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.     

Partition of Ni between olivine and sulfide: the effect of temperature,f_{{\text{O}}_{\text{2}} } and f_{{\text{S}}_{\text{2}} }

The experimental distribution coefficient for Ni/ Fe exchange between olivine and monosulfide (K_D3) is 35.6±1.1 at 1385° C, \(f_{{\text{O}}_{\text{2}} } = 10^{ - 8.87} ,f_{{\text{S}}_{\text{2}} } = 10^{ - 1.02} \) , and olivine of composition Fo96 to Fo92. These are the physicochemical conditions appropriate to hypothesized sulfur-saturated komatiite magma. The present experiments equilibrated natural olivine grains with sulfide-oxide liquid in the presence of a (Mg, Fe)-alumino-silicate melt. By a variety of different experimental procedures, K _D3 is shown to be essentially constant at about 30 to 35 in the temperature range 900 to 1400° C, for olivine of composition Fo97 to FoO, monosulfide composition with up to 70 mol. % NiS, and a wide range of \(f_{{\text{O}}_{\text{2}} } \) and \(f_{{\text{S}}_{\text{2}} } \) .     

P,T, f_{{\text{CO}}_{\text{2}} } and f_{{\text{H}}_{\text{2}} {\text{O}}} during metamorphism of calcareous sediments in the Waterville-Vassalboro area,south-central Maine

In a regional metamorphic terrain where six isograds have been mapped based on mineral reactions that are observed in metacarbonate rocks, the P-T conditions and fugacities of CO₂ and H₂O during metamorphism were quantified by calculations involving actual mineral compositions and experimental data. Pressure during metamorphism was near 3,500 bars. Metamorphic temperatures ranged from 380° C (biotite-chlorite isograd) to 520° C (diopside isograd). \(f_{{\text{CO}}_{\text{2}} }\) and \(f_{{\text{CO}}_{\text{2}} }\) / \(f_{{\text{H}}_{\text{2}} {\text{O}}}\) in general is higher in metacarbonate rocks below the zoisite isograd than in those above the zoisite isograd. Calculated \(f_{{\text{CO}}_{\text{2}} }\) and \(f_{{\text{H}}_{\text{2}} {\text{O}}}\) are consistent with carbonate rocks above the zoisite isograd having equilibrated during metamorphism with a bulk supercritical fluid in which \(P_{{\text{CO}}_{\text{2}} }\) + \(P_{{\text{H}}_{\text{2}} {\text{O}}}\) = P _total. Calculations indicate that below the zoisite isograd, however, \(P_{{\text{CO}}_{\text{2}} }\) + \(P_{{\text{H}}_{\text{2}} {\text{O}}}\) was less than P_total, and that this condition is not due to the presence of significant amounts of species other than CO₂ and H₂O in the system C-O-H-S. Calculated \(P_{{\text{CO}}_{\text{2}} }\) /( \(P_{{\text{CO}}_{\text{2}} }\) + \(P_{{\text{H}}_{\text{2}} {\text{O}}}\) ) is low (0.06–0.32) above the zoisite isograd. The differences in conditions above and below the zoisite isograd may indicate that the formation of zoisite records the introduction of a bulk supercritical H₂O-rich fluid into the metacarbonates. The results of the study indicate that \(f_{{\text{CO}}_{\text{2}} }\) and \(f_{{\text{H}}_{\text{2}} {\text{O}}}\) are constant on a thin section scale, but that gradients in \(f_{{\text{CO}}_{\text{2}} }\) and \(f_{{\text{H}}_{\text{2}} {\text{O}}}\) existed during metamorphism on both outcrop and regional scales.     

