SiO2 Polymorphs Research Articles

Crystal structure prediction and simulations of structural transformations: metadynamics and evolutionary algorithms

Crystal structure prediction is the central problem of computational crystallography and materials design. We review two recently proposed methodologies that address this problem: (1) metadynamics-based approach proposed by R. Martoňák, A. Laio and M. Parrinello, Phys. Rev. Lett. 90 075503 (2003) and (2) ab initio evolutionary algorithm USPEX developed by Glass and Oganov in 2004–2006. The two methods are largely complementary. Metadynamics enables studies of phase transformation mechanisms and can predict new crystal structures, but such simulations require a reasonable starting structure and rely on the choice of a relevant order parameter. Evolutionary simulations cannot find phase transformation mechanisms, but can very efficiently find the stable structure without any knowledge of possible crystal structure or order parameters driving phase transitions. We review several cases where these methods produced important new results: prediction of new phases of MgSiO3 in the Earth's lower mantle, elucidation of plastic behaviour of MgSiO3 phases in the Earth's D'' layer, phase transformation mechanisms of SiO2 polymorphs, prediction of new high-pressure phases of CaCO3, elemental sulphur and carbon. Further developments of the two methods are outlined.

A computational study into the viability of new molecular materials polymorphs based on fully-coordinated inorganic nanoclusters

Spanning the gap between continuously bonded bulk phases and molecular materials, the possibility of employing defect-free fully-coordinated nanoclusters as novel crystal building blocks is computationally explored for the case of SiO2 polymorphs.

Importance of Mineralogical Data for Influencing Properties of Coke: a Reference on Si02 Polymorphs

SiO2 occurs in coking coals as pure quartz and also in complex aluminosilicates. At coking temperatures, pure SiO2 has several polymorphs (α‐ and β‐quartz and β‐tridymite) and transformations from one to another are accompanied by volume changes in the mineral matter that can lead to the formation of cavities and cracks in a coke matrix. These can weaken the coke physical strength and lead to a higher circulation of gases within the pieces. The grain size of the primary quartz crystals in a coal blend is also important for the estimation of coke strength: the larger the crystals that occur in a coal, the larger the cavities and cracks that will ensue (weaker coke). The occurrence of any given SiO2 polymorph indicates the temperature of its formation and can be used to correlate other changes in coke‐forming compounds with certain temperatures. A high amount of free quartz in a coal blend can be considered a negative factor for coking. For a better understanding of the influence of bulk SiO2 on coke quality, mineralogical (phase) analysis and quartz grain size measurements on coking coals can be helpful. Under the blast furnace conditions, SiO2 polymorphs have no substantial influence on the coke physical strength.

Origin of SiO 2-rich components in ordinary chondrites

Silica-rich objects are common minor components in ordinary chondrites (OC), occurring as fragments and as chondrules. Their typical paragenesis is orthopyroxene + SiO 2 (with bulk SiO 2 >65 wt%) and occasionally with additional olivine and/or spinel. Individual silica-rich components (SRC) have previously been studied in various types of OCs, although there is only one comprehensive study of these objects by Brigham et al. [Brigham, C.A., Murrell, M.T., Yabuki, H., Ouyang, Z., El Goresy, A., 1986. Silica-bearing chondrules and clasts in ordinary chondrites. Geochim. Cosmochim. Acta 50, 1655–1666]. Several different explanations of how SRCs formed have been published. The main question is how silica-enrichment was achieved, because CI-chondritic atomic Mg/Si-ratio is 1.07 and as a consequence only olivine and pyroxene, but no free silica should be stable. There are two basic possibilities for the SiO 2-enrichment: (1) a RedOx-mechanism or magmatic fractionation on the parent body and (2) fractional condensation or recycling of chondrule mesostasis in the solar nebula. To better constrain the origin of these objects, we measured major and rare earth elements in SRCs of various types of ordinary chondrites, and in addition, we studied silica polymorphism in these objects using an in situ micro-Raman technique. Bulk chondrule compositions define mixing lines between the compositions of olivine and pyroxene. The SRCs extend these lines to an SiO 2 end member. In contrast, magmatic trends grossly deviate from these mixing lines. Concentrations of CaO, Al 2O 3, and REE in the pyroxenes of the SRCs are low (0.01 to 1× CI) and the CI-normalized REE-patterns are virtually flat, typical of bulk chondrules, but untypical of magmatic trends. We therefore conclude that SiO 2-rich objects are not of magmatic origin. They are the result of fractional condensation in the solar nebula. The silica in SRCs occurs mainly as tridymite and sometimes as cristobalite or—in very rare cases—as quartz. Some SiO 2-phases yielded a yet unknown micro-Raman spectrum, which we were unable to identify. The often chondrule-like shape of SRCs as well as the presence of high-temperature SiO 2-polymorphs lead to the following model for the origin of SRCs: formation of SiO 2-rich precursors in the solar nebula by fractional condensation, reheating to temperatures between 1140 and >1968 K, thereby forming the SRCs,—probably during the chondrule-forming process—followed by rapid cooling.

