Regular Solution Parameter Research Articles

Disorder in Ho2Ti2-x Zr x O7: pyrochlore to defect fluorite solid solution series.

Pyrochlore (A2B2O7) is an important, isometric structure-type because of its large variety of compositions and structural derivatives that are generally related to different disordering mechanisms at various spatial scales. The disordering is key to understanding variations in properties, such as magnetic behavior or ionic conduction. Neutron and X-ray total scattering methods were used to investigate the degree of structural disorder in the Ho2Ti2−xZrxO7 (x = 0.0–2.0, Δx = 0.25) solid solution series as a function of the Zr-content, x. Ordered pyrochlores (Fd3̄m) disorder to defect fluorite (Fm3̄m) via cation and anion disordering. Total scattering experiments with sensitivity to the cation and anion sublattices provide unique insight into the underlying atomic processes. Using simultaneous Rietveld refinement (long-range structure) and small-box refinement PDF analysis (short-range structure), we show that the series undergoes a rapid transformation from pyrochlore to defect fluorite at x ≈ 1.2, while the short-range structure exhibits a linear increase in a local weberite-type phase, C2221, over the entire composition range. Enthalpies of formation from the oxides determined using high temperature oxide melt solution calorimetry support the structural data and provide insight into the effect of local ordering on the energetics of disorder. The measured enthalpies of mixing are negative and are fit by a regular solution parameter of W = −31.8 ± 3.7 kJ mol−1. However, the extensive short-range ordering determined from the structural analysis strongly suggests that the entropies of mixing must be far less positive than implied by the random mixing of a regular solution. We propose a local disordering scheme involving the pyrochlore 48f to 8a site oxygen Frenkel defect that creates 7-coordinated Zr sites contained within local weberite-type coherent nanodomains. Thus, the solid solution is best described as a mixture of two phases, with the weberite-type nanodomains triggering the long-range structural transformation to defect fluorite after accumulation above a critical concentration (50% Ti replaced by Zr).

Application of the modified BET model to concentrated salt solutions with relatively high water activities: Predicting solubility phase diagrams of NaCl + H2O, NaCl + LiCl + H2O, and NaCl + CaCl2 + H2O

Solubility phase diagrams of mixtures of salts and water are of interest in various application fields and can be calculated using the modified BET model. In comparison with other thermodynamic models, the modified BET model requires only two salt-specific model parameters and has shown to possess a predictive capability. In this work, the modified BET equations are extended in order to calculate solubility phase diagrams of concentrated salt solutions with relatively high water activities within the range of undersaturation. As an example, BET parameters of NaCl are determined and applied to calculate solubility phase diagrams of NaCl + H2O, NaCl + LiCl + H2O, and NaCl + CaCl2 + H2O within the temperature range of around 250–500 K. In the ternary systems, the best agreement with solubility data from literature is obtained using constant BET parameters of NaCl and an additional temperature-dependent regular solution parameter to account for salt-salt interaction.

Work of adhesion of interfaces between M2AlC (M = Ti, V, Cr) MAX phases and α-Al2O3

A fast and generic scheme is proposed to calculate the work of adhesion between two different materials or the cohesive energy between two crystal planes in a material. These calculations make use of the regular solution theory. This theory is extended to describe chemical interactions between atoms at either side of an interface. The so-called regular solution parameter is estimated from thermodynamic values tabulated or solution enthalpies obtained from a macroscopic atom model (MAM). Complex surface definitions at either side of an interface, both in composition and position of atoms, can be dealt with.The proposed scheme has been used to calculate the work of adhesion between M2AlC (M = Ti, V, Cr) type MAX phases and α-Al2O3. Next, the cohesive energy of the MAX-phases and alumina were determined. The cohesion of the M2AlC type MAX-phase is the weakest bond present in the M2AlC- α-Al2O3 systems.

Studies on binary mixtures of Pluronic P123 and twin tailed 1-Butyl-3-methyl-imidazolium Aerosol OT - Aggregation behavior and impact on Naproxen and Rifampicin partitioning

Pluronic P123, 1-Butyl-3-methyl-imidazolium Aerosol OT ([Bmim][AOT]) and their binary mixtures at varied mole fractions have been investigated for micellization and rheological properties. The composition of the mixed micelles has been estimated on the basis of Clint, Gibbs adsorption, and Rubingh theories. The mixed micellar systems exhibited synergism for all the investigated mole fraction ranges with more pronounced synergism at intermediate mole fractions of [Bmim][AOT]. The gel behavior of P123 can be tuned by altering suitably mole fraction of surface active ionic liquids in order to tailor the system for desired applications. The investigated single/mixed micellar systems were explored for their solubilization capabilities toward two model hydrophobic drugs, Naproxen and Rifampicin. Regular solution parameter β was compared with deviation ratio R and surfactant-drug interaction parameter B to discuss mixing effect of surfactants on the partitioning of these drugs.

