Thermodynamic properties of almandine-grossular garnet solid solutions

The mixing properties of Fe₃Al₂Si₃O₁₂-Ca₃Al₂Si₃O₁₂ garnet solid solutions have been studied in the temperature range 850–1100° C. The experimental method involves measuring the composition of garnet in equilibrium with an assemblage in which the activity of the Ca₃Al₂Si₃O₁₂ component is fixed. Experiments on the assemblage garnet solid solution, anorthite, Al₂SiO₅ polymorph and quartz at known pressure and temperature fix the activity of the Ca₃Al₂Si₃O₁₂ component through the equilibrium: 1 $$\begin{gathered} {\text{3CaAl}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{8}} \rightleftarrows {\text{Ca}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} \hfill \\ {\text{Anorthite garnet}} \hfill \\ {\text{ + 2Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{ + SiO}}_{\text{2}} \hfill \\ {\text{ sillimanite/kyanite quartz}}{\text{.}} \hfill \\ \end{gathered}$$ This equilibrium, with either sillimanite or kyanite as the aluminosilicate mineral, was used to control \({\text{a}}_{{\text{Ca}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} }^{{\text{gt}}} \) . The compositions of the garnet solutions produced were determined by measurement of their unit cell edges. At 1 bar Fe₃Al₂Si₃O₁₂-Ca₃Al₂Si₃O₁₂ garnets exhibit negative deviations from ideality at the Fe-rich end of the series and positive deviations at the calcium end. With increasing pressure the activity coefficients for the Ca₃Al₂Si₃O₁₂ component increase because the partial molar volume of this component is greater than the molar volume of pure grossular. Previous studies indicate that the activity coefficients for the Ca₃Al₂Si₃O₁₂ component also increase with increasing (Mg/Mg+Fe) ratio of the garnet. The region of negative deviation from ideality implies a tendency towards formation of a stable Fe-Ca garnet component. Evidence in support of this conclusion has been found in a natural Fe-rich garnet which was found to contain two different garnet phases of distinctly different compositions.     

The origin of garnet in the anorthosite-charnockite suite of the Adirondacks

Detailed analysis of textural and chemical criteria in rocks of the anorthosite-charnockite suite of the Adirondack Highlands suggests that development of garnet in silica-saturated rocks of the suite occurs according to the reaction: $$\begin{gathered} {\text{Anorthite}} {\text{Orthopyroxene}} {\text{Quartz}} \hfill \\ {\text{2CaAl}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{8}} + (6 - \alpha )({\text{Fe,Mg}}){\text{SiO}}_{\text{3}} + \alpha {\text{Fe - Oxide + (}}\alpha {\text{ - 2)SiO}}_{\text{2}} \hfill \\ {\text{Garnet}} {\text{Clinopyroxene}} \hfill \\ = {\text{Ca(Fe,Mg)}}_{\text{5}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{6}} {\text{O}}_{{\text{24}}} + {\text{Ca(Fe,Mg)Si}}_{\text{2}} {\text{O}}_{\text{6}} \hfill \\ \end{gathered} $$ , where α is a function of the distribution of Fe and Mg between the several coexisting ferromagnesian phases. Depending upon the relative amounts of Fe and Mg present, quartz may be either a reactant or a product. Using an aluminum-fixed reference frame, this reaction can be restated in terms of a set of balanced partial reactions describing the processes occurring in spatially separated domains within the rock. The fact that garnet invariably replaces plagioclase as opposed to the other reactant phases indicates that the aluminum-fixed model is valid as a first approximation. This reaction is univariant and produces unzoned garnet. It differs from a similar equation proposed by de Waard (1965) for the origin of garnet in Adirondack metabasic rocks, i.e. 6 Orthopyroxene+2 Anorthite = Clinopyroxene+Garnet+2 Quartz, the principle difference being that iron oxides (ilmenite and/or magnetite) are essential reactant phases in the present reactions. The product assemblage (garnet+clinopyroxene+plagioclase ± orthopyroxene ± quartz) is characteristic of the clinopyroxene-almandine subfacies of the granulite facies.     

Assemblages among tephroite,pyroxmangite, rhodochrosite,quartz: Experimental data and occurrences in the Rhetic Alps

Reactions involving the phases quartz-rhodochrosite-tephroite-pyroxmangite-fluid have been studied experimentally in the system MnO-SiO₂-CO₂-H₂O at a pressure of 2 000 bars and resulted in the following expressions 1 $$\begin{gathered} {\text{Rhodochrosite + Quartz = Pyroxmangite + CO}}_2 \hfill \\ {\text{ log}}_{{\text{10}}} K^{{\text{2000 bars}}} = - \frac{{11.765}}{T} + 18.618. \hfill \\ {\text{Rhodochrosite + Pyroxmangite = Tephroite + CO}}_2 \hfill \\ {\text{ log}}_{{\text{10}}} K^{{\text{2000 bars}}} = - \frac{{7.083}}{T} + 11.870. \hfill \\ \end{gathered}$$ which can be used to derive data for the remaining two reactions among the phases under consideration. Field data from the Alps are in agreement with the metamorphic sequence resulting from the experiments.     

