Equilibrium Phase Boundary Research Articles

In situ X-ray observation of the reaction dolomite = aragonite + magnesite at 900–1300 K

To determine the reaction boundary dolomite = aragonite + magnesite, in situ X-ray experiments on dolomite decomposition and synthesis were carried out in the temperature range 900 to 1300 K. Dolomite decomposition experiments were conducted with increasing pressure at constant temperature, and the boundary was determined to be 5.3–5.9 GPa in the temperature range 800–1200 K and 5.9–6.3 GPa at 1300 K. Dolomite synthesis experiments were carried out with decreasing pressure at constant temperature or with increasing temperature at constant press load. The dolomite synthesis boundary was determined to be 6.7–6.9 GPa at 1300 K, 3.7–4.4 GPa at 1100 K, and 2–3 GPa at 800 K. Except at 1300K, the synthesis boundary is much lower in pressure and has a steeper d P /d T slope than the decomposition boundary. The difference in the reaction boundary reflects the different kinetics between decomposition and synthesis reactions, and the former may be closer to the equilibrium phase boundary. The experimental results show that the phase boundary between dolomite and aragonite + magnesite is located at ~6.4 GPa at 1300 K and has a d P /d T slope of 0.001 ± 0.001 GPa/ K in the temperature range 900 to 1200 K.

Effects of B2O3on the Phase Stability of Ba2Ti9O20Microwave Ceramic

Preparation of dense and phase-pure Ba2Ti9O20 is generally difficult using solid-state reaction, since there are several thermodynamically stable compounds in the vicinity of the desired composition and a curvature of Ba2Ti9O20 equilibrium phase boundary in the BaO–TiO2 system at high temperatures. In this study, the effects of B2O3 on the densification, microstructural evolution, and phase stability of Ba2Ti9O20 were investigated. It was found that the densification of Ba2Ti9O20 sintered with B2O3 was promoted by the transient liquid phase formed at 840°C. At sintering temperatures higher than 1100°C, the solid-state sintering became dominant because of the evaporation of B2O3. With the addition of 5 wt% B2O3, the ceramic yielded a pure Ba2Ti9O20 phase at sintering temperatures as low as 900°C, without any solid solution additive such as SnO2 or ZrO2. The facilities of B2O3 addition to the stability of Ba2Ti9O20 are apparently due to the eutectic liquid phase which accelerates the migration of reactant species.

Using shear wave amplitude patterns to detect metastable olivine in subducted slabs

Olivine within the lowest temperature regions of subducting oceanic lithosphere may persist metastably to depths well below the equilibrium phase boundary for transformation to β phase. This may produce a tapering low seismic velocity wedge within the slab in the transition zone; transformational faulting of such metastable olivine has been proposed as a possible explanation of deep earthquakes. Detecting seismic velocity structure associated with metastable olivine within a slab using seismic wave arrival time information alone has proven problematic. Motivated by previous two‐dimensional numerical calculations for upgoing and downgoing seismic waves, a three‐dimensional Gaussian beam method is used to assess whether the azimuthally varying teleseismic amplitude signature produced by a slab with an internal wedge of metastable olivine is distinguishable from that for a slab with equilibrium transitions. Five slab velocity structures are considered: a thermal model with horizontal phase transitions at the same depths as in ambient mantle, two models incorporating equilibrium transitions within the slab, and two models with tongues of metastable olivine. A depth‐ and temperature‐dependent thermal conductivity term and the effect of the latent heat of transformation of olivine to β phase are included in the thermal modeling. Three‐dimensional dynamic ray tracing and Gaussian beam summation are performed for events located at different depths and lateral positions for each of the slab models. For sources near 400 km depth the presence of low‐velocity metastable olivine produces relatively complex azimuthal shear wave amplitude patterns compared to thermal and equilibrium models. Comparison with observed amplitudes for four events in the Kurile slab indicates that allowing for internal slab velocity complexity in the transition zone provides better agreement with observations than simple thermal and equilibrium slab models. This indicates that careful modeling of teleseismic shear wave amplitude patterns may have the resolution to detect and characterize the presence of metastable olivine in deep slabs.

