Fe-Mn partitioning between garnet and ilmenite: experimental calibration and applications

A new mineralogic geothermometer based on the partitioning of Fe and Mn between garnet and ilmenite has been calibrated by reversal experiments in the P-T range 600–900° C, 2 and 5 kbars and for fO₂=QFM. The results constitute a sensitive geothermometer applicable over a broad range of composition and conditions. Garnetilmenite thermometry has advantages relative to existing geothermometers because of its accurate calibration, marked temperature sensitivity and the chemical and structural simplicity of the crystalline solutions involved. Application to natural assemblages reveals that the garnet-ilmenite geothermometer yields temperatures that agree well with other estimates. The reactivity of, and relatively rapid Fe-Mn diffusion in ilmenite may lead to retrograde resetting of high temperature partition values, but these factors may be useful for estimating rock cooling rates. Analysis of the experimental data indicates minor positive deviations from ideality for Fe-Mn garnets and ilmenites. Absolute magnitudes of interaction parameters (W _AB) derived from a regression analysis are subject to considerable uncertainty. The partition coefficient is, however, strongly dependent on the difference between solution parameters. These differences are well constrained with a magnitude of W _FeMn ^ilm –W _FeMn ^gar 300 cal mol^–1. The accuracy and applicability of garnet-ilmenite thermometry will improve with the availability of better thermodynamic data for garnet crystalline solutions.Abbreviations and symbols used in text R universal gas constant (cal/mol/°K) - T absolute temperature (°K or °C) - P pressure (kbars) - V ⁰ volume change of reaction (1) - H _{1, T} ⁰ standard state enthalpy change of reaction (1) at 1 bar and the T of interest, in cal/mole - S _T ⁰ entropy change of reaction (1) at T of interest, in cal/mole/°K - G _P,T ⁰ standard free energy change of reaction (1) at the T and P of interest, in cal/mole - distribution coefficient for Fe-Mn partitioning between garnet and ilmenite - K apparent equilibrium coefficient for reaction (1) - _i ^j activity of component i in phase j - W _A-B binary A-B interaction (Margules) parameter - gar garnet - ilm ilmenite - biot biotite - ol olivine - opx orthopyroxene     

Thermal diffusivity of natural and synthetic garnet solid solution series

Knowledge of heat transport properties as a function of mineral- and rock-composition and temperature is of major relevance to understand and model heat transfer in the Earth’s interior. A systematic study on 13 natural and 4 synthetic garnets was carried out in an attempt to obtain a better systematic understanding of the processes that affect the heat transport in minerals, especially the effect of chemical substitution in solid solution series. It is found that substitution significantly lowers the thermal diffusivity from end-member values for both synthetic and natural garnets with a minimum of thermal diffusivity at an intermediate composition. The thermal diffusivity as a function of the degree of substitution can be described by the approach of Padture and Klemens (J Am Ceram Soc 80 (4):1018–1020, 1997). With increasing temperature the thermal diffusivity decreases due to phonon-phonon-scattering effects. A quantitative analysis of the high-temperature behaviour was carried out by using the model of Roufosse and Klemens (J Geophys Res 79 (5):703–705, 1974), which takes a lower limit of thermal diffusivity at elevated temperatures into account. The model allows for an extrapolation of the deduced room temperature thermal diffusivities to higher temperatures. Furthermore, the model was modified to determine the high temperature limit of the thermal diffusivity for all investigated natural garnets D _min to be 0.64 ± 0.03 mm²/s.     

