Equilibrium Phase Assemblages Research Articles

Rapid densification and reaction sequences in self-reinforced Y- α-SiAlON ceramics with barium aluminosilicate as an additive

Y- α-SiAlON (Y 1/3Si 10Al 2ON 15) ceramics with 5 wt.%BaAl 2Si 2O 8 (BAS) as an additive were synthesized by spark plasma sintering (SPS). The kinetic of densification, phase transformation sequences and grain growth during sintering process were investigated. Full densification could be achieved by 1600 °C without holding and using a heating rate of 100 °C min −1, but the transformation from α-Si 3N 4 to α-SiAlON is not completed simultaneously with the densification process. The equilibrium phase assemblage could be reached after SPS at 1800 °C for 5 min and the resultant material possesses self-reinforced microstructure with high hardness of 19.2 GPa and fracture toughness of 6.8 MPa m 1/2. The complete crystallization of BAS is beneficial to the high temperature mechanical properties. The obtained could maintain the room strength up to 1300 °C.

Composition and structure of hafnia films on silicon

Ellipsometry, electron microscopy, and x-ray photoelectron spectroscopy data indicate that, during HfO2 deposition onto silicon, the native oxide reacts with the HfO2 deposit to form an amorphous intermediate layer which differs in refractive index (≃1.6) from both HfO2 (1.9–2.0) and SiO2 (1.46). Thermodynamic analysis of the Si-SiO2-HfO2-Hf system shows that Si is in equilibrium with Si/HfO2 − y only at low oxygen pressures. Starting at a certain oxygen pressure (equivalent to the formation of a native oxide layer), the equilibrium phase assemblage is Si/HfSiO4/HfO2 − y.

THERIA_G: a software program to numerically model prograde garnet growth

We present the software program THERIA_G, which allows for numerical simulation of garnet growth in a given volume of rock along any pressure–temperature–time (P–T–t) path. THERIA_G assumes thermodynamic equilibrium between the garnet rim and the rock matrix during growth and accounts for component fractionation associated with garnet formation as well as for intracrystalline diffusion within garnet. In addition, THERIA_G keeps track of changes in the equilibrium phase relations, which occur during garnet growth along the specified P–T–t trajectory. This is accomplished by the combination of two major modules: a Gibbs free energy minimization routine is used to calculate equilibrium phase relations including the volume and composition of successive garnet growth increments as P and T and the effective bulk rock composition change. With the second module intragranular multi-component diffusion is modelled for spherical garnet geometry. THERIA_G allows to simulate the formation of an entire garnet population, the nucleation and growth history of which is specified via the garnet crystal size frequency distribution. Garnet growth simulations with THERIA_G produce compositional profiles for the garnet porphyroblasts of each size class of a population and full information on equilibrium phase assemblages for any point along the specified P–T–t trajectory. The results of garnet growth simulation can be used to infer the P–T–t path of metamorphism from the chemical zoning of garnet porphyroblasts. With a hypothetical example of garnet growth in a pelitic rock we demonstrate that it is essential for the interpretation of the chemical zoning of garnet to account for the combined effects of the thermodynamic conditions of garnet growth, the nucleation history and intracrystalline diffusion.

Activation energy and grain growth in nanocrystalline Y-TZP ceramics

Grain growth of nanocrystalline yttria-stabilized tetragonal zirconia polycrystals (Y-TZP) was studied between 1250 and 1650 °C and compared to the Y-TZP data from the literature. All the results exhibited two distinctly different behaviour, where slow and fast grain growth regimes with activation energies ∼280 and ∼546 kJ mol −1 prevail below and above ∼1400 °C, respectively. Analysis of the data with respect to the grain growth mechanisms and the diffusion kinetics was in agreement with limited Y 3+ lattice diffusion within the cubic zirconia nano-grains below ∼1400 °C. This results in slow grain growth kinetics. Redistribution of Y 3+ above ∼1400 °C together with the equilibrium phase assemblage lead to enhanced grain boundary diffusion of Y 3+ and results in enhanced grain growth of the sub-micrometer tetragonal grains.