The Zakłodzie enstatite meteorite: Mineralogy, petrology, origin, and classification

The Zaklodzie meteorite was found in September 1998, about 40 km west of Zamośc, in southeast Poland. Macroscopic and microscopic observations (in transmitted and reflected light), microprobe analyses, cathodoluminescence images, and X-ray diffraction data show that the meteorite is composed of clino- and orthoenstatite, two generations of feldspars, relict olivine (forsterite), a polymorph of SiO2 (apparently cristobalite), and opaque minerals: Fe-Ni alloy (kamacite and taenite), troilite, schreibersite, graphite, and sulfide (Mg, Mn, Fe)S, which is probably keilite. The texture is fine- to inequigranular of cumulate type, locally intergranular. The MgS-FeS thermometer indicates that the sulfides crystallized at ~580-600 oC. Thus, the Zaklodzie meteorite formed by the nearly complete melting of an enstatite chondrite protolith, probably at ~4.4 Ga; the process was likely caused by the decay of the 26Al nuclide in the planetesimal interior. The second stage of its evolution, which could have happened at ~2.1 Ga, involved partial re-melting of most fusible components, probably due to collision with another body. The structure, composition, and origin of the meteorite and its relation to the parent rock indicate that Zaklodzie may represent a primitive enstatite achondrite.

Molecular dynamics study of the high‐temperature elasticity of SiO2 polymorphs: Structural phase transition and elastic anomaly

AbstractThe elastic properties of cristobalite and quartz, the typical polymorphs of SiO2, are studied with particular emphasis on the structural phase transition and the high‐temperature phase. Using the equilibrium molecular dynamics (MD) method with a stress‐fluctuation formula, we have successfully evaluated the adiabatic elastic constants (Cij) of both cristobalite and quartz in a wide temperature range, including the α–β phase‐transition region. In the results for cristobalite, the anomalous property of a negative Poisson's ratio appears over the entire temperature range of 300–1800 K, where the bulk modulus is extremely low compared with the shear modulus. However, the mechanisms differ between the α‐ and β‐phases, according to the structural data obtained from the MD simulations. On the other hand, quartz exhibits a negative Poisson's ratio in the narrow temperature region between ca. 750 and 825 K before the phase transition occurs. After the transition to the β‐phase, the bulk modulus is shown to increase sharply, and a positive value of Poisson's ratio is recovered. For cristobalite as well as quartz, we have confirmed that the recovery of bulk Cij's in the β‐phase can be attributed to internal relaxations, which arise from the cooperative motions of corner‐linked SiO4 tetrahedra. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Molecular volume dependence of the electronic and ionic polarizabilities in TiO2 and SiO2

The molecular volume dependence of the ionic and electronic parts of the molecular polarizability in SiO2 and TiO2 polymorphs is examined. It is demonstrated that their variation should not be neglected when using models such as the “additivity rule” to predict multicomponent oxide dielectric constants.