Thermodynamics of Congruent Oxidation

AbstractCongruent oxidation occurs when an alloy oxidizes at constant oxygen chemical potential and temperature to an oxide in which the ratio of metallic components is the same as in the alloy. In alloys that undergo congruent oxidation concentration gradients near the surface are minimized. In this work thermodynamic conditions for congruent oxidation of binary and ternary alloys are formulated using the regular solution model to describe thermodynamic mixing properties. The conditions under which congruent oxidation can occur are identified. Congruent oxidation of a binary alloy X-Y will occur only if difference in oxygen potential for the oxidation of the two pure metals is less than twice the difference in regular solution parameters for the oxide and alloy phases (Ω0 − ΩA). In the case of ternary alloys, congruency requirements for both two-phase and three-phase equilibria are discussed. Since the conditions for congruent oxidation of ternary alloy X-Y-Z depends on many parameters, the effect of systematic variation of the binary sets of regular solution parameters on the congruent composition is explored by numerical solution of the governing equations.

Improved Tikhonov Regularization Research and Applied in Inverse Problem

The regularization which constructs with the first filter function is precisely the Tikhonov regularization. This article has proven the Tikhonov functional minimization problem is decides suitably, namely satisfies the solution the existence, the solution unique reconciliation to rely on continuously the data stability; and this minimization problem in solves the first class equation equally the normal equation. The numerical simulation experiment's result indicated that distinguishes the inverse with the regular reduction solution parameter to have the numerical precision to be high and the stability is good and convergence rate quick characteristic.

Thermodynamic parameters and counterion binding to the micelle in binary anionic surfactant systems

Competitive counterion binding of sodium and calcium to micelles, and mixed micellization have been investigated in the systems sodium dodecylsulfate (NaDS)/sodium decylsulfate (NaDeS) and NaDS/sodium 4-octylbenzenesulfonate (NaOBS) in order to accurately model the activity of the relevant species in solution. The critical micelle concentration (CMC) and equilibrium micelle compositions of mixtures of these anionic surfactants, which is necessary for determining fractional counterion binding measurements, is thermodynamically modeled by regular solution theory. The mixed micelle is ideal (the regular solution parameter β M = 0) for the NaDS/NaOBS system, while the mixed micelle for NaDS/NaDeS has β M = −1.05 indicating a slight synergistic interaction. Counterion binding of sodium to the micelle is influenced by the calcium ion concentration, and vice versa. However, the total degree of counterion binding is essentially constant at approximately 0.65 charge negation at the micelle’s surface. The counterion binding coefficients can be quantitatively modeled using a simple equilibrium model relating concentrations of bound and unbound counterions.

An attempt to correct the quasichemical model

An attempt was made to correct the quasichemical model to avoid predictions of negative configurational entropy when long-range order is impossible as in liquids. The attempt was successful for negative interaction energies but for positive interaction energies the simplest possible variant of the model predicted two narrow miscibility gaps. It was not possible to improve this by adding regular solution parameters. However, using the next possible variant of the correction term these difficulties may be avoided.

Al2O3 incorporation in MgSiO3 perovskite and ilmenite

First-principles calculations in the MgSiO3–Al2O3 system predict that MgSiO3–perovskite dissolves about 15 mol% Al2O3 at the top of the lower mantle, limited by coexistence with Al-rich ilmenite (corundum). The solubility increases with pressure so that the lower mantle is likely undersaturated in alumina in all but the coldest parts of the uppermost lower mantle. The akimotoite–corundum solid solution is highly non-ideal with a symmetric regular solution parameter W=66 kJ/mol per formula unit at the top of the lower mantle. The critical temperature for exsolution of ilmenite is predicted to be 2000 K. The MgSiO3 solution is also significantly non-ideal; assuming only Tschermak substitutions, the value of W=12 kJ/mol per formula unit. Total energy calculations over a range of compositions and several configurations for each composition are based on density functional theory in the local density approximation. We find that the entropy of solution of both structures is nearly ideal on the basis of random sampling of simulations using semi-empirical interatomic potentials. Results also confirm previous experimental and computational results showing that aluminum has little effect on the elasticity of MgSiO3 perovskite.

