Experimental determination of activity-composition relations in Ni2SiO4− Mg2SiO4 and Co2SiO4-Mg2SiO4 olivine solid solutions at 1200 K and 0.1 MPa and 1573 K and 0.5 GPa

Activity-composition relations in the olivine solid solutions Ni₂SiO₄⁻ -Mg₂SiO₄ and Co₂SiO₄-Mg₂SiO₄ have been determined at 1200 K and 0.1 MPa and at 1573 K and 0.5 GPa by equilibration with the corresponding oxide solutions. Both olivine solutions show small positive deviations from ideal (two site) mixing, which, within the limits of accuracy of the method, may be described by the simple regular solution model with parameters W_Ni+Mg^ol= 0.35 ± 1.0 kJ/g-atom and W_Co-Mg^ol = 1.37 ± 0.9 kJ/g-atom. The requirements of internal consistency between the two systems also show that the recent determination by Brousse et al. (1984) of the enthalpy of formation of Mg₂SiO₄is to be preferred over earlier work, and that their value is also probably more accurate than the uncertainty in their own measurements indicates; activities in the NiO-MgO system are close to ideal.     

Interdiffusion of Mg–Fe in olivine at 1,400–1,600 °C and 1 atm total pressure

The interdiffusion coefficient of Mg–Fe in olivine (D _Mg–Fe) was obtained at 1,400–1,600 °C at the atmospheric pressure with the oxygen fugacity of 10^?3.5–10^?2 Pa using a diffusion couple technique. The D _Mg–Fe shows the anisotropy (largest along the [001] direction and smallest along the [100] direction), and its activation energy (280–320 kJ/mol) is ~80–120 kJ/mol higher than that estimated at lower temperatures. The D _Mg–Fe at temperatures of >1,400 °C can be explained by the cation-vacancy chemistry determined both by the Fe³⁺/Fe²⁺ equilibrium and by the intrinsic point defect formation with the formation enthalpy of 220–270 kJ/mol depending on the thermodynamical model for the Fe³⁺/Fe²⁺ equilibrium in olivine. The formation enthalpy of 220–270 kJ/mol for the point defect (cation vacancy) in olivine is consistent with that estimated from the Mg self-diffusion in Fe-free forsterite. The increase in the activation energy of D _Mg–Fe at >1,400 °C is thus interpreted as the result of the transition of diffusion mechanism from the transition metal extrinsic domain to the intrinsic domain at the atmospheric pressure.     

Experimental testing of olivine–melt equilibrium models at high temperatures

Data are presented on the equilibrium compositions of olivine and melts in the products of 101 experiments performed at 1300–1600°C, atmospheric pressure, and controlled oxygen fugacity by means of new equipment at the Vernadsky Institute. It was shown that the available models of the olivine–melt equilibrium describe with insufficient adequacy the natural systems at temperatures over 1400°C. The most adequate is the model by Ford et al. (1983). However, this model overestimates systematically the equilibrium temperature with underestimating by 20–40°C at 1450–1600°C. These data point to the need for developing a new, improved quantitative model of the olivine–melt equilibrium for high-temperature magnesian melts, as well as to the possibility of these studies on the basis of the equipment presented.     

Fe–Mg diffusion in olivine II: point defect chemistry,change of diffusion mechanisms and a model for calculation of diffusion coefficients in natural olivine

