High-temperature Phase Relations Research Articles

Note on holographic torus stress tensor correlators in AdS3 gravity

In the AdS3/CFT2 framework, the Euclidean BTZ black hole corresponds to the dominant high-temperature phase of its dual field theory. We initially employ perturbative methods to solve the Einstein equations as boundary value problems, providing correlators for the energy-momentum tensor operator at low points. Utilizing operator equations established in our previous work, we further compute arbitrary high-point correlators for the energy-momentum tensor operator in the high-temperature phase and recursive relations for these high-point functions. Concurrently, we employ the Chern-Simons formalism to derive consistent results. Further, using the cut-off AdS/TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformed CFT duality, we calculate the energy-momentum tensor correlators, contributing to the comprehensive understanding of the system’s dynamics. Finally, stress tensor correlators enable us to ascertain the corresponding KdV operator correlators at low-temperature.

High-temperature phase relations of hydrous aluminosilicates at 22 GPa in the AlOOH-AlSiO3OH system

Abstract The stabilities of the minerals that can hold water are important for understanding water behavior in the Earth’s deep interior. Recent experimental studies have shown that the incorporation of aluminum enhances the thermal stabilities of hydrous minerals significantly. In this study, the phase relations of hydrous aluminosilicates in the AlOOH-AlSiO3OH system were investigated at 22 GPa and 1400–2275 K using a multi-anvil apparatus. Based on the X-ray diffraction measurements and composition analysis of the recovered samples, we found that the AlSiO4H phase Egg forms a solid solution with δ-AlOOH above 1500 K. Additionally, at temperatures above 1800 K, two unknown hydrous aluminosilicates with compositions Al2.03Si0.97O6H2.03 and Al2.11Si0.88O6H2.11 appeared, depend ing on the bulk composition of the starting materials. Both phases can host large amounts of water, at least up to 2275 K, exceeding the typical mantle geotherm. The extreme thermal stability of hydrous aluminosilicates suggests that deep-subducted crustal rocks could be a possible reservoir of water in the mantle transition zone and the uppermost lower mantle.

Phase equilibria and microwave dielectric properties in the ternary La2O3–TiO2–Nb2O5 system

High-temperature phase relations in the La2O3–TiO2–Nb2O5 ternary system were investigated at 1290 °C using SEM, EDS and XRD, and a subsolidus phase equilibrium diagram was constructed. It was demonstrated that the addition of the La1/3NbO3 to the La2O3:3TiO2 mixture completely stabilizes a perovskite-La2/3TiO3 compound, which is otherwise not stable at stoichiometric composition. On the other hand, a mixture La2O3:TiO2 =1:3 dissolves in La1/3NbO3 up to 15 mol% TiO2. Moreover, a newly defined composition of compound La30Ti16Nb4O87 formed in the La2O3-rich part of the system and a solid solution La3Ti5Nb10O39.5–La2Ti2Nb8O27 were proposed. In the binary subsystem LaTiNbO6-La0.462Ti0.386Nb0.614O3, the components exhibit opposite temperature dependence of resonant frequency in the microwave frequency range. Thus, the dielectric properties of the prepared ceramics can be tailored by varying the component concentration and thermally stable dielectric properties can be achieved for a composition with a LaTiNbO6/La0.462Ti0.386Nb0.614O3 molar ratio of 0.27.

High-pressure and high-temperature phase relations in the systems KAlSiO4-MgAl2O4 and CaAl2O4-MgAl2O4: Stability fields of NAL phases

