Phase Transitions In Minerals Research Articles

Phase transitions in minerals: strain and elasticity

Phase transitions in minerals: strain and elasticity

Rigid unit modes in crystal structures with octahedrally coordinated atoms

The rigid unit mode analysis was initially developed to understand the phase transitions in aluminosilicate minerals containing corner-linked tetrahedra. Here the model is applied to a range of minerals with crystal structures that can be described as frameworks of linked octahedral and tetrahedral units, including garnet, sillimanite, titanite, and ellenbergerite. Consistent with a constraint analysis, there are no rigid unit modes in these minerals. Generalizing these results suggests that there will not be any easy ways to distort structures that have frameworks containing octahedral units. This result explains why polyhedraltilting displacive phase transitions are not common in such minerals, whereas they occur in most aluminosilicate minerals containing only tetrahedral units. It also explains that it will be necessary for the tetrahedra and octahedra to distort when solid solutions are formed.

高温高圧下におけるマントル鉱物の相転移とその熱力学的性質

This paper reviews the author's studies on phase transitions of mantle minerals at high pressures and high temperatures. Two experimental techniques, high-pressure high-temperature experiment and calorimetry, have been applied to clarify the phase transitions and thermodynamic properties of mantle minerals. The author's researches are described in the trend of mineral physics studies in recent decades. Current status and future development in mineral physics are also briefly discussed.

Relationship between order-disorder and elastic phase transitions in framework minerals

Abstract Two processes are important in the high-temperature behaviour of many framework silicates: (1) order/disorder of tetrahedral cations in the framework, (2) elastic instabilities of the framework itself. These processes frequently couple via a common strain. The nature and effect of such coupling is considered for albite, cordierite and leucite. There is a stark contrast in the dependence of macroscopic spontaneous strain in each of these minerals: while Q and Qod are strongly coupled in albite, the high-temperature behaviour of Q in leucite seems independent of Qod. Leucite analogues, such as K2MgSi5O12, show strong strain—order/disorder interactions, however, and illustrate the importance of the size of the ordering cations on the interaction between Q and Qod. Results for the kinetic controlled ordering of K-bearing cordierite emphasize the role chemical inhomogeneity has in enhancing the development of tweed microstructures.

Physico-mechanical property changes associated with mineral phase transition in granite

Variations in elastic wave velocity, low-frequency internal friction and acoustic emission in granite were experimentally studied as a function of temperature. It is found that the wave velocity and Young’s modulus tend to decrease with temperature. In association with theα — β transition of quartz a sharp internal friction peak can be recognized accompanied by a drastic drop in wave velocity and modulus and by a second peak of acoustic emission rate.

Calculations of pressure-induced phase transitions in mantle minerals

The crystal structures and energies of SiO2 stishovite, MgO periclase, Mg2SiO4 spinel, and MgSiO3 perovskite were calculated as a function of pressure with the polarization-included electron gas (PEG) model. The calculated pressures of the spinel to perovskite phase transitions in the Mg2SiO4 and MgSiO3 systems are 26.0 GPa and 27.0 GPa, respectively, compared to the experimental zero temperature extrapolations of 27.4 GPa and 27.7 GPa. The two oxide phases are found to be the most stable form in the pressure range 24.5 GPa to 31.5 GPa, compared to the experimental zero temperature extrapolation of 26.7 GPa to 28.0 GPa. The volume changes associated with the phase transitions are in good agreement with experiment. The transition pressures calculated with the PEG model, which allows the ions to distort from spherical symmetry, are in much better agreement with experiment than those calculated with the modified electron gas (MEG) model, which constrains the ions to be spherical.

Phase Transitions in Minerals: From Equilibrium Properties Towards Kinetic Behaviour Progress Report

Landau theory is derived from a simple atomistic model. The Gibbs free energy can be written in the displacive limit as where Ts = 1/2Θs is the saturation temperature due to quantum fluctuations. The coefficients A, B,… and degeneracies of the order parameter are determined by the conventional symmetry constraints. For T > Θs, G is the classic Landau potential. Solutions for non-displacive systems and coupled order parameters are discussed. – The theory is applied to some model-minerals such as quartz, Na-feldspar, and calcite as typical examples. It is argued that the structural complexity of minerals is often related to several thermodynamic degrees of freedom. The transition leads to coupling phenomena, which are reviewed in some detail. – Non-equilibrium features in crystals which are “nearly” in thermodynamic equilibrium are domain walls. It is shows that domain walls react very sensitively to small changes in the thermodynamic state of the material. New structural configurations are generated in the wall which do not exist in the bulk. – Kinetic processes with continuous order parameters can be analysed using a general rate equation which contains δG/δQ (G is often a Landau potential, Q is the order parameters) as a driving force. This theory draws, thus, a connection between the equilibrium Landau-type theories and kinetic rate theories.