Phase transitions and short timescale sinusoidal motions

While the effects of phase transitions of mantle materials are considered in convection studies, models of geophysical processes that occur on shorter timescales, such as seismic normal modes and Earth tides, often ignore these effects. A common justification is that the latent heat released from the material changing phase could not conduct away from the boundary on timescales shorter than those of convection, and thus the phase transition would not proceed. In this study, we first examine the behavior of a phase boundary to a periodic pressure perturbation by solving the heat equation. If all the latent heat is released at an infinitely thin boundary, we find that the phase transitions do not proceed. However, if the latent heat is released over a region of 1–5 km thickness, which might occur due to the divariant nature of the phase boundaries, then some of the material changes phase regardless of the period of the forcing. We apply these results to predictions of seismic normal mode center frequencies and elastic Love numbers. The perturbations to the normal mode frequencies can be two orders of magnitude greater than the differences between the observed frequencies and those predicted using the Preliminary Reference Earth Model. However, we have not considered kinetics, the energetics of the mechanisms of the phase transitions, in this formulation. This work suggests a greater knowledge of the kinetics near equilibrium phase boundaries is required because the kinetics may be the limiting factor in these short period, small amplitude motions.

Calorimetric study of perovskite solid solutions in the CaSiO 3 -CaGeO 3 system

Enthalpies of drop solution (ΔHdrop-sol) of CaGeO3, Ca(Si0.1Ge0.9)O3, Ca(Si0.2Ge0.8)O3, Ca(Si0.3Ge0.7)O3 perovskite solid solutions and CaSiO3 wollastonite were measured by high-temperature calorimetry using molten 2PbO · B2O3 solvent at 974 K. The obtained values were extrapolated linearly to the CaSiO3 end member to give ΔHdrop-sol of CaSiO3 perovskite of 0.2 ± 4.4 kJ mol−1. The difference in ΔHdrop-sol between CaSiO3, wollastonite, and perovskite gives a transformation enthalpy (wo → pv) of 104.4 ± 4.4 kJ mol−1. The formation enthalpy of CaSiO3 perovskite was determined as 14.8 ± 4.4 kJ mol−1 from lime + quartz or −22.2 ± 4.5 kJ mol−1 from lime + stishovite. A comparison of lattice energies among A2+B4+O3 perovskites suggests that amorphization during decompression may be due to the destabilizing effect on CaSiO3 perovskite from a large nonelectrostatic energy (repulsion energy) at atmospheric pressure. By using the formation enthalpy for CaSiO3 perovskite, phase boundaries between β-Ca2SiO4 + CaSi2O5 and CaSiO3 perovskite were calculated thermodynamically utilizing two different reference points [where ΔG(P,T )=0] as the measured phase boundary. The calculations suggest that the phase equilibrium boundary occurs between 11.5 and 12.5 GPa around 1500 K. Its slope is still not well constrained.

Excess Enthalpies (HE) for 2-Butoxyethanol/Water and Determination of Liquid-Liquid Equilibrium Phase Boundaries from Fits to HE of Redlich-Kister, Pade, and Critical-Scaling Equations.

Excess enthalpies (HE) for the binary n-butanol/water measured by isothermal flow calorimetry at 30 and 50°C, and nonionic amphiphile 2-butoxyethanol/water at 10 different temperatures (from 48.5 to 70°C) reported in the literature were analyzed for the determination of phase boundaries. HE exhibited S-shape behavior in the former system and U-shape behavior in the latter system. When the HE data in the single-phase were fitted by semi-empirical polynomials and critical-scaling equations, plots of specific HE vs. weight fraction provided more accurate fitting with fewer parameters than conventionally drawn molar HE vs. mole fraction plots. This was due to the enhanced symmetry of specific HE vs. weight fraction plots. Liquid-liquid equilibrium phase boundaries between the single- and two-phase regions were determined from HE. The phase boundary points were obtained as the intersections of the curve and the straight line, which describe the composition dependence of HE for the single- and two-phase regions, respectively. When Redlich-Kister (RK) and Pade polynomials were employed, the phase boundary points could be determined for the n-butanol/water but not for the 2-butoxyethanol/water. These results imply that correct phase boundaries may not be obtained with the semi-empirical polynomials when HE behavior is of the U-type. However, when the critical-scaling equations for HE of binary mixtures were used, the phase boundaries were obtained accurately, irrespective of the type of HE data.