(Ca,Mg)2Si2O6 clinopyroxenes: A solution model based on nonconvergent site-disorder

Experiments at high pressure and temperature indicate that excess Ca may be dissolved in diopside. If the (Ca, Mg)₂Si₂O₆ clinopyroxene solution extends to more Ca-rich compositions than CaMgSi₂O₆, macroscopic regular solution models cannot strictly be applied to this system. A nonconvergent site-disorder model, such as that proposed by Thompson (1969, 1970), may be more appropriate. We have modified Thompson's model to include asymmetric excess parameters and have used a linear least-squares technique to fit the available experimental data for Ca-Mg orthopyroxene-clinopyroxene equilibria and Fe-free pigeonite stability to this model. The model expressions for equilibrium conditions \(\mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction A) and \(\mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction B) are given by: 1 $$\begin{gathered} \Delta \mu _{\text{A}}^{\text{O}} = {\text{RT 1n}}\left[ {\frac{{(X_{{\text{Mg}}}^{{\text{opx}}} )^2 }}{{X_{{\text{Mg}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} }}} \right] - \frac{1}{2}\{ W_{21} [2(X_{{\text{Ca}}}^{{\text{M2}}} )^3 - (X_{{\text{Ca}}}^{{\text{M2}}} ] \hfill \\ {\text{ + 2W}}_{{\text{22}}} [X_{{\text{Ca}}}^{{\text{M2}}} )^2 - (X_{{\text{Ca}}}^{{\text{M2}}} )^3 + \Delta {\text{G}}_{\text{*}}^{\text{0}} (X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Ca}}}^{{\text{M2}}} )\} \hfill \\ {\text{ + W}}^{{\text{opx}}} (X_{{\text{Wo}}}^{{\text{opx}}} )^2 \hfill \\ \Delta \mu _{\text{B}}^{\text{O}} = {\text{RT 1n}}\left[ {\frac{{(X_{{\text{Ca}}}^{{\text{opx}}} )^2 }}{{X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Ca}}}^{{\text{M2}}} }}} \right] - \frac{1}{2}\{ 2W_{21} [2(X_{{\text{Mg}}}^{{\text{M2}}} )^2 - (X_{{\text{Mg}}}^{{\text{M2}}} )^3 ] \hfill \\ {\text{ + W}}_{{\text{22}}} [2(X_{{\text{Mg}}}^{{\text{M2}}} )^3 - (X_{{\text{Mg}}}^{{\text{M2}}} )^2 + \Delta {\text{G}}_{\text{*}}^{\text{0}} (X_{{\text{Mg}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} )\} \hfill \\ {\text{ + W}}^{{\text{opx}}} (X_{{\text{En}}}^{{\text{opx}}} )^2 \hfill \\ \hfill \\ \end{gathered} $$ where 1 $$\begin{gathered} \Delta \mu _{\text{A}}^{\text{O}} = 2.953 + 0.0602{\text{P}} - 0.00179{\text{T}} \hfill \\ \Delta \mu _{\text{B}}^{\text{O}} = 24.64 + 0.958{\text{P}} - (0.0286){\text{T}} \hfill \\ {\text{W}}_{{\text{21}}} = 47.12 + 0.273{\text{P}} \hfill \\ {\text{W}}_{{\text{22}}} = 66.11 + ( - 0.249){\text{P}} \hfill \\ {\text{W}}^{{\text{opx}}} = 40 \hfill \\ \Delta {\text{G}}_*^0 = 155{\text{ (all values are in kJ/gfw)}}{\text{.}} \hfill \\ \end{gathered} $$ . Site occupancies in clinopyroxene were determined from the internal equilibrium condition 1 $$\begin{gathered} \Delta G_{\text{E}}^{\text{O}} = - {\text{RT 1n}}\left[ {\frac{{X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} }}{{X_{{\text{Ca}}}^{{\text{M2}}} \cdot X_{{\text{Mg}}}^{{\text{M1}}} }}} \right] + \tfrac{1}{2}[(2{\text{W}}_{{\text{21}}} - {\text{W}}_{{\text{22}}} )(2{\text{X}}_{{\text{Ca}}}^{{\text{M2}}} - 1) \hfill \\ {\text{ + }}\Delta G_*^0 (X_{{\text{Ca}}}^{{\text{M1}}} - X_{{\text{Ca}}}^{{\text{M2}}} ) + \tfrac{3}{2}(2{\text{W}}_{{\text{21}}} - {\text{W}}_{{\text{22}}} ) \hfill \\ {\text{ (1}} - 2X_{{\text{Ca}}}^{{\text{M1}}} )(X_{{\text{Ca}}}^{{\text{M1}}} + \tfrac{1}{2})] \hfill \\ \end{gathered} $$ where δG _E ⁰ =153+0.023T+1.2P. The predicted concentrations of Ca on the clinopyroxene Ml site are low enough to be compatible with crystallographic studies. Temperatures calculated from the model for coexisting ortho- and clinopyroxene pairs fit the experimental data to within 10° in most cases; the worst discrepancy is 30°. Phase relations for clinopyroxene, orthopyroxene and pigeonite are successfully described by this model at temperatures up to 1,600° C and pressures from 0.001 to 40 kbar. Predicted enthalpies of solution agree well with the calorimetric measurements of Newton et al. (1979). The nonconvergent site disorder model affords good approximations to both the free energy and enthalpy of clinopyroxenes, and, therefore, the configurational entropy as well. This approach may provide an example for Febearing pyroxenes in which cation site exchange has an even more profound effect on the thermodynamic properties.     