Thermodynamic modelling in the ZrO2–La2O3–Y2O3–Al2O3system

AbstractThe thermodynamic database for the ZrO2– La2O3– Y2O3– Al2O3system has been derived using previous descriptions for the six binary systems and the ternary ZrO2– La2O3– Al2O3system. The parameters of the Y2O3– Al2O3system were adjusted due to changes in the Y2O3thermody-namic parameters. The thermodynamic parameters of the La2O3– Y2O3system were slightly changed to get consistency between calculations and new experimental results for the ZrO2– La2O3– Y2O3ternary system. Diverse kinds of phase diagrams of the ZrO2– La2O3– Y2O3and La2O3– Y2O3– Al2O3ternary systems have been calculated. The present thermodynamic description of the quaternary system is consistent with available experimental results for lower-order systems. It was used to calculate isoplethal sections for compositions related to thermal barrier coating (TBC) and its interaction with thermally grown oxide Al2O3. TheT0-lines have been calculated for diffusionless transformations between fluorite, tetragonal, monoclinic and pyrochlore phases in the ZrO2– LaO1.5system as well as driving forces for partitioning of non-equilibrium phase into equilibrium phase assemblages. These data could be applied for determination of desirable ranges of material composition for TBC.

Phase relations in the Ba–Y–Cu–O films on SrTiO3 for the ex situ BaF2 process

In situ x-ray diffraction was used to establish the phase relations in high-Tc superconductor Ba–Y–Cu–O films grown on SrTiO3 through the ex situ BaF2 process. These relations differ from bulk equilibrium phase assemblages in the BaO–Y2O3–CuOx system. In particular, BaY2CuO5 (the “green phase”), a common impurity phase in bulk processing, is absent in the films. Because of the absence of this green phase, the compositional stability field of Ba2YCu3O6+x expands considerably as compared to that of the bulk system, resulting in the tie lines Ba2YCu3O6+x–Y2O3 and Ba2YCu3O6+x–Y2Cu2O5.

Experimental data on Fe and Mg partitioning between coexisting sapphirine and spinel: an empirical geothermometer and its application

Specially designed experiments were carried out in the temperature range 950-1100 °C at 800 MPa to grow coexisting sapphirine and spinel-bearing metapelitic assemblages in the KFMASH system. Equilibrium phase assemblages contain these two phases with stoichiometric compositions. Compositional data obtained from the two coexisting phases indicate a strong dependence of the Mg-Fe distribution coefficient on temperature. An empirical thermometric expression has been formulated from the experimentally constrained relationship, lnKD = -6277/T(°K) + 6.4202, where KD = (XMg/XFe)Spr.(XFe/XMg)Spl. Application of this thermometer to natural mineral pairs indicate that earlier temperature estimates based on sapphirine-spinel need to be revised upward by 120-160 °C.

Crystallization conditions in the Upper Pollara magma chamber, Salina Island, Southern Tyrrhenian Sea

Pyroclastites erupted from the Upper Pollara magma chamber (13 ka, Salina Island, Aeolian Archipelago) resulted from mingling and mixing of rhyolitic and andesitic magmas. An experimental study has been conducted on the rhyolitic end-member to constrain the pre-eruptive conditions of the magma. In order to check for the role of mixing on the equilibrium phase assemblage, three different starting compositions, corresponding to three different mixing degrees, have been used. The crystallization experiments were conducted at two different oxygen fugacities and at variable temperature and fluid contents. The results indicate that the natural mineralogical assemblage can only be reproduced from a composition showing a certain degree of mixing. Assuming a pressure of 200 MPa (generally accepted for the Aeolian Islands), the pre-eruptive temperature of the magmas is estimated between 755 and 800 °C and the water content of the melt was higher than 4–4.5 wt.%.

