Mineral behaviour at extreme conditions

Edited by Ronald Miletich


Extreme conditions and their effects on matter and materials are currently fashionable topics in modern science. Perhaps the fascination derives from the unimaginable dimensions that grab our attention and push the boundaries of our imagination. Imagine the pressures in extremely dense neutron stars where electrons and protons are fused together and atoms collapse to the density of an atomic nucleus; imagine temperatures of thousands of degrees Kelvin at the solar surface, or multimegabar and terapascal pressures deep within the interior of our planets. But even a simple droplet of water represents an extreme environment when it comes into contact with an otherwise stable crystal of rock salt, causing the crystal to dissolve as external conditions are drastically changed. We have an inherent desire to understand these diverse kinds of phenomena in nature, the mechanisms of the material changes involved, as well as the extreme conditions which are becoming increasingly demanded to achieve the extraordinary performance of new engineering materials. This rapidly evolving area of science is necessarily interdisciplinary, as it combines fundamental physics, chemistry and biology with geoplanetary and materials science, in addition to increasingly becoming one of the keys to engineering and technology aimed at process optimisation. Current experimental methods permit materials to be studied at pressures of several megabars, temperatures of tens of thousands of degrees Kelvin, and to achieve magnetic fields of several thousand teslas. Moreover, the rapid surge in computer technology has, in turn, permitted the solution of many previously intractable problems, and now even allows the behaviour of matter to be predicted far beyond the range of conditions currently accessible to experimentation. Previously unknown phenomena such as the formation of new phases, new forms of electronic and magnetic order, melting, atomic and electronic excitation, ionisation or the formation of a plasma state might result from exposing matter to extreme conditions well beyond those which were characteristic of the equilibria at the time of formation. With this volume of EMU Notes in Mineralogy we have endeavoured to provide up-to-date reviews of our understanding of the behaviour of minerals and geomaterials at exterior conditions that are sufficiently extreme to induce changes. In total 18 chapters reflect the diversity of this theme, but also demonstrate how strongly interdisciplinary this domain of modern mineralogy has become, bringing together physicists, chemists and geologists as well as experimentalists and computer scientists. The present volume contains the contributions of the lectures presented at the 7th EMU School, held at the University of Heidelberg from June 19 to June 25, 2005.

  1. Page 1

    The first experimental studies on minerals and rocks under high temperature and high pressure were probably carried out by Sir James Hall (1761–1832). At that time, some geologists still debated the magmatic origin of basalts. In a series of meltingand crystallisation experiments carried out in furnaces used at that time in the ceramic and glass industry, Hall was able to reproduce the textures and mineral assemblages of natural basalts. Experimentally much more demanding were his studies on the recrystallisation of limestone (Eyles, 1961). In order to reach high pressures and high temperatures simultaneously, Hall sealed the sample together with some water into gun barrels. By heating the sealed gun barrels in a furnace (Fig 1), he was probably able to reach pressures close to 0.1 GPa and temperatures around or above 600 °C simultaneously. Limestone subjected to these conditions converted to marble and Hall therefore simulated for the first time metamorphic processes in the laboratory. In order to accurately measure pressure, Hall devised a dead-weight pressure gauge, which determines the force on a piston by balancing it with a weight (Fig 2). In principle, the same type of instrument is still in use today for the high-precision calibration of gauges.

    Hall’s ingenious experiments were far ahead of his time and it appears that not much progress was made in experimental mineralogy and petrology for almost one century following his work. At the same time, however, physicists and chemists became interested in high-pressure and high-temperature phenomena such as the behaviour of gases under extreme conditions.

  2. Page 31

    The classic picture of mineral structures is dominated by the periodic repetition of the asymmetric unit over infinite distances. This picture is governed by the principles of symmetry and it has its merits for the description of bulk structures of minerals and their associated equilibrium properties.

    However, apart from bulk structure, the properties of the actual mineral assemblies found in nature in the form of rocks are equally determined by mineral surfaces, grain boundaries and sub-grain microstructures. These diverse features require a description of minerals at very different length scales, ranging from the properties of atoms at the sub-ångström range (1 Å = 10−10 m), to the now fashionable nanometre range that would encompass a relatively small and still enumerable number of atoms in a world governed by the forces of quantum mechanics (Fig. 1).

    Going on to the micrometre length scales of mineral microstructure and further to the length scales directly accessible to the human eye, i.e. millimetre grain sizes or rock deformations ranging from the metre to the kilometre range, the properties of these structures are more and more dictated by classical mechanics.

