2SiO4 Olivine Research Articles

Experimental investigation of mixing properties of (Ca,Fe,Mg)<sub>2</sub>SiO<sub>4</sub> olivine: Fe-Mg exchange with Ca-rich clinopyroxene and phase relations in olivine quadrilateral

To constrain the mixing properties of (Ca,Fe,Mg)2SiO4 olivine, Fe-Mg exchange experiments have been carried out on the assemblages of low-Ca olivine+clinopyroxene, low-Ca olivine+high-Ca olivine+clinopyroxene and high-Ca olivine+clinopyroxene with bulk Fe/(Fe+Mg) in the range of 0.4 to 0.6, mainly about 0.5, at pressures from 1 atm to 2.0 GPa and temperatures from 1100°C to 1300°C, mainly at 1 atm and 1150°C. The phase relations of (Ca,Fe,Mg)2SiO4 olivine have been also determined at 1 atm and 1150°C. Experiments under 1 atm were performed in an electric furnace equipped with CO2/H2 control device. The oxygen fugacity around the sample space in the furnace was kept to that realized with the iron-wustite buffer. High-pressure experiments were carried out using a piston-cylinder apparatus. The Fe-Mg distribution coefficient between olivine and clinopyroxene, KD [=(XMgCpx XFeOl)/(XFeCpx XMgOl)], increases with bulk Ca/(Ca+Fe+Mg) content, but insensitive to pressure. The solvus between low-Ca and high-Ca olivines becomes narrow with pressure and Fe/(Fe+Mg) of the system, but the pressure effect on the solvus is very small. Thermodynamic analyses were made on the present and previous data to refine the compositional dependence on KD of olivine-clinopyroxene pair and the solvus of quadrilateral (Ca,Fe,Mg)2SiO4 olivine using the Fe-Mg mixing data, and the free energy changes of the Fe-Mg exchange reactions between these phases and in olivine. The symmetric and asymmetric two-site regular solution models were applied to (Ca,Fe,Mg)2SiO4 olivines in terms of the Fe-Mg intracrystalline exchange between M1 and M2 sites and the excess energies of Ca-Fe-Mg mixing. In the present model, it is assumed that substitution of Ca is limited to M2 sites alone whereas Fe and Mg substitute on both M1 and M2 sites. The mixing parameters of the asymmetric Ca-Mg and symmetric Fe-Mg and Ca-Fe models are evaluated as WCaMg=36.31±0.19, WMgCa=32.73±0.18, WCaFe=21.34±0.06, WCaFeMg=6.12±0.98, δ1=2.24±1.30 and δ2=−8.45±0.94 (unit in kJ), whereas the symmetric Ca-Fe-Mg mixing model (WCaFeMg=0) resulted as WCaMg=WMgCa=34.20±0.18, WCaFe=23.75±0.58, δ1=−1.50±2.35 and δ2=−10.20±1.37. The present results are consistent with the previous analyses of miscibility gaps in Ca-Fe-Mg olivines. The Ca-Mg mixing is slightly less non-ideal than the previous estimates on the forsterite-monticellite solvus. Considerations about the Fe-Mg intracrystalline exchange show a slight preference of Fe in M1 site in Ca-free olivines, and indicate preferential order of Fe to M2 site with increase of Ca contents of olivine.

Thermodynamics of multicomponent olivines and the solution properties of (Ni,Mg,Fe)2SiO4 and (Ca,Mg,Fe)2SiO4olivine—Reply