Experimental determination of the reaction paragonite=jadeite+kyanite+H2O,and internally consistent thermodynamic data for part of the system Na2O−Al2O3−SiO2−H2O,with applications to eclogites and blueschists

Hydrothermal reversal experiments have been performed on the upper pressure stability of paragonite in the temperature range 550–740 ° C. The reaction $$\begin{gathered} {\text{NaAl}}_{\text{3}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{1 0}}} ({\text{OH)}}_{\text{2}} \hfill \\ {\text{ paragonite}} \hfill \\ {\text{ = NaAlSi}}_{\text{2}} {\text{O}}_{\text{6}} + {\text{Al}}_{\text{2}} {\text{SiO}}_{\text{5}} + {\text{H}}_{\text{2}} {\text{O}} \hfill \\ {\text{ jadeite kyanite vapour}} \hfill \\ \end{gathered}$$ has been bracketed at 550 ° C, 600 ° C, 650 ° C, and 700 ° C, at pressures 24–26 kb, 24–25.5 kb, 24–25 kb, and 23–24.5 kb respectively. The reaction has a shallow negative slope (? 10 bar °C^?1) and is of geobarometric significance to the stability of the eclogite assemblage, omphacite+kyanite. The experimental brackets are thermodynamically consistent with the lower pressure reversals of Chatterjee (1970, 1972), and a set of thermodynamic data is presented which satisfies all the reversal brackets for six reactions in the system Na₂O-Al₂O₃-SiO₂-H₂O. The Modified Redlich Kwong equation for H₂O (Holloway, 1977) predicts fugacities which are too high to satisfy the reversals of this study. The P-T stabilities of important eclogite and blueschist assemblages involving omphacite, kyanite, lawsonite, Jadeite, albite, chloritoid, and almandine with paragonite have been calculated using thermodynamic data derived from this study.     

Some geobarometers involving cordierite in the FeO-Al2O3-SiO2(±H2O) system: refinements,thermodynamic calibration,and applicability in granulite facies rocks

Five geobarometers involving cordierite have been formulated for quantitative pressure sensing in high grade metapelites. The relevant reactions in the FeO-Al₂O₃-SiO₂ (±H₂O) system are based on the assemblages (A) cordierite-garnet-sillimanite-quartz, (B) cordierite-spinel-quartz, (C) cordierite-garnet-spinel-sillimanite, (D) cordierite-garnet-orthopyroxene-quartz and (E) cordierite-orthopyroxene-sillimanite-quartz. Application of the barometric formulations to a large number of granulite grade rocks indicates that the cordierite-garnet-sillimanite-quartz equilibrium is widely applicable and registers pressures which are in good agreement with the “consensus” pressure estimates. The dispersion in the computed P values, expressed as one standard deviation, is within ±1.2 kbar. The geobarometers (B) and (C) also yield pressures which are reasonable and compare well with those computed from equilibrium (A). The estimated pressures from (D) and (E), both involving orthopyroxene, are at variance with these estimates. It has been argued that the discrepancy in pressures obtained from these geobarometers stems from an inadequate knowledge of activity-composition relations and/or errors in input thermodynamic data of aluminous orthopyroxene. The convergence of pressure values estimated from the barometric formulations, especially (A), (B) and (C), implies that the present formulations are more dependable than the existing formulations and are also capable of setting limits on P values in response to varying $$\begin{gathered} {\text{1/2Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} \hfill \\ {\text{ = 1/3Fe}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} {\text{ + 2/3Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{ + 5/6SiO}}_{\text{2}} {\text{. (A)}} \hfill \\ {\text{1/2Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} {\text{ = FeAl}}_{\text{2}} {\text{O}}_{\text{4}} {\text{ + 5/2SiO}}_{\text{2}} {\text{. (B)}} \hfill \\ {\text{Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} {\text{ + FeAl}}_{\text{2}} {\text{O}}_{\text{4}} \hfill \\ = {\text{Fe}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} {\text{ + 2Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{. (C)}} \hfill \\ {\text{1/2Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} {\text{ + Fe}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} \hfill \\ = {\text{Fe}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} {\text{ + 3/2SiO}}_{\text{2}} .{\text{ (D)}} \hfill \\ {\text{1/2Fe}}_{\text{2}} {\text{Al}}{}_{\text{4}}{\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} \hfill \\ = 1/2{\text{Fe}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} {\text{ + Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{ + 1/2SiO}}_{\text{2}} .{\text{ (E)}} \hfill \\ \end{gathered}$$ . The present communication addresses the calibration, applicability and reliability of these barometers with reference to granulite facies metapelites.     