Phase relations in the system KAlSiO4-MgAl2O4 were determined up to 28 GPa and 1500 °C. A hexagonal aluminous (NAL) phase is stable above 16 GPa with a narrow compositional range of (1-x)KAlSiO4·xMgAl2O4, x ≈ 0.61–0.65. The stability field of NAL phase in the CaAl2O4-MgAl2O4 system was also determined up to 29 GPa and 1200 °C, resulting in a compositional range of NAL phase of (1-x)CaAl2O4·xMgAl2O4, x ≈ 0.67–0.74. Compared with the above compositional widths of NAL phases, the stability field of NAL phase in the NaAlSiO4-MgAl2O4 system is much wider, (1-x)NaAlSiO4·xMgAl2O4, x ≈ 0.47–0.70 (Ono et al., 2009). The difference may be caused by the fact that both of Na+ and Mg2+ with similar cation sizes enter 6-fold trigonal prism sites in the NAL structure. In the system KAlSiO4-MgAl2O4, KAlSiO4 kalsilite and MgAl2O4 spinel coexist below ~8 GPa, above which an assemblage of MgAl2O4 spinel, corundum, K2Mg2Si2O7-rich phase X and pyrope becomes stable. The assemblage further changes into NAL phase at 16 GPa. These results and compositional similarity suggest that composite inclusions consisting of MgAl2O4-rich spinel and kalsilite-nepheline solid solution found in diamonds in the Juina-5 kimberlite, Brazil, were formed below ~8 GPa presumably by decomposition of K-rich NAL phase trapped in diamonds in the lower mantle conditions.

Thermodynamic properties of ZrSiO4 zircon and reidite and of cotunnite-type ZrO2 with application to high-pressure high-temperature phase relations in ZrSiO4

Enthalpies of high-pressure phase transitons in ZrSiO4 were measured by high-temperature drop-solution calorimetry. The enthalpies for the zircon-reidite transition in ZrSiO4 and for dissociation of reidite to cotunnite-type ZrO2 + SiO2 stishovite were obtained to be 27.5 ± 3.3 and 50.3 ± 3.0 kJ/mol, respetively, at 298 K. By thermal relaxation method, low-temperature isobaric heat capacities of ZrSiO4 reidite and cotunnite-type ZrO2 were measured, giving standard entropies at 298 K of 77.29 ± 0.04 and 49.10 ± 0.04 J/mol·K, respectively. Combining the measured enthalpies and entropies with other available thermophysical data, the transition boundaries in ZrSiO4 were calculated. The calculated zircon-reidite transiton boundary is consistent with that by in situ high-pressure expreiments by Ono et al. (2004a) within the errors. The calculated dissociation boundary of reidite has a smaller slope than that by high-pressure quench expreiments by Tange and Takahashi (2004). The equilibrium zircon-reidite transition pressure is calculated to be 8 GPa at 298 K, which is by 12–15 GPa lower than the transition pressures observed by room-temperature static compression experiments. Our results suggest that zircon transforms to reidite and dissociates into the two phases at 330 and 610 km depths, respectively, along the normal mantle geotherm. Combining the calculated phase relations with kinetics estimated from the first principles calculation may provide some insights to P, T conditions which reidites found in impact ejecta layers and craters experienced.

Experimental and thermodynamic investigations on the stability of Mg14Si5O24anhydrous phase B with relevance to Mg2SiO4forsterite, wadsleyite, and ringwoodite

High-pressure high-temperature phase relation experiments in Mg 14 Si 5 O 24 were performed using a 6-8 multi-anvil high-pressure apparatus in the pressure range of 12–22 GPa and temperature range of 1673–2173 K. We first found that Mg 14 Si 5 O 24 anhydrous phase B (Anh-B) dissociates to Mg 2 SiO 4 wadsleysite (Wd) and MgO periclase (Per) at about 18 GPa and 1873 K. From the results of the high-pressure experiments, the phase boundaries of 5 Mg 2 SiO 4 forsterite (Fo) + 4 Per = Anh-B and Anh-B = 5 Wd + 4 Per were determined. In addition, the isobaric heat capacity ( C P ) of Anh-B was measured by differential scanning calorimetry in the temperature range of 300–770 K and the thermal relaxation method using a Physical Property Measurement System (PPMS) in the range of 2–303 K. From the measured low-temperature C P , the standard entropy ( S ∘ 298.15 ) of Anh-B was determined to be 544.4(2) J/(mol·K). We also performed high-temperature X-ray diffraction measurements in the range 303–773 K to determine the thermal expansivity (α) of Anh-B. The obtained C P and α were theoretically extrapolated to higher temperature region using a lattice vibrational model calculation partly based on Raman spectroscopic data. Thermodynamic calculations by adopting the thermochemical and thermoelastic data for Anh-B obtained in this study and the estimated formation enthalpy for Anh-B of –13 208 kJ/mol gave phase equilibrium boundaries for 5 Fo + 4 Per = Anh-B and Anh-B = 5 Wd + 4 Per that were consistent with those determined by the present high-pressure high-temperature experiments. The results clarified that, in the Mg 14 Si 5 O 24 system, Anh-B is stable between 12 and 18 GPa at the expected temperatures of the Earth’s mantle.