Fleet (2000) criticizes several aspects of the thermodynamic model for (Ni,Mg,Fe)2SiO4-bearing olivine from Hirschmann (1991) and its subsequent recalibration in my Ph.D. thesis (Hirschmann 1992). He also justifies the thermodynamic methods used by Fleet (1989) to extract activity coefficients of NiSi0.5O2 in olivine. I am pleased that somebody has taken the time to read parts of my Ph.D. thesis and will take this opportunity to reply to Fleet’s comments on some of my early work and elaborate on the problems with Fleet (1989). Fleet (2000) finds fault with three aspects of the thermodynamic model for (Ni,Mg,Fe)2SiO4 olivine from Hirschmann (1991 Hirschmann (1992). He criticizes the formulation of the model, but his contentions reflect misapprehensions regarding thermodynamic models that account for long-range ordering. He questions the quality of the ordering data used to calibrate the model, but does not acknowledge available data that corroborate the site occupancy measurements. He also disparages the accuracy of the predicted activity-composition relations, but fails to account for experimental uncertainties and discounts considerable evidence for agreement between the model and experimental constraints on NiSi0.5O2 olivine activities. Fleet (2000) also defends the activity coefficients for NiSi0.5O2 extracted in the thermodynamic analysis of Fleet (1989). He suggests that there is a posteriori evidence that silica activity was nearly constant in a suite of experiments that were not designed to buffer silica but, as detailed below, there is good reason to suspect significant silica activity variation in these experiments. He reiterates evidence presented in Fleet (1989) suggesting that the oxysulfide liquids in the experiments of interest are reasonable approximations of FeS-NiS binary solutions. However, these liquids are unlikely to be close to monosulfide composition because their reported compositions are critically …

Thermodynamics of multicomponent olivines and the solution properties of (Ni,Mg,Fe)2SiO4and (Ca,Mg,Fe)2SiO4olivines—Comment

Article Thermodynamics of multicomponent olivines and the solution properties of (Ni,Mg,Fe)2SiO4 and (Ca,Mg,Fe)2SiO4 olivines—Comment was published on October 1, 2000 in the journal American Mineralogist (volume 85, issue 10).

In situ complex impedance spectroscopy of mantle minerals measured at 20 GPa and 1400°C

Electrical conductivities of mantle silicate minerals (Mg0·9Fe0·1)2SiO4 olivine, wadsleyite and ringwoodite were determined at pressures up to 20 GPa and temperatures up to 1400°C using complex impedance spectroscopy in a high pressure multianvil apparatus. All samples were polycrystalline, synthesized in separate high pressure experiments prior to the electrical measurements. Olivine conductivities up to 10 GPa are very close to values determined at ambient pressure under controlled oxygen fugacities in previous studies indicating a very small pressure dependence. The conductivities of wadsleyite at 15 GPa and ringwoodite at 20 GPa are similar, and both about 100 times greater than for olivine. When compared to conductivity models of Earth's mantle, these results suggest that the steep increase in conductivity near the transition zone is mainly due to the olivine to wadsleyite phase transformation at 410 km depth, with only minor changes in conductivity occurring over the wadsleyite to ringwoodite transformation near 520 km depth.

Polymorphic transformations between olivine, wadsleyite and ringwoodite: mechanisms of intracrystalline nucleation and the role of elastic strain

AbstractKinetic models and rate equations for polymorphic reconstructive phase transformations in polycrystalline aggregates are usually based on the assumptions that (a) the product phase nucleates on grain boundaries in the reactant phase and (b) growth rates of the product phase remain constant with time at fixed P-T. Recent observations of experimentally-induced transformations between (Mg,Fe)2SiO4 olivine (α) and its high pressure polymorphs, wadsleyite (β) and ringwoodite (γ), demonstrate that both these assumptions can be invalid, thus complicating the extrapolation of experimental kinetic data. Incoherent grain boundary nucleation appears to have dominated in most previous experimental studies of the α–β–γ transformations because of the use of starting materials with small (<10–20 µm) grain sizes. In contrast, when large (0.6 mm) olivine single crystals are reacted, intracrystalline nucleation of both β and γ becomes the dominant mechanism, particularly when the P-T conditions significantly overstep the equilibrium boundary. At pressures of 18–20 GPa intracrystalline nucleation involves (i) the formation of stacking faults in the olivine, (ii) coherent nucleation of γ-lamellae on these faults and (iii) nucleation of β on γ. In other experiments, intracrystalline nucleation is also observed during the β-γ transformation. In this case coherent nucleation of γ appears to occur at the intersections of dislocations with (010) stacking faults in β, which suggests that the nucleation rate is stress dependent. Reaction rims of β/γ form at the margins of the olivine single crystals by grain boundary nucleation. Measurements of growth distance as a function of time indicate that the growth rate of these rims decreases towards zero as transformation progresses. The growth rate slows because of the decrease in the magnitude of the Gibbs free energy (stored elastic strain energy) that develops as a consequence of the large volume change of transformation. On a longer time scale, growth kinetics may be controlled by viscoelastic relaxation.