Using tert-Butyl Alcohol as an Adductive Agent for Separation of an m-Cresol and 2,6-Xylenol Mixture

The solid−liquid equilibrium (SLE) phase boundaries of the ternary mixture of m-cresol, 2,6-xylenol, and tert-butyl alcohol and those of the three constituent binary mixtures were experimentally determined by means of the solid-disappearance method. Each of the m-cresol + 2,6-xylenol and tert-butyl alcohol + 2,6-xylenol mixtures exhibits one eutectic point, whereas the m-cresol + tert-butyl alcohol mixture exhibits one congruent point and two eutectic points. The approach proposed by Ott and Goates (J. Chem. Thermodyn. 1983, 15, 267) was used to represent the melting point temperatures as functions of the mole fraction of one of the components. The formulation developed by Stoicos and Eckert (Chem. Eng. Sci. 1987, 42, 1137) for SLE calculations was used with the NRTL activity coefficient model of Renon and Prausnitz (AIChE J. 1968, 14, 135) to correlate the experimental data for the binary systems. On the basis of the information presented in the phase diagram, which shows all the eutectic and congruent points and the liquidus isotherms for the ternary system, two conceptual possible processes involving the use of tert-butyl alcohol as the adductive agent for separating a mixture of m-cresol and 2,6-xylenol are proposed.

Measurements and model prediction of the solid–liquid equilibria of organic binary mixtures

Solid–liquid equilibria of three binary mixtures consisting of benzoic acid, 2-aminobenzoic acid and 1-naphthol were measured in this study using differential scanning calorimetry (DSC). Simple eutectic phase diagrams were observed, and the experimental data were well correlated by either the Wilson equation or the UNIFAC activity coefficient model. A new method by employing the DSC experiment and the theoretical calculations to detect the fractional transformation of solid–liquid equilibrium of organic mixture is proposed. Deconvolution method was employed to obtain the ideal equilibrium solid–liquid DSC curve. The heat generation rate and fraction of transformation were calculated using the Gray's model. Applying this theoretical approach, the eutectic points and the equilibrium liquidus temperatures were easily determined from the fractional transformation curve. An easier procedure to confirm the composition of eutectic point is presented. It is also demonstrated that the solid–liquid equilibrium phase boundaries are predicted with good agreement to the experimental results.

Nanometer-size alpha-PbO(2)-type TiO(2) in garnet: A thermobarometer for ultrahigh-pressure metamorphism

A high-pressure phase of titanium dioxide (TiO(2)) with an alpha-PbO(2)-type structure has been identified in garnet of diamondiferous quartzofeldspathic rocks from the Saxonian Erzgebirge, Germany. Analytical electron microscopy indicates that this alpha-PbO(2)-type TiO(2) occurred as an epitaxial nanometer-thick slab between twinned rutile bicrystals. Given a V-shaped curve for the equilibrium phase boundary of alpha-PbO(2)-type TiO(2) to rutile, the stabilization pressure of alpha-PbO(2)-type TiO(2) should be 4 to 5 gigapascals at 900 degrees to 1000 degrees C. This suggests a burial of continental crustal rocks to depths of at least 130 kilometers. The alpha-PbO(2)-type TiO(2) may be a useful pressure and temperature indicator in the diamond stability field.

Liquidus temperature determination in multicomponent alloys by thermal analysis

Thermal analysis is often used to determine equilibrium phase boundary temperatures such as the liquids. Accurate measurements require proper calibration procedures, which are standard for given instruments. In multicomponent alloys such as RENE N5 and PWA 1484 superalloys, a complex melting behavior associated with the solidification structure was exposed by examining the melting response at different heating rates. The observed variability in the melting signal is related to the sample processing history and is not addressed by the various standard calibration methods or supplemental procedures for different heating rates. The liquidus temperature can be determined under conditions approaching full compositional equilibrium by the application of an interrupted-heating thermal analysis protocol. The approach provides a new strategy for the reliable determination of phase boundary temperatures by thermal analysis.