The ferric-ferrous ratio of natural silicate liquids equilibrated in air

Results of chemical analyses of glasses produced in 46 melting experiments in air at 1,350° C and 1,450° C on rocks ranging in composition from nephelinite to rhyolite have been combined with other published data to obtain an empirical equation relating in \((X_{{\text{Fe}}_{\text{2}} {\text{O}}_{\text{3}} }^{{\text{liq}}} /X_{{\text{FeO}}}^{{\text{liq}}} )\) to T, \(\ln f_{{\text{O}}_{\text{2}} } \) and bulk composition. The whole set of experimental data range over 1,200–1,450° C and oxygen fugacities of 10^?9.00 to 10^?0.69 bars, respectively. The standard errors of temperature and \(\log _{10} f_{{\text{O}}_{\text{2}} } \) predictions from this equation are 52° C and 0.5 units, respectively, for 186 experiments.     

Experimentelle Untersuchung der Reaktion Dolomit + Kalifeldspat + H2O ⇌ Phlogopit + Calcit + CO2

The equilibrium curve for the reaction 3 dolomite + 1 K-feldspar + 1 H₂O=1 phlogopite + 3 calcite + 3 CO₂ was determined experimentally at a total gas pressure of 2000 bars using two different methods.

1. In the first case water alone was added to the reactants. The CO₂ component of the gas phase was producted solely by the reaction under favourable P-T conditions. This manner of carrying out the reaction is called the “water method”. With this method sufficient time must be allowed for the gas phase to attain a constant composition (see Fig. 1). Reverse reactions were carried out using reaction products of the forward reaction.
2. In the second case silver oxalate + water were added to the reactants. Breakdown of the silver oxalate leads to formation of a CO₂-H₂O gasphase of definite composition. At constant temperature and gas pressure the \(X_{{\text{CO}}_{\text{2}} } \) determines whether the reaction products will be phlogopite + calcite or dolomite + K-feldspar. In this case it is not necessary to wait for equilibrium to be attained. This method is abbreviated the “oxalate method”. Reactants for reverse reactions are not identical with the products of the forward reaction.

At high temperatures the results of the two different methods agree well (see Tables 1 and 2). Equilibrium was attained in one case at 490° C and \(X_{{\text{CO}}_{\text{2}} } \) of approximately 0.77, and in the other case at 520° C and \(X_{{\text{CO}}_{\text{2}} } \) of 0.90. At lower temperatures there are considerable differences in the results. With the water method an \(X_{{\text{CO}}_{\text{2}} } \) of about 0.25 was reached at 450° C. With the oxalate method dolomite K-feldspar and water still react with each other at even higher \(X_{{\text{CO}}_{\text{2}} } \) values. Phlogopite, calcite and CO₂ are formed together with metastable talc. There are no criteria to indicate which of the methods is the correct one at lower temperatures and in Fig. 2, therefore, both equilibrium curves are plotted.     

Experimental investigation of the mechanism of the reaction: 1 tremolite+11 dolomite ⇌ 8 forsterite+13 calcite+9 CO2+1H2O

Stoichiometric mixtures of tremolite and dolomite were heated to 50° C above equilibrium temperatures to form forsterite and calcite. The pressure of the CO₂-H₂O fluid was 5 Kb and \(X_{{\text{CO}}_{\text{2}} }\) varied from 0.1 to 0.6. The extent of the conversion was determined by the amount of CO₂ produced. The resulting mixtures of unreacted tremolite and dolomite and of newly-formed forsterite and calcite were examined with a scanning electron microscope. All tremolite and dolomite grains showed obvious signs of dissolution. At fluid compositions with \(X_{{\text{CO}}_{\text{2}} }\) less than about 0.4, the forsterite and calcite crystals are randomly distributed throughout the charges, indicating that surfaces of the reactants are not a controlling factor with respect to the sites of nucleation of the products. A change is observed when \(X_{{\text{CO}}_{\text{2}} }\) is greater than about 0.4; the forsterite and calcite crystals now nucleate and grow at the surface of the dolomite grains, thus indicating a change in mechanism at medium CO₂ concentrations. As the reaction progresses, the dolomite grains become more and more surrounded by forsterite and calcite, finally forming armoured relics of dolomite. Under experimental conditions this characteristic texture can only be formed if the CO₂-concentration is greater than about 40 mole %. These findings make it possible to estimate the CO₂-concentration from the texture of the dolomite+tremolite+forsterite+calcite assemblage. The results suggest a dissolution-precipitation mechanism for the reaction investigated. In a simplified form it consists of the following 4 steps:

1. Dissolution of the reactants tremolite and dolomite.
2. Diffusion of the dissolved constituents in the fluid.
3. Heterogeneous nucleation of the product minerals.
4. Growth of forsterite and calcite from the fluid.