Analysis of existing data and models on point defects in pure (Fe,Mg)-olivine (Phys Chem Miner 10:27–37,1983; Phys Chem Miner 29:680–694, 2002) shows that it is necessary to consider thermodynamic non-ideality of mixing to adequately describe the concentration of point defects over the range of measurement. In spite of different sources of uncertainties, the concentrations of vacancies in octahedral sites in (Fe,Mg)-olivine are on the order of 10⁻⁴ per atomic formula unit at 1,000–1,200 °C according to both the studies. We provide the first explicit plots of vacancy concentrations in olivine as a function of temperature and oxygen fugacity according to the two models. It is found that in contrast to absolute concentrations at ∼1,100 °C and dependence on fO₂, there is considerable uncertainty in our knowledge of temperature dependence of vacancy concentrations. This needs to be considered in discussing the transport properties such as diffusion coefficients. Moreover, these defect models in pure (Fe,Mg)-olivine need to be extended by considering aliovalent impurities such as Al, Cr to describe the behavior of natural olivine. We have developed such a formulation, and used it to analyze the considerable database of diffusion coefficients in olivine from Dohmen et al. (Phys Chem Miner this volume, 2007) (Part - I) and older data in the literature. The analysis documents unequivocally for the first time a change of diffusion mechanism in a silicate mineral—from the transition metal extrinsic (TaMED) to the purely extrinsic (PED) domain, at fO₂ below 10⁻¹⁰  Pa, and consequently, temperatures below 900 °C. The change of diffusion mechanism manifests itself in a change in fO₂ dependence of diffusivity and a slight change in activation energy of diffusion—the activation energy increases at lower temperatures. These are consistent with the predictions of Chakraborty (J Geophys Res 102(B6):12317–12331, 1997). Defect formation enthalpies in the TaMED regime (distinct from intrinsic defect formation) lie between −66 and + 15 kJ/mol and migration energies of octahedral cations in olivine are most likely ∼ 260 kJ/mol, consistent with previous inferences (Phys Chem 207:147–162, 1998). Plots are shown for diffusion at various constant fO₂ as well as along fO₂ buffers, to highlight the difference in behavior between the two. Considering all the diffusion data and constraints from the point defect models, (Fe–Mg) diffusion in olivine along [001] is best described by the Master equations: (1) At oxygen fugacities greater than 10⁻¹⁰ Pa:

Fe–Mg Interdiffusion in (Mg,Fe)O

We have performed a series of interdiffusion experiments on magnesiowüstite samples at room pressure, temperatures from 1,320° to 1,400°C, and oxygen fugacities from 10^?1.0 Pa to 10^?4.3 Pa, using mixed CO/CO₂ or H₂/CO₂ gases. The interdiffusion couples were composed of a single-crystal of MgO lightly pressed against a single-crystal of (Mg_1-x Fe _x )_1-δO with 0.07<x<0.27. The interdiffusion coefficient was calculated using the Boltzmann–Matano analysis as a function of iron content, oxygen fugacity, temperature, and water fugacity. For the entire range of conditions tested and for compositions with 0.01<x<0.27, the interdiffusion coefficient varies as $$\tilde D\, =\,2.9\times10^{ - 6}\,f_{{\text{O}}_2 }^{0.19}\,x^{0.73}\,{\text{e}}^{ - (209,000\, -\,96,000\,x)/RT}\,\,{\text{m}}^{\text{2}} {\text{s}}^{ -1} $$ These dependencies on oxygen fugacity and composition are reasonably consistent with interdiffusion mediated by unassociated cation vacancies. For the limited range of water activity that could be investigated using mixed gases at room pressure, no effect of water on interdiffusion could be observed. The dependence of the interdiffusion coefficient on iron content decreased with increasing iron concentration at constant oxygen fugacity and temperature. There is a close agreement between our activation energy for interdiffusion extrapolated to zero iron content (x=0) and that of previous researchers who used electrical conductivity experiments to determine vacancy diffusivities in lightly doped MgO.     