Phase Equilibria Studies of Hf44.5Ti5Cu27Ni13.5Al10 and Hf44.5Nb5Cu27Ni13.5Al10

AbstractWe report the equilibrium phase assemblage of two bulk-metallic-glass-forming alloys, Hf44.5Ti5Cu27Ni13.5Al10 and Hf44.5Nb5Cu27Ni13.5Al10. Using thermal analysis, scanning electron microscopy, and x-ray microanalysis, we examined the phase equilibria of the major components - Hf, Cu, and Ni. We then examined the effect of additions or substitutions of Nb, Ti, and Al on equilibrium phase assemblage and melting behavior.

Phase equilibria of hydrated Portland cement

A model is described for predicting the equilibrium phase assemblage in hydrated Portland cement and for calculating the relative contents and composition of phases present in the assemblage, from the chemical composition of the cement and the water/cement ratio. The method is also used to calculate the content of capillary pores using the best available data for the densities for each of the phases. These calculations were carried out on three different Portland cements (two white Portland cements and one grey) at water/cement ratios of 0.70. Energy dispersive spectroscopy (EDS) analysis on the SEM was used to verify the presence of all phases predicted by the model. A density for the C-S-H phase of approximately 2.10 g/cm 3 and an evaporable water content in the C-S-H of approximately 19% provided the best agreement between the predicted values of chemical shrinkage, loss of ignition and content of evaporable water, and experimental data. Other results included compositional data on the C-S-H phase corresponding to molar ratios of Al/Ca=0.04 and S/Ca=0.03 in all cements investigated, and Fe/Ca=0.02 in the grey Portland cement.

Phase relations in silicic systems at one-atmosphere pressure

An important control on magma rheology is the extent to which the magma crystallizes during ascent as a result of the effective undercooling created by volatile exsolution. To assess this undercooling, we need to know the final (anhydrous) one-atmosphere phase relations of silicic magmas. For this reason, we have performed one-atmosphere controlled-fO2 crystallization experiments on dacitic to rhyolitic melt compositions (67–78 wt% SiO2) and determined equilibrium phase assemblages, melt fractions, and some phase compositions over a range of temperatures. Experiments were run at oxygen fugacities between NNO+1 and NNO+2 and temperatures of 1,000 to 1,250°C. Constant phase compositions and sample crystallinities in runs longer than 3.5 days suggest that these runs closely approached compositional equilibrium. Additionally, melting experiments with similar compositions yielded results closely resembling those obtained in crystallization experiments. All samples have liquidus temperatures between 1,250 and 1,200 °C, with plagioclase the liquidus phase for the two most mafic samples and quartz for the most silicic sample. When associated glass compositions are projected into the Qz-Ab-Or system they define a revised one-atmosphere quartz-feldspar cotectic 5–10% less quartz normative than previously estimated. Glass compositions from each sample plot along this cotectic between 1,100 and 1,000 °C, consistent with the plagioclase-quartz co-crystallization textures found in runs at these temperatures. This cotectic constrains glass compositions to a maximum silica content of 76±1 wt% SiO2. Reported glass compositions in excess of 77 wt% SiO2 in volcanic samples suggest non-equilibrium crystallization, perhaps a consequence of large melt undercoolings.

Reaction sequences occurring in dense Li-doped sialon ceramics: influence of temperature and holding time