Mixing behavior in quaternary garnet solid solution and an extended Ellis and Green garnet-clinopyroxene geothermometer

Applications of the different formulations of garnet-clinopyroxene geothermometers to crustal granulites and particularly to metamorphosed manganese formations show a wide scatter of estimates. This is primarily related to the uncertainty associated with the formulation of the activity-composition relationship in garnet solid solution besides that in the clinopyroxene solid solution. The largest uncertainty appears to have resulted from the adopted Mg-Mn interaction parameter in garnet which is yet to be experimentally determined. A fresh statistical regression of eleven pairs of garnet and clinopyroxene equilibrated at identical P-T conditions from a manganese formation in India yields W _Mg-Mn ^Gt (=W_Mn-Mg) value of 1600±500 cal/mols. An extension of the Ellis and Green (1979) geothermometer, known to work well in normal granulites, incorporating terms associated with the activity coefficients of the exchangeable cations, now yields consistent temperature estimation from normal granulites as well as from metamorphosed manganese formations. The geothermometer, however, will not work well for garnet having X_Fe0.65 and clinopyroxenes containing appreciable Na, Al and/or Fe³⁺.     

Cation diffusion in aluminosilicate garnets: experimental determination in spessartine-almandine diffusion couples,evaluation of effective binary diffusion coefficients,and applications

We present new experimental data on diffusion of divalent cations in almandine-spessartine diffusion couples in graphite capsules in the P-T range of 14–35 kb, 1100–1200° C. The tracer diffusion coefficients of the major divalent cations, viz. Fe, Mg and Mn, retrieved from the multicomponent diffusion profiles, have been combined with earlier data from our laboratory at 29–43 kb, 1300–1480° C (Loomis et al. 1985) to derive expressions of the P-T dependence of the diffusion coefficients at fO₂ approximately corresponding to that defined by equilibrium in the system graphite-O₂. We review the conditions, discussed earlier by Cooper, under which the flux of a component in a multicomponent system becomes proportional to its concentration gradient (Fickian diffusion), as if the entire solvent matrix behaves as a single component, and also suggest a method of incorporating the thermodynamic effect on diffusion in the same spirit. Regardless of the magnitude or sign of the off-diagonal terms of the D matrix, it is always possible to define an effective binary diffusion coefficient (EBDC) of a component in a semi-infinite multicomponent diffusion-couple experiment such that it has the property of the Fickian diffusion coefficient, provided that there is no inflection on the diffusion profiles. It is shown that the success of Elphick et al. in fitting the experimental diffusion profiles of all components over a limited concentration range by a single diffusion coefficient is due to fortuitous similarity of the EBDCs of the components (Fe, Mg, Mn and Ca) in their diffusion couple experiments. In common metapelitic garnets showing compositional zoning, the EBDCs of the divalent cations do not differ from each other by more than a factor of 2.5. However, the EBDC of a component changes from core to rim by a factor of 3 to 12, depending on the composition. We suggest a method of volume averaging of the EBDC which should prove useful in approximate calculations of diffusion flux during relaxation of compositional zoning. The EBDC of Mn is found to reduce essentially to D _MnMn, the main diagonal term of the D matrix, and consequently can be calculated quite easily. Evaluation of EBDC of Fe, Mg and Mn in garnets from a prograde Barrovian sequence did not reveal any significant dependence on the extent of relaxation of garnet. The diffusion data have been applied to calculate the cooling rate of natural biotite-garnet diffusion couple from eastern Finland and diffusional modification of growth zoning in garnet in early Proterozoic Wopmay orogen, Canada. The results are in good agreement with geochronological and other independent constraints.Symbols and abbreviations a Radius of a spherical garnet crystal - BSE Back-scattered electron imaging - C Column vector of (n-1) independent components - D Diffusion coefficient matrix - D _ij An element of the diffusion matrix on the i th row and j th column - D _* ⁱ Tracer diffusion coefficient of component i - D(i) Effective interdiffusion coefficient (EIC) of various components in a multicomponent solution rich in the component i - D(i-j) Interdiffusion coefficient of components i and j in a binary solution - D _i (EB) Effective binary diffusion coefficient of component i in a multicomponent solution - D _i (EB:Ideal) D _i (EB) under condition of ideal thermodynamic mixing of the diffusing species - D _i (EB:thermo) Thermodynamic component of D _i(EB) - D _O ^A Interdiffusion coefficient at peak temperature T ₀ in the phase A - D ₀ Pre-exponential factor in an Arrhenius relation - EBDC Effective binary diffusion coefficient between a solute and a multicomponent solvent matrix - FEC Fixed edge composition model - EIC Effective interdiffusion coefficient - f _i Fugacity of component i - HM Hematite-magnetite oxygen fugacity buffer - kb Kilobars - P Pressure - Q Activation energy (enthalpy) of diffusion - Extent of relaxation defined as the difference between core and rim compositions normalized to the same difference in the initial zoning profile - R Gas constant - s Cooling rate - T ₀, T _Ch Peak temperature and characteristic temperature, respectively - t Time - VEC Variable edge composition model - V ⁺ Activation volume - W _ij Simple mixture interaction parameter between i and j - W _i(EB) Effective simple mixture interaction parameter of a component i in a multicomponent solution - _ij Margules interaction parameter between i and j - X _i Mole fraction of component i - _i Activity coefficient of component i - A dimensionless variable =D t/a ² - _ij Kronecker delta (i=j, _ij =1; ij, _ij =0) - Z_i Charge on the ion i     