Constitution of the mantle. 2. Petrological models of transition zone based on FMS phase diagram

Abstract A detailed picture is presented of phase transformations in the mantle transition zone, based upon the study of phase relations and topologies in the FeOMgOSiO2 (FMS) system. The (P - T)x diagram for the composition close to pyrolite (SiO2 = 40 mol.% and Fe/(Fe + Mg) = 0.12) is used in modelling the structure of the mantle transition zone, to connect phase transitions in minerals to the observed seismic discontinuities. The mineralogical nature of the first seismic discontinuity, at a depth of about 400 km, is associated either with a univariant transformation Px + α + γ → α + β + Px or with a sharp divariant transformation α + Px → α + β + Px → β + Px, which should be closer to 420 km. For the fixed composition close to pyrolite at a depth of about 650 km neither univariant nor invariant equilibria are observed in the FMS system. It has been found that, in the FMS system, two extremely narrow (1–2 km wide) stability fields of divariant mineral assemblages γ + Pv + St and γ + Pv + Mw, separated by a trivariant zone γ + Pv (about 5 km wide) might be responsible for the nature of the 650 km discontinuity. Because of the negative slope of the phase boundaries, the second seismic discontinuity in the cold subducting slab is deeper than in the surrounding mantle.

A silica-rich sodium pyroxene phase with six-coordinated silicon

Phase transitions in minerals and melts that involve a change in the coordination of silicon from fourfold to sixfold are generally accompanied by large changes in material properties such as density, bulk modulus and elastic moduli. When such transformations occur within the Earth, these large changes in material properties can result in seismic discontinuities. The presence of six-coordinated silicon in minerals such as majorite garnet at upper-mantle pressures is therefore of crucial importance to an understanding of the properties of this region of the Earth. The silicate pyroxenes are also believed to comprise a significant portion of the upper mantle1, and to provide a host for large cations such as sodium and calcium. It has long been assumed that silicon is restricted to the tetrahedral sites within the pyroxene structure. Here, however, we report the high-pressure synthesis and characterization of single crystals of a pyroxene of nominal stoichiometry Na(Mg0.5Si0.5)Si2O6, which is the first pyroxene known to contain both tetrahedrally and octahedrally coordinated silicon.

The spread of subducted lithospheric material along the mid-mantle boundary

Studies of phase transitions in silicate minerals at high temperatures and pressures suggest that the bulk density of subducted lithosphere at the mid-mantle boundary is intermediate between the densities of the upper and lower mantle. We argue that, if this is the case, then the lithospheric material will intrude along the mid-mantle boundary driven by buoyancy forces resulting from the compositional density differences between the intrusion and its surroundings. The rate of spread of the intrusion is given by a balance between these buoyancy forces and the viscous resistance of the mantle to motion. Using results from our recent studies of the fluid mechanics of such viscous gravity currents, we find that lithospheric material can propagate between one thousand and two thoudand kilometres in a hundred million years and can cover the entire boundary in one to six billion years. This spreading may be reflected in the global distribution of the isotopic characteristics of oceanic basalts.

The effect of material parameters on the shape of the phase separation surfaces within the earth's mantle

The effects of compressibility, thermal expansion and changes in entropy of transformations on the shape of a phase equilibrium curve (the Clausius-Clapeyron curve) have been studied. The curve has been found to take a dimensionless polynomial form and to conform to the following relations y=Cx(1 + ax + bx 2), x=(T−T 0)/T 0, y=(P−P 0)/P 0 where P 0 and T 0 denote reference point coordinates, and coefficients C, a, b are constants dependent on material factors. Based on data from the literature, the phase equilibrium equation appears to take the following forms for the selected mineral transitions ( P in GPa, T in kelvins): 1. (a)|for Mg 2SiO 4: olivine → spinel P=7.82 + 4.57 X 10 -13T−0.70X10 -6T 2+0.007X10 -9T 3,700 K<T<2000 K 2. (b)|for Mg 2SiO 4 → SiO 2 + 2 MgO (spinel → oxides) P=25.95 − 2.81 X 10 -3T+0.89 X 10 -6T 2+0.059 X 10 -9T 3,700 K<T<2000 K 3. (c)|for quartz → coesite P=1.42 + 1.27 X 10 -3T−0.69 X 10 -6T 2+0.78 X 10 -9T 3,600 K<T<1600 K It is concluded on the basis of calculations of mineral phase transitions taking place in the Earth's mantle that the influence of compressibility and thermal expansion should not be neglected. It is insignificant in the olivine → spinel transition, but in the quartz → coesite transition or spinel decomposition it is essential. Moreover, compressibility and thermal expansion shift the minimum of the Clausius-Clapeyron curve, e.g., in the spinel → oxides decomposition (Fig. 3b). Based on the equations for the phase equilibrium curves, the different shapes possibly taken by the phase separation surfaces in the Earth's mantle within the descending slab and its surroundings have been discussed. Of special interest are the olivine → spinel transition in which the surface is shaped as an upward convexity about 60 km high, and the surface of the spinel → oxides transition which is almost unaffected by the descending slab.

鉱物の相変化の過程と機構

鉱物の相変化の過程と機構

Phase Transition of Silicate Minerals under High Temperature and High Pressure and the Structure of the Earth's Mantle

Phase Transition of Silicate Minerals under High Temperature and High Pressure and the Structure of the Earth's Mantle