Computational DFT Study of ZrSiO4 Polymorphs: Microelectronic, Nuclear Safety and Geological Implications

AbstractZirconium silicate is an extremely durable materials with the variety of useful optical and electronic properties and broad range of existing and potential applications. Using Density Functional Theory (DFT) in local density approximation (LDA) and generalized gradient approximation (GGA) with plane wave (PW) basis set we have revealed eight new polymorphs of ZrSiO4 within the energy range ∼1 eV above the most stable zircon which have higher and lower density than experimentally known zircon and reidite. Two structures, which have both silicon and zirconium atoms six-fold coordinated, orthorhombic AlTaO4-like (alumotantite) and monoclinic PbWO4-like (raspite), have similar energies at GGA level ∼0.35 eV above reidite and density intermediate between zircon and reidite. Among two low-density structures, which can be potentially revealed experimentally in the nanocrystalline thin films, the orthorhombic CaSO4-like form has energy similar to reidite but much lower density. We also conducted a comparative study of existing ZrO2 and SiO2 polymorphs, which demonstrates the higher accuracy of GGA approach.

High-temperature structure and dynamics of coesite (SiO2) from numerical simulations

The 1-bar structure and properties of the high-pressure SiO2 polymorph coesite have been simulated by lattice and molecular dynamics up to 1600 and 2100 K, respectively. In agreement with available experimental data, the monoclinic structure was found metastable (with respect to cristobalite or SiO2 liquid) up to the highest temperatures investigated. Thermal expansion of coesite is small because of restricted rotations of SiO4 tetrahedra. Above about 1000 K, the structure of coesite becomes dynamically disordered and similar to those reported for the β-phases of quartz and cristobalite. Disorder sets smoothly, however, in contrast to its abrupt onset in quartz and cristobalite, which have α–β transitions. The radial distribution functions for all bond distances indicate that order then prevails only for the nearest neighbors whereas the angle distributions widen markedly so that the monoclinic form of coesite with an Si–O–Si angle of 180° is only a time-averaged structure.

Geothermobarometry of UHP and HP eclogites and schists – an evaluation of equilibria among garnet–clinopyroxene–kyanite–phengite–coesite/quartz

AbstractGeothermometry of eclogites and other high pressure (HP)/ultrahigh‐pressure (UHP) rocks has been a challenge, due to severe problems related to the reliability of the garnet–clinopyroxene Fe–Mg exchange thermometer to omphacite‐bearing assemblages. Likewise, reliable geobarometers for eclogites and related HP/UHP rocks are scarce. In this paper, a set of internally consistent geothermobarometric expressions have been formulated for reactions between the UHP assemblage garnet–clinopyroxene–kyanite–phengite–coesite, and the corresponding HP assemblage garnet–clinopyroxene–kyanite–phengite–quartz. In the system KCMASH, the end members grossular (Grs) and pyrope (Prp) in garnet, diopside (Di) in clinopyroxene, muscovite (Ms) and celadonite (Cel) in phengite together with kyanite and coesite or quartz define invariant points in the coesite and quartz stability field, respectively, depending on which SiO2 polymorph is stable. Thus, a set of net transfer reactions including these end members will uniquely define equilibrium temperatures and pressures for phengite–kyanite–SiO2‐bearing eclogites. Application to relevant eclogites from various localities worldwide show good consistency with petrographic evidence. Eclogites containing either coesite or polycrystalline quartz after coesite all plot within the coesite stability field, while typical quartz‐bearing eclogites with no evidence of former coesite fall within the quartz stability field. Diamondiferous coesite–kyanite eclogite and grospydite xenoliths in kimberlites all fall into the diamond stability field. The present method also yields consistent values as compared with the garnet–clinopyroxene Fe–Mg geothermometer for these kinds of rocks, but also indicates some unsystematic scatter of the latter thermometer. The net transfer geothermobarometric method presented in this paper is suggested to be less affected by later thermal re‐equilibration than common cation exchange thermometers.