Use of FePt alloys to eliminate the iron loss problem in 1 atmosphere gas mixing experiments: Theoretical and practical considerations

Theoretical and practical considerations are combined to place limits on the iron content of an FePt alloy that is in equilibrium with silicate melt, olivine and a gas phase of known \(f_{{\text{O}}_{\text{2}} }\) . Equilibrium constants are calculated for the reactions: (1) $$2{\text{Fe}}^{\text{o}} + {\text{SiO}}_{\text{2}} + {\text{O}}_{\text{2}} \rightleftharpoons {\text{Fe}}_{\text{2}} {\text{SiO}}_{\text{4}}$$ (2) $${\text{Fe}}^{\text{o}} + \frac{1}{2}{\text{O}}_{\text{2}} \rightleftharpoons {\text{FeO}}$$ . These equilibria may be used to choose an appropriate iron activity for the FePt alloy of an experiment. The temperature dependence of the equilibrium constants is calculated from experimental data. The Gibbs free energy of reaction (1) obtained using thermochemical data is in close agreement with ΔG_rxn calculated from the experimental data. Reaction (1) has the advantage that it is independent of the Fe²⁺/Fe³⁺ ratio of the melt, but is limited to applications where olivine is a crystallizing phase and requires a formulation for \(a_{{\text{SiO}}_{\text{2}} }^{{\text{liq}}}\) . Reaction (2) uses an empirical approximation for the FeO/Fe₂O₃ ratio of the liquid, and is independent of olivine saturation. However, it requires a formulation for a _FeO ^liq . Either equilibrium constant may be used to calculate the appropriate FePt alloy in equilibrium with a silicate melt. If experiments are conducted at an \(f_{{\text{O}}_{\text{2}} }\) parallel that of a buffer assemblage, a small range of FePt alloys may be used over a large temperature interval. For example, an alloy containing from 6 % to 9 % Fe by weight is in equilibrium with olivine-saturated tholeiites and komatiites at the quartzfayalite-magnetite buffer over the temperature interval 1,400° C to 1,100° C. Lunar basalt liquids in equilibrium with olivine at 1/2 log unit below the iron-wüstite buffer require an FePt alloy that contains 30–50 wt. % iron over a similar temperature interval.     

Ephesite,Na(LiAl2) [Al2Si2O10] (OH)2: I. thermal stability and standard state thermodynamic properties

Ephesite, Na(LiAl₂) [Al₂Si₂O₁₀] (OH)₂, has been synthesized for the first time by hydrothermal treatment of a gel of requisite composition at 300≦T(° C)≦700 and \(P_{H_2 O}\) upto 35 kbar. At \(P_{H_2 O}\) between 7 and 35 kbar and above 500° C, only the 2M₁ polytype is obtained. At lower temperatures and pressures, the 1M polytype crystallizes first, which then inverts to the 2M₁ polytype with increasing run duration. The X-ray diffraction patterns of the 1M and 2M₁ poly types can be indexed unambiguously on the basis of the space groups C2 and Cc, respectively. At its upper thermal stability limit, 2M₁ ephesite decomposes according to the reaction (1) $$\begin{gathered} {\text{Na(LiAl}}_{\text{2}} {\text{) [Al}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{{\text{10}}} {\text{] (OH)}}_{\text{2}} \hfill \\ {\text{ephesite}} \hfill \\ {\text{ = Na[AlSiO}}_{\text{4}} {\text{] + LiAl[SiO}}_{\text{4}} {\text{] + }}\alpha {\text{ - Al}}_{\text{2}} {\text{O}}_{\text{3}} {\text{ + H}}_{\text{2}} {\text{O}} \hfill \\ {\text{nepheline }}\alpha {\text{ - eucryptite corundum}} \hfill \\ \end{gathered}$$ Five reversal brackets for (1) have been established experimentally in the temperature range 590–750° C, at \(P_{H_2 O}\) between 400 and 2500 bars. The equilibrium constant, K, for this reaction may be expressed as (2) $$log K{\text{ = }}log f_{{\text{H}}_{\text{2}} O}^* = 7.5217 - 4388/T + 0.0234 (P - 1)T$$ where \(f_{H_2 O}^* = f_{H_2 O} (P,T)/f_{H_2 O}^0\) (1,T), with T given in degrees K, and P in bars. Combining these experimental data with known thermodynamic properties of the decomposition products in (1), the following standard state (1 bar, 298.15 K) thermodynamic data for ephesite were calculated: H _f,298.15 ⁰ =-6237372 J/mol, S _298.15 ⁰ =300.455 J/K·mol, G _298.15 ⁰ =-5851994 J/mol, and V _298.15 ⁰ =13.1468 J/bar·mol.     