Viscosity of andesitic melts—new experimental data and a revised calculation model

The viscosity of a synthetic andesite-like melt was measured in the low viscosity range (10¹-10⁶ Pa s) using the falling sphere(s) method and in the high viscosity range (10⁸-10¹³ Pa s) using parallel-plate viscometry. Falling sphere experiments with melts containing 2.3 and 5.6 wt.% H₂O were carried out in an internally heated gas pressure vessel (IHPV) at 500 MPa confining pressure. The sinking velocity of Pt and Pd spheres and in one case of a corundum sphere was used to measure the melt viscosity. In addition, a creep experiment was performed at ambient pressure using a glass containing 2.73 wt.% H₂O . A more water-rich glass (5.6 wt.% H₂O ) was investigated with a high pressure parallel-plate viscometer at 400 MPa confining pressure in an IPHV. By combining our new data with previous results for a similar melt composition we derived the following expression to describe the viscosity η (in Pa s) as a function of temperature T (in K) and water content w (in wt.%)

     

Thermodynamics and crystal chemistry of the hematite–corundum solid solution and the FeAlO3 phase

High-temperature oxide-melt calorimetry and Rietveld refinement of powder X-ray diffraction patterns were used to investigate the energetics and structure of the hematite–corundum solid solution and ternary phase FeAlO₃ (with FeGaO₃ structure). The mixing enthalpies in the solid solution can be described by a polynomial ΔH_mix=WX _hem(1?X _hem) with W=116 ± 10 kJ mol^?1. The excess mixing enthalpies are too positive to reproduce the experimental phase diagram, and excess entropies in the solid solution should be considered. The hematite–corundum solvus can be approximately reproduced by a symmetric, regular-like solution model with ΔG _excess=(W _H ?TW _S )X _hem X _cor, where W _H= 116 ± 10 kJ mol^?1 and W _S =32 ± 4 J mol^?1 K^?1. In this model, short-range order (SRO) of Fe/Al is neglected because SRO probably becomes important only at intermediate compositions close to Fe:Al=1:1 but these compositions cannot be synthesized. The volume of mixing is positive for Al-hematite but almost ideal for Fe-corundum. Moreover, the degree of deviation from Vegard's law for Al-hematite depends on the history of the samples. Introduction of Al into the hematite structure causes varying distortion of the hexagonal network of oxygen ions while the position of the metal ions remains intact. Distortion of the hexagonal network of oxygen ions attains a minimum at the composition (Fe_0.95Al_0.05)₂O₃. The enthalpy of formation of FeAlO₃ from oxides at 298 K is 27.9 ± 1.8 kJ mol^?1. Its estimated standard entropy (including configurational entropy due to disorder of Fe/Al) is 98.9 J mol^?1 K^?1, giving the standard free energy of formation at 298 K from oxides and elements as +19.1 ± 1.8 and ?1144.2 ± 2.0 kJ mol^?1, respectively. The heat capacity of FeAlO₃ is approximated as C _p (T in K)= 175.8 ? 0.002472T ? (1.958 × 10⁶)/T ²? 917.3/T ^0.5+(7.546 × 10^?6) T ² between 298 and 1550 K, based on differential scanning calorimetric measurements. No ferrous iron was detected in FeAlO₃ by Mössbauer spectroscopy. The ternary phase is entropy stabilized and is predicted to be stable above about 1730 ± 70 K, in good agreement with the experiment. Static lattice calculations show that the LiNbO₃-, FeGaO₃-, FeTiO₃-, and disordered corundum-like FeAlO₃ structures are less stable (in the order in which they are listed) than a mechanical mixture of corundum and hematite. At high temperatures, the FeGaO₃-like structure is favored by its entropy, and its stability field appears on the phase diagram.     