Two possible explanations are discussed for the development of the amoured texture at \(X_{{\text{CO}}_{\text{2}} }\) above 0.4. The first is based upon the assumption that dolomite has a lower rate of dissolution than tremolite at high \(X_{{\text{CO}}_{\text{2}} }\) values resulting in preferential calcite and forsterite nucleation and growth on the dolomite surface. An alternative explanation is the formation of a raised CO₂ concentration around the dolomite grains at high \(X_{{\text{CO}}_{\text{2}} }\) values, leading to product precipitation on the dolomite crystals.     

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.     

Gehlenite stability in the system CaO-Al2O3-SiO2-H2O-CO2

P, T, \(X_{{\text{CO}}_{\text{2}} }\) relations of gehlenite, anorthite, grossularite, wollastonite, corundum and calcite have been determined experimentally at P _f =1 and 4 kb. Using synthetic starting minerals the following reactions have been demonstrated reversibly

1. 2 anorthite+3 calcite=gehlenite+grossularite+3 CO₂.
2. anorthite+corundum+3 calcite=2 gehlenite+3 CO₂.
3. 3anorthite+3 calcite=2 grossularite+corundum+3CO₂.
4. grossularite+2 corundum+3 calcite=3 gehlenite+3 CO₂.
5. anorthite+2 calcite=gehlenite+wollastonite+2CO₂.
6. anorthite+wollastonite+calcite=grossularite+CO₂.
7. grossularite+calcite=gehlenite+2 wollastonite+CO₂.

In the T, \(X_{{\text{CO}}_{\text{2}} }\) diagram at P _f =1 kb two isobaric invariant points have been located at 770±10°C, \(X_{{\text{CO}}_{\text{2}} }\) =0.27 and at 840±10°C, \(X_{{\text{CO}}_{\text{2}} }\) =0.55. Formation of gehlenite from low temperature assemblages according to (4) and (2) takes place at 1 kb and 715–855° C, \(X_{{\text{CO}}_{\text{2}} }\) =0.1–1.0. In agreement with experimental results the formation of gehlenite in natural metamorphic rocks is restricted to shallow, high temperature contact aureoles.     

An empirical Redlich-Kwong-type equation of state for water to 1,000 °C and 200 Kbar

An empirically derived Redlich-Kwong type of equation of state (ERK) is proposed for H₂O, expressing a, the term related to the attraction between the molecules, as a pressure-independent function of temperature, and b, the covolume, as a temperature-independent function of pressure. The coefficients of a(T) and b(P) were derived by least squares non-linear regression, using P-V-T data given by Burnham et al. (1969b) and Rice and Walsh (1957) in conjunction with more precise recent data obtained by Tanishita et al. (1976), Hilbert (1979) and Schmidt (1979): $$a(T) = 1.616 x 10^8 - 4.989 x 10^4 T - 7.358 x 10^9 T^{ - 1} $$ and $$ = \frac{{1 + 3.4505x 10^{--- 4} P + 3.8980x 10^{--- 9} P^2 - 2.7756x 10^{--- 15} P^3 }}{{6.3944x 10^{--- 2} + 2.3776x 10^{--- 5} + 4.5717x 10^{--- 10} P^2 }}$$ , where T is expressed in Kelvin and P in bars. The ERK works very well at upper mantle conditions, at least up to 200 kbar and 1,000 °C. At subcritical conditions and those somewhat above the critical point, it still reproduces the molar Gibbs energy, \(\tilde G_{{\text{H}}_{\text{2}} {\text{O}}} \) , with a maximum deviation of 400 joules. Thus, for the purpose of calculation of geologically interesting heterogeneous equilibria, it predicts the thermodynamic properties of H₂O well enough. The values of molar volume, \(\tilde V_{{\text{H}}_{\text{2}} {\text{O}}} \) , and \(\tilde G_{{\text{H}}_{\text{2}} {\text{O}}} \) are tabulated in the appendix over a considerable P-T range. A FORTRAN program generating these functions as well as a FORTRAN subroutine for calculating the fugacity values, \(f_{{\text{H}}_{\text{2}} {\text{O}}} \) for incorporation into existing programs, are available upon request.     

