Introduction

Phase diagrams are determined by recording the state of a material at a series of thermodynamic conditions, for example, whether the sample is molten or crystalline as a function of temperature, composition, and pressure. Although phase boundaries are thermodynamically well defined, the experimental observations that constrain phase diagrams often display significant scatter about the equilibrium boundaries. The scatter may be evident either within a single set of measurements or between distinct experiments from different laboratories.

Introduction

It is now two decades since it was found (unexpectedly to many) that key properties of liquid and glassy SiO2 could be reproduced semiquantitatively by molecular-dynamics (MD) computer simulations in which the Si and the O components are treated as simple ions with full formal charges [1]. The internal energy at 300 K was obtained to within 3%, and the qualitatively unique features of (1) high liquid compressibility contrasting with low liquid expansivity, (2) anomalous increase of diffusivity with pressure, and (3) large pressure-induced glass densification were also demonstrated.

Introduction

Although an x-ray diffraction experiment may have very high precision, there are many factors that need to be controlled if an accurate result is to be obtained. This paper discusses the potential systematic errors arising from peak asymmetry that are due to axial divergence, sample positioning errors, and nonhydrostatic stress distributions.

Axial Divergence

Axial divergence, the effect that causes peak asymmetry for diffraction maxima near 0° or 180° 2θ in powder-diffraction patterns, arises from the elliptical shape of the intersection of diffraction cones with the cylinder that describes the opening of the detector as it is swept through 2θ. The description of this effect and a method for calculating the resulting profile have been presented by Finger et al. [1]. This correction can be applied directly for data measured with monochromatic radiation and a diffractometer. Axial divergence should not affect monochromatic powder patterns measured with flat-plate detectors, such as imaging plates or CCD detectors. Such patterns are usually processed to convert the circular rings on the flat two-dimensional detector into a pseudo-one-dimensional pattern by dividing the pattern into a number of wedges and integrating each piece [2].

If you look at the cosmic abundance of elements, oxygen, carbon, neon, nitrogen, magnesium, and silicon are the top six (apart from hydrogen and helium); most of them are indeed the main constituents of rock-forming minerals. If the goal of modern mineralogy is to understand classes of materials on an atomic scale, this is also the aim of modern condensed-matter physics. Therefore it is natural that condensed-matter physics should be applied to mineralogy and earth sciences, just as particle physics is a key tool in understanding cosmology.

This book is intended to give a state-of-the-art description of intensive interactions between geophysics and condensed-matter physics that recent years have witnessed. Although you might assume that, given the maturity of the solid-state physics, the crystalline structures of materials must have been readily understood in atomistic, nonempirical terms, this rather naive expectation has not been satisfied until quite recently.

Although traditional mineralogical principles had remained largely empirical, a few individuals pursued the idea that modern theoretical solid-state physics must become the foundation of mineralogy and geophysical sciences. One of the pioneers in this respect is Professor Yoshito Matsui in Japan. Following the tradition of Goldschmidt, he realized the importance of identifying and characterizing the underlying physics that controls geochemical, geophysical, and geological phenomena over the entire range of pressure and temperature relevant to the Earth. In so doing, he, in collaboration with Dr. Eiji Ito, directed the development of new experimental high-pressure facilities that would be required for understanding the rich and sometimes unexpected behaviour of minerals under conditions found deep within the Earth.

Introduction

Although quantum mechanics laid a solid foundation for condensed-matter physics earlier this century, we are now witnessing a new era in that branch of physics in which we begin to understand crystal structures in nonempirical ways. As stressed in the Preface of this volume, this has been particularly fruitful in understanding rock-forming minerals. It is indeed fascinating if we can predict crystal structures of minerals or other materials in general from a knowledge of the chemical composition alone. This also opens up a way to search for novel crystal structures, either in denser or open-structured forms.

The purpose of this chapter is twofold. One is to take silica as an example for elaborating on various crystal structures, obtained from a nonempirical computer-simulation study. Silica comprises the two most abundant elements on the Earth, i.e., silicon and oxygen. Silica, along with silicates, is an important ingredient in rock-forming minerals. Crystal-to-crystal phase transformations, as well as pressure-induced amorphisation, are described.