Spark Plasma Sintering (SPS) has been used to consolidate a lithium-doped duplex α–β sialon with the overall composition Li0.5Si9.5Al2.5O2.0N14. The kinetics of densification has been studied, and the phase transformation, reactions and grain growth occurring in the dense compacts upon further heat treatment have been investigated. Two sources of Si3N4 powders were used, namely α- and β-Si3N4. Green bodies heated at a rate of 100 °C min−1 yielded fully dense compacts at 1450 °C (α-Si3N4) and 1500 °C (β-Si3N4) without holding, and these compacts consisted mainly of a locally formed liquid and precursor Si3N4 particles. Upon further heating it was observed that α-sialon is formed initially, irrespectively of whether α-Si3N4 or β-Si3N4 powder is used as Si3N4 source; and when α-Si3N4 is used as starting powder, almost monophasic α-sialon compacts are formed before any transformation to β-sialon takes place on further heating. When β-Si3N4 is used as starting powder the formation of β-sialon is kinetically promoted, and compacts containing α-sialon, β-sialon and β-Si3N4 are obtained before the equilibrium phase assemblage is reached, i.e. a lithium-doped duplex α–β sialon ceramic. These observations can be interpreted in terms of the Ostwald step rule. Grain growth does not occur until the equilibrium phase assemblage has been established. The separation of grain growth from densification and phase transformation has implications for preparing Si3N4-based nano-ceramics and provides possibility for further studies of the kinetics of grain growth in Si3N4-based ceramics.

Hydrothermal crystallization of ceramics

In broad terms, hydrothermal synthesis is a technology for crystallizing materials (chemical compounds) directly from aqueous solution by adept control of thermodynamic variables ( temperature, pressure and composition). The objective of this chapter is to introduce the field of hydrothermal materials synthesis and slow how understanding solution thermodynamics of the aqueous medium can be used for engineering hydrothermal crystallization processes. In the first section, we will focus on hydrothermal synthesis as a materials synthesis technology by providing history, process definitions, technological merits and comments on its current implementation in industry. In the second section, we will describe how thermodynamic modeling is being developed as an engineering tool to predict equilibrium phase assemblages and use this predictive power as an engineering tool for development of hydrothermal technology for materials synthesis.

Phase equilibria in the systems Fe 2 O 3 -MgO-TiO 2 and FeO-MgO-TiO 2 between 1173 and 1473 K, and Fe 2+ -Mg mixing properties of ilmenite, ferrous-pseudobrookite and ulvöspinel solid solutions

Detailed phase relations have been determined within the systems Fe2O3-MgO-TiO2 and FeO-MgO-TiO2. Experiments were performed over the temperature interval 1173–1473 K by equilibrating pelletized, fine-grained oxide mixtures in either inert calcia-stabilized zirconia pots (Fe2O3-MgO-TiO2 system) or evacuated silica tubes (FeO-MgO-TiO2 system). Equilibrium phase assemblages were determined by combined optical microscope, X-ray diffraction and EMP examination. Phase relations in the Fe2O3-MgO-TiO2 ternary are dominated by the instability of the M2O3 solid solution relative to the phase assemblage M3O4 + M3O5. A miscibility gap along the M2O3 binary also gives rise to two, 3-phase fields (α-M2O3 + M3O5 + M3O4 and α′-M2O3 + M3O5 + M3O4) separated by the M3O4 + M3O5 phase field. Phase relations in the FeO-MgO-TiO2 ternary were divided into two sub-systems. For the FeTiO3-MgTiO3-TiO2 sub-ternary, there is complete solid solution along the M2O3 and M3O5 binary joins at high temperature. At low temperatures (T < 1373 K) the M3O5 pseudobrookite solid solution decomposes to M2O3 + TiO2. Increasing the concentration of MgO in M3O5 phase results in a decrease in the temperature at which M3O5 becomes unstable and compositional tie lines linking M2O3 and TiO2 fan out, before the appearance of a three-phase region where M2O3, M3O5, and TiO2 coexist. Within the expanded FeO-MgO-TiO2 system, at temperatures above ∼1273 K there is a continuous solid solution along the M3O4 binary. At low temperatures (T < 1273 K) the Mg2TiO4 end-member breaks down to MgO and MgTiO3. The M3O4 phase shows significant non-stoichiometry, down to at least 1173 K. Fe2+-Mg partitioning data were obtained for coexisting M2O3-M3O5 and M2O3-M3O4 pairs in the FeO-MgO-TiO2 ternary. Assuming a regular solution mixing model for all phases, the M2O3 and M3O4 solid solutions were both found to exhibit moderate positive deviations from ideality (∼2600 J/mol), whereas the data for the M3O5 binary suggest close to ideal behaviour.