The equilibrium phase boundary between hexagonal and cubic boron nitride

Abstract The equilibrium phase boundary between hexagonal and cubic boron nitride was determined over the pressure range 3–6 GPa and the temperature range 1200–2200°C. Absolute pressure and temperature were estimated based on the minimum P–T point of diamond formation in the conventional metal catalyst system using the Kennedy–Kennedy equilibrium line between graphite and diamond. Above 3.8 GPa, we determined the phase boundary by detecting the formation of cubic BN in the catalyst-containing system and by the reverse transformation from cubic BN to hexagonal BN. Below 3.8 GPa, we determined the boundary by careful observation of the transformation behavior of cubic BN powder. The rate of phase transformation from cubic BN to hexagonal BN was evaluated from the ratio of X-ray diffraction peak intensities of both phases. We found that the amount of cubic BN phase clearly changed at the phase boundary. Two sets of the results could be plotted with a uniquely determined boundary line expressed by the equation P(GPa)=T(°C)/465+0.79, which is located about 300°C higher at 5 GPa than the line determined by Bundy and Wentorf in 1963.

The role of undercooling in producing igneous zoning trends in pyroxenes and maskelynites among basaltic Martian meteorites

Pyroxene and maskelynite are major minerals in basaltic Martian meteorites (Shergotty, Zagami, EETA79001, and QUE94201). They are chemically zoned in both major and minor elements, offering useful information on their crystallization history. Pigeonite and augite show two distinct textural occurrences of zoning patterns. In Shergotty and Zagami, pigeonite and augite are usually present as separate grains that are zoned from Mg-rich core to Fe-rich rim, respectively. Both pigeonite and augite usually have homogeneous cores, considered to be cumulus phases. Zagami pyroxenes are not zoned as extensively as those in Shergotty, but their mineralogy is quite similar. On the other hand, pigeonite and augite in EETA79001 and QUE94201 are both present in individual composite grains. These pyroxenes are complexly zoned, and typically the cores are Mg-rich pigeonites, mantled by Mg-rich augite, and the rims are Fe-rich pigeonite. Pyroxenes in lithology A of EETA79001 are small and show irregular zoning patterns, but most of them show similar zoning patterns to lithology B of EETA79001 and QUE94201. Maskelynite compositions also correspond to differences in pyroxene zoning. Maskelynites in Shergotty and Zagami are more alkali-rich than those in EETA79001 and QUE94201. Shergotty and Zagami maskelynites apparently nucleated on pyroxene crystals and grew outward (to lower An content) into interstitial melts, whereas EETA79001 and QUE94201 maskelynites have the most An-rich portions in the centers of grains, showing normal core-to-rim zoning. FeO in the maskelynite cores is different between Shergotty and Zagami (0.5–0.6 wt%) and EETA79001 and QUE94201 (0.3–0.4 wt%). The lower Fe content of EETA79001 and QUE94201 maskelynite cores reflects earlier crystallization of plagioclase. Al zoning in pyroxenes also marks the beginning of plagioclase crystallization. Decrease of the Al/Ti ratios observed in Al–Ti plots of pyroxenes further suggests plagioclase crystallization, and the Al–Ti distribution shows a clear difference between Shergotty and Zagami on one hand and EETA79001 and QUE94201 on the other. Such mineralogical differences of EETA79001 and QUE94201 from Shergotty and Zagami can be understood by undercooling of the magmas from which they have crystallized. We believe that Shergotty and Zagami experienced only slight undercooling, resulting initially in cotectic growth of pigeonite and augite, later joined by plagioclase. On the other hand, EETA79001 and QUE94201 experienced significant undercooling of their melts, and their crystallization sequence was pigeonite, augite, plagioclase, and then Fe-rich pigeonite, with each phase crystallizing metastably alone, because the melt compositions did not follow the equilibrium phase boundaries. Lithology A of EETA79001 also experienced undercooling effects, but they are not so extensive as in lithology B, inasmuch as lithology A shows some features similar to Shergotty and Zagami. All of these inferences concerning supercooling are consistent with field emission gun scanning electron microscopy (FEG-SEM) observation of pyroxene microstructures if we consider that magmatic cooling rates are related to subsolidus cooling rates. That is, the pyroxene cores of Shergotty and Zagami have fine exsolution lamellae (a few tens to a few hundreds nm), whereas those of EETA79001 and QUE94201 do not contain such exsolution lamellae, indicating faster cooling rate even at subsolidus.