    Any consideration of the composition, structure and properties of matter leads to the existence of atoms as its basic building units. Atoms may be approximated as spherical, with a diameter between 1 and 5 × 10−10 m. However, they are not indivisible (“ατομοσ”) as stated by Democritus, and modern physics of the past 100 years revealed the three fundamental particles protons, electrons, and neutrons.

  3. Page 65

    The study of the physical properties of silicate melts is now at an exciting point. Given that a large amount of data exists for average melts at average conditions, we can now build on this knowledge to investigate melts at extreme conditions, to observe the unusual behaviour of melts. The combination of the average data that already exist and newer observations from extreme conditions illustrates how challenging the understanding of silicate melts is. Melts at extreme conditions do not show the physical properties extrapolated from the measurements at average conditions.

    There is a range of extreme conditions for silicate melts:

    1. Structure: structure varies with temperature, pressure and composition (T, P, X) and controls the physical properties of melts.

    2. Composition: both Si-rich and Si-poor melts are yet to be investigated thoroughly, as well as Al-rich and Al-poor melts.

    3. Temperature: both high- and low-temperature conditions - this means low and high viscosities, respectively.

    4. Pressure: viscosity will either increase or decrease with pressure depending upon composition.

    5. Time: the investigation of the change in physical properties with time as the melt structure equilibrates with the change in applied stress or temperature.

    Although the physical properties of melts at these different conditions will be discussed separately, they are inter-related. The physical properties are a function of structure, which in turn is a function of composition, temperature, pressure and time.

    In studying silicate melts the properties density, viscosity, surface tension, compressibility, electrical conductivity, and their dependence on pressure, temperature and composition are determined.

  4. Page 95

    Since the formulation of the “Law of Spring”, Ut Pondus sic Tensio by Robert Hooke in 1678, elastic properties of solids have been subject of intensive research in various fields of basic and applied sciences. For example, as the interior of our planet is not directly accessible by experiment, models of the structure of the Earth are mainly based on seismic data. The interpretation of seismic wave propagation and the derivation of equations of state in geosciences require a profound knowledge of the elastic and visco-elastic properties of the constituting mineral phases. All geological materials undergo phase transitions at certain thermodynamical conditions, which can lead to dramatic variations in their elastic properties. Often the influence of the transition extends over a wide temperature and pressure range. Therefore, elasticity serves as a highly sensitive probe for the investigation of structural instabilities related to phase transitions (Carpenter & Salje, 1998). Although most people are not aware, we cannot imagine life today without piezoelectric single crystals and ceramics. Most electronic devices make use of specific interactions between elastic and piezoelectric properties of crystal species like α-quartz and tourmaline. The so-called electromechanical coupling effects allow for conversion of mechanical into electrical energy and vice versa. Examples for technical applications are frequency filters and delay lines in communication technologies, ultrasound generators and clock oscillators. The pure piezoelectric effect is used in pressure sensors in combustion engines and gas turbines.

    In view of the importance of elasticity and piezoelectricity it is rather surprising that relatively little is known about these basic physical properties of crystals.

  5. Page 117

    Most of the Earth’s material exists at high pressures and temperatures inside the planet. Since experiments in this p-T regime often turn out to be difficult or plain impossible, it is often necessary to do simulations, which avoid some of the important problems encountered in experiments.

    For a more specific look on the topics of this chapter we refer the reader to Kohn (1999), Martin (2004), Oganov et al. (2002), Payne et al. (1992) and Stixrude et al. (1998). In this chapter we describe how to calculate the energy of a crystal with ab initio methods. It will shortly touch the historical origins of today’s methods and will end with the state-of-the-art quantum-mechanical calculations.

    When we want to investigate a mineral system we start with the Gibbs free energy. Every system in equilibrium likes to be in the state with the lowest Gibbs free energy G at given pressure and temperature condition. The Gibbs free energy is then given by minimising the following equation:

    where E is the energy, p the pressure, V the volume, T the temperature and S the entropy of the system. From statistical mechanics, knowing the energy of different states of the system (i.e. the energies of different vibrational and electronic quantum levels or of different atomic configurations) one can calculate the entropy and the free energy1, the link being provided by the partition function Z:

    The total energy of a non-relativistic electron-nuclear system and all its energy levels can be calculated by solving the Schrodinger equation, where H is the Hamilton operator and ψ is the wave function for the N electrons and the M nuclei.