Free Energy Minimization by Simulated Annealing with Applications to Lithospheric Slabs and Mantle Plumes

An optimization algorithm based upon the method of simulated annealing is of utility in calculating equilibrium phase assemblages as functions of pressure, temperature, and chemical composition. Operating by analogy to the statistical mechanics of the chemical system, it is applicable both to problems of strict chemical equilibrium and to problems involving metastability. The method reproduces known phase diagrams and illustrates the expected thermal deflection of phase transitions in thermal models of subducting lithospheric slabs and buoyant mantle plumes. It reveals temperature-induced changes in phase transition sharpness and the stability of Fe-rich γ phase within an α + γ field in cold slab thermal models, and it suggests that transitions such as the possible breakdown of silicate perovskite to mixed oxides can amplify velocity anomalies.

Phase relations in the Cu 2 S-PbS-Sb 2 S 3 system; an experimental appraisal and application to natural polymetallic sulfide ores

The system Cu 2 S-PbS-Sb 2 S 3 has been experimentally studied at 500 degrees , 440 degrees , and 300 degrees C by the evacuated silica tube (+ or - halide flux) technique. Additionally, the ambient sulfur fugacity of equilibrium phase assemblages has been monitored by the two-pyrrhotite indicator method. Contrary to the earlier results of Hoda and Chang (1975), the extents of solid solubility in meneghinite and phase Z are distinctly smaller and the Cu 2 S- and Sb 2 S 3 -rich melt fields at 500 degrees C are more extensive. There is also a marked shift in the position of the Cu 2 S-rich melt field. The meneghinite field gradually tapers down away from its PbS-rich end to the Sb 2 S 3 -rich end and the Cu 2 S-poor boundary moves away from the PbS-Sb 2 S 3 binary with increasing Sb 2 S 3 . The earlier claim that tintinaite is the natural analogue of phase Z is corroborated. Falkmanite appears as a distinct phase at 500 degrees and 440 degrees C. Cu-free meneghinite can possibly be stable at a temperature > or = 550 degrees C. The absence of meneghinite and phase Z at 300 degrees C is a major deviation from the earlier study of Hoda and Chang (1975). Further, robinsonite disappears and semseyite appears leading to the establishment of bournonite-boulangerite, bournonite-semseyite, and chalcostibite-semseyite tie lines. Variations in f (sub s 2 ) at 500 degrees and 440 degrees C within the three-phase fields and on the two-phase boundaries are consistent. The f (sub s 2 ) -imposed experiments in the chalcostibite-zinkenite-stibnite field at 440 degrees C reveal that famatinite forms according to the sulfidation reaction: 3 chalcostibite + 1/2S 2 = famatinite + stibnite.Mineralogy and composition of pertinent natural sulfosalt-bearing assemblages from a wide variety of polymetallic ore deposits are successfully explained in the light of the present experimental results. Significantly, the compositions of natural meneghinites plot at the PbS-rich boundary of the meneghinite field on the Cu 2 S-poor side. The virtual absence of natural Sb 2 S 3 -rich meneghinites can be explained by the requirement of more copper for their stability which is not geologically realistic in a model hydrothermal fluid. Additionally, relatively low f (sub S 2 ) values essential for the stability of meneghinites may be another possibility. Rarity of phases such as chalcostibite and skinnerite can be explained by the extremely low sulfur fugacity values, beyond the Bartonian f (sub S 2 ) -T regime, that are essential for their stability.