Quaternary acid magma in New Zealand

The voluminous Pleistocene—Recent Taupo rhyolites typically contain phenocrysts of plagioclase (oligoclase-labradorite), quartz, titanomagnetite, ilmenite, and ferromagnesian silicates. Ferromagnesian assemblages correlate with well defined Fe-Ti oxide equilibration temperature ranges and allow the rhyolites to be subdivided as follows: (1) Cummingtonite (c)—calcic hornblende (hb)—orthopyroxene (opx); 725–755°C, (2) Hb-opx, 750–825°C, (3) Biotite-hb-(c-opx), 720–765°C, (4) Opx-clinopyroxene (cpx), 860–915°C, (5) Fe olivine-opx-cpx, one sample with temperature of 900°C. Plagioclase and orthopyroxene phenocryst compositions typically exhibit a range of composition up to ～20 mol.%. Calculated average phenocryst equilibration pressures (P _total) range between 0.5–4.9 kb, and average 2.2 kb (～7–8 km depth), indicating upper crustal crystallization. These calculations are very sensitive to variations in phenocryst composition. Calculated \(/_{{\text{H}}_2 {\text{O}}} \) for the amphibole and biotite-bearing rhyolites indicate phenocryst equilibration under \(P_{{\text{H}}_2 {\text{O}}} \simeq P_{{\text{total}}} \) , with \(X_{{\text{H}}_2 {\text{O}}} \) ～0.17–0.24 (5–8 wt. %). The precipitation of cummingtonite is thus temperature dependent, the upper limit being close to 760°C. Eruptive mechanisms of the lavas, pumices, and ash-flow deposits are evidently not primarily controlled by temperature, P _total, \(P_{{\text{H}}_2 {\text{O}}} \) , or crystal content of the magmas, and explanations must lie in kinetic and fluid dynamic behavior of the magmas. For the Taupo rhyolites, it is suggested that the critical size of a magma body (i.e. Rayleigh number) is a controlling factor in that it will influence the convective regime; fully turbulent convection is deduced to have occurred within the larger magma bodies. One consequence is intense vesiculation, prior to eruption, within the uppermost zones of these magma chambers, and the voluminous pumice deposits are believed to emanate from such chambers. Oscillatory compositional zoning within pyroxene phenocrysts is consistent with magma convection.     

Instability of sapphirine at high pressures

The stability field of Mg-sapphirines is limited at high pressures through the solid-solid breakdown reaction sapphirine?pyrope = corundum+spinel, the univariant curve originating from an invariant point located at 22 kb, 880°C to 30 kb, 1350°C. Under water pressures less than 22 kb sapphirines exhibit the same low-temperature breakdown into the assemblage chlorite+corundum+spinel as determined by Seifert (1974) between 1 kb and 7 kb thus resulting in one continuous univariant lower stability limit extending from 1 kb, about 650°C through 10 kb, 770°C to the invariant point at 22 kb, 880°C. If \(P_{{\text{H}}_{\text{2}} {\text{0}}} < P_{{\text{total}}} \) , the stability field of sapphirine will expand towards lower temperatures. The occurrence of sapphirine in mantle depths requires rather aluminous bulk compositions, high geothermal gradients and/or \(P_{{\text{H}}_{\text{2}} {\text{0}}} < P_{{\text{total}}} \) , with total pressures not exceeding 30 kb. Thus sapphirine is probably not a stable phase in the lower portions of lithospheric plates and the underlying asthenosphere.     

