Oxygen isotope thermometry of basic lavas and mantle nodules

Measurements have been made of the oxygen isotope and chemical composition of glass and phenocrysts in lavas and coexisting minerals in mantle nodules. Temperatures of formation of these assemblages have been estimated from various chemical thermometers and range from 855° to 1,300° C. The permil fractionations between coexisting orthopyroxene and clinopyroxene in the lavas and nodules are all near zero. The fractionations between pyroxene and olivine vary from +1.2 to –1.4 and are a smooth function of temperature over the entire range. This function is given by T(° C)=1151-173 (px-d)-68²(px-d) and has an uncertainty of ±60° (2). At temperatures above 1,150° C, olivine in the nodules becomes more¹⁸O-rich than coexisting clinopyroxene, orthopyroxene, and plagioclase. In combination with the experimental work of Muehlenbachs and Kushiro (1974), the olivine-pyroxene fractionations indicate that olivine also becomes substantially more¹⁸O-rich than basaltic liquids above 1,200° C. Geothermometers based on the oxygen isotope equilibration of basaltic liquid with olivine, pyroxene, and plagioclase are presented.     

Study on the compositional dependence of the apparent partition coefficient of iron and magnesium between coexisting garnet and clinopyroxene solid solution

Compositional dependence of apparent partition coefficient of iron and magnesium between coexisting garnet and clinopyroxene from Mt. Higasiakaisi is studied by means of a multicomponent regular solution model. It is shown that garnet and clinopyroxene solid solutions are positively non-ideal, and the non-ideal parameters according to the symmetric regular solution model are 2.58 kcal and 2.39 kcal, respectively, assuming the equilibration temperature of the mass to be 550° C.Notations a _i ^h activity of component i in phase h - _ij interaction parameter of component i and j in a solid solution - _i activity coefficient of component i - X _i mole fraction of component i - K partition coefficient of Fe and Mg between coexisting garnet and clinopyroxene - K apparent partition coefficient of Fe and Mg between coexisting garnet and clinopyroxene - G ⁰ difference in free energy of the partition reaction - H ⁰ difference in enthalpy of the partition reaction - S ⁰ difference in entropy of the partition reaction - R gas constant - G garnet - Alm almandine component - Py pyrope component - Gr grossular component - Sp spessartine component - CPx clinopyroxene - Hd hedenbergite component - Di diopside component - Jd jadeite component - Ts Tschermac's molecule component Deceased on April 17, 1974.     

Mean and turbulent velocity measurements of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some largescale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity ( _u /U).List of Symbols a speed of sound - b total mixing layer thickness betweenU ₁ – 0.1U andU ₂ + 0.1U - f normalized third moment ofu-velocity,f u ³/(U)³ - g normalized triple product ofu ² v,g u ² v/(U)³ - h normalized triple product ofu v ², h uv' ²/(U)³ - l _u axial distance for similarity in the mean velocity - l _u axial distance for similarity in the turbulence intensity - M Mach number - M _c convective Mach number (for ₁=₂),M _c (U ₁–U ₂)/(a ₁+a ₂) - P static pressure - r freestream velocity ratio,rU ₂/U ₁ - Re unit Reynolds number,Re U/ - s freestream density ratio,s ₂/ ₁ - T _t total temperature - u instantaneous streamwise velocity - u deviation ofu-velocity,u u–U - U local mean streamwise velocity - U ₁ primary freestream velocity - U ₂ secondary freestream velocity - U average of freestream velocities, ¯U (U ₁ +U ₂)/2 - U freestream velocity difference,U U ₁ –U ₂ - v instantaneous transverse velocity - v deviation ofv-velocity,v v – V - V local mean transverse velocity - x streamwise coordinate - y transverse coordinate - y ₀ transverse location of the mixing layer centerline - ensemble average - ratio of specific heats - boundary layer thickness (y-location at 99.5% of free-stream velocity) - similarity coordinate, (y –y ₀)/b - compressible boundary layer momentum thickness - viscosity - density - standard deviation - dimensionless velocity, (U –U ₂)/U - 1 primary stream - 2 secondary stream A version of this paper was presented at the 11th Symposium on Turbulence, October 17–19, 1988, University of Missouri-Rolla     

F-OH exchange equilibria between mica-amphibole mineral pairs

Fluoride-hydroxyl exchange equilibria between phlogopite-pargasite and phlogopite-tremolite mineral pairs were experimentally determined at 1,173K, 500 bars and 1,073–1,173 K, 500 bars respectively. The distribution of fluorine between phlogopite and pargasite was found to favor phlogopite slightly, G _ex ^. (1,173 K)=–1.71 kJ anion^–1, while in the case of phlogopite-tremolite, fluorine was preferentially incorporated in the mica, G _ex ^. (1,073)=– 5.67 kJ anion^–1 and G _ex ^. (1,173K)=–5.84 kJ anion^–1. These results have yielded new values of entropy and Gibbs energy of formation for fluortremolite, S _f =–2,293.4±16.0JK^–1 mol^–1 and G _f = –11,779.3±25.0 kJ mol^–1, respectively. In addition, F-OH mineral exchange equilibria support a recent molten oxide calorimetric value for the Gibbs energy of fluorphlogopite, G _f =–6,014.0±7.0 kJ mol^–1, which is approximately 40 kJ mol^–1 more exothermic than the tabulated value.This work performed in part at Sandia National Laboratories supported by the U.S. Department of Energy, DOE, under contract number DE-AC04-76DP00789     