Redox state of deep off-craton lithospheric mantle: new data from garnet and spinel peridotites from Vitim, southern Siberia

Oxygen fugacity (fO₂) affects melting, metasomatism, speciation of C–O–H fluids and carbon-rich phases in the upper mantle. fO₂ of deep off-craton mantle is poorly known because garnet-peridotite xenoliths are rare in alkali basalts. We examine the redox and thermal state of the lithospheric mantle between the Siberian and North China cratons using new Fe³⁺/ΣFe ratios in garnet and spinel obtained by M?ssbauer spectroscopy, major element data and P–T estimates for 22 peridotite xenoliths as well as published data for 15 xenoliths from Vitim, Russia. Shallow spinel-facies mantle is more oxidized than deep garnet peridotites (average, ?0.1 vs. ?2.5 ΔlogfO₂(FMQ)). For intermediate garnet–spinel peridotites, fO₂ estimates from spinel-based oxybarometers are 1.5–3.2 ΔlogfO₂(FMQ) lower than those from garnet-based oxybarometers. These rocks may be out of phase and chemical inter-mineral equilibrium because the spinel–garnet reaction and concomitant changes in mineral chemistry do not keep up with P–T changes (e.g., lithospheric heating by recent volcanism) due to slow diffusion of trivalent cations and because gar-, gar-spl and spl-facies rocks may coexist on centimeter–meter scale. The spinel-based fO₂ estimates may not be correct while garnet-based fO₂ values provide conditions before the heating. The T (780–1,100?°C) and fO₂ ranges of the Vitim xenoliths overlap those of coarse garnet and spinel cratonic peridotites. However, because of a higher geothermal gradient, the deepest Vitim garnet peridotites are more reduced (by 0.5–2.0 ΔlogfO₂(FMQ)) than cratonic garnet peridotites at similar depths, and the “water maximum” conditions (>80?% H₂O) in the off-craton mantle exist in a more shallow and narrow depth range (60–85?km) than in cratonic roots (100–170?km). The base of the off-craton lithospheric mantle (≥90?km) at 2.5?GPa and 1,150?°C has fO₂ of ?3.0 ?logfO₂(FMQ), with dominant CH₄ and H₂O and minor H₂ in the fluid. Melting near the base of off-craton mantle lithosphere may be induced by increasing water share in migrating fluids due to oxidation of methane.     

Transformation kinetics of polycrystalline aragonite to calcite: new experimental data,modelling, and implications

Experimental data are used to model the transformation rate of polycrystalline aragonite (grain diameter 80 m) to calcite. Optimized values for nucleation and growth rates were obtained by numerically fitting the overall transformation rates from 280° to 380°C and 0.10 MPa to an expression for a grain-boundary-nucleated and interface-controlled transformation. The nucleation rate is 4–5 orders of magnitude faster than for calcite nucleated within aragonite grains, and the growing in rate is slower below 300°C than for calcite growing in aragonite single crystals. The activation enthalpy for growth in polycrystalline aggregate is 247kJ/mol compared to 163 kJ/mol for growth in single crystals. Permanent deformation of the phases limits the elastic strain energy due to the 7% volume change and reduces the coherency of the calcite/aragonite interace. Theoretical expressions are used to extrapolate the data for nucleation and growth to other temperatures, and data from 0.10 to 400 MPa are used to evaluate the effect of pressure on the grain-boundary nucleation rate. Because of permanent deformation of the phases, the effective strain energy for nucleation is 0.55 kJ/mol, which is less than a quarter of the value for purely elastic deformation. These data are used to predict the percent transformation for various P-T-t paths; without heating during uplift partial preservation of aragonite in dry blueschist facies rocks can occur if the calcite stability field is entered at 235° C, and the kinetic data are also consistent with published P-T-t paths which include heating during uplift. The predicted percent transformation is relatively insensitive to variations in the initial grain size of the aragonite, but strongly dependent on the effective strain energy.     