Effects of slab mineralogy on subduction rates

Although velocities of subducting slabs should be controlled primarily by their negative thermal buoyancies, their mineralogy can also have significant effects. We explore this by using thermo‐kinetic modeling to predict mineralogy and compare the resultant buoyant (driving) force to the opposing viscous drag. Phase transitions of (Mg, Fe)2SiO4 in subducting slabs depend on thermal structure in two ways. First, equilibrium phase boundaries should be deflected, causing local buoyancy anomalies whose sign depends upon that of the Clapeyron slope. As slabs first enter the transition zone, negative anomalies should accelerate them, but positive anomalies that arise when they fully penetrate the transition zone should slow them. Such effects may induce geologically abrupt changes in plate motions. Second, olivine that persists metastably in slabs will form regions of positive buoyancy which should reduce slab velocities. The coldest and fastest slabs should be slowed more greatly, thus narrowing the range of feasible subduction rates. Decreased descent rates, however, allow slabs to warm and metastable wedges to thermally erode. Such negative feedback mechanisms may serve to regulate subduction rates.

Application of New, Modified BWR Equations of State to the Corresponding-States Prediction of Natural Gas Properties

The accurate description of mixtures includes both single-phase (bulk) properties and the location of phase equilibrium boundaries, e.g., properties that depend upon partial molar properties. In order to estimate these properties, many variants of corresponding-states theory have been developed, especially for nonpolar mixtures such as those found in natural gas systems, In this work we have developed two new, modified BWR equations of state for two natural gas components (n-pentane and n-heptane) and used these equations in a reformulated (Teja-like) Lee–Kesler model. The reformulated model has been tested on bulk-phase properties of hydrocarbon systems, in both the pure and the mixed states. Results have been obtained using the original Lee–Kesler model, the extended corresponding-states theory, and the multifluid corresponding-states principle using several combinations of reference fluids chosen from this and previous equation of state studies. Details of the new equations of state and theoretical comparisons are reported.

Chemical reactions and phase equilibria of model halocarbons and salts in sub- and supercritical water (200–300 bar, 100–600°C)

Experimental data and theoretical predictions of hydrolysis reaction kinetics of model halocarbons and phase equilibria of their associated neutralized salt reaction products are reported for a range of hydrothermal conditions. Specifically, the results of a study of hydrolysis and oxidation of methylene chloride (CH 2Cl 2) to produce CO 2, H 2O, and HCl as final mineralized products are presented. An analysis of hydrolysis kinetics and heat transfer was used to generate kinetic parameters for comparison with theoretical predictions based on a modified form of the Kirkwood solution model to show density dependent effects as a function of the dielectric strength of the reaction solvent medium. Phase equilibria data for the ternary NaCl–Na 2SO 4–H 2O, system at 200 and 250 bar were measured and correlated. A modified form of the Anderko–Pitzer semi-empirical PVTx i model was used to predict equilibrium phase boundaries for the NaCl–H 2O system at 210, 250, and 300 bar. Molecular simulation results for the NaCl–H 2O binary was used to illustrate changes in the solvation power of water as a function of density.

Optical-Cell Evidence for Superheated Ice under Gas-Hydrate-Forming Conditions

We previously reported indirect but compelling evidence that fine-grained H2O ice under elevated CH4 gas pressure can persist to temperatures well above its ordinary melting point while slowly reacting to form methane clathrate hydrate. This phenomenon has now been visually verified by duplicating these experiments in an optical cell while observing the very slow hydrate-forming process as the reactants were warmed from 250 to 290 K at methane pressures of 23 to 30 MPa. Limited hydrate growth occurred rapidly after initial exposure of the methane gas to the ice grains at temperatures well within the ice subsolidus region. No evidence for continued growth of the hydrate phase was observed until samples were warmed above the equilibrium H2O melting curve. With continued heating, no bulk melting of the ice grains or free liquid water was detected anywhere within the optical cell until hydrate dissociation conditions were reached (292 K at 30 MPa), even though full conversion of the ice grains to hydrate requires 6−8 h at temperatures approaching 290 K. In a separate experimental sequence, unreacted portions of H2O ice grains that had persisted to temperatures above their ordinary melting point were successfully induced to melt, without dissociating the coexisting hydrate in the sample tube, by reducing the pressure overstep of the equilibrium phase boundary and thereby reducing the rate of hydrate growth at the ice−hydrate interface. Results from similar tests using CO2 as the hydrate-forming species demonstrated that this superheating effect is not unique to the CH4−H2O system.