Experimental determination of uranium (IV) speciation in HF solutions at 500°C and 1000 bar

Uraninite solubility in HF solutions (0.0001–0.5 m) was experimentally studied at 500°C, 1000 bar, and hydrogen fugacity corresponding to the Ni/NiO buffer. It was shown that the predominant U(IV) species in aqueous solution are U(OH)₄⁰, U(OH)₃F⁰, and U(OH)₂ F₂⁰. Using the results of uraninite solubility measurement, the Gibbs free energies of the uranium (IV) species were calculated at 500°C and 1000 bar (kJ/mol): −986.55 for UO₂(aq), −1712.42 for U(OH)₃F⁰, −1755.53 for U(OH)₂F₂⁰, and the equilibrium constants of the uraninite solubility in water and HF solutions were estimated: UO₂(κ) = UO₂(aq), which is similar to UO₂(cr) + 2H₂O = U(OH)₄⁰, pK₀ = 6.64; UO₂(cr) + HF⁰ + H₂O = U(OH)₃F⁰, K₁ = 0.0513; UO₂(cr) + 2HF⁰ = U(OH)₂F₂⁰K₂ = 7.00 × 10⁻⁴. Approximate values K₃ = 5.75 × 10⁻³ and K₄ = 6.7 × 10⁻² were obtained for equilibria UO₂(cr) + 4HF⁰ =UF₄⁰ + 2H₂O and UO₂(cr) + 4HF = UF₄⁰ + 2H₂O. Maximum observed in the uranium concentration curve as a function of HF concentration can be explained by the decrease (to < 1) of activity coefficient ratio of HF⁰ to U(OH)₃F⁰ with increasing HF concentrations.     

Experimental investigation of the α-β transformation of San Carlos olivine single crystal

Single crystalline San Carlos olivine (1 mm cube) was transformed to (Mg,Fe)₂SiO₄β-phase at 13.5–15 GPa, 1030–1330 °C for 0–600 min using a multi-anvil high pressure apparatus. The α-β transformation occurred by incoherent surface nucleation and interface-controlled growth and recovered partially transformed samples showed sharply defined reaction rim. The growth rate of the β-phase rim significantly decreased with time and the growth eventually ceased. TEM observations revealed that many dislocations were created in both the relict olivine just near the α-β interface and the β-phase in the rim, which show evidence for deformation caused by interfacial stresses associated with the misfit elastic strain of the transformation. The observed tangled dislocation texture in β-phase suggested that the β-phase rim was hardened and relaxation of the interfacial stress was retarded. This probably caused a localized pressure drop in the relict olivine and decreased the growth rate. Time-dependent growth rates of β-phase is possibly controlled by the rheology of β-phase, which must be considered for the prediction of the olivine metastability in the subducting slabs. Received: 24 January 1997 / Revised, accepted: 24 July 1998     

Thermochemical study of Mg–Fe chlorites

The thermochemical study of two natural trioctahedral Mg–Fe chlorites—clinochlores was carried out using high-temperature melt solution calorimetry with a Tian–Calvet microcalorimeter. The enthalpies of formation of clinochlores of compositions (Mg_4.9Fe _0.3 ²⁺ Al_0.8)[Si_3.2Al_0.8O₁₀](OH)₈ (–8811 ± 12 kJ/mol) and (Mg_4.3Fe _0.7 ²⁺ Al_1.0)[Si_3.0Al_1.0O₁₀](OH)₈ (–8696 ± 13 kJ/mol) from elements were determined. The values of the standard entropies and the Gibbs energies of formation of the studied natural minerals as well as thermodynamic properties of Mg–Fe chlorites of theoretical composition were estimated.     

Electronic state of Fe2+ in (Mg,Fe)(Si,Al)O3 perovskite and (Mg,Fe)SiO3 majorite at pressures up to 81 GPa and temperatures up to 800 K