The origin of coarse garnet peridotites in cratonic lithosphere: new data on xenoliths from the Udachnaya kimberlite, central Siberia

We report new textural and chemical data for 10 garnet peridotite xenoliths from the Udachnaya kimberlite and examine them together with recent data on another 21 xenoliths from the 80–220 km depth range. The samples are very fresh (LOI near zero), modally homogeneous and large (>100 g). Some coarse-grained peridotites show incipient stages of deformation with <10 % neoblasts at grain boundaries of coarse olivine. Such microstructures can only be recognized in very fresh rocks, because fine-grained interstitial olivine is strongly affected by alteration, and may have been overlooked in previous studies of altered peridotite xenoliths in the Siberian and other cratons. Some of the garnet peridotites are similar in composition to low-opx Udachnaya spinel harzburgites (previously interpreted as pristine melt extraction residues), but the majority show post-melting enrichments in Fe and Ti. The least metasomatized coarse peridotites were formed by 30–38 % of polybaric fractional melting between 7 and 4 GPa and ≤1–3 GPa. Our data together with experimental results suggest that garnet in these rocks, as well as in some other cratonic peridotites elsewhere, may be a residual mineral, which has survived partial melting together with olivine and opx. Many coarse and all deformed garnet peridotites from Udachnaya underwent modal metasomatism through interaction of the melting residues with Fe-, Al-, Si-, Ti-, REE-rich melts, which precipitated cpx, less commonly additional garnet. The xenoliths define a complex geotherm probably affected by thermal perturbations shortly before the intrusion of the host kimberlite magmas. The deformation in the lower lithosphere may be linked to metasomatism.     

Study on the compositional dependence of the apparent partition coefficient of iron and magnesium between coexisting garnet and clinopyroxene solid solution

Compositional dependence of apparent partition coefficient of iron and magnesium between coexisting garnet and clinopyroxene from Mt. Higasiakaisi is studied by means of a multicomponent regular solution model. It is shown that garnet and clinopyroxene solid solutions are positively non-ideal, and the non-ideal parameters according to the symmetric regular solution model are 2.58 kcal and 2.39 kcal, respectively, assuming the equilibration temperature of the mass to be 550° C.Notations a _i ^h activity of component i in phase h - _ij interaction parameter of component i and j in a solid solution - _i activity coefficient of component i - X _i mole fraction of component i - K partition coefficient of Fe and Mg between coexisting garnet and clinopyroxene - K apparent partition coefficient of Fe and Mg between coexisting garnet and clinopyroxene - G ⁰ difference in free energy of the partition reaction - H ⁰ difference in enthalpy of the partition reaction - S ⁰ difference in entropy of the partition reaction - R gas constant - G garnet - Alm almandine component - Py pyrope component - Gr grossular component - Sp spessartine component - CPx clinopyroxene - Hd hedenbergite component - Di diopside component - Jd jadeite component - Ts Tschermac's molecule component Deceased on April 17, 1974.     

