Orthopyroxene Solid Solutions Research Articles

Thermal equation of state of synthetic orthoferrosilite at lunar pressures and temperatures

Iron-rich orthopyroxene plays an important role in models of the thermal and magmatic evolution of the Moon, but its density at high pressure and high temperature is not well-constrained. We present in situ measurements of the unit-cell volume of a synthetic polycrystalline end-member orthoferrosilite (FeSiO3, fs) at simultaneous high pressures (3.4–4.8 GPa) and high temperatures (1,148–1,448 K), to improve constraints on the density of orthopyroxene in the lunar interior. Unit-cell volumes were determined through in situ energy-dispersive synchrotron X-ray diffraction in a multi-anvil press, using MgO as a pressure marker. Our volume data were fitted to a high-temperature Birch–Murnaghan equation of state (EoS). Experimental data are reproduced accurately, with a \(\varDelta P\) standard deviation of 0.20 GPa. The resulting thermoelastic parameters of fs are: V0 = 875.8 ± 1.4 A3, K0 = 74.4 ± 5.3 GPa, and \(\frac{{\text d}K}{{\text d}T} = -0.032 \pm 0.005\,\hbox{GPa K}^{-1}\), assuming \({K}^{\prime}_{0} = 10 \). We also determined the thermal equation of state of a natural Fe-rich orthopyroxene from Hidra (Norway) to assess the effect of magnesium on the EoS of iron-rich orthopyroxene. Comparison between our two data sets and literature studies shows good agreement for room-temperature, room-pressure unit-cell volumes. Preliminary thermodynamic analyses of orthoferrosilite, FeSiO3, and orthopyroxene solid solutions, (Mg1−xFex) SiO3, using vibrational models show that our volume measurements in pressure–temperature space are consistent with previous heat capacity and one-bar volume–temperature measurements. The isothermal bulk modulus at ambient conditions derived from our measurements is smaller than values presented in the literature. This new simultaneous high-pressure, high-temperature data are specifically useful for calculations of the orthopyroxene density in the Moon.

Model independent phase equilibrium constraints on the ferrosilite activity in the binary Fe-Mg orthopyroxene solid solution

Compositional reversals of orthopyroxene solid solution (Opx) on the enstatite (En, MgSiO 3 )-ferrosilite (Fs, FeSiO 3 ) join equilibrated with hematite (Hm, Fe 2 O 3 ), magnetite (Mt, Fe 3 O 4 ), and quartz (Qz) were obtained in piston-cylinder apparatus in the pressure range 10–25 kbar at temperatures of 800 and 950 °C. A double-capsule technique with the Hm-Mt external buffer was employed to ensure the presence of both Fe oxides in the run products. Starting materials were crystalline mixtures of synthetic Opx with X Fs [=Fe/(Fe+Mg)] = 0.05 and 0.45, reagent Mt, Hm, and natural Qz. Run products were carefully examined using optical microscopy, back-scattered (BSE) imaging, and wavelength dispersive electron microprobe analysis. Despite the differences in the rates of forward and backward reactions Fs (in Opx) + Hm = Mt + Qz (1), very tight compositional brackets (less than 0.01 X Fs ) were obtained at each P - T . At 800 °C, midpoints of the compositional brackets are: 0.195/10 kbar, 0.24/15, 0.29/20, and 0.34/25; at 950 °C: 0.21/15 kbar, 0.25/20, and 0.295/25 kbar. Activities of Fs, recalculated from these compositions using either Berman and Aranovich (1996) or Holland and Powell (1998) data sets for the pure end-member reaction (1), show negative deviation from ideal mixing. Strongly temperature dependent enthalpy of mixing is required to make these activity values consistent with the configurational entropy of the solid solution deduced from the site occupancy measurements. A simple mixing model with a linearly varying temperature-dependent W term, similar to that of Berman and Aranovich (1996), adequately reproduces the experimental data.