Electrical Conductivities of Mantle Minerals: In-situ High-Pressure High-Temperature Complex Impedance Spectroscopy.

Electrical conductivities for olivine at 10 GPa, wadsleyite at 15 GPa and ringwoodite at 20 GPa, all with San Carlos (Mg0. 9Fe0. 1) 2SiO4 olivine starting composition were determined by complex impedance spectroscopy in a multianvil apparatus. Results for olivine are in good agreement with previous studies, both at elevated pressure and ambient pressure, suggesting that its conductivity is only weakly dependent on pressure. Conductivities for wadsleyite and ringwoodite are significantly higher than olivine (about 2 orders of magnitude), but with slightly lower activation energies. These differences can be attributed to the likely presence of ferric iron in the wadsleyite and ringwoodite.

High-temperature order-disorder in (Fe0.5Mn0.5)2SiO4 and (Mg0.5Mn0.5)2SiO4 olivines: an in situ neutron diffraction study

Time-of-flight neutron powder diffraction has been used to determine the time-temperature dependence of M-site occupancies and crystal structures of MgMnSiO4 and FeMnSiO4 olivines between room temperature and 1000°C. In each sample Mn shows a preference for the M2 site at low temperature, but becomes increasingly disordered between M1 and M2 on increasing temperature. The equilibrium non-convergent disordering behaviour is described by a Landau expression for the free-energy change due to ordering. The kinetics of non-convergent ordering of the M-site cations in these samples have been analysed using a Ginzburg-Landau model, giving an activation energy for Fe-Mn exchange between M1 and M2 of 193 ± 3 kJ/mol and for Mg-Mn exchange of 172 ± 3 kJ/mol. The M-site occupancy at room temperature is shown to be a function of the cooling rate of the crystal, indicating the possibility that (Mg,Fe)2SiO4 olivine might be useful as a geospeedometer for relatively rapid cooling events, such as the cooling of small high-level basaltic intrusions. The relationship between M-site ordering in these Mn-bearing samples and structural parameters such as bond lengths, octahedral bond-angle variance, and cell parameters is described.

Subsolidus Phase Relations in the System MgO–SiO2–Cr–O and Thermodynamic Properties of Related Cr2+–Containing End–members

Abstract Subsolidus phase relations have been determined in the systems SiO2–Cr–O and MgO–SiO2–Cr–O in equilibrium with metallic Cr, at 1100 to 1500°C and 0 to 2.88 GPa. The results show that there are no ternary phases in the SiO2–Cr–O system at these conditions, i.e., only the assemblage eskolaite–Cr–metal–quartz (or tridymite) is found. In the MgO–containing system, however, extensive substitution of Cr2+ for Mg is observed in (Mg, Cr2+)2SiO4 olivine, (Mg, Cr2+)2Si2O6 pyroxene, and (Mg, Cr2+)Cr2O4 spinel. Cr3+ levels in olivine and pyroxene are below detection limits. The pyroxene is orthohombic at XPxCr2+ <0.2, monoclinic at higher XPxCr2+. The structure of the spinels becomes tetragonally distorted at XPxCr2+ >0.2. The experimental data have been fitted to a thermodynamic model, and the authors obtained the mixing parameter (W) of Mg‐Cr2+ in olivine, pyroxene and spinel, and the relation between temperatures and free energies of formation for the end–members: Cr2+–olivine (Cr2SiO4), Cr2+–pyroxene (Cr2Si2O6) and Cr2+–spinel (Cr3O4).