  6. Page 139

    Among the structural phase transitions, displacive phase transitions comprise those that only require small collective displacements of individual atoms. A small displacement of atoms in this context amounts to fractions of the nearest neighbour interatomic distances, i.e. generally at most a few tenths of an ångstrom. Displacive transitions occur spontaneously and reversibly at specific pressure and temperature conditions. Because of this, their direct observation is inextricably linked to the use of in situ methods, usually requiring a non-trivial sample environment, e.g. high-pressure cells, furnaces or cryostats. This definition puts displacive phase transitions in contrast to those structural phase transitions that involve significant diffusion of atoms, e.g. cation ordering transitions or entirely reconstructive phase transitions.

    As this introductory text should serve as a guide to the analysis of experimental data, it will be predominantly concerned with the theory of displacive phase transitions and not with the experimental techniques employed to obtain the necessary data. Alarge number of in-depth review articles and textbooks devoted to the subject has already appeared in the recent past. It is therefore not the aim of this text to introduce every imaginable aspect of displacive phase transitions. Many of the details that are necessarily being omitted can be found elsewhere (e.g. Binder, 1987; Salje, 1992a, 1992c, 1993; Dove, 1997; Carpenter et al., 1998a; Carpenter & Salje, 1998). What this text is trying to achieve is to transport a general picture of the theory and its application to experimental data, accompanied by an explanation of technical terms where they might appear.

  7. Page 173

    Our knowledge of physical properties of crystals is rather limited compared to the number of solved crystal structures. Mainly the basic tensorial properties of numerous crystal species belonging to simple structure types like halite-, CsCl-, fluorite-, perovskite-, spinel- and garnet-type have been extensively studied over the years. On the basis of these data relations between chemical composition and certain physical properties could be established. For instance, the mean values of magnetic susceptibility of para- and diamagnetic crystals, dielectric constants, optical refractivity and the Faraday effect can be easily estimated by additivity rules as sums of quasi-persistent contributions of individual atoms, ions or molecules. A well-known example is the Clausius–Mosotti equation

    which relates the mean dielectric constant ε of a crystal to the polarisabilities αj of its constituents. nj is the number of particles of type j per unit volume and ε0 denotes the permittivity of vacuum.

    In contrast to such physical properties, elasticity exclusively arises from interactions between the constituents of a crystal. The mean elastic stiffness is therefore closely correlated to the lattice energy, and the elastic anisotropy directly reflects the anisotropy of the crystal’s bonding system. The modifications of carbon, SiO2 and Mg2SiO4 provide instructive examples (Fig. 1). Due to their higher tensorial rank, already the second-order elastic properties (Hooke’s law) behave anisotropically even in crystals possessing cubic symmetry (Fig. 2). Consequently, elasticity provides one of the most powerful probes for the investigation of structure-property relationships. Further, a series of rules on the qualitative interpretation of the structural dependence of many other physical properties can be derived from the elastic behaviour. Examples are listed in Table 1.

  8. Page 199

    Over the decades that Earth scientists have been studying the solids and fluids of the Earth, our traditional mineralogical and geochemical methods have taught us a great deal about the composition and properties of the materials that make up our surroundings in nature and also about the materials of the deep Earth and the Universe. Through this information, we have been able to form conceptual models about the reactions that take place at mineral surfaces, at the interface between solid and fluid – be it a gas, a solution, or a melt. An interface is a boundary between phases. It is at the interface, the growing or dissolving front of the solid, where composition of both solid and fluid are defined and mineral structure and morphology are determined. Even processes such as solid-state diffusion and mineral transformation under heat and pressure, begin at a point or a line that may be a physical defect or a chemical inhomogeneity, and continue along a front that separates properties that are slightly different than in the rest of the solid.

    Earth scientists have many bulk analytical methods at their disposal. Typically, we have been able to choose among: X-ray diffraction (XRD), electron microprobe (EPMA), scanning electron microscopy (SEM), inductively coupled plasma mass or atomic emission spectroscopy (ICP-MS or ICP-AES), atomic absorption spectroscopy (AAS), optical and other forms of microscopy, infrared, Mössbauer and other forms of spectroscopy, potentiometry, chromatography and other wet-chemistry methods. These techniques give us information about the morphology, composition and structure of minerals

  9. Page 217

    There are two experimental techniques capable of generating the very high pressure and temperature conditions of the deep interior of planets: laser-heated diamond cells and shock compression. In laser-heated diamond cells temperatures of over 4000 K have been achieved at pressures up to 200 GPa (2 Mbar) (Boehler, 1993). The main advantage in using diamond cell over shock experiments is that P-T conditions can be kept constant for long periods of time (hours), and this allows a large variety of visual, spectroscopic and X-ray diffraction measurements. The principal drawback to the diamond cell are small sample size, temperature gradients, and in some cases chemical reaction of the sample with the diamond or the pressure medium. The installation of high-pressure beam lines at synchrotron facilities, along with recent developments in X-ray diffraction techniques, have significantly improved our ability to measure the phase behaviour of many materials at extreme pressure and temperature conditions.