Thermodynamic Modeling of the YO1.5–ZrO2 System

The YO1.5–ZrO2 system consists of five solid solutions, one liquid solution, and one intermediate compound. A thermodynamic description of this system is developed, which allows calculation of the phase diagram and thermodynamic properties. Two different solution models are used—a neutral species model with YO1.5 and ZrO2 as the components and a charged species model with Y3+, Zr4+, O2−, and vacancies as components. For each model, regular and subregular solution parameters are derived from selected phase equilibrium and thermodynamic data. The neutral species and charged species modeling results are compared.

Internally consistent database for sulfides and sulfosalts in the system Ag 2S–Cu 2S–ZnS–Sb 2S 3–As 2S 3

An updated thermodynamic database for Ag 2S–Cu 2S–ZnS–Sb 2S 3–As 2S 3 sulfides and sulfosalts applicable to temperatures above 119°C is developed to calculate phase relations for polybasite-pearceite- and fahlore-bearing assemblages. It is based on pre-existing and new constraints on activity-composition, Ag–Cu and As–Sb partitioning, and other relations, and on experiments (200–300°C, evacuated silica tubes) conducted to define the stability of the polybasite-pearceite [(Ag 1− x ,Cu x ) 16(Sb 1− y ,As y) 2S 11] + ZnS sphalerite assemblage with respect to assemblages containing (Ag,Cu) 2S sulfides coexisting with (Cu, Ag) 10Zn 2(Sb,As) 4S 13 fahlore sulfosalts. It was found that the thermodynamics of mixing of bcc– and hcp–(Ag,Cu) 2S solutions, which are fast-ion conductors, may be described by using site multiplicities of metals α Ag,Cu > 2 and temperature-dependent regular solution parameters. We obtained estimates for the Gibbs energies of formation for Ag 16Sb 2S 11 and Cu 16Sb 2S 11 polybasite endmembers from the simple sulfides (Ag 2S, Cu 2S, and Sb 2S 3) of −30.79 and −4.07 kJ/gfw at 200°C, and −32.04 and −0.59 kJ/gfw at 400°C, respectively, that are about one half kJ/gfw more positive and about 6 kJ/gfw more negative than those estimated by Harlov and Sack (1995b). The corresponding estimates for formation energies of Ag 10Zn 2Sb 4S 13 and Cu 10Zn 2Sb 4S 13 fahlores (−20.29 and −105.29 kJ/gfw at 200°C and −23.72 and −105.76 kJ/gfw at 400°C) are comparable to, and roughly 110 kJ/gfw more positive than, the corresponding estimates of Ebel and Sack (1994). We also determined that the Gibbs energies of the As–Sb exchange reactions: 1 4 Ag 10 Zn 2 Sb 4 S 13 + 1 2 Ag 16 As 2 S 11 = 1 2 Ag 16 Sb 2 S 11 + 1 4 Ag 10 Zn 2 As 4 S 13 Sb–fahlore pearceite polybasite As–fahlore and Ag 3 SbS 3 + 1 2 Ag 16 As 2 S 11 = 1 2 Ag 16 Sb 2 S 11 + Ag 3 AsS 3 pyrargyrite pearceite polybasite proustite are, respectively, 8.75 and 0.40 kJ/gfw in the range 150–350°C, and these predictions are consistent with As–Sb partitioning relations observed in nature and produced in laboratory studies. Finally, we obtain estimates for the Gibbs energies of formation of Cu 10Fe 2Sb 4S 13 and Ag 10Fe 2Sb 4S 13 fahlores (−63.92 and +11.46 kJ/gfw at 200°C and −75.73 and −3.31 kJ/gfw at 400°C).

Thermochemistry of sulfide liquids. II. Associated solution model for sulfide liquids in the system O-S-Fe

We present a new formulation to describe the thermodynamics of liquids in the system O-S-Fe. The model is based on an associated regular solution formulation. According to this model, liquids in the O-S-Fe ternary are made up of an equilibrium solution of the six melt species S, Fe, FeO, FeO1.5, FeS and FeOS. The model presented here represents oxygen and sulfur fugacities as well as phase equilibria with stoichiometric solid phases better than models from the literature on O-Fe and S-Fe binaries. Furthermore, this model represents a substantial improvement on the model of Kress (1997), which is the only other thermodynamic model available in the ternary system. Asymmetric regular solution parameters are required along the FeO join in order to reproduce experimental data with the chosen list of species. Symmetric regular solution parameters are required along the Fe-S binary. Mixing between any of the species considered and FeOS close to ideal. The associated solution model presented here will serve as a more solid foundation for future models in O-S-Fe- Ni-Cu liquids. Efficient and robust strategies for calculating equilibrium speciation and estimating model parameters are presented.

