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

矿物是地球的基本物质，如果我们想要了解形成地球的过程，并继续改变地球的景观和人类环境，我们需要了解矿物在地球上经历的各种条件下的行为。这项建议侧重于各种各样的矿物，试图了解影响其组成和行为的原子尺度因素，并利用这一理解在宏观尺度上对其行为进行合理化和预测。我使用各种形式的辐射(X射线、中子)，通过衍射在原子尺度上看到一种矿物，并得出构成它的原子的排列。关于原子无序的详细信息可以通过使用其他形式的辐射(例如红外线、伽马射线)的光谱学来查看。由此得到的矿物的原子尺度细节为我们提供了信息，从中我们可以了解矿物是如何形成的，在什么条件下形成，在什么条件下是稳定的。为什么矿物会有它们所拥有的化学式？为什么它们有自己特定的结构安排？为什么矿物在特定的pH、Eh、温度、压力和组分活度范围内是稳定的？晶体结构与生成焓、熵和吉布斯自由能有什么关系？我们如何才能得出地质过程的原子尺度机制呢？数学复杂性与矿物结构和矿物在平衡和非平衡过程中的行为有什么关系？这些问题是矿物学本身的基本问题，但在过去却被忽视了，因为它们不容易受到物理学和化学中既定理论技术的影响。这里提出的工作从根本上解决了其中的几个问题，并将进一步加深我们对不同地球材料以及它们对环境变化的反应方式的理解。这项建议的一个主要部分涉及进一步发展一种回答这些问题的理论方法，一种基于空间化学键的拓扑(连通性)的方法。我将使用数学(图论、组合拓扑学、复杂性理论)和化学(固体能量密度的矩方法)的各个方面[1]建立键连接性模式(键拓扑学)和它们的能量含量之间的联系；[2]研究这些联系如何决定矿物的化学成分和结构连接性；以及[3]这些因素如何影响矿物如何参与地质过程。这项理论工作得到了一项广泛的矿物表征实验计划的支持，该计划涉及角闪石和电气石、宝石矿物、TS块矿物、新矿物以及其他可以受益于我们当地的实验能力和理论专业知识的不同项目。

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.