Phase relations of osumilite and dehydration melting in pelitic rocks: a simple thermodynamic model for the KFMASH system

Thermodynamic modelling of (1) osumilite solid solutions and (2) dehydration melting in pelitic compositions within the KFMASH system is quite successful in reproducing the invariant and univariant reactions determined in experimental studies. Even though rather preliminary, such melt thermodynamic models may be very useful in interpolating and extrapolating the limited information available from a small number of experimental runs. These methods allow the compositions of all phases to be monitored as a function of pressure, temperature and equilibrium phase assemblage for any desired bulk composition. Locating the higher variance phase fields (e.g. quadrivariant, quinivariant) is often difficult or impossible by inspection, but is made relatively easy using thermodynamic software such as thermocalc. In the KFMASH system the calculated partition of Fe and Mg between osumilite, garnet, cordierite, orthopyroxene and biotite are shown to be in good agreement with experimental and natural data and allow reliable calculation of mineral compositions coexisting with quartz-saturated and H2O-undersaturated melts for a variety of bulk compositions. These phase diagram calculations allow quite tight limits to be placed on the pressure, temperature and water activity conditions which accompanied metamorphism of natural osumilite occurrences in Nain, Namaqualand, and Rogaland. At fixed bulk composition, the initial melting of pelites by dehydration of biotite can occur via univariant, divariant or trivariant equilibria depending upon pressure of metamorphism. Of particular interest is that, for low pressures or more magnesian bulk compositions, fluid-absent melting begins by generating liquid from the high-variance assemblage biotite+cordierite+K-feldspar+ quartz. This type of modelling allows investigation, at least qualitatively, of the fine scale details of melt production as a function of changes in pressure, temperature and bulk composition.

SiAlON Composites Containing Rare‐Earth Melilite and Neighboring Phases

Sintering aids with a formulation of rare‐earth (R) melilite solid solution M'(R) have been introduced to several SiAlON composites to obtain high‐density bodies by pressureless and gas‐pressure sintering. These compositions include ones along the Si3N4–R2O3:9AlN line, which contain no Al2O3 and are known to have excellent strength but very poor sinterability. Phase analysis and property (hardness, toughness, strength, and oxidation resistance) measurements reveal a complex set of structure–property–processing relationships that are composition‐dependent. Of the most importance is the Al—O content in various phases, which is dictated by the starting composition as well as Al—O solubility in M'(R). This influences the sinterability, strength, and phase assemblage through the compositions of the intermediate liquid and the final β'‐SiAlON. La2O3 is further established as an effective sintering aid that does not affect the equilibrium phase assemblage. Overall, M'(R) and La2O3 show promise as SiAlON sintering aids that allow high density to be achieved without compromising intrinsic mechanical and thermal properties.

Minerals and calculated low-temperature phase equilibria in the pseudoternary system Tl2S-As2S3-Sb2S3

The experimental determination of phase relations in the pseudoternary system Tl2 S-As2S3-Sb2S3 below 200°C is practically impossible, especially so under dry condensed conditions. As thallium sulfosalts are naturally formed at low temperatures equilibrium phase assemblages at 100 and 200°C were calculated by application of thermochemical approximations for the free enthalpies of formation of the sulfosalts. A comparison of the calculated conode configurations with the results of syntheses under dry condensed conditions at 200°C yielded good agreement between experiment and calculations.

New software models thermodynamics of magmatic systems

A new software package, MELTS, is now available for modeling crystal‐liquid equilibria in magmatic systems. MELTS is based on experimentally calibrated models for the thermodynamics of solution of magmatic liquids and solids [Ghiorso and Sack, 1994; Hirschmann and Ghiorso, 1994]. The package computes equilibrium phase assemblages—the compositions and proportions of coexisting liquids and solids—by direct minimization of the thermodynamic potential of the system [Ghiorso and Kelemen, 1987]. MELTS has a menu driven, interactive, graphical user interface and may be used to model a range of igneous processes including equilibrium or fractional crystallization of specified bulk compositions, crystallization paths under specified T‐f02, total enthalpy, total entropy, or total volume constraints, and assimilation or magma mixing in evolving magmatic systems.