Reactions between molten iron and silicate melts at high pressure: Implications for the chemical evolution of Earth's core

Reactions between molten iron and silicate melt were investigated with mixtures of pure iron and silicates (1Fe + 3MgSiO3 enstatite and 1Fe + 3(Mg0.9Fe0.1)2SiO4 olivine in volumetric ratio) as starting materials at pressures of 10–26 GPa and temperatures of about 2500°C. The results show that a certain amount of Si (up to about 2%) dissolves in molten iron from silicate melt and that the dissolution is enhanced with increasing pressure. Many small spherical blobs composed of SiO2 and FeO present in coalesced iron grains were interpreted as quenched immiscible liquid formed during cooling. Therefore O also dissolves in molten iron under the experimental conditions. No evidence for dissolution of Mg was obtained. The present study also indicates that Si and O are important light elements of Earth's core if core segregation occurred in the deep magma ocean. The chemical evolution of Earth's core is discussed on the bases of the current core formation model and the present experimental results.

Compression and amorphization of (Mg,Fe)2SiO4 olivines: An X-ray diffraction study up to 70 GPa

The effect of (Mg,Fe) substitution on the compression and pressure-induced amorphization of olivines has been investigated up to more than 50 GPa in a diamond anvil cell through energy-dispersive X-ray diffraction experiments with synchrotron radiation. For the four (Mg1−x , Fe x )2SiO4 olivines studied, the compressibility is the highest along the b axis and the smallest along the a axis. For compositions with x = 0, 0.17, 0.66, and 1, the slope of the volume-pressure curves shows a rapid decrease at pressures of around 42, 34, 20 and 10 GPa, respectively. Assuming K′0 = 4, we obtained at lower pressures with a Birch-Murnaghan equation of state essentially the same room-pressure bulk modulus for all olivines, namely K 0 = 131 ± 6 GPa, in agreement with previous single-crystal compression and ultrasonic measurements. At higher pressures, the compression becomes nearly isotropic and the materials very stiff. These changes could precede partial transformation of olivines to a high-pressure polymorph related to the spinel structure. Only a small fraction of olivines seems to transform actually to this phase, however, because most of the material undergoes instead pressure-induced amorphization which take place at considerably higher pressures for Mg-than for Fe-rich olivines.

Impedance Spectroscopy of Upper Mantle Earth Materials

ABSTRACTEarth scientists study electrical properties of Earth materials to understand mechanisms of transport and deformation under conditions existing in the Earth's interior, and for comparison with direct determinations of the conductivity – depth structure of the Earth. We have performed impedance spectroscopic studies of natural and artificial (hot-pressed and sintered) rocks composed of (Mg9Fe1)2SiO4 olivine, a major constituent of the Earth's upper mantle between 40 and 400 km depth. The studies were performed over the frequency range 105 to 10−4 Hz at 1 bar total pressure and temperatures of 800 – 1400 °C under controlled oxygen atmospheres. Complex impedance plane analysis of the results shows depressed impedance arcs corresponding to grain interior and grain boundary transport in series, analogous to the behavior of zirconia and other materials. Distinct grain boundary phases that might cause the resistive grain boundary behavior are not observed. The exponent of the oxygen pressure dependence of the grain boundary conductivity ranges from 0.02 to −0.08, which is very different than the 1/5.5 to 1/7 dependence of the polaronic grain interior mechanism. However, lack of constraints on the composition of the intergranular material limit interpretation of these exponents in terms of mechanism. Key issues for application to the Earth's interior are determination of the mechanism and pressure dependence of the grain boundary transport.