A note on the significance of the assemblage calcite-quartz-plagioclase-paragonite-graphite

The biotite zone assemblage: calcite-quartz-plagioclase (An₂₅)-phengite-paragonite-chlorite-graphite, is developed at the contact between a carbonate and a pelite from British Columbia. Thermochemical data for the equilibrium paragonite+calcite+2 quartz=albite+ anorthite+CO₂+H₂O yields: $$\log f{\text{H}}_{\text{2}} {\text{O}} + \log f{\text{CO}}_{\text{2}} = 5.76 + 0.117 \times 10^{ - 3} (P - 1)$$ for a temperature of 700°K and a plagioclase composition of An₂₅. By combining this equation with equations describing equilibria between graphite and gas species in the system C-H-O, the following partial pressures: \(P{\text{H}}_2 {\text{O}} = 2572{\text{b, }}P{\text{CO}}_2 = 3162{\text{b, }}P{\text{H}}_2 = 2.5{\text{b, }}P{\text{CH}}_4 = 52.5{\text{b, }}P{\text{CO}} = 11.0{\text{b}}\) are obtained for \(f{\text{O}}_2 = 10^{ - 26}\) . If total pressure equals fluid pressure, then the total pressure during metamorphism was approximately 6 kb. The total fluid pressure calculated is extremely sensitive to the value of \(f{\text{O}}_2\) chosen.     

Manganese thermometer for mantle peridotites

The temperature dependence of the Mn-Mg distribution between garnet and clinopyroxene, originally proposed by Carswell, was confirmed by Shimizu and Allègre (1978) using ion microprobe and electron microprobe data. High precision electron microprobe analyses of a larger set of 52 Iherzolites from S. Africa and Malaita, Solomon Islands show considerable scatter in the temperature dependence of this distribution, and correlation with the CaO content of the garnet is indicated. A new distribution coefficient is based on the reaction: $$\begin{gathered} \operatorname{Mn} _{\text{2}} \operatorname{Si} _2 \operatorname{O} _6 {\text{ + }}\operatorname{CaAl} _{2/3} \operatorname{SiO} _4 {\text{ + }}\operatorname{MgAl} _{2/3} \operatorname{SiO} _4 \hfill \\ {\text{Mn - pyroxene grossular pyrope}} \hfill \\ {\text{ }} \rightleftharpoons \operatorname{CaMgSi} _2 \operatorname{O} _6 {\text{ + }}2\operatorname{MnAl} _{2/3} \operatorname{SiO} _4 \hfill \\ {\text{ diopside spessartine}} \hfill \\ \end{gathered} $$ It was calibrated against temperature determined from two independent thermometers (Wells pyroxene and O'Neill-Wood garnet-olivine) for Iherzolitic assemblages, and shown to to be sensitive to within + 50 °C for most specimens in the range 900 °– 1,300 ° C. This distribution coefficient appears independent of pressure within the uncertainty of the available data, and has the potential to be a third independent thermometer for use in garnet Iherzolites and possibly eclogites.     

Stabilitätsbeziehungen zwischen Chlorit,Cordierit und Almandin bei der Metamorphose

The stability relations between cordierite and almandite in rocks, having a composition of CaO poor argillaceous rocks, were experimentally investigated. The starting material consisted of a mixture of chlorite, muscovite, and quartz. Systems with widely varying Fe²⁺/Fe²⁺+Mg ratios were investigated by using two different chlorites, thuringite or ripidolite, in the starting mixture. Cordierite is formed according to the following reaction: $${\text{Chlorite + muscovite + quartz}} \rightleftharpoons {\text{cordierite + biotite + Al}}_{\text{2}} {\text{SiO}}_{\text{5}} + {\text{H}}_{\text{2}} {\text{O}}$$ . At low pressures this reaction characterizes the facies boundary between the albite-epidotehornfels facies and the hornblende-hornfels facies, at medium pressures the beginning of the cordierite-amphibolite facies. Experiments were carried out reversibly and gave the following equilibrium data: 505±10°C at 500 bars H₂O pressure, 513±10°C at 1000 bars H₂O pressure, 527±10°C at 2000 bars H₂O pressure, and 557±10°C at 4000 bars H₂O pressure. These equilibrium data are valid for the Fe-rich starting material, using thuringite as the chlorite, as well as for the Mg-rich starting mixture with ripidolite. At 6000 bars the equilibrium temperature for the Mg-rich mixture is 587±10°C. In the Fe-rich mixture almandite was formed instead of cordierite at 6000 bars. The following reaction was observed: $${\text{Thuringite + muscovite + quartz}} \rightleftharpoons {\text{almandite + biotite + Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{ + H}}_{\text{2}} {\text{O}}$$ . Experiments with the Fe-rich mixture, containing Fe²⁺/Fe²⁺+Mg in the ratio 8∶10, yielded three stability fields in a P,T-diagram (Fig.1):

1. Above 600°C/5.25 kb and 700°C/6.5 kb almandite+biotite+Al₂SiO₅ coexist stably, cordierite being unstable.
2. The field, in which almandite, biotite and Al₂SiO₅ are stable together with cordierite, is restricted by two curves, passing through the following points:
   1. 625°C/5.5 kb and 700°C/6.5 kb,
   2. 625°C/5.5 kb and 700°C/4.0 kb.
3. At conditions below curves 1 and 2b, cordierite, biotite, and Al₂SiO₅ are formed, but no garnet.

An appreciable MnO-content in the system lowers the pressures needed for the formation of almandite garnet, but the quantitative influence of the spessartite-component on the formation of almandite could not yet be determined. the Mg-rich system with Fe²⁺/Fe²⁺+Mg=0.4 garnet did not form at pressures up to 7 kb in the temperature range investigated. Experiments at unspecified higher pressures (in a simple squeezer-type apparatus) yielded the reaction: $${\text{Ripidolite + muscovite + quartz}} \rightleftharpoons {\text{almandite + biotite + Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{ + H}}_{\text{2}} {\text{O}}$$ . Further experiments are needed to determine the equilibrium data. The occurence of garnet in metamorphic rocks is discussed in the light of the experimental results.     