    In comparison to the wide range of temperatures and pressures accessible to the diamond cell method, shock experiments using guns or lasers provide measurements of densities and sound velocities only along a material-specific, nearly adiabatic P-T path (Hugoniot). Another drawback to the shock method is the short experimental time scale. However, the maximum pressures attainable by shock methods are virtually unlimited.

    In this paper the experimental technique for obtaining reliable data at simultaneously high pressure and high temperature employing the laser-heated diamond cell is described. A schematic cross-section of a laser-heated diamond cell is shown in Figure.

    The principal components of a diamond cell are two diamond anvils compressing a gasket.

  10. Page 225

    The term “fluid” is used in different ways in the geologic literature. Sometimes “fluid” is used to denote any kind of mobile phase, including silicate melts. In this chapter, we will, for purely pragmatic reasons, define a fluid as a mobile phase which is not a silicate or carbonate melt. Sometimes the term is defined even more narrowly as a mobile phase in a regime of pressure and temperature where no distinction between “vapour” and “liquid” is possible anymore. We will not follow this use, i.e. a “fluid” in the sense as it will be used in this chapter can have either “vapour-like” or “liquid-like” or transitional properties, unless otherwise stated.

    Evidence for the composition of fluids in the Earth’s interior comes essentially from three sources of evidence: (i) the analysis of volcanic gases, (ii) the investigation of fluid inclusions and (iii) considerations of phase equilibria. Gases from volcanoes with a non-explosive eruption style can sometimes be directly sampled, while direct sampling is impossible during major explosions. Naturally, this introduces some bias in the data on volcanic gas compositions, since gas analyses can be much more easily acquired from basaltic magmas than from the often highly explosive andesitic and rhyolitic ones. However, in recent years remote sensing of gas compositions by infrared spectroscopy has become possible and it is to be expected that the further development of these methods will ultimately allow a more representative sampling of volcanic gases from a variety of magma sources and tectonic environments. In any case, although there are quite significant variations, virtually all available analyses show that the predominant constituents

  11. Page 253

    Humanity has a long history of curiosity about the solids of the Earth and applying them as objects of beauty, wealth, power and practical advantage. From the first use of a stone tool, through the bronze age, iron age, the time of the alchemists, the ageof coal, steam and steel and now the silicon age, we have exploited minerals and shaped them to our purposes. For a couple of centuries, analytical tools have allowed us to identify mine-rals and describe their physical and chemical properties, so their bulkcomposition and structure are reasonably well characterised. Likewise, methods have been available for defining the compositionofsolutions and gases. Interactions between solids and fluids have been explored and conceptual models have been proposed for how atoms come to and leave surfaces, but only recently have we been able to confirm or disprove these models through direct observation at the molecular scale. It is the reactions that take place at the interface between phases that determine the properties of them both. An understanding of the mechanisms responsible offers scientists a powerful tool in pre-dicting the behaviour of the natural world and in engineering materials that continue to suit our purposes.

    Whether Earth scientists are interested in the crystallisation of a melt in a magma chamber, or the recrystallisation that results in a diagenetic cement in a sandstone, or the accumulation of precious elements to form an ore deposit, or a hydrocarbon reservoir, or in the wide dispersal of contaminants throughout environmental systems, or the uptake or release of gases by a soil ora subduction zone, the chemical processes are the same.

  12. Page 273

    The melting temperature of iron at high pressure is key to deriving the temperature in the Earth’s interior because theboundary between the solid inner core and the liquid outer core at about 3.3 Mbar is due to the melting (or freezing) of an iron-rich alloy. Data at core pressures measured in the laser-heated diamond cell (up to 200 GPa) have been reported over ten years ago (Boehler, 1993). In the last few years the experimental data obtained with this technique have converged, but there is still considerable disagreement between shock data, theory and diamond cell measurements. Thispaper will provide some of the latest dateon the phase diagram of iron and compare its melting curve with some other transition metals. This comparison is useful to understand systematic behaviour in transition metal melting.