High-pressure high-temperature phase relations in FeTiO3 up to 35 GPa and 1600 °C

Phase relations in FeTiO3 were precisely determined at 25–35 GPa and 600–1600 °C using multianvil high-pressure experiments with tungsten carbide anvils. Pressure generation up to about 36 GPa at 1600 °C was evaluated using Al2O3 solubility in MgSiO3 perovskite (Pv) in the system MgSiO3–Al2O3. At about 28 GPa, FeTiO3 Pv dissociates into an assemblage of calcium titanate (CT)-type Fe2TiO4 + orthorhombic-I (OI)-type TiO2 below 1200 °C. However, above 1200 °C at 28 GPa, FeTiO3 Pv decomposes into a new, denser phase assemblage of CT-type Fe2TiO4 + a new compound of FeTi2O5. The new phase FeTi2O5 was recovered as an amorphous phase at 1 atm. In situ X-ray diffraction experiments at 35.1 GPa indicated that the new phase (N-p) FeTi2O5 has orthorhombic symmetry with cell parameters a = 8.567(2) A, b = 5.753(1) A and c = 5.257(1) A. In addition, the assemblage of CT-type Fe2TiO4 + OI-type TiO2 changes to FeO wustite (Wu) + OI-type TiO2 at about 33 GPa below 1000 °C. The phase assemblages in FeTiO3 are denser in the order: FeTiO3 (Pv) → 1/2Fe2TiO4 (CT) + 1/2TiO2 (OI) → 1/3Fe2TiO4 (CT) + 1/3FeTi2O5 (N-p) → FeO (Wu) + TiO2 (OI). Our results indicate that the upper stability limit of FeTiO3 Pv is about 28 GPa at 600–1600 °C. This puts a constraint on peak shock pressure for formation of naturally discovered lithium niobate-type FeTiO3 which was interpreted to be retrograde transition product of FeTiO3 Pv on release of shock pressure.

Phase diagram of the Sr–Co–O system

Abstract The phase diagram of Sr–Co–O system was assessed based on the analysis of thermodynamic behavior of solid samples in air atmosphere. Samples of several compositions were prepared by standard ceramic route consisting of solid state reaction and sintering for long time periods followed by slow cooling to ensure the formation of thermodynamically stable phases. The equilibrated samples were then analyzed by DTA/TG and high temperature phase relations were studied by numbers of quenching experiments. The thermodynamic data of the involved phases were assessed based on the experimental results and the phase diagram for air atmosphere was calculated using the FactSage program.

Tetragonal almandine pyrope phase (TAPP): retrograde Mg-perovskite from subducted oceanic crust?

Laser heated diamond-anvil-cell experiments performed on a “tetragonal almandine pyrope phase” (TAPP) bulk composition constrain high-temperature phase relations between 6 and 48 GPa. Phase assemblages determined by synchrotron X-ray diffraction consist of TAPP + garnet ± pseudobrookite ± enstatite from 6 to 10 GPa, garnet from 13 to 22 GPa, Mg-perovskite + garnet from 23 to 30 GPa, and Mg-perovskite above 30 GPa. TAPP has the same structure at 1 atm and at high pressure based on in situ X-ray diffraction data, and is stable at a maximum pressure of 10–13 GPa at 1300–1700 K. These results rule out direct incorporation of TAPP in diamond at transition-zone or lower-mantle pressures. Possible origins of TAPP are (1) entrapment by diamonds in the upper mantle, and (2) retrograde formation from a high-pressure garnet or Mg-perovskite precursor. We suggest that single-phase TAPP inclusions and possibly composite TAPP-bearing inclusions originated as Mg-perovskite in the lower mantle in mafic protoliths, and that TAPP forms upon retrograde conversion at pressures below 13 GPa upon exhumation of the diamonds from the lower mantle to shallower depths of less than 400 km.