Experimental investigation of the reaction forsterite + H2O ⇌ serpentine + brucite

A new determination of the equilibrium reaction: $$\begin{gathered} 2{\text{ Mg}}_{\text{2}} [{\text{SiO}}_{\text{4}} ] + 3{\text{ H}}_{\text{2}} {\text{O}} \rightleftharpoons {\text{1 Mg}}_{\text{3}} [({\text{OH)}}_{\text{4}} |{\text{Si}}_{\text{2}} {\text{O}}_{\text{5}} ] + 1{\text{ Mg(OH)}}_{\text{2}} \hfill \\ \hfill \\ {\text{ forsterite serpentine brucite}} \hfill \\ \end{gathered} $$ yielded equilibrium temperatures which lie (at identical H₂O-pressures) about 60° C lower than all previously published data (Bowen and Tuttle, 1949; Yoder, 1952; Kitahara et al., 1966; Kitahara and Kennedy, 1967). It has been shown that the above authors have determined not the stable equilibrium curve but instead a metastable “synthesis boundary”. The actual (stable) equilibrium curve is located at 0,5 kb and 350° C 2,0 kb and 380° C 3,5 kb and 400° C 5,0 kb and 420° C 6,5 kb and 430° C.     

Talc paragenesis in some siliceous dolomitic rocks,and its sedimentologic significance

Thin (0.5–4 mm), contorted stringers of talc, associated with apatite and minor pyrite, are containdy Formation in eastern Alabama. The form, position and lithologic distribed within generally saccharoidal dolomite-quartz marbles of the Cambrian Shaution of the stringers strongly suggest an algalstromatolitic origin, with interlaminar trapped dolomitic muds. Metamorphic formation of talc plus apatite proceeded only within the stringers, whereas surrounding marble remained as unreacted dolomite plus quartz. Talc generation is best explained by the reaction $${\text{dolomite}} + {\text{silica}} + {\text{water}} + {\text{P}}_{\text{2}} {\text{O}}_{\text{5}} = {\text{talc}} + {\text{apatite}} + {\text{CO}}_{\text{2}}$$ in which the phosphate was supplied to the reaction from organic matter contained within the stromatolitic layers. The system was probably open to CO₂ during metamorphism, and \(P_{{\text{CO}}_{\text{2}} }\) remained relatively low.     

Oxygen isotope fractionation between rutile and water

Synthetic rutile-water fractionations (1000 ln α) at 775, 675, and 575° C were found to be ?2.8, ?3.5, and ?4.8, respectively. Partial exchange experiments with natural rutile at 575° C and with synthetic rutile at 475° C failed to yield reliable fractionations. Isotopic fractionation within the range 575–775° C may be expressed as follows: 1 $$1000\ln \alpha ({\rm T}i{\rm O}_{2 } - H_2 O) = - 4.1 \frac{{10^6 }}{{T_{k^2 } }} + 0.96$$ . Combined with previously determined quartz-water fractionations, the above data permit calibration of the quartz-rutile geothermometer: 1 $$1000\ln \alpha ({\text{S}}i{\rm O}_{2 } - Ti{\rm O}_{2 } ) = 6.6 \frac{{10^6 }}{{T_{k^2 } }} - 2.9$$ . When applied to B-type eclogites from Europe, as an example, the latter equation yields a mean equilibration temperature of 565° C.     

The Reaction Titanite+Kyanite=Anorthite+Rutile and Titanite-Rutile Barometry in Eclogites

Titanite and rutile are a common mineral pair in eclogites, and many equilibria involving these phases are potentially useful in estimating pressures of metamorphism. We have reversed one such reaction,

Intrinsic oxygen Fugacity measurements on chromites from the Bushveld Complex and their petrogenetic significance