Despite a large number of studies of iron spin state in silicate perovskite at high pressure and high temperature, there is still disagreement regarding the type and P–T conditions of the transition, and whether Fe²⁺ or Fe³⁺ or both iron cations are involved. Recently, our group published results of a Mössbauer spectroscopy study of the iron behaviour in (Mg,Fe)(Si,Al)O₃ perovskite at pressures up to 110 GPa (McCammon et al. 2008), where we suggested stabilization of the intermediate spin state for 8- to 12-fold coordinated ferrous iron (^[8–12]Fe²⁺) in silicate perovskite above 30 GPa. In order to explore the behaviour in related systems, we performed a comparative Mössbauer spectroscopic study of silicate perovskite (Fe_0.12Mg_0.88SiO₃) and majorite (with two compositions—Fe_0.18Mg_0.82SiO₃ and Fe_0.11Mg_0.88SiO₃) at pressures up to 81 GPa in the temperature range 296–800 K, which was mainly motivated by the fact that the oxygen environment of ferrous iron in majorite is quite similar to that in silicate perovskite. The ^[8–12]Fe²⁺ component, dominating the Mössbauer spectra of majorites, shows high quadrupole splitting (QS) values, about 3.6 mm s^?1, in the entire studied P–T region (pressures to 58 GPa and 296–800 K). Decrease of the QS of this component with temperature at constant pressure can be described by the Huggins model with the energy splitting between low-energy e _g levels of ^[8–12]Fe²⁺ equal to 1,500 (50) cm^?1 for Fe_0.18Mg_0.82SiO₃ and to 1,680 (70) cm^?1 for Fe_0.11Mg_0.88SiO₃. In contrast, for the silicate perovskite dominating Mössbauer component associated with ^[8–12]Fe²⁺ suggests the gradual change of the electronic properties. Namely, an additional spectral component with central shift close to that for high-spin ^[8–12]Fe²⁺ and QS about 3.7 mm s^?1 appeared at ~35 (2) GPa, and the amount of the component increases with both pressure and temperature. The temperature dependence of QS of the component cannot be described in the framework of the Huggins model. Observed differences in the high-pressure high-temperature behaviour of ^[8–12]Fe²⁺ in the silicate perovskite and majorite phases provide additional arguments in favour of the gradual high-spin—intermediate-spin crossover in lower mantle perovskite, previously reported by McCammon et al. (2008) and Lin et al. (2008).     

Details of Interaction between CaCO3 and Fe at 4 GPa and 1400‒1500°C

Doklady Earth Sciences - The issue of the stability of carbonate matter (CaCO3) in subduction zones under reduced conditions remains topical. In addition, carbonates may be one of the key sources...     

A refined garnet - biotite Fe−Mg exchange geothermometer and its application in amphibolites and granulites

A new formulation of garnet-biotite Fe–Mg exchange thermometer has been developed through statistical regression of the reversed experimental data of Ferry and Spear. Input parameters include available thermo-chemical data for quaternary Fe–Mg–Ca–Mn garnet solid solution and for excess free energy terms, associated with mixing of Al and Ti, in octahedral sites, in biotite solid solution. The regression indicates that Fe–Mg mixing in biotite approximates a symmetrical regular solution model showing positive deviation from ideality withW _FeMg ^bi =1073±490 cal/mol. H _r and S _r for the garnet-biotite exchange equilibrium were derived to be 4301 cal and 1.85 cal respectively. The resultant thermometer gives consistent results for rocks with a much wider compositional range than can be accommodated by earlier formulations.     

Mg–Fe interdiffusion rates in wadsleyite and the diffusivity jump at the 410-km discontinuity