Evaluation of thermochemical data on Fe-Mg olivine,orthopyroxene, spinel and Ca-Fe-Mg-Al garnet

Thermochemical data on Fe-Mg olivine, orthopyroxene, spinel and Ca-Fe-Mg garnet have been tested and reevaluated in reproducing experimental equilibrium data. All data (except of spinel) adjusted in this process lie within the error limits of original calorimetric experiments. For spinel, an enthalpy of −2307.2 kJ/mol and an entropy of 81.5 J/mol-K has been recommended. Recommended interaction parameters for the spinel-hercynite and forsterite-fayalite solutions are as follows:Spinel: W_{spinel-hercynite} = 9124.0 J/mol. W_{hercynite-spinel} = 0.0 J/molOlivine: W = 4500.0 J/mol for 1 cation.Excess entropies (on 1 cation basis) necessary to reproduce phase equilibria for the pyrope-almandine and almandine-grossular solutions are as follows:Mg-Fegarnet: W^s_{pyrope-almandine} = 11.760 − 0.00167 J/mol-K. W^s_{almandine-pyrope} = −10.146 +0.0037T J/mol-K.Fe-Ca garnet: W^s = −16.07 + 0.0126T J/mol-K.     

Thermodynamics of minerals of variable composition: Andradite-grossularite and pistacite-clinozoisite solid solutions

Exchange-mineral equilibria with Al and Fe³⁺ aqueous chloride solutions (aq.), Andr + AlCl _aq ³ = FeCl _aq ³ + Gros, (1) Psc + AlCl _aq ³ = FeCl _aq ³ + Czo, (2) were studied under the following experimental conditions: 500°;C and 580°;C and 1 and 2 kbar, respectively, with an overall concentration of metals in the aqueous solutions of about 0.5 M and pH 3. The mixing functions of the components in garnet and epidote were calculated from the experimental data. Thermodynamic treatment of experimental evidence for reaction (1) led to the conclusion that, within the accuracy of experiment, garnet in the andradite-grossularite series was an ideal solid solution. However, epidote solid solution markedly departed from the ideal, as was shown by concentration and pressure-temperature (PT) dependencies of Gibbs's molar excess energies and by mixing-volume concentration dependence.     

Analysis of experimental data on divalent cation diffusion kinetics in aluminosilicate garnets with application to timescales of peak Barrovian metamorphism,Scotland

We present a new statistical framework to analyze the diffusion data for divalent cations (Fe, Mg, Mn, and Ca) in aluminosilicate garnet using published experimental data and an Arrhenius relationship that accounts for dependence on temperature, pressure, garnet unit-cell dimension, and oxygen fugacity. The regression is based on Bayesian statistics and is implemented by the Markov chain Monte Carlo approach. All reported experimental uncertainties are incorporated, and the data are weighted by the precision of the experimental conditions. We also include a new term, the inter-experiment bias, to compensate for possible inconsistencies among experiments and to represent any experimental variability not explicitly presented in the Arrhenius relationship (e.g., water content, defect density). At high temperatures where most experiments were conducted, the diffusion coefficients calculated with the new parameters agree well with previous diffusion models (e.g., Chakraborty and Ganguly in Contrib Mineral Petrol, 111:74–86, 1992; Carlson in Am Mineral, 91:1–11, 2006). However, the down-temperature extrapolation leads to notable differences at lower temperatures for common petrological applications. For example, at 600 °C, the diffusion coefficients of Fe and Mn are one half-to-one order of magnitude faster and the diffusion coefficient of Ca is about one order of magnitude slower than calculated with parameters in Carlson (2006). Our statistical analysis also provides well-defined uncertainty bounds for timescale estimates based on garnet diffusion profiles. Application of the newly derived coefficients indicates that the timescale of the thermal peak of Barrovian metamorphism (Dalradian belt of Scotland) is about four to seven times longer than that estimated using previously published diffusion coefficients. The peak is still geologically brief, however—of the order of 10⁶ years (0.75 Myr +0.70/?0.36 Myr; ±1σ). This brevity requires pulsed advective heat input, as provided by syn-orogenic mafic magmatism in these rocks.     