High-pressure and high-temperature phase transitions in FeTiO3 and a new dense FeTi3O7 structure

High-pressure and high-temperature phase relations of FeTiO 3 were investigated up to a pressure of about 74 GPa and 2600 K by synchrotron X-ray diffraction and analytical transmission electron microscopy. We conclude that FeTiO 3 ilmenite transforms into the following phase(s) with increasing pressure: FeTiO 3 (perovskite) at 20-30 GPa, Fe 2 TiO 4 (Ca 2 TiO 4 -type) + TiO 2 (OI-type) at 30-44 GPa and high temperature, FeO (wüstite) + TiO 2 (OI) at 30-44 GPa and low temperature, and wüstite + FeTi 3 O 7 (orthorhombic phase) above 44 GPa. Among these dense high-pressure polymorphs, FeTi 3 O 7 is a new compound and its structure analysis was tried using particle swarm optimization simulation. This method successfully found a new high-density FeTi 3 O 7 structure, and Rietveld refinement based on this model structure gave an excellent fit with the experimentally obtained X-ray diffraction pattern. This new high-density FeTi 3 O 7 structure consists of polyhedra for monocapped FeO 7 prisms, bicapped TiO 8 prisms, and tricapped TiO 9 prisms, which develop on the b-c plane and stack along the a axis. The dense compound assemblage found in FeTiO 3 is promising for investigating the behavior of ABX 3 compounds under ultrahigh pressures.

Crystal structure and high temperature phase relations of monoclinic and orthorhombic pyroxene-compounds MnGeO3: a comparison

Crystal structure and high temperature phase relations of monoclinic and orthorhombic pyroxene-compounds MnGeO3: a comparison

Microfabrication of controlled-geometry samples for the laser-heated diamond-anvil cell using focused ion beam technology

The pioneering of x-ray diffraction with in situ laser heating in the diamond-anvil cell has revolutionized the field of high-pressure mineral physics, expanding the ability to determine high-pressure, high-temperature phase boundaries and equations of state. Accurate determination of high-pressure, high-temperature phases and densities in the diamond-anvil cell rely upon collinearity of the x-ray beam with the center of the laser-heated spot. We present the development of microfabricated samples that, by nature of their design, will have the sample of interest in the hottest portion of the sample. We report initial successes with a simplified design using a Pt sample with dimensions smaller than the synchrotron-based x-ray spot such that it is the only part of the sample that absorbs the heating laser ensuring that the x-rayed volume is at the peak hotspot temperature. Microfabricated samples, synthesized using methods developed at The Ohio State University's Mineral Physics Laboratory and Campus Electron Optics Facility, were tested at high P-T conditions in the laser-heated diamond-anvil cell at beamline 16 ID-B of the Advanced Photon Source. Pt layer thicknesses of ≤0.8 μm absorb the laser and produce accurate measurements on the relative equations of state of Pt and PtC. These methods combined with high-purity nanofabrication techniques will allow for extension by the diamond-anvil cell community to multiple materials for high-precision high-pressure, high-temperature phase relations, equations of state, melting curves, and transport properties.