Oxygen Fugacity measurements were carried out on chromites from the Eastern Bushveld Complex (Maandagshoek) and are compared with former measurements on chromites from the western Bushveld Complex (Zwartkop Chrome Mine). These results together with those of Hill and Roeder (1974) yield the following conditions of formation for the massive chromitite layers: Western Bushveld Complex (Zwartkop Chrome Mine) $$\begin{gathered} Layer{\text{ }}T(^\circ C) p_{O_2 } (atm) \hfill \\ LG3{\text{ 1160}} - {\text{1234 10}}^{ - {\text{5}}} - 10^{ - 7.6} \hfill \\ LG4{\text{ 1175}} - {\text{1200 10}}^{ - 6.35} - 10^{ - 7.20} \hfill \\ LG6{\text{ 1162}} - {\text{1207 10}}^{ - 6.20} - 10^{ - 7.50} \hfill \\ \hfill \\ \end{gathered} $$ Eastern Bushveld Complex (Farm Maandagshoek) $$\begin{gathered} {\text{LXI 1115}} - {\text{1150 10}}^{ - 7.80} - 10^{ - 8.80} \hfill \\ ( = {\text{Steelpoort Seam)}} \hfill \\ {\text{LX 1125 10}}^{ - 8.25} \hfill \\ {\text{V 1120 10}}^{ - 8.55} \hfill \\ {\text{LII 1120 10}}^{ - 8.0} - 10^{ - 8.60} \hfill \\ \end{gathered} $$ The comparison of the data shows, that the chronitite layers within each particular sequence were formed under approximately identicalp _{o 2}- andT-conditions. The chromites from the western Bushveld Complex, however, were formed at higher temperatures and higher oxygen fugacities than the chromites from the eastern Bushveld Complex. Fromp _{o 2}-T-curves of disseminated chromites and the temperatures derived above, the following conditions of formation for the host rocks were obtained: Western Bushveld Complex $$T = 1200^\circ {\text{C; }}p_{{\text{o}}_{\text{2}} } = 10^{ - 7.25} - 10^{ - 7.50} $$ Eastern Bushveld Complex $$T = 1125^\circ {\text{C; }}p_{{\text{o}}_{\text{2}} } = 10^{ - 8.50} - 10^{ - 9.25} $$ Consequently, the host rocks in the Zwartkop-Chrome-Mine, were formed under higher temperatures and higher oxygen fugacities than the host rocks at Maandagshoek. The rock sequence in the Zwartkop-Chrome-Mine therefore originated in an earlier stage of the differentiation of the Bushveld magma. Comparison of the chromites from the host rocks with the chromites from massive layers supports Ulmer's (1969) thesis that an increase of the oxygen fugacity is responsible for the formation of massive chromitite layers. The values in this investigation show that increases of only about 0.5–1.0 log units are necessary to enhance chromitite layer formation.     

Moon—An albite depleted giant Skaergaard?

The chemical composition of 2188 terrestrial igneous rocks ranging from ultrabasic to granitic composition was analyzed statistically using the method of factor analysis (principal components). The resultant first and second factors were: $$\begin{gathered} {\text{ }}F_1 = 0.933{\text{ Na}}_{\text{2}} {\text{O + 0}}{\text{.143 SiO}}_{\text{2}} + 0.206{\text{ K}}_{\text{2}} {\text{O}} - 0.346{\text{ CaO}} - 0.263{\text{ MgO}} - \hfill \\ .203{\text{ FeO}} \pm \cdot \cdot \cdot \hfill \\ {\text{ }}F_2 = 0.979{\text{ Al}}_{\text{2}} {\text{O}}_{\text{3}} - 0.269{\text{ MgO}} - 0.151{\text{ SiO}}_{\text{2}} - 0.112{\text{ FeO}} \pm \cdot \cdot \cdot \hfill \\ \end{gathered} $$ where oxides are in weight percent. A plot of the first factor against the second results in a useful igneous variation diagram. When the compositions of the 2188 terrestrial rocks and 604 lunar rocks are plotted on this diagram, the two groups of rocks are clearly separated within an albite-anorthite-forsterite-fayalite-quartz polygon. None of the terrestrial differentiation trends are significant for lunar rocks. The major difference in the chemistry of lunar and terrestrial rocks lies in the former being albite poor. Removal of most of the albite from the compositions of terrestrial layered intrusives such as the Skaergaard results in an excellent match between the compositions of the two groups of rocks. Albite subtracted compositions of Skaergaard rocks in particular cover the entire range of chemical variation in the lunar rocks. The statistical results prompt us to speculate further on the similarity of the moon and Skaergaard. We note that the average composition of the moon (Wanke et al., 1974) is similar to the albite subtracted composition of the Skaergaard magma. The lunar crust and a significant part of the lunar interior may match the albite subtracted and somewhat Mg enriched Skaergaard magma.     

Systematic study of liquidas phase relations in olivine melilitite +H2O +CO2 at high pressures and petrogenesis of an olivine melilitite magma

Near-liquidus phase relationships of a spinel lherzolite-bearing olivine melilitite from Tasmania were investigated over a P, T range with varying , , and . At 30 kb under MH-buffered conditions, systematic changes of liquidus phases occur with increasing ( = CO₂/CO₂ +H₂O+olivine melilitite). Olivine is the liquidus phase in the presence of H₂O alone and is joined by clinopyroxene at low . Increasing eliminates olivine and clinopyroxene becomes the only liquidus phase. Further addition of CO₂ brings garnet+orthopyroxene onto the liquidus together with clinopyroxene, which disappears with even higher CO₂. The same systematic changes appear to hold at higher and lower pressures also, only that the phase boundaries are shifted to different . The field with olivine- +clinopyroxene becomes stable to higher with lower pressure and approaches most closely the field with garnet+orthopyroxene+clinopyroxene at about 27 kb, 1160 °C, 0.08 and 0.2 (i.e., 6–7% CO₂+ 7–8% H₂O). Olivine does not coexist with garnet+orthopyroxene+clinopyroxene under these MH-buffered conditions. Lower oxygen fugacities do not increase the stability of olivine to higher and do not change the phase relationships and liquidus temperatures drastically. Thus, it is inferred that olivine melilitite 2927 originates as a 5% melt (inferred from K_{2 O} and P₂O₅ content) from a pyrolite source at about 27kb, 1160 dg with about 6–7% CO₂ and 7–8% H₂O dissolved in the melt. The highly undersaturated character of the melt and the inability to find olivine together with garnet and orthopyroxene on the liquidus (in spite of the close approach of the respective liquidus fields) can be explained by reaction relationships of olivine and clinopyroxene with orthopyroxene, garnet and melt in the presence of CO₂.     