Solubility and migration ability of rhodium in natural conditions: model experimental data

The contents of dissolved rhodium species in the near-neutral environments have been studied for the first time and data on the interaction of Rh with organic matters of natural waters and its sorption behavior during contact with the components of geochemical barriers were obtained. The solubility method was used to analyze the behavior of rhodium hydroxide in the Rh(OH)_x–H₂O and Rh(OH)_x–H₂O–FA (fulvic acids) systems. The possible contents of inorganic species of rhodium and its compounds with humic organic ligands were determined within the pH range typical of surface waters. The solubility of rhodium shows a twoorder- of magnitude increase in the presence of humic matters (FA). The sorption interaction of the soluble rhodium species with the main components of geochemical barriers such as iron oxyhydroxides (III), (including fulvic-acid modified ones), alumosilicates, and precipitates of humic acids in contact with natural waters was studied. It was revealed that rhodium has the high affinity to all studied materials; its species are sorbed by ferrihydrite within several hours. It is suggested that rhodium is mainly transferred as colloid with suspended particulate matters of waters and then is accumulated in bottom sediments. The differences revealed in the sorption behavior of Pt(IV), Pd(II) and Rh(III) may be used to predict the distribution of the considered platinum group elements between the components of ecosystems.     

AuPdFe ternary solution model and applications to understanding the fO2 of hydrous, high-pressure experiments

This study provides an experimental calibration of the equilibrium constant for AuPdFe alloys with Fe-bearing silicate melts. The ideal metal capsules for H₂O-bearing experiments are pure Au, because of its slow hydrogen diffusivity. However, above the melting point of Au, other materials must be used. The solution to this problem is to use AuPd alloy capsules. However, under most relevant fO₂ conditions, this alloy absorbs Fe from the coexisting silicate melt, thus changing the bulk composition of the experimental charge. This study combines previous work on the Au–Pd, Pd–Fe, and Au–Fe binary systems to develop a ternary thermodynamic solution model for AuPdFe. This solution model is used with experiments to calculate an equilibrium reaction coefficient for the FeO_melt → Fe_alloy + 1/2O₂ exchange reaction. Using a non-ideal ternary solution model, the fO₂ conditions of hydrous, piston cylinder experiments can be estimated by analyzing the sample capsule alloy and the coexisting liquid composition.     

Distinct local environments for Ca along the non-ideal pyrope–grossular solid solution: A new model based on crystallographic and EXAFS analysis

A multi-technique approach (based on electron microprobe analysis, structure refinement, and EXAFS analysis at the Ca K-edge) was used to characterise the local geometry of Ca in synthetic and natural garnet compositions referable to the pyrope–grossular solid solution. Multi-shell fits of the EXAFS data indicate that Ca assumes the standard [4 + 4]-fold coordination (the polyhedral shape being a triangular dodecahedron with Ca1–O = 2.30–2.31(1) and Ca2–O = 2.45–2.46(1) Å) when Ca > 1.50 atoms per formula unit (apfu), but assumes a nearly regular [8]-fold coordination with Ca–O = 2.35–2.36 (1) Å when (Mg, Fe²⁺, Mn²⁺) > 1.50 apfu. Therefore, in the pyrope-dominant structure the Ca1–O distance lengthens and the Ca2–O distance shortens to converge towards the value observed for the Mg2–O bond in pyrope. This finding is consistent with many distinct structural features observed in solid solution terms with (Mg, Fe²⁺, Mn²⁺) > 1.50 apfu or Ca > 1.50 apfu, as well as with the anomalous properties of the intermediate terms observed both in the short-range and in the long-range perspective. The presence of two distinct Ca coordinations in the pyrope (almandine, spessartine)-like and in the grossular-like structure, and thus of an isosymmetric transition at the intermediate composition, can help to explain both the strong and asymmetric non-ideality of the solid solution between pyrope (almandine) and grossular, as well as the differences in the ability to incorporate some trace elements (such as REE and actinides) which are commonly used as process-specific indicators. This feature must be taken into account when building theoretical models of the garnet solid solutions, which are at the moment the most promising approach for calculating thermodynamic properties or for interpreting and predicting trace-element behaviour in this crucial mineral phase.     

Fe2+-Mg2+ partition between coexisting cordierite and garnet — a discussion of the experimental data

The partition of iron and magnesium between cordierite and garnet depends on as well as temperature. The apparently conflicting experimental data on the values of K _D may be reconciled by considering the pertaining during the different experiments.