MgO, periclase, is the simplest oxide and has been a subject of intense experimental and theoretical study. Oxides and silicates make up the bulk of the Earth's mantle and crust, and thus it is important to understand and predict their behavior. The behavior of MgO, as the prototypical oxide, is the key to understanding mineral and rock behavior in the bulk of the Earth. An important feature of MgO is the nonrigid behavior of the oxygen O2– ion, which makes the interactions not describable by pairwise interactions. All other more complex oxides share this feature and add additional complications as well. MgO is simple in that it is an ionic material with no solid-state phase transitions until over 500 GPa according to the best computations. If we understand MgO we will not immediately understand all other oxides and silicates, but if we cannot understand MgO, we cannot understand any other oxide or silicate.

There is an enormous literature on MgO, and a comprehensive review is impossible here. Instead the main thrust is on the underlying fundamental physics of MgO. First-principles methods, as opposed to empirical methods, are emphasized. Properties that are addressed range from the thermal equation of state and elasticity to properties of defects, surfaces, and impurities.

Introduction

Magmatic processes within the Earth are controlled to a large extent by transport properties of silicate liquids. For example, both rates of magma ascent and rates of crystal settling during fractionation processes are controlled by the viscosity of silicate melts. In addition, ionic diffusion in silicate liquids controls rates of magma mixing, homogenization, and chemical equilibration and is therefore an important controlling parameter at all stages of magma evolution, from initial partial melting at depth to eruption or emplacement at or near the Earth's surface. Because a knowledge of the transport properties of silicate melts is essential for quantifying magmatic processes in the Earth, the viscosities of such melts have been studied extensively as functions of temperature and chemical composition at 1 bar with a range of experimental techniques [1].

Introduction

Silica is one of the most intensively studied materials under a wide range of pressure and temperature conditions because of its importance in earth science as well as in material science. In spite of its simple chemical formula, many different polymorphs are formed, depending on the pressure and the temperature conditions. Moreover, recent room-temperature compression studies of various polymorphs clarified the formation of variety of metastable phases [1–5], and the situation is complicated. It is likely that the formation of some of the metastable phases is related to the nonhydrostatic nature of applied pressure. Here we report a new example of the formation of completely different high-pressure structures that depend on the hydrostaticity of applied pressure.

Introduction

The hydrogen bond (X—H… Y) is one of the most studied bond geometries in the mineralogical, biological, and solid-state organic chemical communities [1, 2]. For nonmineral and mineral structures alike, the published literature, consisting mainly of crystal-structure determinations at ambient pressure, provides a means to study the bond as donor (X) and acceptor (Y) vary over a variety of structures and chemistries [3, 4]. The secondary environment, however, is important in considering the effects of structure on H-bond geometry [5]; in many cases gross changes in this environment from one structure type to the next make it difficult to separate the effects of the relatively weak H bonding from the steric effects because of the framework making up the remainder of the structure [5].

Introduction

It has long been recognized that atomic interactions are key in understanding large-scale geological phenomena, which is an approach dating at least as far back as the days of Goldschmidt [1]. Conversely, a study of the materials that comprise the planets can tell us much about fundamental physics and chemistry. This line of approach is subsequently exemplified by Pauling's development of the theory of chemical bonding from the structural studies of minerals [2].

Among many facets that revolutionized modern earth science are plate tectonic theory, discoveries in planetary astronomy, and extraordinary technical advances that provide windows on our planet's deep interior. Modern condensed-matter physics, on the other hand, has acquired much impetus from the discovery of new phenomena, the development of new experimental methods, and vast improvements in computational methods. Although physics and mineralogy have continued largely on distinct and disparate trajectories, many recent advances in both earth science and physics stem from science done at the crossroads of the two fields.

Introduction

The high-pressure phases of metal monoxides [including alkaline-earth-metal monoxides, transition-metal monoxides (TMMOs), etc.], with the rock-salt (Bl) structure at normal pressure and room temperature, are important for both condensed-matter physics and earth science because their crystal structure is simple and moreover MgO and FeO are considered to be important constituents of the Earth's deep mantle.

Introduction

Shock Compression Method for Solids

The dynamic compression method using shock wave has been utilized for highpressure research on solids. The method can easily generate high pressures to more than 100 GPa. In principle, the nature of the dynamic compression is understood by hydrodynamical considerations [1]: When a shock wave travels in solids with a supersonic speed (U) and accelerates particles to a particle velocity (w), the shock front is generated as a discontinuity boundary of pressure and density. In real solids, the discontinuity is observed as a very steep change of pressure in solids and the transition interval is only several nanoseconds.