Les glaucophanites et roches associées de l'île de Groix (Morbihan,France): étude minéralogique et pétrogénétique

The petrographic and mineralogic study of the different rock facies on île de Groix shows that two metamorphic episodes have affected the alkaline basic rocks and associated pelitic schists. The first is represented by a zonation (west-east): II-III-II-I-II where I= eclogite facies glaucophanites (8,5 bars, 530°C), II=glaucophane-epidote-garnet facies (8 kbars, 500°C), III=greenschist facies containing blue-green amphibole (7,5 kbars, 470°C). The second metamorphic episode has partially transformed these rocks to the albite-chlorite-epidote-blue green amphibole facies (6,5 kbars, 470°C). The variations of \(P_{O_2 } \) and \(P_{{\text{H}}_{\text{2}} {\text{O}}}\) as they affect local assemblages is detailed.     

Experimental delineation of the “e” ⇌ I\bar 1 and “e” ⇌ C\bar 1 transformations in intermediate plagioclase feldspars

Approximately 125 hydrothermal annealing experiments have been carried out in an attempt to bracket the stability fields of different ordered structures within the plagioclase feldspar solid solution. Natural crystals were used for the experiments and were subjected to temperatures of ～650°C to ～1,000°C for times of up to 370 days at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =600 bars, or \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =1,200 bars. The structural states of both parent and product materials were characterised by electron diffraction, with special attention being paid to the nature of type e and type b reflections (at h+k=(2n+1), l=(2n+1) positions). Structural changes of the type C \(\bar 1\) → I \(\bar 1\) , C \(\bar 1\) → “e” structure, I \(\bar 1\) → “e” and “e” structure → I \(\bar 1\) have been followed. There are marked differences between the ordering behaviour of crystals with compositions on either side of the C \(\bar 1\) ? I \(\bar 1\) transition line. In the composition range ～ An₅₀ to ～ An₇₀ the e structure appears to have a true field of stability relative to I \(\bar 1\) ordering, and a transformation of the type I \(\bar 1\) ? e has been reversed. It is suggested that the e structure is the more stable ordered state at temperatures of ～ 800°C and below. For compositions more albite-rich than ～ An₅₀ the upper temperature limit for long range e ordering is lower than ～ 750°C, and there is no evidence for any I \(\bar 1\) ordering. The evidence for a true stability field for “e” plagioclase, which is also consistent with calorimetric data, necessitates reanalysis both of the ordering behaviour of plagioclase crystals in nature and of the equilibrium phase diagram for the albite-anorthite system. Igneous crystals with compositions of ～ An₆₅, for example, probably follow a sequence of structural states C \(\bar 1\) → I \(\bar 1\) → e during cooling. The peristerite, Bøggild and Huttenlocher miscibility gaps are clearly associated with breaks in the albite, e and I \(\bar 1\) ordering behaviour but their exact topologies will depend on the thermodynamic character of the order/disorder transformations.     