Thermodynamics and phase equilibria involving the spinel solid solution Fe X Mg1−X Cr2O4

Activities of FeCr2O4 in the spinel solid solutions Fe X Mg1−X Cr2O4 (0<X<1) in equilibrium with pure iron and Cr2O3 have been measured in the temperature range 1050 to 1350 K by employing a bielectrolyte solid-state galvanic cell of the type Pt, Fe + Fe X Mg1−X Cr2O4 + Cr2O3//(Y2O3) ThO2/(CaO) ZrO2//Fe + FeCr2O4 + Cr2O3, Pt Activities of both the components exhibit small negative deviation from the ideal behavior, characterized by the regular solution parameter Ω s =−2260 (±200) J/mol. The lattice parameter of the spinel solid solutions quenched from 1200 K was found to obey Vegard’s law. The phase relations in the FeO-MgO-Cr2O3 system have been deduced from the results obtained in this study together with other relevant thermodynamic data from the literature. The tie-lines between the solid solutions with rock salt and spinel structures represent the influence of intercrystalline ion exchange. The tie-lines are skewed toward the FeCr2O4 corner, primarily because of the higher stability of FeCr2O4 compared to MgCr2O4, with respect to their component binary oxides. The oxygen partial pressure corresponding to the two three-phase regions, Fe + Fe X Mg1−X Cr2O4 + Cr2O3 and Fe + Fe Y Mg1−Y O + Fe X Mg1−X Cr2O4, have been evaluated as a function of composition at 1200 K.

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The solubilization of hydrocarbon and fluorocarbon alcohols in single and mixed aqueous solutions containing fluorocarbon surfactant has been studied. Surfactants used are lithium dodecyl sulfate (LiDS), lithium perfluorooctane sulfonate (LiFOS), lithium perfluorooctanoate (LiPFO), and hexaethyleneglycol dodecyl ether (6ED). In single surfactant systems, the partition coefficients of the alcohols between anionic micelles and water are greater for the surfactants which have the same kind of alkyl chain as the alcohols than for the surfactants having a different kind of alkyl chain to the alcohols. The standard free energies calculated from the partition coefficients indicate that the transfer of the alcohols occurs more favorably to the micelles consisting of the same kind of alkyl chain as the alcohols than of the different kind of alkyl chain. Also, the mixed surfactant systems LiDS-LiFOS, LiFOS-LiPFO and 6ED-LiFOS have been characterized by the regular solution parameter β and the alcohol partition coefficient. In the LiDS-LiFOS system with a positive β value, the partition coefficients of both hydrocarbon and fluorocarbon alcohols are greater than in single surfactant systems. In the LiFOS-LiPFO system exhibiting almost ideal mixing, the partition coefficients of both hydrocarbon and fluorocarbon alcohols change ideally, whereas the partition coefficients of the fluorocarbon alcohols are greater than those of the hydrocarbon alcohols. By contrast, in the 6ED-LiFOS system with negative β values, the partition coefficients of both alcohols are lower than in single surfactant systems.

H 2 O activity in concentrated KCl and KCl-NaCl solutions at high temperatures and pressures measured by the brucite-periclase equilibrium