Hypothetical Uninodal Zeolite Structures: Comparison of AlPO4 and SiO2 Compositions Using Computer Simulation.

A total of 126 hypothetical zeolite structures have been modeled in the composition AlPO4. The framework topologies are those derived by tiling theory and comprise uninodal structures based on simple or quasi-simple tilings. Atomistic calculations have been used to optimize and evaluate each structure, and compare it to that of the SiO2 polymorph possessing the same topology. Characteristic properties including relative lattice energies, framework density, coordination sequences, accessible volumes, surface areas, average bond distances and angles, and the degree of distortion of the TO4 tetrahedra were calculated. The AlPOs are found to be more stable relative to berlinite than the zeolites are relative to quartz. The AlPO and SiO2 polymorphs show the same relationships between framework density and lattice energies, as well as between framework density and accessible volume, enabling us to predict whether individual hypothetical AlPO/silica polymorphs can be expected to be thermodynamically feasible. We...

Age and temperature of shock metamorphism of Martian meteorite Los Angeles from (U-Th)/He thermochronometry

Mineralogic features attributed to impact-induced shock metamorphism are commonly observed in meteorites and terrestrial impact craters. Partly because the duration of shock metamorphism is very short, constraining the timing and temperature of shock events has been problematic. We measured (U-Th)/He ages of single grains of merrillite and chlorapatite from the Martian meteorite Los Angeles (LA). Merrillite and chlorapatite ages cluster at 3.28 6 0.15 Ma (2s) and 2.18 6 0.19 (2s) Ma, respectively. The mean age of the merrillites, which are larger than chlorapatites, is indistinguishable from cosmic-ray exposure ages (3.1 6 0.2 Ma), suggesting that impact-induced shock metamorphism was coeval with ejection of the LA precursor from Mars. To constrain the initial temperature of shock metamorphism in the LA precursor body, we modeled diffusive loss of He from merrillite as a function of diffusion domain size, LA precursor body size, and ablation depth. From these calculations, we suggest that the metamorphic temperature of the shock event was higher than 450 8C. These results support the idea that shock pressures of the Martian meteorite Shergotty were higher than 45 GPa, as inferred from the presence of post-stishovite SiO2 polymorphs. Single-grain (U-Th)/He dating of phosphates may provide unique constraints on the timing and pressure-temperature dynamics of shock metamorphism in a wide variety of extraterrestrial materials.

Hypothetical Uninodal Zeolite Structures: Comparison of AlPO4 and SiO2 Compositions Using Computer Simulation

A total of 126 hypothetical zeolite structures have been modeled in the composition AlPO4. The framework topologies are those derived by tiling theory and comprise uninodal structures based on simple or quasi-simple tilings. Atomistic calculations have been used to optimize and evaluate each structure, and compare it to that of the SiO2 polymorph possessing the same topology. Characteristic properties including relative lattice energies, framework density, coordination sequences, accessible volumes, surface areas, average bond distances and angles, and the degree of distortion of the TO4 tetrahedra were calculated. The AlPOs are found to be more stable relative to berlinite than the zeolites are relative to quartz. The AlPO and SiO2 polymorphs show the same relationships between framework density and lattice energies, as well as between framework density and accessible volume, enabling us to predict whether individual hypothetical AlPO/silica polymorphs can be expected to be thermodynamically feasible. We...

Extreme crustal oxygen isotope signatures preserved in coesite in diamond.