The effect of Cr on the solubility of Al in orthopyroxene: experiments and thermodynamic modelling

The partitioning of chromium and aluminium between coexisting orthopyroxene and spinel in equilibrium with forsterite in the system MgO–Al2O3–SiO2–Cr2O3 (MAS–Cr) has been experimentally determined as a function of temperature, pressure and Cr/(Cr + Al) ratio. Experiments were conducted at temperatures between 1300 and 1500 °C and at pressures from 5 to 54 kbar. Previous experimental results on the (Al, Cr)2O3 and Mg(Al, Cr)2O4 solid solutions have been combined with the present results plus relevant data from the CMAS system to derive a thermodynamic model for Al–Cr-bearing orthopyroxenes, spinels and corundum–eskolaite solid solutions. The orthopyroxene solid solution can be modelled within the accuracy of all experimental constraints as a ternary solid solution involving the components Mg2Si2O6 ( E), MgAl2SiO6 (M) and MgCr2SiO6 (C), in which the activities are related to composition through the equations:

Fe 2+ -Mg order-disorder in orthopyroxene: equilibrium fractionation between the octahedral sites and thermodynamic analysis

The equilibrium intracrystalline distribution coeAcient, k D ,o f Fe (i.e. Fe 2+ + Mn) and Mg between the M1 and M2 sites of three natural nearly binary Fe 2+ -Mg orthopyroxene crystals (Fs14 ,F s15 and Fs49) were determined by annealing experiments at several temperatures between 550 and 1000 ∞C and single crys- tal X-ray structure refinements. In addition, the X-ray data of an orthopyroxene crystal (Fs23), which were collected earlier by Molin et al. (1991) between 700 and 1000 ∞C, were re-refined. The data were processed through two diAerent refinement programs (SHELXL- 93 and RFINE90) using both unit and individual weights and also both ionic and atomic scattering fac- tors. The calculated site occupancies were found to agree within their estimated standard errors. However, the use of ionic scattering factors led to significantly better goodness of fit and agreement index, and smaller standard deviations of the site occupancies than those obtained from the use of atomic scattering factors. Furthermore, the weighted refinements yielded signifi- cantly smaller standard deviations of the site occupan- cies than the unweighted refinements even when the same set of reflections was used in the two procedures. The site occupancy data from this study were combined with selected published data to develop expressions of k D as a function of temperature and composition. Cal- culation of the excess configurational entropy, DS XS , suggests that orthopyroxene should be treated as a two parameter symmetric solution instead of as a ''simple mixture''. The calculated DS XS values and the excess Gibbs free energy of mixing suggested by available cat- ion exchange data lead to a slightly negative enthalpy of mixing in the orthopyroxene solid solution.

Garnet-spinel-olivine-orthopyroxene equilibria in the FeO-MgO-Al2O3-SiO2-Cr2O3 system: II. Thermodynamic analysis

Experimental results for the four-phase assemblage in the MASCr (Doroshev et al., 1997) and FMASCr (Brey et al., 1999) systems are evaluated with respect to exchange (Fe-Mg and Cr-Al) and displaced equilibrium reactions (Al solubility in orthopyroxene and spinel-orthopyroxene to garnet-olivine transition). These equilibria are considered on the basis of the thermodynamic data of Berman (1988). The effects of non-ideal mixing in solid solutions is approximated by a subregular Margules formulation, independent for each site of spinel, garnet, and orthopyroxene solid solutions. Mixing parameters were calculated by linear programming considering each experimental point as an independent half-bracket for the concentration term in the respective equilibrium. Cr-Al mixing in all phases is not ideal, but the magnitudes of excess mixing energies are not large. Spinel solid solution shows asymmetric Cr-Al and Mg-Fe excess mixing energy. Cr-Al mixing in garnet is close to an ideal model with a symmetric Margules parameter 0 to 6 kJ/mol. Standard state properties of knorringite, Mg 3 Cr 2 Si 3 O 12 and orthopyroxene end-member MgCrAlSiO 6 are estimated. The major factor determining concentration dependencies of equilibrium constants is the Gibbs free energy changes of reciprocal reactions FeCr+MgAl = FeAl+MgCr in spinel and garnet. The derived thermodynamic parameters are used to calculate phase relationships in the four-mineral region of the FMASCr system, which models depleted mantle harzburgite. The Cr/(Cr+Al) ratio of garnet increases with both pressure and temperature, while that of spinel depends mainly on pressure. The distribution of Cr and Al between spinel and garnet in equilibrium with orthopyroxene and olivine may be used as a thermobarometer for deep mantle xenoliths and inclusions in diamonds.