H2O activities in supercritical fluids in the system KCl-H2O-(MgO) were measured at pressures of 1, 2, 4, 7, 10 and 15 kbar by numerous reversals of vapor compositions in equilibrium with brucite and periclase. Measurements spanned the range 550–900 °C. A change of state of solute KCl occurs as pressures increase above 2 kbar, by which H2O activity becomes very low and, at pressures of 4 kbar and above, nearly coincident with the square of the mole fraction (xH2O). The effect undoubtedly results primarily from ionic dissociation as H2O density (ρH2O) approaches 1 gm/cm3, and is more pronounced than in the NaCl-H2O system at the same P-T-X conditions. Six values of solute KCl activity were yielded by terminal points of the isobaric brucite-periclase T-xH2O curves where sylvite saturation occurs. The H2O mole fraction of the isobaric invariant assemblage brucite-periclase-sylvite-fluid is near 0.52 at all pressures, and the corresponding temperatures span only 100 °C between 1 and 15 kbar. This remarkable convergence of the isobaric equilibrium curves reflects the great influence of pressure on lowering of both KCl and H2O activities. The H2O and KCl activities can be expressed by the formulas: aH2O = γH2O[xH2O+(1 + (1 + α)xKCl)], and aKCL = γKCl[(1 + α)xKCl/(xH2O +(1 + α)xKCl)](1 + α), where α is a degree of dissociation parameter which increases from zero at the lowest pressures to near one at high pressures and the γ's are activity coefficients based on an empirical regular solution parameter W: ln γi = (1 − xi)2W. Least squares fitting of our H2O and KCl activity data evaluates the parameters: α = exp(4.166 −2.709/ρH2O) − 212.1P/T, and W = (−589.6 − 23.10P) /T, with ρH2O in gm/cm3, P in kbar and T in K. The standard deviation from the measured activities is only ± 0.014. The equations define isobaric liquidus curves, which are in perfect agreement with previous DTA liquidus measurements at 0.5–2 kbar, but which depart progressively from their extrapolation to higher pressures because of the pressure-induced dissociation effect. The great similarity of the NaCl-H2O and KCl-H2O systems suggests that H2O activities in the ternary NaCl-KCl-H2O system can be described with reasonable accuracy by assuming proportionality between the binary systems. This assumption was verified by a few reconnaissance measurements at 10 kbar of the brucite-periclase equilibrium with a Na/(Na + K) ratio of 0.5 and of the saturation temperature for Na/(Na + K) of 0.35 and 0.50. At that pressure the brucite-periclase curves reach a lowest xH2O of 0.45 and a temperature of 587 °C before salt saturation occurs, values considerably lower than in either binary. This double-salt eutectic effect may have a significant application to natural polyionic hypersaline solutions in the deep crust and upper mantle in that higher solute concentrations and very low H2O activities may be realized in complex solutions before salt saturation occurs. Concentrated salt solutions seem, from this standpoint, and also because of high mechanical mobility and alkali-exchanging potential, feasible as metasomatic fluids for a variety of deep-crust and upper mantle processes.

Synthesis, characterization, and enthalpy of mixing of the (Fe,Mg)C0 3 solid solution

Solid solutions along the magnesite-siderite join have been synthesized from mechanical mixtures of iron oxalate and basic magnesium carbonate using hydrothermal synthesis techniques at 500°C and about 2 kilobars. The double capsule method was used to provide the atmosphere necessary to prevent decomposition and oxidation of the Fe 2+-bearing carbonate. The synthetic samples were characterized by x-ray diffraction (XRD) and thermogravimetric analysis (TGA). Unit cell parameters, determined from x-ray diffraction in step scan mode, show a linear relationship with composition. The compositions and homogeneity of the sample were confirmed by electron microprobe analysis.Enthalpy of mixing was measured using a Calvet-type calorimeter at 770°C. A two step calorimetric method was developed and confirmed to be successful in determining the energetics of the Fe 2+-bearing carbonates. The first step involved decomposition of the sample in an oxygen atmosphere, and then the decomposition of the sample in an oxygen atmosphere, and then the decomposition products (a mixture of a spinel phase, MgFe 2O 4, and MgO or hematite) were dissolved in lead borate solvent in air as the second step. The enthalpies of mixing are slightly positive, with a regular solution parameter of 4.44 ± 0.75 kJ/mol. Under the assumption of regular solution, the phase diagram of the FeC0 3MgCO 3 system has been calculated, and the critical temperature for exsolution is about −6°C. Thus, the (Fe,Mg) CO 3 solid solution is expected to be complete and nearly ideal in all geological environments.

Position sensitive atom probe study of segregation in molybdenum alloys.

Three dimensional atom-probe measurements have been carried out to study the segregation behaviour of Mo(x)W((1-x)) alloys (x = 0.9; 0.75; 0.5; 0.25). As predicted from alloy thermodynamics, on in situ annealed specimens a significant surface enrichment of molybdenum has been observed. For alloys with tungsten contents above 25% the composition profiles measured are in a good agreement with the theoretical predictions. The positive regular solution parameter of this binary system gives reason for a random distribution of alloy components. In the three-dimensional reconstructions local agglomerations and combined features of tungsten atoms are to observe in alloys with Mo as major component.