The system Fe-Si-O: Oxygen buffer calibrations to 1,500K

The five solid-phase oxygen buffers of the system Fe-Si-O, iron-wuestite (IW), wuestite-magnetite (WM), magnetite-hematite (MH), quartz-iron-fayalite (QIF) and fayalite-magnetite-quartz (FMQ) have been recalibrated at 1 atm pressure and temperatures from 800°–1,300° C, using a thermogravimetric gas mixing furnace. The oxygen fugacity, \(f_{{\text{O}}_{\text{2}} }\) was measured with a CaO-doped ZrO₂ electrode. Measurements were made also for wuestite solid solutions in order to determine the redox behavior of wuestites with O/Fe ratios varying from 1.05 to 1.17. For FMQ, additional determinations were carried out at 1 kb over a temperature range of 600° to 800° C, using a modified Shaw membrane. Results agree reasonably well with published data and extrapolations. The reaction parameters K, ΔG _r ^o , ΔH _r ^o , and ΔS _r ^o were calculated from the following log \(f_{{\text{O}}_{\text{2}} }\) /T relations (T in K): $$\begin{gathered} {\text{IW }}\log f_{{\text{O}}_{\text{2}} } = - 26,834.7/T + 6.471\left( { \pm 0.058} \right) \hfill \\ {\text{ }}\left( {{\text{800}} - 1,260{\text{ C}}} \right), \hfill \\ {\text{WM }}\log f_{{\text{O}}_{\text{2}} } = - 36,951.3/T + 16.092\left( { \pm 0.045} \right) \hfill \\ {\text{ }}\left( {{\text{1,000}} - 1,300{\text{ C}}} \right), \hfill \\ {\text{MH }}\log f_{{\text{O}}_{\text{2}} } = - 23,847.6/T + 13.480\left( { \pm 0.055} \right) \hfill \\ {\text{ }}\left( {{\text{1,040}} - 1,270{\text{ C}}} \right), \hfill \\ {\text{QIF }}\log f_{{\text{O}}_{\text{2}} } = - 27,517.5/T + 6.396\left( { \pm 0.049} \right) \hfill \\ {\text{ }}\left( {{\text{960}} - 1,140{\text{ C}}} \right), \hfill \\ {\text{FMQ }}\log f_{{\text{O}}_{\text{2}} } = - 24,441.9/T + 8.290\left( { \pm 0.167} \right) \hfill \\ {\text{ }}\left( {{\text{600}} - 1,140{\text{ C}}} \right). \hfill \\ \end{gathered}$$ These experimentally determined reaction parameters were combined with published 298 K data to determine the parameters G_f, H_f, and S_f for the phases wuestite, magnetite, hematite, and fayalite from 298 K to the temperatures of the experiments. The T? \(f_{{\text{O}}_{\text{2}} }\) data for wuestite solid solutions were used to obtain activities, excess free energies and Margules mixing parameters. The new data provide a more reliable, consistent and complete reference set for the interpretation of redox reactions at elevated temperatures in experiments and field settings encompassing the crust, mantle and core as well as extraterrestrial environments.     

Experimental investigation and application of the equilibrium rutile + orthopyroxene = quartz + ilmenite

Equilibria in the Sirf (Silica-Ilmenite-Rutile-Ferrosilite) system: $${\text{SiO}}_{\text{2}} + ({\text{Mg,Fe}}){\text{TiO}}_{\text{3}} {\text{ + (Mg,Fe)SiO}}_{\text{3}} $$ have been calibrated in the range 800–1100° C and 12–26 kbar using a piston-cylinder apparatus to assess the potential of the equilibria for geobarometry in granulite facies assemblages that lack garnet. Thermodynamic calculations indicate that the two end-member equilibria involving quartz + geikielite = rutile + enstatite, and quartz + ilmenite = rutile + ferrosilite, are metastable. We therefore reversed equilibria over the compositional range Fs_40–70, using Ag₈₀Pd₂₀ capsules with \(f_{{\text{O}}_{\text{2}} } \) buffered at or near iron-wüstite. Ilmenite compositions coexisting with orthopyroxene are \(X_{{\text{MgTiO}}_{\text{3}} }^{{\text{Ilm}}} \) of 0.06 to 0.15 and \(X_{{\text{Fe}}_{\text{2}} {\text{O}}_{\text{3}} }^{{\text{Ilm}}} \) of 0.00 to 0.01, corresponding toK _D values of 13.3, 10.2, 9.0 and 8.0 (±0.5) at 800, 900, 1000 and 1100° C, respectively, whereK _D =(XMg/XFe)^Opx/(XMg/XFe)^Ilm. Pressures have been calculated using equilibria in the Sirf system for granulites from the Grenville Province of Ontario and for granulite facies xenoliths from central Mexico. Pressures are consistent with other well-calibrated geobarometers for orthopyroxeneilmenite pairs from two Mexican samples in which oxide textures appear to represent equilibrium. Geologically unreasonable pressures are obtained, however, where oxide textures are complex. Application of data from this study on the equilibrium distribution of iron and magnesium between ilmenite and orthopyroxene suggests that some ilmenite in deep crustal xenoliths is not equilibrated with coexisting pyroxene, while assemblages from exposed granulite terranes have reequilibrated during retrogression. The Sirf equilibria are sensitive to small changes in composition and may be used for determination of activity/composition (a/X) relations of orthopyroxene if an ilmenite model is specified. A symmetric regular solution model has been used for orthopyroxene in conjunction with activity models for ilmenite available from the literature to calculatea/X relations in orthopyroxene of intermediate composition. Data from this study indicate that FeSiO₃?MgSiO₃ orthopyroxene exhibits small, positive deviations from ideality over the range 800–1100°C.     