High-pressure high-temperature phase relations in MgAl2O4

High-pressure high-temperature phase relation experiments in MgAl2O4 were performed in the pressure and temperature ranges of 18-27 GPa and 1400-2500 °C using a Kawai-type multi-anvil high-pressure apparatus. It was clarified that MgAl2O4 spinel directly transforms to the Mg2Al2O5 + Al2O3 assemblage at about 20 GPa and temperature higher than 2100 °C. The experimental results indicates that the phase assemblage of Mg2Al2O5 + Al2O3 is stable in the P-T region of 20 < P < 25 GPa and T > 2000 °C. The crystal structure of the Mg2Al2O5 phase was refined by the Rietveld method using a structure model based on that of ludwigite. The calculated density of ρcalc = 3.801(1) g/cm3 for the Mg2Al2O5 phase is very consistent with the phase relations determined by the high-pressure high-temperature experiments.

High P-T phase relation of magnesian (Mg0.7Fe0.3) staurolite compositon in the system FeO-MgO-Al2O3-SiO2-H2O: Implications for prograde high-pressure history of ultrahigh-temperature metamorphic rocks

High-pressure and high-temperature phase relation on Mg 0.74 Fe 0.26 -staurolite composition with excess water in the system FeO-MgO-Al 2 O 3 -SiO 2 -H 2 O was experimentally determined at 12-19 kbar and 850-1050 °C, with a focus on the lower-pressure stability limit of magnesian staurolite. The experimental results show that the stability field of staurolite in the system shifts to higher temperatures as compared to that of pure-Mg staurolite. At 950 °C, the lower-pressure stability limit is located between 15 and 14 kbar. This study demonstrates that staurolite breaks down with isothermal decompression by a series of reactions at 950 °C: St → Opx + Crn + Melt and St + Opx → Spr + Melt. The Mg' [=Mg/(Fe+Mg)] of staurolite in the former reaction is 0.7. When staurolite coexists with orthopyroxene in run products, the staurolite Mg' is decreased to 0.6-0.5. Moderate-Mg staurolite (Mg' = ∼0.5) in natural occurrences has been reported as inclusion minerals in poikiloblastic garnets within ultrahigh-temperature (UHT) metamorphic rocks from major collisional orogenic belts in southern India and southern Africa. The experimental data presented in our study suggest the possibility that the staurolite-bearing UHT metamorphic rocks had experienced high-pressure metamorphism and/or UHT extreme metamorphism during the prograde metamorphic stage.

High-pressure–high-temperature phase relations ofMgGeO3: First-principles calculations

The high-pressure--high-temperature behavior of $\mathrm{Mg}\mathrm{Ge}{\mathrm{O}}_{3}$ has been investigated by first-principles computations. It is found that at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the first transformation from ilmenite to orthorhombic perovskite at $24--38\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ is followed by the second one to the $\mathrm{Ca}\mathrm{Ir}{\mathrm{O}}_{3}$ structure at $51--56\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Quasiharmonic free energy calculations suggest that the first transformation has a negative Clapeyron slope ($\ensuremath{-}9.3\phantom{\rule{0.3em}{0ex}}\mathrm{MPa}∕\mathrm{K}$ at $1000\phantom{\rule{0.3em}{0ex}}\mathrm{K}$), whereas the second one has a less temperature-sensitive positive Clapeyron slope ($+7.8\phantom{\rule{0.3em}{0ex}}\mathrm{MPa}∕\mathrm{K}$ at $1000\phantom{\rule{0.3em}{0ex}}\mathrm{K}$). It is also confirmed that the $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_{3}$ structure does not have its own stability $P,T$ conditions. Pressure dependence of the Goldschmidt tolerance factor indicates a clear correlation between distortion of the perovskite structure and relative stability of perovskite and postperovskite structures.