Pressure dependence of the electrical conductivity of (Mg0.9Fe0.1)SiO3 perovskite

The electrical conductivity of (Mg0.9Fe0.1)SiO3 perovskite has been measured at pressures of 0–8 GPa and ambient temperature using a DIA‐6 cubic‐anvil apparatus. At ambient conditions, the electrical conductivity of the (Mg0.9Fe0.1)SiO3 perovskite is found to be 7.6 (±2.0) ×10−9 S/m. The conductivity of the perovskite increases with increasing pressure, and the activation volume for electrical conduction is determined to be −0.12 (±0.04) cm3/mol. As a cross‐check with previous electrical conductivity measurements, an assemblage of the perovskite and magnesiowüstite synthesized from the (Mg0.89Fe0.11)2SiO4 olivine has been examined in the present study using a laser‐heated diamond anvil cell at ∼ 48 GPa and in the temperature range of 295–3500 K. The results for this assemblage are consistent with those for the pure (Mg0.9Fe0.1)SiO3 perovskite. The present experimental data show that the electrical conductivity of the crystalline (Mg0.9Fe0.1)SiO3 perovskite remains below 10−5 S/m at 300 K and lower mantle pressures.

High‐pressure and high‐temperature reactions between silicates and liquid iron alloys, in the diamond anvil cell, studied by analytical electron microscopy

We report new experimental results on mixtures of iron alloys and silicates (Fe + forsterite, Fe + (Mg0.89,Fe0.11)SiO3 enstatite, Fe + (Mg0.89,Fe0.11)2SiO4 olivine, Fe + FeS + (Mg0.83,Fe0.17)2SiO4 olivine, and FeS + (Mg0.83,Fe0.17)2SiO4 olivine) reacted at about 70 GPa and 130 GPa, at high temperature in a laser‐heated diamond anvil cell. The recovered samples were studied by analytical transmission electron microscopy. We found that chemical reactions occurred between molten iron alloys and solid oxides, leading to a dissolution of oxygen in the molten metallic phase, and a drastic depletion of iron in the oxides in contact with the metallic phase. Chromium and manganese partition into the liquid iron. Oxygen is therefore a serious candidate for being a light element in the Earth's core, and oxides which have experienced a high‐pressure contact with molten iron should have a rather low Fe/Fe+Mg ratio.

Pressure-induced structural modifications and amorphization in olivine compounds

(Mg,Fe)2SiO4 olivine, recovered from temperatures lower than 700°C and pressures exceeding 30 GPa displays some quenchable phase transformations. If the maximum pressure of the experiment is > 70 GPa, the recovered phase is largely amorphous. This phenomenon is interpreted as a metastable pressure-induced amorphization. If the maximum pressure of the experiment is between 30 and 70 GPa, a phase is recovered which displays a partial amorphous character. It actually consists of a quasi ideally close-packed oxygen sublattice and an amorphous cation “sublattice” indicated by diffuse rings in the diffraction patterns. We interpret this phase as the result of a pressure-induced disordering of the cation sublattice in the olivine structure. Similar observations have been made in numerous other compounds with the olivine structure (Ca2GeO4. Mg2GeO4 and Mn2GeO4). In parallel, we present numerical simulations of the forsterite structure and lattice dynamics at high pressure which show that a dynamical instability of the structure appears at ambient temperature and 30 GPa. The very same instability is shown to appear in simulations of the melting of forsterite at ambient pressure. This reinforces the idea that the phenomena observed at high pressure are simply interpreted as pressure-induced metastable “premelting” and “melting” processes.

Magnon-phonon coupling in Fe 2SiO 4

In a Fe 2SiO 4-olivine single crystal we have investigated the magnetic collective excitations by means of FIR-spectroscopyv and inelastic neutron scattering. All eight magnon branches predicted by model calculations have been found and examined in the principal directions. The experimental data correspond well to a theoretical spin-wave model but they also show evidence of magnon-phonon coupling. Strong magnetic inelastic scattering intensities have been observed even in Brillouin zones with vanishing structure factors of the magnetic Bragg peaks. In those zones some magnon branches follow different dispersion relations. Further, anticrossing effects between magnons and phonons have been found in several q-directions.