Mg–Fe interdiffusion rates have been measured in wadsleyite aggregates at 16.0–17.0 GPa and 1230–1530 °C by the diffusion couple method. Oxygen fugacity was controlled using the NNO buffer, and water contents of wadsleyite were measured by infrared spectroscopy. Measured asymmetric diffusion profiles, analyzed using the Boltzmann–Matano equation, indicate that the diffusion rate increases with increasing iron concentration and decreasing grain size. In the case of wadsleyite containing 50–90 weight ppm H₂O, the Mg–Fe interdiffusion coefficients at compositions of Mg/(Mg + Fe)=0.95 in the coarse-grained region (about 60 m) and 0.90 in the fine-grained region (about 6 m) were determined to be a D_Xmg = 0.95 (m² s^–1)=1.24 × 10^–9 exp[–172 (kJ mol^–1)/RT] and D_Xmg = 0.90 (m² s^–1)=1.77 × 10^–9 exp[–143 (kJ mol^–1)/RT], respectively. Grain-boundary diffusion rates were estimated to be about 4 orders of magnitude faster than the volume diffusion rate. Grain-boundary diffusion dominates when the grain size is less than a few tens of microns. Results for the nominally dry diffusion couple in the present study are roughly consistent with previous studies, taking into account differences in pressure and grain size, although water contents of samples were not clear in previous studies. We observed that the diffusivity is enhanced by about 1 order of magnitude in wadsleyite containing 300–2100 wt. ppm H₂O at 1230 °C, which is almost identical to the enhancement associated with a 300 °C increase in temperature. It is still not conclusive that a jump in diffusivity exists between olivine and wadsleyite because water contents of olivine in previous diffusion studies and effects of water on the olivine diffusivity are uncertain.     

Influence of hydrogen on Fe–Mg interdiffusion in (Mg,Fe)O and implications for Earth’s lower mantle

Interdiffusion of Fe and Mg in (Mg,Fe)O has been investigated experimentally under hydrous conditions. Single crystals of MgO in contact with (Mg_0.73Fe_0.27)O were annealed hydrothermally at 300 MPa between 1,000 and 1,250°C and using a Ni–NiO buffer. After electron microprobe analyses, the dependence of the interdiffusivity on Fe concentration was determined using a Boltzmann–Matano analysis. For a water fugacity of ∼300 MPa, the Fe–Mg interdiffusion coefficient in Fe _x Mg_1−x O with 0.01 ≤ x ≤ 0.25 can be described by with and C = −80 ± 10 kJ mol⁻¹. For x = 0.1 and at 1,000°C, Fe–Mg interdiffusion is a factor of ∼4 faster under hydrous than under anhydrous conditions. This enhanced rate of interdiffusion is attributed to an increased concentration of metal vacancies resulting from the incorporation of hydrogen. Such water-induced enhancement of kinetics may have important implications for the rheological properties of the lower mantle.

Experimental characterization of diamond crystallization in melts of mantle silicate-carbonate-carbon systems at 7.0–8.5 GPa

Diamond crystallization from carbon solutions in compositionally variable melts of model eclogite with dolomite [CaMg(CO₃)₂], potassium carbonate (K₂CO₃), and multicomponent K-Na-Ca-Mg-Fe carbonates was studied at 7.0–8.5 GPa. Concentration barriers for the nucleation of the diamond were determined at a standard pressure of 8.5 GPa for variable proportions of silicate and carbonate components in the growth solutions. They correspond to 35, 65, and 40 wt % of silicate components for systems with dolomite, K₂CO₃, and carbonatites, respectively. At higher contents of silicates in silicate-carbonate melts, the nucleation of diamond phase ceases, but diamond crystallization on seed crystals continues and is accompanied by the spontaneous crystallization of thermodynamically unstable graphite. In melts of the albite (NaAlSi₃O₈)-K₂CO₃-C compositions, the concentration barrier of diamond nucleation at 8.5 GPa is up to 90–92 wt % of the albite component, and diamond growth on seeds was observed in albite-carbon melts. Using mineralogical and experimental data, we developed a model of mantle carbonate-silicate (carbonatite) melts as the main parental media for natural diamonds; it was shown that the composition of the silicate constituent of such parental melts is variable and corresponds to the mantle ultrabasic-basic series. With respect to concentration contributions and dominant role in the genesis of diamond in the Earth’s mantle, major (carbonate and silicate) and minor or admixture components were distinguished. The latter include both soluble in carbonate-silicate melts (oxides, phosphates, chlorides, carbon dioxide, and water) and insoluble components (sulfides, metals, and carbides). Both major and minor components may affect the position of the concentration barriers of diamond nucleation in natural parent media.     