Phase Behavior of Colloids in Binary Liquid Mixtures

Partially miscible binary liquids containing silica colloids show equilibrium phase boundaries and critical lines. The phase separation is ternary in nature, and measurements allow construction of the ternary phase prism for colloids dispersed in binary fluid mixtures. Comparison with earlier aggregation studies strongly suggests that the aggregation phenomena observed for colloidal particles in binary liquid mixtures is in fact a true phase separation in the ternary mixture.

Analysis of the β′Ni2TiAl/βNiTi equilibrium in Ni-Ti-Al alloys by the cluster variation method

Abstract The cluster variation method with the Lennard-Jones potential, previously used to analyze the γ′(L1 2 Ni 3 Al)/γ(fcc Ni) equilibrium in Ni-Al base multicomponent alloys, was used to calculate the β′(L2 1 Ni 2 TiAl)/β (B2 NiTi) equilibrium phase boundaries in the Ni-Ti-Al system. Results are compared with the isothermal and vertical sections of the ternary phase diagram in the literature. The lattice misfit between β′ and β compound lattices, which is considered to play an important role for the formation of a rafted structure, passed through a minimum at 50%Ni, but was considerably larger compared to γ′/γ alloys. It is thus necessary to consider alloying addition for the optimization of high temperature properties of β′/β alloys by controlling the size and distribution of the β′ phase and the lattice misfit. © 1997 Elsevier Science Limited. All rights reserved

Computer simulation of the kinetics of order-disorder and phase separation during precipitation of δ′ (Al 3Li) in AlLi alloys

A computer simulation study has been performed of the reaction paths for the precipitation of δ′ (Al 3Li) ordered particles from a disordered matrix (α) in AlLi alloys, using microscopic Langévin diffusion equations. It is found that the precipitation of δ′ occurs either by a congruent ordering process followed by decomposition, or by a non-classical nucleation mechanism which requires critical fluctuations of both composition and order parameter, except in a narrow range of compositions near the equilibrium phase boundary of the disordered phase, where classical nucleation theory seems to be applicable. Composition and order parameter profiles across a critical nucleus were obtained for different compositions in the nucleation and growth regime, and compared with those obtained from the continuum non-classical nucleation theory. Possible origins for the discrepancies in the precipitation mechanism, obtained from different theoretical and experimental studies, are suggested.

Bubble shapes in rotating two-phase fluid systems: a thermodynamic approach

A method is reported for predicting the shape of the phase boundary in two-phase isothermal constant-volume constant-mass rotating fluid systems. In contrast to previous methods that have employed the continuum concept of pressure, the proposed method uses the thermodynamic concept. The latter requires, in addition to the usual condition of a force balance existing at the boundary, that the equilibrium phase boundary shape be such that there is no net mass flux. The latter condition is imposed by requiring that the chemical potentials in the different phases be equal at the phase boundary. A non-dimensional parameter is defined that allows one to determine when the effects of a gravitational field acting at 90 to the axis of rotation may be neglected. Experiments have been performed under conditions where this restriction is satisfied. With known values of the experimentally controllable variables, the proposed method has been used to predict the length of the vapour phase. To within the experimental error, the predicted lengths are found to be in agreement with the measurements. If, however, a gravitational field of a sufficient magnitude is imposed the vapour phase has been found to become unstable and to break into two or more separate bubbles. Using the variable-gravity environment of an aircraft following a parabolic flight path, this instability has been investigated. By approximating the gravitational effects, the theoretical description has been extended and a method proposed to determine the conditions under which the phase boundary becomes unstable. If the angle of action of the net viscous shear force on the bubble were known, a prediction of the breakup could be made entirely in terms of experimentally controllable parameters. Using arguments for the value of this angle, bounds on the breakup condition are compared with experimental results.