Energetics of hydration of cordierite and water barometry in cordierite-granulites

The Gibbs free energy and volume changes attendant upon hydration of cordierites in the system magnesian cordierite-water have been extracted from the published high pressure experimental data at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =P _total, assuming an ideal one site model for H₂O in cordierite. Incorporating the dependence of ΔG and ΔV on temperature, which was found to be linear within the experimental conditions of 500°–1,000°C and 1–10,000 bars, the relation between the water content of cordierite and P, T and \(f_{{\text{H}}_{\text{2}} {\text{O}}} \) has been formulated as $$\begin{gathered} X_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{crd}}} = \hfill \\ \frac{{f_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{P, T}}} }}{{\left[ {{\text{exp}}\frac{1}{{RT}}\left\{ {64,775 - 32.26T + G_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{1, }}T} - P\left( {9 \times 10^{ - 4} T - 0.5142} \right)} \right\}} \right] + f_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{P, T}}} }} \hfill \\ \end{gathered} $$ The equation can be used to compute H₂O in cordierites at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) <1. Our results at different P, T and partial pressure of water, assuming ideal mixing of H₂O and CO₂ in the vapour phase, are in very good agreement with the experimental data of Johannes and Schreyer (1977, 1981). Applying the formulation to determine \(X_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{crd}}} \) in the garnet-cordierite-sillimanite-plagioclase-quartz granulites of Finnish Lapland as a test case, good agreement with the gravimetrically determined water contents of cordierite was obtained. Pressure estimates, from a thermodynamic modelling of the Fe-cordierite — almandine — sillimanite — quartz equilibrium at \(P_{{\text{H}}_{\text{2}} {\text{O}}} = 0\) and \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =P_total, for assemblages from South India, Scottish Caledonides, Daly Bay and Hara Lake areas are compatible with those derived from the garnetplagioclase-sillimanite-quartz geobarometer.     

The reversed alumina contents of orthopyroxene in equilibrium with spinel and forsterite in the system MgO-Al2O3-SiO2

Equilibrium alumina contents of orthopyroxene coexisting with spinel and forsterite in the system MgO-Al₂O₃-SiO₂ have been reversed at 15 different P-T conditions, in the range 1,030–1,600° C and 10–28 kbar. The present data and three reversals of Danckwerth and Newton (1978) have been modeled assuming an ideal pyroxene solid solution with components Mg₂Si₂O₆ (En) and MgAl₂SiO₆ (MgTs), to yield the following equilibrium condition (J, bar, K): $$\begin{gathered} RT{\text{ln(}}X_{{\text{MgTs}}} {\text{/}}X_{{\text{En}}} {\text{) + 29,190}} - {\text{13}}{\text{.42 }}T + 0.18{\text{ }}T + 0.18{\text{ }}T^{1.5} \hfill \\ + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP = 0,} \hfill \\ \end{gathered} $$ where $$\begin{gathered} + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP} \hfill \\ = [0.013 + 3.34 \times 10^{ - 5} (T - 298) - 6.6 \times 10^{ - 7} P]P. \hfill \\ \end{gathered} $$ The data of Perkins et al. (1981) for the equilibrium of orthopyroxene with pyrope have been similarly fitted with the result: $$\begin{gathered} - RT{\text{ln(}}X_{{\text{MgTs}}} \cdot X_{{\text{En}}} {\text{) + 5,510}} - 88.91{\text{ }}T + 19{\text{ }}T^{1.2} \hfill \\ + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP = 0,} \hfill \\ \end{gathered} $$ where $$\begin{gathered} + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP} \hfill \\ = [ - 0.832 - 8.78{\text{ }} \times {\text{ 10}}^{ - {\text{5}}} (T - 298) + 16.6{\text{ }} \times {\text{ 10}}^{ - 7} P]{\text{ }}P. \hfill \\ \end{gathered} $$ The new parameters are in excellent agreement with measured thermochemical data and give the following properties of the Mg-Tschermak endmember: $$H_{f,970}^0 = - 4.77{\text{ kJ/mol, }}S_{298}^0 = 129.44{\text{ J/mol}} \cdot {\text{K,}}$$ and $$V_{298,1}^0 = 58.88{\text{ cm}}^{\text{3}} .$$ The assemblage orthopyroxene+spinel+olivine can be used as a geothermometer for spinel lherzolites, subject to a choice of thermodynamic mixing models for multicomponent orthopyroxene and spinel. An ideal two-site mixing model for pyroxene and Sack's (1982) expressions for spinel activities provide, with the present experimental calibration, a geothermometer which yields temperatures of 800° C to 1,350° C for various alpine peridotites and 850° C to 1,130° C for various volcanic inclusions of upper mantle origin.