Experimental study of Pd hydrolysis in aqueous solutions at 25–70°C

The hydrolysis of the Pd²⁺ ion in HClO₄ solutions was examined at 25–70°C, and the thermodynamic constants of equilibrium K ₍₁₎⁰ and K ₍₂₎⁰were determined for the reactions Pd²⁺ + H₂O = PdOH⁺ + H⁺ and Pd²⁺ + 2H₂O = Pd(OH)₂⁰ + 2H⁺, respectively. The values of log K ₍₁₎⁰ = −1.66 ± 0.5 (25°C) and −0.65 ± 0.25 (50°C) and log K ₍₂₎⁰ = −4.34 ± 0.3 (25°C) and −3.80 ± 0.3 (50°C) were derived using the solubility technique at 0.95 confidence level. The values of log K ₍₁₎⁰ = −1.9 ± 0.6 (25°C), −1.0 ± 0.4 (50°C), and −0.5 ± 0.3 (70°C) were obtained by spectrophotometric techniques. The palladium ion is significantly hydrolyzed at elevated temperatures (50–70°C) even in strongly acidic solutions (pH 1–1.5), and its hydrolysis is enhanced with increasing temperature.     

Fe–Mg interdiffusion rates in clinopyroxene: experimental data and implications for Fe–Mg exchange geothermometers

Chemical interdiffusion of Fe–Mg along the c-axis [001] in natural diopside crystals (X _Di = 0.93) was experimentally studied at ambient pressure, at temperatures ranging from 800 to 1,200 °C and oxygen fugacities from 10^?11 to 10^?17 bar. Diffusion couples were prepared by ablating an olivine (X _Fo = 0.3) target to deposit a thin film (20–100 nm) onto a polished surface of a natural, oriented diopside crystal using the pulsed laser deposition technique. After diffusion anneals, compositional depth profiles at the near surface region (~400 nm) were measured using Rutherford backscattering spectroscopy. In the experimental temperature and compositional range, no strong dependence of D ^Fe–Mg on composition of clinopyroxene (Fe/Mg ratio between Di₉₃–Di₆₅) or oxygen fugacity could be detected within the resolution of the study. The lack of fO₂-dependence may be related to the relatively high Al content of the crystals used in this study. Diffusion coefficients, D ^Fe–Mg, can be described by a single Arrhenius relation with $$D^{{{\text{Fe}} - {\text{Mg}}}} = 2. 7 7\pm 4. 2 7\times 10^{ - 7} {\text{exp(}}-3 20. 7\pm 1 6.0{\text{ kJ}}/{\text{mol}}/{\text{RT)m}}^{ 2} /{\text{s}}.$$ D ^Fe–Mg in clinopyroxene appears to be faster than diffusion involving Ca-species (e.g., D ^Ca–Mg) while it is slower than D ^Fe–Mg in other common mafic minerals (spinel, olivine, garnet, and orthopyroxene). As a consequence, diffusion in clinopyroxene may be the rate-limiting process for the freezing of many geothermometers, and compositional zoning in clinopyroxene may preserve records of a higher (compared to that preserved in other coexisting mafic minerals) temperature segment of the thermal history of a rock. In the absence of pervasive recrystallization, clinopyroxene grains will retain compositions from peak temperatures at their cores in most geological and planetary settings where peak temperatures did not exceed ~1,100 °C (e.g., resetting may be expected in slowly cooled mantle rocks, many plutonic mafic rocks, or ultra-high temperature metamorphic rocks).     