Garnet-spinel-olivine-orthopyroxene equilibria in the FeO-MgO-Al2O3-SiO2-Cr2O3 system: I. Composition and molar volumes of minerals

Experiments in the FMASCr system at pressures of 30-50 kbar and temperatures of 1200-1500 degrees C model mineral equilibria in depleted mantle harzburgite. Special emphasis was on the partitioning of chromium between garnet, spinel and orthopyroxene and the influence of chromium on the garnet to spinel peridotite transition. The experiments were carried out using mixtures of synthetic minerals as starting materials with different initial compositions of phases, approaching the conditions of reversed experiments. The equilibrium between minerals was attained rapidly with respect to Fe-Mg exchange, whereas a considerable scatter in Cr/(Cr-+Al) values was observed in all phases studied. The extreme compositions of phases in reversed experiments give insight on the equilibrium phase composition. Cr/(Cr+Al) ratio of garnet coexisting with orthopyroxene, olivine and spinel increases with pressure and temperature, exceeding 0.4 at 50 kbar and 1500 degrees C. At high pressure spinel becomes also more chromian, while orthopyroxene composition approaches the enstatite-ferrosilite join. After quench, the minerals were studied by X-ray diffraction in order to obtain unit-cell parameters of solid solutions and refine their volume properties. Spinels in the system (Mg, Fe)(Cr, Al) 2 O 4 show negative deviation from ideal mixing volume at high Cr contents and positive deviation in Al-rich composition (Margules excess mixing volume parameters: W CrAl = 0.017 and W AlCr = -0.007 J/bar). Small negative excess volume of mixing is related to Fe-Mg mixing in spinel. Cr-Al mixing in garnet is characterised by a small excess mixing volume, which may be approximated by a symmetrical model (W V AlCr = W V CrAl = 0.018 J/bar). Our results are compatible with zero excess mixing volume of orthopyroxene solid solution. All the excess volumes of mixing are small and their influence on equilibria is substantial only at very high pressures (>50 kbar).

An XAFS study of the crystal chemistry of Fe in orthopyroxene

X-ray absorption fine-structure (XAFS) spectra at the Fe K edge in Bamble enstatite (Mgo88Feo,,)Si03 were analyzed in conjunction with theoretical XAFS spectra to determine the bonding configuration of Fe in this structure. The structural analysis involved determination of the Fe distribution between the octahedral M1 and M2 sites, and Fe-O bond lengths in the M2 site, into which Fe strongly partitions. Our analysis yielded bond lengths for Fe in the M2 site of 1.97(2), 1.98(2), 2.09(2), 2.16(2), 2.43(2), and 2.65(10) A, in agreement with bond lengths determined from X-ray and neutron-diffraction analysis of the two orthopyroxene end-members. The average Fe-O bond length in the M2 site is 2.22(2) A, longer than that of the Mg end-member (2.151 A) but approximately the same as that of the Fe end-member (2.228 A) of the orthopyroxene solid-solution series. Octahedral distortion of the M2 site may be greater than that of either the Fe or Mg endmember. The presence of a minor amount of Fe3+ was inferred by our analysis of the M I site and was also suggested by our bond-valence calculations, which yielded a charge of 2.07 for Fe in the M2 site and a charge of 2.78 for Fe in the Ml site. Simple calculations using our data and those of other studies show that the average Fe-O bond length in the M2 site is constant along the Fe-Mg join in the orthopyroxene solid-solution series.

Orthopyroxene-magnetite-quartz oxygen barometer for Mnbearing rocks (experimental calibration)

The compositions of orthopyroxene, associated with magnetite and quartz in the system FeO-MgO-MnO-SiO2 were determined experimentally at temperatures of 700, 750, 800°C and pressures ranging between 3 and 5 kbar. On the basis of data obtained the value of the Guggenheim parameter of orthopyroxene solid solution was calculated: AFe. Mn = 2400 ±500 cal. For rocks rich in MnO, a modified version of orthopyroxene-magnetite-quartz oxygen barometer is suggested.

Fe-Ti oxide geothermometry: thermodynamic formulation and the estimation of intensive variables in silicic magmas