Physicochemical parameter charts for gases in fluid inclusions

A great wealth of analytical data for fluid inclusions in minerals indicate that the major species of gases in fluid inclusions are H₂O, CO₂, CO, CH₄, H₂ and O₂. Three basic chemical reactions are supposed to prevail in rock-forming and ore-forming fluids: $$\begin{gathered} H_2 + 1/2{\text{ O}}_{\text{2}} = H_2 O, \hfill \\ CO + 1/2{\text{ O}}_{\text{2}} = CO_2 , \hfill \\ CH_4 + 2{\text{O}}_{\text{2}} = CO_2 + 2H_2 O, \hfill \\ \end{gathered} $$ and equilibria are reached among them. \(\lg f_{O_2 } - T,{\text{ }}\lg f_{CO_2 } - T\) and Eh-T charts for petrogenesis and minerogenesis in the supercritical state have been plotted under different pressures. On the basis of these charts \(f_{O^2 } ,{\text{ }}f_{CO_2 } \) , Eh, equilibrium temperature and equilibrium pressure can be readily calculated. In this paper some examples are presented to show their successful application in the study of the ore-forming environments of ore deposits.     

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.     

Thermodynamics of coexisting cummingtonite-hornblende Pairs

The activity-composition relations for calcium-rich and calcium-poor amphiboles are calculated from the composition of coexisting cummingtonite-hornblende pairs from a suite of New Zealand rhyolites. The activities are formulated in terms of site occupancies and the regular solution model is used to represent non-ideal mixing of the cations on each site. The regular solution parameters for each site are calculated from the compositions of the coexisting amphiboles. The resulting activity-composition relations are used to calibrate the standard Gibbs energy change for the reaction $${\text{7MgSiO}}_{\text{3}} {\text{ + SiO}}_{\text{2}} {\text{ + H}}_{\text{2}} {\text{O = Mg}}_{\text{7}} {\text{Si}}_{\text{8}} {\text{O}}_{{\text{22}}} {\text{(OH)}}_{\text{2}} $$ assuming that the lowest temperature rhyolites in this suite crystallised at \(P_{{\text{H}}_2 {\text{O}}} = P_{{\text{total}}} \)      

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.     

X-ray topographic study of quartz crystals twinned according to japan twin law

Quartz crystals twinned according to Japan twin law were investigated by means of X-ray topography in order to understand the origin of characteristic morphology of twin crystals. It is demonstrated that the flattened and elongated morphology characteristic of quartz twins is due to preferential growth at twin junctions where dislocations with the Burgers vector direction 〈11 \(\overline {\text{2}} \) 1〉 concentrate, and that such preferential growth operates only when {10 \(\overline {\text{1}} \) 1} faces meet at the twin junction. Once {10 \(\overline {\text{1}} \) 0} faces appear at the twin junction due to the change of growth conditions, the effect diminishes sharply and the characteristic morphology becomes less pronounced. This leads to the conclusion that the characteristic morphology of quartz crystals twinned according to Japan twin law is formed at the earlier stage of growth and becomes less pronounced at the later stage of growth.