Pressure dependence of Néel transition in (Mg,Fe)O

Pressure dependence of Néel temperature (T _N) in (Mg_0.20Fe_0.80)O, (Mg_0.25Fe_0.75)O, and (Mg_0.30Fe_0.70)O was newly measured up to 1.14 GPa, using superconducting quantum interference device magnetometer and piston–cylinder-type pressure cell under hydrostatic condition. The dT _N/dP values of (Mg_0.20Fe_0.80)O, (Mg_0.25Fe_0.75)O, and (Mg_0.30Fe_0.70)O were determined as 4.0 ± 0.3, 2.7 ± 0.3, and 4.4 ± 0.4 K/GPa, respectively, in linear approximation; however, the T _N deviated from the linearity under nonhydrostatic conditions. The compositional dependence of dT _N/dP in (Mg_1?X Fe _X )O showed a rapid decay with increasing Mg components at X ≥ 0.75 and the trend ended at X = 0.70. The estimated Néel transition pressure at room temperature by extrapolating these linearities are very similar to the rhombohedral distortion determined by previous X-ray diffraction studies for X ≥ 0.75, which suggests that the rhombohedral phase of (Mg_1?X Fe _X )O (X ≥ 0.75) at room temperature is antiferromagnetic under hydrostatic conditions.     

A Raman spectroscopic study of Fe–Mg olivines

End-member synthetic fayalite and forsterite and a natural solid-solution crystal of composition (Mg_1.80,Fe_0.20)SiO₄ were investigated using Raman spectroscopy. Polarized single-crystal spectra were measured as a function of temperature. In addition, polycrystalline forsterite and fayalite, isotopically enriched in ²⁶Mg and ⁵⁷Fe, respectively, were synthesized and their powder spectra measured. The high-wavenumber modes in olivine consist of internal SiO₄ vibrations that show little variation upon isotopic substitution. This confirms conclusions from previous spectroscopic studies that showed that the internal SiO₄ vibrations have minimal coupling with the lower-wavenumber lattice modes. The lowest wavenumber modes in both forsterite and fayalite shift in energy following isotopic substitution, but with energies less than that which would be associated with pure Mg and Fe translations. The low-wavenumber Raman modes in olivine are best described as lattice modes consisting to a large degree of mixed vibrations of M(2) cation translations and external vibrations of the SiO₄ tetrahedra. The single-crystal spectra of forsterite and Fo₉₀Fa₁₀ were recorded at a number of temperatures from room temperature to about 1200 °C. From these data the microscopic Grüneisen parameters for three different A_g modes for both compositions were calculated, and also the structural state of the solid solution crystal was investigated. Small discontinuities observed in the wavenumber behavior of a low-energy mixed Mg/T(SiO₄) mode between 700 and 1000 °C may be related to minor variations in the Fe–Mg intracrystalline partitioning state in the Fo₉₀Fa₁₀ crystal, but further spectroscopic work is needed to clarify and quantify this issue. The mode wavenumber and intensity behavior of internal SiO₄ vibrations as a function of temperature are discussed in terms of crystal field and dynamic splitting and also ₁ and ₃ coupling. Crystal-field splitting increases only very slightly with temperature, whereas dynamical-field splitting is temperature dependent. The degree of ₁–₃ coupling decreases with increasing temperature.     

Non-ideal mixing in the phlogopite-annite binary: constraints from experimental data on Mg−Fe partitioning and a reformulation of the biotite-garnet geothermometer