A new thermodynamic formulation of the Fe−Ti oxide geothermometer/oxygen barometer is developed. The method is based upon recently calibrated models for spinel solid solutions in the quinary system (Fe2+, Mg)(Al,Fe3+,Cr)2O4−(Fe2+, Mg)2TiO4 by Sack and Ghiorso, and rhombohedral oxides in the quaternary system (Fe2+,Mg,Mn)TiO3−Fe2O3 (this paper). The formulation is internally consistent with thermodynamic models for (Fe2+,Mg)-olivine and -orthopyroxene solid solutions and end-member thermodynamic properties tabulated by Berman. The constituent expressions account for compositional and temperature dependent cation ordering and reproduce miscibility gap features in all of the component binaries. The calibration does not account for the excess Gibbs energy resulting from compositional and temperature dependent magnetic ordering in either phase. This limits application of the method to assemblages that equilibrated at temperatures above 600° C. Practical implementation of the proposed geothermometer/oxygen barometer requires minimal use of projection algorthms in accommodating compositions of naturally occurring phases. The new formulation is applied to the estimation of temperature and oxygen fugacity in a wide variety of intermediate to silicic volcanic rocks. In combination with previous work on olivine and orthopyroxene thermodynamics, equilibration pressures are computed for a subset of these volcanics that contain the assemblage quartz, oxides and either ferromagnesian silicate. The calculated log10fO2-T relations are reflected in coexisting ferromagnesian mineral assemblages. Volcanics with the lowest relative oxygen fugacity (Δlog10fO2) are characterized by the assemblage olivine-quartz, those with slightly higher Δ log10fO2 s, by the assemblage orthopyroxene-quartz. The sequence proceeds with the necessary phases biotite-feldspar, then hornblende-quartz-clinopyroxene, and finally at the highest Δ log10fO2 s, sphene-quartz-clinopyroxene. Quantitative analysis of these trends, utilizing thermodynamic data for the constituent phases, establishes that, in most cases, the T-log10fO2value computed from the oxides is consistent with the compositions of coexisting silicate phases, indicating that phenocryst equilibrium was achieved prior to eruption. There is, however, considerable evidence of oxide-silicate disequilibrium in samples collected from more slowly cooled domes and obsidians. In addition, T-log10fO2trends from volcanic rocks that contain biotite and orthopyroxene are interpreted to imply a condition of Fe2+−Mg exchange disequilibrium between orthopyroxene and coexisting ferromagnesian silicates and melt. It is suspected that many biotite-feldspar-quartz-orthopyroxene bearing low temperature volcanic rocks inherit orthopyroxene xenocrysts which crystallized earlier in the cooling history of the magma body.

The effects of serpentinization on density and magnetic susceptibility: a petrophysical model

Abstract New measurements are presented of initial magnetic susceptibility and density for serpentinized harzburgites from the Josephine Peridotite (Oregon). An inverse correlation between density and susceptibility, which is typical of these rocks and similar rocks from other localities, is not explained by simple serpentinization reactions. Calculations of density and susceptibility as a function of reaction progress for reactions that produce magnetite show susceptibilities that are larger than those observed at low degrees of serpentinization. Susceptibilities of Fe-bearing serpentine and brucite are calculated from a molecular field model initially developed for the olivine and orthopyroxene solid solutions. At high degrees of serpentinization, susceptibilities that are lower than those observed are predicted by reactions where iron is sequestered by serpentine and brucite. Observed density-susceptibility trends of serpentinized harzburgites fall between the values predicted by these limiting reactions. The observed properties may be modelled by multiple reactions involved in multi-stage serpentinization processes such that the production of magnetite increases with the degree of serpentinization. The empirical and calculated properties provide a complementary characterization of density and susceptibility values of serpentinites.

Importance of considerations of mixing properties in establishing an internally consistent thermodynamic database: thermochemistry of minerals in the system Mg2SiO4-Fe2SiO4-SiO2