High-temperature phase relations and topological constraints in the quaternary system MgO-Al2O3-SiO2-Cr2O3: An experimental study

Phase relationships in the system MgO-Al 2 O 3 -SiO 2 -Cr 2 O 3 (MASCr) were investigated experimentally from 1250 to 1560 °C using a 1-atm vertical quench furnace on 12 oxide mixtures covering a wide range of chemical compositions. Spinel, corundum, mullite, and sapphirine were found to display a wide range of solid solutions toward CR-rich end-members, whereas enstatite, cordierite, forsterite, and glasses were always Cr-poor. Glasses formed in relatively MgO-rich bulk compositions from 1250 °C, in assemblage with cordierite, enstatite, forsterite, and spinel, suggesting a lowering of the eutectic minimum in MASCr compared to available melting relationships in the model system MAS. Although unexpected, the relatively low-temperature melting of Cr-bearing mixtures is supported by topological constraints in the subsystems SACr and MSCr. The extent of Cr solubility in mullite has been found to reach ~14 wt% at 1560 °C, and 33 wt% in sapphirine at 1340 °C, which are the highest Cr values reported so far for these minerals. Liquidus surfaces are constrained by glass compositions that are displaced systematically toward silica compared to corresponding liquids in the ternary system MAS. As a consequence, the primary crystallization fields of Cr-spinel, Cr-sapphirine, and Cr-mullite are found to face the cristobalite/tridymite primary fields. A tentative liquidus diagram for the system MgO-Al 2 O 3 -SiO 2 -Cr 2 O 3 is proposed, which could serve as a basis for the interpretation of the high-temperature evolution of planetary materials as well as for the development of new ceramic materials.

A high pressure and temperature phase relations in MgAl2O4

a high pressure and temperature phase relations in MgAl2O4

GASPARIK, T. 2003. Phase Diagrams for Geoscientists. An Atlas of the Earth's Interior. xi+462 pp. Berlin, Heidelberg, New York: Springer-Verlag. Price Euros 149.95 (plus VAT at local rate), SFr 242.50, £105.00, US $ 169.00 (hard covers). ISBN 3 540 00248 0

GASPARIK, T. 2003. Phase Diagrams for Geoscientists. An Atlas of the Earth's Interior. xi+462 pp. Berlin, Heidelberg, New York: Springer-Verlag. Price Euros 149.95 (plus VAT at local rate), SFr 242.50, £105.00, US $ 169.00 (hard covers). ISBN 3 540 00248 0 - Volume 142 Issue 2

High-Temperature Phase Relations in Selected MnO-CrOx-Containing Systems

Phase relations in the pseudobinary MnO-CrOx system were studied by the reaction of the individual oxides in the temperature range 1400°-1750°C under a reducing atmosphere with a CO:CO2 volume ratio of 4.8, yielding oxygen partial pressures in the range 10-9.98-10-6.97 atm. In the pseudoternary MnO-CrOx-containing systems that constitute the pseudoquaternary MnO-CrOx-CaO-SiO2 system, phase relations were determined only at 1500°C under an oxygen partial pressure of 10−8.99 atm. Characteristic of these MnO-CrOx-containing systems was the dominance of the (Mn,Cr)3O4 spinel phase.

Importance of fine ore chemical composition and high temperature phase relations: applications to iron ore sintering and pelletising

In the iron ore industry significant emphasis is placed throughout the mining process on meeting chemical composition specifications for the export of fine ores. However, little has been published on the implications of ore chemical composition for iron ore sinter and pellet product quality. The ore bulk composition and the nature of the minerals in the fine ore both play a critical role in determining the type of high temperature bonding phases that form during sintering and pelletising. This paper uses the experimental determination of phase relations in model sinter and pellet systems such as Fe2O3-CaO-SiO2 (FCS) and Fe2O3-Al2O3-CaO-SiO2 (FACS) to examine the links between iron ore chemical composition and the temperatures used during sintering and pellet firing. The phase relations help to establish the critical thermal and compositional parameters that control the bonding phase chemistry, which in turn influences the physical characteristics of the sinter or pellet matrix. Results show that lower Fe grade (<62%Fe) ores and concentrates will typically form SFCA as part of the final assemblage, medium grade (62-65%Fe) ores will form a mixture of SFCA and SFCA-I, while high grade (65-68%Fe) ores will form largely SFCA-I. The SFCA-I phase is the most desirable bonding phase in iron ore sinter and pellets since microstructures composed entirely of SFCA-I show higher physical strength and higher reducibility than microstructures composed predominantly of SFCA.