The existing experimental data [Ferry and Spear 1978; Perchuk and Lavrent'eva 1983] on Mg?Fe partitioning between garnet and biotite are disparate. The underlying assumption of ideal Mg?Fe exchange between the minerals has been examined on the basis of recently available thermochemical data. Using the updated mixing parameters for the pyrope-almandine asymmetric regular solution as inputs [Ganguly and Saxena 1984; Hackler and Wood 1984], thermodynamic analysis points to non-ideal mixing in the phlogopite-annite binary in the temperature range of 550°C–950°C. The non-ideality can be approximated by a temperature-independent, one constant Margules parameter. The retrieved values for enthalpy of mixing for Mg?Fe biotites and the standard state enthalpy and entropy changes of the exchange reaction were combined with existing thermochemical data on grossular-pyrope and grossular-almandine binaries to obtain geothermometric expressions for Mg?Fe fractionation between biotite and garnet. [T in K] $$\begin{gathered} {\text{T(HW) = [20286 + 0}}{\text{.0193P - \{ 2080(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{)}}^{\text{2}} {\text{ - 6350(X}}_{{\text{Fe}}}^{{\text{Gt}}} {\text{)}}^{\text{2}} \hfill \\ {\text{ - 13807(X}}_{{\text{Ca}}}^{{\text{Gt}}} {\text{)(1 - X}}_{{\text{Mn}}}^{{\text{Gt}}} {\text{) + 8540(X}}_{{\text{Fe}}}^{{\text{Gt}}} {\text{)(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{)(1 - X}}_{{\text{Mn}}}^{{\text{Gt}}} {\text{)}} \hfill \\ {\text{ + 4215(X}}_{{\text{Ca}}}^{{\text{Gt}}} {\text{)(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{ - X}}_{{\text{Fe}}}^{{\text{Gt}}} {\text{)\} + 4441}}{{{\text{(2X}}_{{\text{Mg}}}^{{\text{Bt}}} {\text{ - 1)]}}} \mathord{\left/ {\vphantom {{{\text{(2X}}_{{\text{Mg}}}^{{\text{Bt}}} {\text{ - 1)]}}} {{\text{[13}}{\text{.138}}}}} \right. \kern-\nulldelimiterspace} {{\text{[13}}{\text{.138}}}} \hfill \\ {\text{ + 8}}{\text{.3143 InK}}_{\text{D}} {\text{ + 6}}{\text{.276(X}}_{{\text{Ca}}}^{{\text{Gt}}} ){\text{(1 - X}}_{{\text{Mn}}}^{{\text{Gt}}} )] \hfill \\ {\text{T(GS) = [13538 + 0}}{\text{.0193P - \{ 837(X}}_{{\text{Mg}}}^{{\text{Gt}}} )^{\text{2}} {\text{ - 10460(X}}_{{\text{Fe}}}^{{\text{Gt}}} )^2 \hfill \\ {\text{ - 13807(X}}_{{\text{Ca}}}^{{\text{Gt}}} )(1{\text{ - X}}_{{\text{Mn}}}^{{\text{Gt}}} {\text{) + 19246(X}}_{{\text{Fe}}}^{{\text{Gt}}} ){\text{(X}}_{{\text{Mg}}}^{{\text{Gt}}} ){\text{(1 - X}}_{{\text{Mn}}}^{{\text{Gt}}} ) \hfill \\ {\text{ }}{{{\text{ + 5649(X}}_{{\text{Ca}}}^{{\text{Gt}}} ){\text{(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{ - X}}_{{\text{Fe}}}^{{\text{Gt}}} ){\text{\} + 7972(2X}}_{{\text{Mg}}}^{{\text{Bt}}} {\text{ - 1)]}}} \mathord{\left/ {\vphantom {{{\text{ + 5649(X}}_{{\text{Ca}}}^{{\text{Gt}}} ){\text{(X}}_{{\text{Mg}}}^{{\text{Gt}}} {\text{ - X}}_{{\text{Fe}}}^{{\text{Gt}}} ){\text{\} + 7972(2X}}_{{\text{Mg}}}^{{\text{Bt}}} {\text{ - 1)]}}} {{\text{[6}}{\text{.778}}}}} \right. \kern-\nulldelimiterspace} {{\text{[6}}{\text{.778}}}} \hfill \\ {\text{ + 8}}{\text{.3143InK}}_{\text{D}} {\text{ + 6}}{\text{.276(X}}_{{\text{Ca}}}^{{\text{Gt}}} )(1{\text{ - X}}_{{\text{Mn}}}^{{\text{Gt}}} )] \hfill \\ \end{gathered} $$ The reformulated geothermometer is an improvement over existing biotite-garnet geothermometers because it reconciles the experimental data sets on Fe?Mg partitioning between the two phases and is based on updated activity-composition relationship in Fe?Mg?Ca garnet solid solutions.