The anomalously high and low oxygen isotope values observed in eclogite xenoliths from the upper mantle beneath cratons have been interpreted as indicating that the parent rock of the eclogites experienced alteration on the ancient sea floor. Recognition of this genetic lineage has provided the foundation for a model of the evolution of the continents whereby imbricated slabs of oceanic lithosphere underpin and promote stabilization of early cratons. Early crustal growth is thought to have been enhanced by the addition of slab-derived magmas, leaving an eclogite residuum in the upper mantle beneath the cratons. But the oxygen isotope anomalies observed in eclogite xenoliths are small relative to those in altered ocean-floor basalt and intermediate-stage subduction-zone eclogites, and this has hindered acceptance of the hypothesis that the eclogite xenoliths represent subducted and metamorphosed ocean-floor basalts. We present here the oxygen isotope composition of eclogitic mineral inclusions, analysed in situ in diamonds using an ion microprobe/secondary ion mass spectrometer. The oxygen isotope values of coesite (a polymorph of SiO2) inclusions are substantially higher than previously reported for xenoliths from the subcratonic mantle, but are typical of subduction-zone meta-basalts, and accordingly provide strong support for the link between altered ocean-floor basalts and mantle eclogite xenoliths.

First-principles calculation of vibrational Raman spectra in large systems: signature of small rings in crystalline SiO2.

We present an approach for the efficient calculation of vibrational Raman intensities in periodic systems within density functional theory. The Raman intensities are computed from the second order derivative of the electronic density matrix with respect to a uniform electric field. In contrast to previous approaches, the computational effort required by our method for the evaluation of the intensities is negligible compared to that required for the calculation of vibrational frequencies. As a first application, we study the signature of 3- and 4-membered rings in the Raman spectra of several polymorphs of SiO2, including a zeolite (H-ZSM-18) having 102 atoms per unit cell.

Carbonate-Bearing UHPM Rocks from the Tso-Morari Region, Ladakh, India: Petrological Implications

Evidence of ultrahigh-pressure metamorphism (UHPM) of subducted Indian continental crust in the form of carbonate-bearing coesite eclogite is preserved in the Tso-Morari Crystalline Complex (TMC) in eastern Ladakh, India. These eclogites, which occur as boudins in kyanite/sillimanite—grade rocks of the Puga Formation, contain essential mineral assemblages (garnet, clinopyroxeneomphacite, phengite, rutile, epidote-zoisite/clinozoisite and quartz), as well as coesite, talc, kyanite, magnesite, aragonite, dolomite, and Mg-calcite. Coesite, magnesite, and dolomite occur as inclusions in zoned garnet. The carbonate-bearing coesite eclogite underwent three stages of metamorphism—prograde, peak, and retrograde. The prograde assemblage is characterized by the presence of magnesite and a SiO2 polymorph, which is stable throughout the metamorphic process from the prograde to retrograde stage. At ultrahigh-pressure (27 kbar) and a temperature of 650°C, quartz transforms to coesite. Peak metamorphism was characterized by the development of coesite in garnet coexisting with high-Si phengite, clinopyroxene, magnesite, aragonite, dolomite, zoisite/clinozoisite, kyanite, and talc at a pressure of >39 kbar and temperature of >750°C. This is in good agreement with the estimated peak pressure and temperature judging from the composition of phengite, jadeite barometry, and garnet-clinopyroxene, garnet-phengite thermometry. Enstatite formed with talc and kyanite at a pressure of >31 kbar and temperature of 750°C. With a subsequent decrease in pressure, retrogression is constrained by the development of chlorite and chloritoid, which surround the garnet at a minimum pressure of 4-5 kbar and temperature of <500°C. Mineral assemblages in the carbonate-bearing coesite eclogite reveal that prograde metamorphism started with greenschist-facies conditions and reached the ultrahigh-pressure eclogite facies, passing through the intermediate blueschist facies. During UHP metamorphism, pressure abruptly doubled with a slight change of temperature, defining a geothermal gradient of 6–7°C/km. The UHP material was brought back to the surface along a path by rapid and almost isothermal exhumation.

Accurate first principles prediction of 17O NMR parameters in SiO2: assignment of the zeolite ferrierite spectrum.