    What is the melting temperature of iron at 3.3 Mbar? This question has addressed by many researchers over the past 20 years and the answers reach from 2000 to 10000 K. Figure 1 represents the latest solutions obtained from shock experiments, diamond cell experiments and from theory, and clearly indicates the difficulties associated with the question.

    The experimental techniques for generating high temperatures in the laser-heated diamond cell, pressure and temperature measurements are described in Chapter 9 in this volume (Boehler, 2005). Melting can be detected in situ for most materials by several methods: 1) by measuring discontinuous changes of the absorption of the laser radiation, 2) from changes in the reflectivity of the sample at a wavelength different from that of the heating laser, and 3) direct visual observation of melting on the sample surface.

  13. Page 281

    Following the discovery of X-ray scattering on crystalline materials, crystallography and the experimental application of diffraction techniques have resulted in our current understanding of the atomic arrangements and bonding in condensed phases.

    Soon after Max von Laue’s famous experiments in 1912 (Fig. 1), for which he received the Nobel Prize in Physics in 1914, a period of pioneering work began. Starting with father and son Bragg in the early twenties, the “century of crystal-structure determination” brought insight to the atomic view of solid matter, which only had been a matter of speculation before the discovery of scattering by crystals. Scattering techniques were de-veloped over the subsequent years, not only using X-ray radiation, but also involving electron and neutron scattering phenomena. Nowadays, with the evolution of powerful radiation sources, such as neutron spallation sources or synchrotron radiation facilities, the nature of atomic structure can be visualised even for the most complex macromolec-ular systems which include thousands of atoms.

    The pioneering work of structure solution was carried out at ambient conditions, starting with basic structures such as of sodium chloride, zincblende or diamond. Structure solution was not straightforward from the beginning. The so-called “phase problem”, i.e. the fact that the amount of phase shift on wave interference could not be determined experimentally from diffraction data, kept crystallographers busy for decades. It resulted in fundamental approaches, such as the Fourier summation of a set of squared (but not phased) amplitudes as introduced by A.L. Patterson (1934). H. Hauptman and J. Karle (1950) employed statistics and probability distributions as applied in the “direct methods” to overcome the phase problem.

  14. Page 339

    The Earth is a hot, dynamically evolving planet as shown at the surface either by slow, progressive manifestations (plate motion, continental drift) or more violent ones (earthquakes, volcanoes). Mantle convection, which underlies most geological processes, involves large-scale flow of rocks at high pressure and high temperature. Studying the rheological properties of deep-mantle materials is thus one of the biggest issues in mineral physics. It is also one of the most challenging as most of the deep Earth’s minerals are stable only at high pressure. We now have a broad range of experimental techniques allowing us to cover most of the entire P-T conditions range of the inner Earth. However, the usual methods used for mechanical testing - creep at constant stress, deformation at constant strain rate and stress relaxation - can usually not be achieved under those conditions. Measuring strain and stress is in itself a challenging problem at high pressure. The primary aim of this chapter is to give a rapid overview of the recent advance in the field of experimental deformation of minerals at high pressure.

    The most traditional experiment consists of applying a confining pressure to a cylindrical sample on to which an independent axial load is superimposed in order to generate differential stresses. The strain rate is usually held constant while the force on the piston is monitored with time and total deformation. Pressure can be applied by means of a gas as in the system designed by Paterson (Paterson, 1970). This apparatus has the great advantage of high accuracy with regard to axial stress

  15. Page 357

    About half a century ago the first experimental shock techniques and the basic laws governing the propagation of shock waves have been developed. During these early post-war years Russian and American pioneers were already able to experimentally compress solids to half of their specific volumes (see Trunin, 1998, or Zel’dovich & Raizer, 2002, for a review), i.e. pressures prevailing in the Earth’ s core were reproducible in laboratory shock experiments long before static compression techniques such as the diamond anvil cell approached this limit. The strength of shock experiments particularly lies in the fact that a combination of high pressures and high temperatures can be achieved, while the attainment of high temperatures is still problematic in diamond anvil cell experiments.

    In Earth and planetary sciences there are numerous basic interests in employing shock techniques. On one hand, shock experiments are devoted to the measurement of the shock wave equation of state of minerals and rocks at extreme conditions (Wackerle, 1962; Grady, 1977; Marsh, 1980; Ahrens, 1987, 1993; Boslough & Ahrens, 1984; Ahrens & Johnson, 1995a, 1995b). Virtually, the entire range of pressures and temperatures prevailing in the Earth’ s and planetary interiors can be reproduced in the laboratory. In this context, important applications of shock wave data are the correlation of the pressure–density function with the inner structure of planets and the assessment of the melting temperatures at which planetary magma oceans can be produced.

