterns of bond connectivity (bond topology) and their energetic content; [2] examine how these connections dictate the chemical compositions and structural connectivities of minerals; and [3] how these factors affect how minerals participate in geological processes. This theoretical work is supported by an extensive experimental program of mineral characterization involving amphiboles and tourmalines, gem minerals, TS-block minerals, new minerals, and other diverse projects that can benefit from our local experimental capabilities and theoretical expertise.