17O NMR parameters, both the chemical shifts and the quadrupolar parameters, are calculated for SiO2 polymorphs using density functional theory with the generalized gradient-corrected PBE functional. The gauge including projector augmented wave (GIPAW) method (Pickard, C. J.; Mauri, F. Phys. Rev. B2001, 63, 245101) ensures the reproduction of all electron results while using computationally efficient pseudopotentials. The use of plane-waves permits fully converged calculations to be performed on structures containing 144 atoms in the unit cell, without the need to resort to the cluster approximation. The calculated NMR parameters of cristobalite, quartz, coesite, and faujasite are in excellent agreement with experimental data. This demonstrates that density functional theory is able to reproduce with high accuracy the 17O NMR parameters in SiO2 systems. This precision is used to assign the spectrum of the zeolite ferrierite. The data calculated for SiO2 are used to confirm that no simple correlation between the chemical shift and Cq NMR parameters and Si-O-Si angle exists, emphasizing the importance of predictive theories in this field.

Phase transitions and their effects on the thermal diffusivity behaviour of some SiO2 polymorphs

Thermal diffusivity is a material physical property important in all problems involving non-steady state heat transfer calculations, being a decisive parameter in the response of materials subjected to thermal shock. In this work it is presented a fundamental study related to how the phase transitions may influence the thermal diffusivity behaviour as a function of temperature in the phase transforming SiO2. The experimental technique employed was the flash thermal diffusivity technique, and measurements were carried out from 100 ºC up to approximately 1200 ºC. It was found a strong dependence on the thermal diffusivity with the high and low temperature forms of the quartz and cristobalite phases.

Characterization of a high-pressure phase of silica from the Martian meteorite Shergotty

Recently, there has been substantial interest in post-stishovite high-pressure polymorphs of SiO2, discovered as extraterrestrial minerals, or synthesized in the laboratory. Previous investigators reported the presence of “α-PbO2-like” and “baddeleyite-like” SiO2 in the Martian meteorite Shergotty, and also the synthesis of an a-PbO2-like phase at pressures of 60-80 GPa in a laser-heated diamond anvil cell. To provide definitive information about the nature of the natural “a-PbO2 phase,” we recovered a small sample from the Shergotty meteorite, obtained powder X-ray diffraction patterns, and performed a Rietveld refinement of the structure. The resulting cell parameters and space group are a = 4.097(1) Å, b = 5.0462(9) Å, c = 4.4946(8) Å, and Pbcn. The structure refinement confirms that this sample does have the α-PbO2 structure

Inelastic neutron scattering and lattice dynamics of minerals

This paper reviews the inelastic-neutron-scattering measurements and theoretical lattice-dynamics calculations, which have aimed at providing a microscopic understanding of the vibrational and thermodynamic properties of geophysically important minerals. In the last decade, detailed inelastic-neutron-scattering measurements supported by extensive model calculations have extended our knowledge of the nature of phonon-dispersion relations and density of states of minerals and their variations in various mineral phases in the Earth's mantle. An accurate understanding of these vibrational properties of minerals is crucial for predicting the phase transitions and thermodynamic properties of minerals at the pressures and temperatures prevalent in the Earth's mantle. The mineral studies reviewed here include the olivine end members forsterite and fayalite, the pyroxene end member enstatite, the garnet minerals pyrope, almandine, grossular and spessartine, the silicate perovskite MgSiO3, the mineral zircon, the aluminium-silicate minerals sillimanite, kyanite and andalusite, the layer silicates vermiculite and muscovite, the oxide minerals MgO, FeO, Al2O3 and the SiO2 polymorphs, and the carbonate minerals rhodochrosite and calcite. Inelastic-neutron-scattering measurements using reactors and spallation sources on single crystals and powder samples have provided data of their phonon-dispersion relations and density of states, which have been interpreted using theoretical calculations. While quantum mechanical ab initio calculations have been successfully employed to understand the vibrational properties of minerals like MgO, Al2O3, MgSiO3 perovskite etc ., theoretical studies of structurally more complex minerals have largely employed an atomistic approach involving semi-empirical interatomic potentials. The calculations enabled microscopic interpretations of the experimental data and have been very useful in providing an atomic-level understanding of the vibrational and thermodynamic properties of these minerals.