  16. Page 389

    Multiscale modelling and computation is becoming one of the most active research areas in materials science. This evolution is driven by the rapid growth in available computing power and by the development of many innovative algorithms and techniques. In mineral physics, the issue of mantle rheology, controlled by the deformation of high-pressure mineral assemblages, can be addressed by this new approach. In contrast with thermodynamic properties like the equation of state, which are fully determined at the atomic length scale, mechanical properties are inherently multiscale: they depend on the interrelationship between processes operating at the scale of the atom, the crystal, the rock and the whole planet. Moreover, these different scales are often strongly coupled to each other, which makes the problem even more challenging.

    Mechanical properties of real materials are controlled by crystal defects such as point defects, dislocations, stacking faults and grain boundaries. Taken individually, these defects can be described at the fundamental level through their atomic and electronic structures, which can be found by solving the Schrödinger equation. First-principles calculations and molecular dynamics are used to address such problems. At the scale of a grain, the mechanical properties are often the result of the collective behaviour of these defects in response to the loading conditions. Newly developed three-dimensional dislocation dyna-EMU Notes in Mineralogy, Vol. 7 (2005), Chapter 16, 389–415 mics simulation techniques are aimed to take these interactions between defects into account to provide insights about single-crystal plasticity. Constitutive laws for single-crystal plasticity can be ultimately transferred to the scale of the polycrystal. Polycrystal plasticity models and finite-element methods based on continuum mechanics examine how an aggregate (with possibly several phases) will deform in response to an applied stress.

  17. Page 417

    The study of the Earth’s interior is based upon the comparison of laboratory data on longitudinal and shear wave speeds of minerals with the seismic wave speeds from the Earth (see Fig. 1). This requires

    • (1)

      laboratory measurements of the temperature- and pressure-dependence of single-crystal elastic moduli to be recast in terms of wave speeds and densities of polycrystalline materials of possible mantle compositions and mineralogies; together with

    • (2)

      highly accurate information on seismic wave speeds as a function of depth in the mantle, together with

    • (3)

      jumps in wave speeds due to phase transitions,

    • (4)

      a temperature profile of the Earth,

    • (5)

      a density profile of the Earth,

    • (6)

      a pressure profile of the Earth, together with

    • (7)

      a petrological model of the Earth as a function of depth.

    While seismologists and petrologists have been acquiring their data, mineral physicists have been working on new, varied and imaginative methods of measuring wave speed first in single crystals, and more recently in polycrystalline materials at the temperature and pressure conditions of the Earth.

    There are a range of different methods used to determine the speed at which stress waves travel through materials at high-pressure and temperature conditions (see Fig. 2). These methods include the following:

    Shock wave measurements involve shooting a projectile at the sample of interest. The resulting collision creates high temperature, high pressure conditions within the sample, and the speed at which the shock wave travels through the sample is measured (e.g. Jackson & Ahrens, 1979; Watt & Ahrens, 1986; Luo et al., 2002; Panero et al., 2003; Langenhorst & Hornemann, 2005).

  18. Page 441

    Basic theory behind first-principles simulations has been reviewed by many authors, e.g. Jung & Oganov (2005b) in this volume, or by Oganov et al. (2002) and Cohen (1999); the main focus of this chapter is on applications of such simulation techniques, illustrating the power of modern simulation approaches. There are two main problems thatsimulations have to be able to solve in order to be useful:

    1. prediction of crystal structure topology, i.e. of the structure type of the stable and possible metastable phases for a given chemical composition;

    2. once structural topology is known, optimisation of the structure for given PT conditions and calculation of physical properties.

    While the second problem is practically solved for most properties, the first problem still poses great challengesand has no general practical solution. In principle, one should explore the entire energy surface and locate all local minima and the global minimum. However, the dimensionality of this surface is so overwhelmingly high that it is difficult to explore it efficiently. Nevertheless, there have been some recent successes in this direction and it seems that soon this problem may become tractable.

    The method of Martonak et al. (2003) seems promising and using it Oganov et al. (inprep.) have been able to predict, at a fully ab initio level, several highpressure forms of MgSiO3. Since the problem of structure type prediction is still far from its solution, here we review what can be done once the structure type is known – e.g., how accurate the theoretically optimised structures are, how accurate the predicted simulations helped to resolve several important problems in mineral sciences.

Purchase Chapters

Recommended Reading