A thermodynamic solution model is developed for minerals whose compositions lie in the two binary systems Mg2SiO4-Fe2SiO4 and Mg2Si2O6-Fe2Si2O6. The formulation makes explicit provision for nonconvergent ordering of Fe2+ and Mg2+ between M1 and M2 sites in orthopyroxenes and non-zero Gibbs energies of reciprocal ordering reactions in both olivine and orthopyroxene. The calibration is consistent with (1) constraints provided by available experimental and natural data on the Fe-Mg exchange reaction between olivine and orthopyroxene ± quartz, (2) site occupancy data on orthopyroxenes including both crystallographic refinements and Mossbauer spectroscopy, (3) enthalpy of solution data on olivines and orthopyroxenes and enthalpy of disordering data on orthopyroxene, (4) available data on the temperature and ordering dependence of the excess volume of orthopyroxene solid solutions, and (5) direct activity-composition determinations of orthopyroxene and olivine solid solutions at elevated temperatures. Our analysis suggests that the entropies of the exchange [Mg(M2)Fe(M1)⇔Fe(M2)Mg(M1)] and reciprocal ordering reactions [Mg(M2)Mg(M1)+ Fe(M2)Fe(M1)⇔Fe(M2)Mg(M1)+Mg(M2)Fe(M1)] cannot differ significantly (± 1 cal/K) from zero over the temperature range of calibration (400°–1300° C). Consideration of the mixing properties of olivine-orthopyroxene solid solutions places tight constraints on the standard state thermodynamic quantities describing Fe-Mg exchange reactions involving olivine, orthopyroxene, pyralspite garnets, aluminate spinels, ferrite spinels and biotite. These constraints are entirely consistent with the standard state properties for the phasesα-quartz,β-quartz, orthoenstatite, clinoenstatite, protoenstatite, fayalite, ferrosilite and forsterite which were deduced by Berman (1988) from an independent analysis of phase equilibria and calorimetric data. In conjunction with these standard state properties, the solution model presented in this paper provides a means of evaluating an internally consistent set of Gibbs energies of mineral solid solutions in the system Mg2SiO4-Fe2SiO4-SiO2 over the temperature range 0–1300° C and pressure interval 0.001–50 kbars. As a consequence of our analysis, we find that the excess Gibbs energies associated with mixing of Fe and Mg in (Fe, Mg)2SiO4 olivines, (Fe, Mg)3Al2Si3O12 garnets, (Fe, Mg)Al2O4 and (Fe, Mg)Fe2O4 spinels, and K(Mg, Fe)3AlSi3O10(OH)2 biotites may be satisfactory described, on a macroscopic basis, with symmetric regular solution type parameters having values of 4.86±0.12 (olivine), 3.85±0.09 (garnet), 1.96±0.13 (spinel), and 3.21±0.29 kcals/gfw (biotite). Applications of the proposed solution model demonstrate the sensitivity of petrologic modeling to activity-composition relations of olivine-orthopyroxene solutions. We explore the consequences of estimating the activity of silica in melts forming in the mantle and we develop a graphical geothermometer/geobarometer for metamorphic assemblages of olivine+orthopyroxene+quartz. Quantitative evaluation of these results suggests that accurate and realistic estimates of silica activity in melts derived from mantle source regions,P-T paths of metamorphism and other intensive variables of petrologic interest await further refinements involving the addition of “trace” elements (Al3+ and Fe3+) to the thermodynamic formulation for orthopyroxenes.

Pyroxene-melt equilibria: an updated model

An updated model for pyroxene-melt equilibria at 1 atm has been developed and calibrated using new and existing experimental data in order to refine calculations of liquid lines of descent, which simulate the effect of igneous differentiation processes. We combine the Davidson and Lindsley (1985) model for activities of components in clinopyroxene and orthopyroxene solid solutions, aip, where i represents a quadrilateral endmember, with the Nielsen and Drake (1979) expressions for component activities in the melt, aiL(two-lattice melt model). The chemical potential differences for pyroxene-melt equilibria are expressed in the form: $$\Delta \mu _{\iota } = 0 = In \left( {{{a_i^p } \mathord{\left/{\vphantom {{a_i^p } {a_i^L }}} \right.\kern-\nulldelimiterspace} {a_i^L }}} \right) + A_i + {{B_i } \mathord{\left/{\vphantom {{B_i } T}} \right.\kern-\nulldelimiterspace} T}$$

An experimental study on partition of magnesium and manganese between olivine and orthopyroxene

The partition of Mn and Mg between coexisting synthetic olivine, orthopyroxene and Ca-rich clinopyroxene was studied. The apparent equilibrium constant for the partition of Mn and Mg between olivine and orthopyroxene, K′ (=(Mn/Mg) Ol (Mg/Mn) Opx), was measured under the conditions of 1200 °C, 30 kb; 1000 °C, 30 kb; and 1050 °C, 0 kb. The pressure dependence of ln K′ was found to be −0.0040/kb (±0.0010) at 1000 °C in the composition range around Mn/(Mn+Mg) = 0.05. This value agrees quite well with the theoretical value, −0.0043/kb, based on unit cell parameter data. Composition and temperature dependences of K′ were also observed. In the systems containing Ca-rich clinopyroxene, the reaction rate was so small that no equilibrated samples were obtained. The formation condition of a garnet peridotite xenolith in South African kimberlite was estimated by thermodynamic analysis of the partition of MnMg and CoMg between olivine and orthopyroxene, assuming the binary regular solution model. It was concluded that the garnet peridotite xenolith had been formed at a temperature of about 100 °C lower and at a pressure of about 60 kb higher than the Itinomegata spinel lherzolite nodule. Unit cell parameters of synthetic MnMg olivine and orthopyroxene solid solutions are reported in the Appendix.