Dissolution of Silicon and Oxygen in Molten Iron at High Pressure and Temperature.

Reaction between molten iron and silicate at high pressure and temperature was examined by employing a mixture of pure iron and (Mg0.9Fe0.1)2SiO4 olivine as the starting material. The experimental charge quenched at 24 GPa and 2550°C demonstrated that certain amount of SiO2 component (at least 2wt% of Si) dissolved into mol ten iron fromthe silicate melt. It is suggested that the dissolving would be enhanced with increasing pressure. The experimental results indicate that Si and O are the important alloying light-elements in the earth's core if the core segregation proceeded in the magma ocean of the proto-earth. Concurrently, SiO2 contents of the mantle should be substantially reduced from its primitive content.

Ion Beam-Induced Amorphization of (Mg, Fe)2SiO4 Olivine Series: An In Situ Transmission Electron Microscopy Study

ABSTRACTEffects of ion beam irradiation of five members of the (Mg, Fe)2SiO4 olivine series, from synthetic pure fayalite (Fe2SiO4) to naturally occurring (Mg0.88Fe0.12)2SiO4, have been studied by in situ transmission electron microscopy (TEM). Under 1.5 MeV Kr+ ion room temperature irradiations, all of the samples have been amorphized. The critical amorphization dose or the total collision energy loss required for amorphization increased rapidly with the increasing Mg:Fe ratio which coincides with an increasing melting temperature (bond strength) and an increasing average bond ionicity. A 400 keV He+ ion irradiation of (Mg0.88Fe0.12)2-SiO4, which mainly results in ionization energy loss in the sample, did not cause amorphization even at a much higher dose rate and a much higher final dose. This indicates nuclear interactions (collisions) are primarily responsible for ion beam induced amorphization. Also, high resolution electron microscopy (HREM) images of the defect structure at a low ion dose have been obtained and compared with the displacement cascade structure generated by computer modelling.

The strength of mantle silicates at high pressures and room temperature: implications for the viscosity of the mantle

THE rheological properties of the upper mantle, important in convective and tectonic processes, have long been studied through low-pressure creep experiments on olivine1–5. In comparison, our understanding of deformation in the deep Earth is incomplete, because there are few experimental constraints on the rheology of the transition zone (400–670 km depth) and the lower mantle. Estimates of the viscosity at these depths have had to rely on geophysical models of, for example, post-glacial uplift, the geoid and changes in the Earth's rate of rotation6–13. Recently we developed techniques for measuring solid-state creep at mantle pressures14, and here we use these methods to make direct laboratory measurements of the strength of key mantle minerals. We study (Mg, Fe)2SiO4 olivine (representative of about 60% of the upper mantle), (Mg, Fe)2SiO4 γ-spinel (which constitutes a large fraction of the transition zone) and (Mg, Fe)SiO3 perovskite and perovskite + (Mg, Fe)O magnesiowiistite assemblages (which comprise most of the lower mantle), all at room temperature and pressures of up to 60 GPa. Our results suggest that the transition zone may form a layer of relatively high viscosity or strength between the upper and lower mantle. A simple Theological model shows that this behaviour may be compatible with current geophysical observations.

Electron microscopy of high-pressure phases synthesized from natural olivine in diamond anvil cell

The products of the transformation of natural (Mg0.83Fe0.17)2SiO4 olivine have been prepared at various high pressures (between 25 GPa and 90 GPa), and high temperature in a laser-heated diamond-anvil cell (DAC). Studies of the high-pressure phases have been made by transmission electron microscopy (TEM), and X-ray microanalysis.

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.