Tie lines and activities in the system NiO-MgO-SiO2 at 1373 K

The isothermal section of the phase diagram for the system NiO-MgO-SiO2 at 1373 is established. The tie lines between (NixMg1-x)O solid solution with rock salt structure and orthosilicate solid solution (NiyMg1-y)Si0.5O2 and between orthosilicate and metasilicate (NizMg1-z)SiO3 crystalline solutions are determined using electron probe microanalysis (EPMA) and lattice parameter measurement on equilibrated samples. Although the monoxides and orthosilicates of Ni and Mg form a continuous range of solid solutions, the metasilicate phase exists only for 0 < Z < 0.096. The activity of NiO in the rock salt solid solution is determined as a function of composition and temperature in the range of 1023 to 1377 using a solid state galvanic cell. The Gibbs energy of mixing of the monoxide solid solution can be expressed by a pseudo-subregular solution model: ΔGex = X(l - X)[(-2430 + 0.925T)X + (-5390 + 1.758T)(1 - X)] J/mol. The thermodynamic data for the rock salt phase are combined with information on interphase partitioning of Ni and Mg to generate the mixing properties for the orthosilicate and the metasilicate solid solutions. The regular solution model describes the orthosilicate and the metasilicate solid solutions at 1373 K within experimental uncertainties. The regular solution parameter ΔGex/Y(1-Y) is -820 (±70) J/mol for the orthosilicate solid solution. The corresponding value for the metasilicate solid solution is -220 (±150) J/mol. The derived activities for the orthosilicate solid solution are discussed in relation to the intracrystalline ion exchange equilibrium between Ml and M2 sites. The tie line information, in conjunction with the activity data for orthosilicate and metasilicate solid solutions, is used to calculate the Gibbs energy changes for the intercrystalline ion exchange reactions. Combining this with the known data for NiSi0.5O2, Gibbs energies of formation of MgSi0.5O2, MgSiO3, and metastable NiSiO3 are calculated. The Gibbs energy of formation of NiSiO3, from its component oxides, is equal to 7.67 (±0.6)kJ/mol at 1373K.

Modelling of Phase Diagram Boundaries at Equilibrium of Two Binary Regular Phases

The conditions of occurrence of extremes on the solidus and liquidus curves in a binary isobaric phase diagram are specified. The solid and liquid phases are regarded as regular solutions in equilibrium. Two simplifying assumptions are made: (i) the Gibbs function of melting of the pure components is a linear function of temperature; (ii) the two phases in equilibrium are regular solutions with a temperature-dependent regular solution parameter. The conditions of occurrence of inflexion points on the solidus and/or liquidus curves are obtained by modelling.

The partitioning of Fe and Mg between olivine and carbonate and the stability of carbonate under mantle conditions

We have investigated the effect of Fe on the stabilities of carbonate (carb) in lherzolite assemblages by determining the partitioning of Fe and Mg between silicate (olivine; ol) and carbonates (magnesite, dolomite, magnesian calcite) at high pressures and temperatures. Fe enters olivine preferentially relative to magnesite and ordered dolomite, but Fe and Mg partition almost equally between disordered calcic carbonate and olivine. Measurement of Kd(XFecarbXMgol/XFeolXMgcarb) as a function of Fe/ Mg ratio indicates that Fe−Mg carbonates deviate only slightly from ideality. Using the regular solution parameter for olivine WFeMgolof 3.7±0.8 kJ/mol (Wiser and Wood 1991) we obtain for (FeMg)CO3 a WFeMgcarbof 3.05±1.50 kJ/mol. The effect of Ca−Mg−Fe disordering is to raise Kd substantially enabling us to calculate WCaMgcarb-WCaFecarbof 5.3±2.2 kJ/mol. The activity-composition relationships and partitioning data have been used to calculate the effect of Fe/Mg ratio on mantle decarbonation and exchange reactions. We find that carbonate (dolomite and magnesian calcite) is stable to slightly lower pressures (by 1 kbar) in mantle lherzolitic assemblages than in the CaO−MgO−SiO2(CMS)−CO2 system. The high pressure breakdown of dolomite + orthopyroxene to magnesite + clinopyroxene is displaced to higher pressures (by 2 kbar) in natural compositions relative to CMS. CO2. We also find a stability field of magnesian calcite in lherzolite at 15–25 kbar and 750–1000°C.