Origin and differentiation of picritic arc magmas,Ambae (Aoba), Vanuatu

Key aspects of magma generation and magma evolution in subduction zones are addressed in a study of Ambae (Aoba) volcano, Vanuatu. Two major lava suites (a low-Ti suite and high-Ti suite) are recognised on the basis of phenocryst mineralogy, geochemistry, and stratigraphy. Phenocryst assemblages in the more primitive low-Ti suite are dominated by magnesian olivine (mg 80 to 93.4) and clinopyroxene (mg 80 to 92), and include accessory Cr-rich spinel (cr 50 to 84). Calcic plagioclase and titanomagnetite are important additional phenocryst phases in the high-Ti suite lavas and the most evolved low-Ti suite lavas. The low-Ti suite lavas span a continuous compositional range, from picritic (up to 20 wt% MgO) to high-alumina basalts (<5 wt% MgO), and are consistent with differentiation involving observed phenocrysts. Melt compositions (aphyric lavas and groundmasses) in the low-Ti suite form a liquid-line of descent which corresponds with the petrographically-determined order of crystallisation: olivine + Cr-spinel, followed by clinopyroxene + olivine + titanomagnetite, and then plagioclase + clinopyroxene + olivine + titanomagnetite. A primary melt for the low-Ti suite has been estimated by correcting the most magnesian melt composition (an aphyric lava with 10.5 wt% MgO) for crystal fractionation, at the oxidising conditions determined from olivine-spinel pairs (fo₂ FMQ + 2.5 log units), until in equilibrium with the most magnesian olivine phenocrysts. The resultant composition has 15 wt% MgO and an mg ^Fe2 value of 81. It requires deep (3 GPa) melting of the peridotitic mantle wedge at a potential temperature consistent with current estimates for the convecting upper mantle (T _p 1300°C). At least three geochemically-distinct source components are necessary to account for geochemical differences between, and geochemical heterogeneity within, the major lava suites. Two components, one LILE-rich and the other LILE- and LREE-rich, may both derive from the subducting ocean crust, possibly as an aqueous fluid and a silicate melt respeetively. A third component is attributed to either differnt degrees of melting, or extents of incompatible-element depletion, of the peridotitic mantle wedge.     

Mineralogical applications of the lattice constant variance-covariance matrices

Summary Direct and reciprocal lattice constant variance-covariance matrices when involved in the Law of Propagation of Errors can be used to gain a full evaluation of the error terms in mineralogical quantities expressed in terms of lattice constants. Properties and relationships which mutually connect the two matrices are discussed, with emphasis placed on physical dimensions. A practical application is given by calculating the error terms in the structural indicators (bc) and (^**) of alkali feldspars. The differences between values obtained by using both variances plus covariances and those obtained using variances alone, are very small. However, as the calculations are completely automated, the full formulation using variances plus covariances represents a suitable better approach.

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Mineralogische Anwendungen der Varianz-Kovarianz-Matrizen der Gitterkonstanten

Zusammenfassung Varianz-Kovarianz-Matrizen der direkten und reziproken Gitterkonstanten können beim Fehlerfortpflanzungsgesetz benützt werden, um eine vollständige Auswertung der Fehlerausdrücke mineralogischer Größen, ausgedrückt durch Gitterkonstanten, zu erhalten. Eigenschaften und Beziehungen, welche diese beiden Matrizen gegenseitig verknüpfen, werden mit Betonung physikalischer Dimensionen diskutiert. Eine praktische Anwendung wird gegeben, indem die Fehlerausdrücke der strukturellen Indikatoren (bc) und (^**) von alkalifeldspäten berechnet werden. Die Differenzen zwischen den Werten, die bei Benützung von Varianzen und Kovarianzen, bzw. nur von Varianzen erhalten wurden, sind sehr klein. Da aber die Berechnungen voll automatisiert sind, bietet die vollständige Formulierung mit Varianzen plus Kovarianzen eine brauchbare bessere Methode.

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The distortion index in anhydrous Mg-Cordierite

The mechanism of the hexagonal-orthorhombic transition in anhydrous Mg-cordierite has been studied by isothermal annealing experiments on synthetic samples. Products have been characterized by X-ray powder diffractometry and transmission electron microscopy. The transformation is first order and at temperatures below about 1,450° C the stable phase is orthorhombic cordierite with a distortion index,0.25. Under non-equilibrium conditions the transformation takes place via a modulated structure which on annealing, coarsens to produce an apparently continuous sequence of metastable intermediate values. The limitations of the distortion index as an indicator of the structural state of anhydrous Mg-cordierite are discussed in terms of short-range and long-range distortions associated with the transition.     

Structural explanation for Δ (α*γ*) from α* vs. γ* in alkali feldspar

Summary As suggested bySmith (1968) and supported by most structural data published since, in alkali feldspar the ^** plot can be used for estimating (^**), i. e. the difference in Al confent between 0 andm subsites. The present study investigates the topologically identical plot on the basis of the configuration of the alkali feldspar tetrahedral framework. Changes in Al content ofT-sites are functionally related to changes in cosines of and . While the total Al causing changes in cos is directly equal to the difference in Al content between 0 andm subsites, the total Al causing changes in cos is expressed by a complicated function which is equal with a very good approximation to three fourths of the difference in Al content betweenm and 0 subsites. This relation of quasiproportionality. like the feasible substitution in alkali feldspar of the diagram cos vs. cos by the plot, represents two simplifying assumptions which permit the difference in Al content to be calculated, as previously predicted.

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Strukturelle Deutung für (^**) aus dem ^*/^* der Alkalifeldspäte

Zusammenfassung Nach einem Vorschlag vonSmith (1968) und in Übereinstimmung mit den meisten seither publizierten Strukturdaten kann man in Alkalifeldspäten das ^*/^* zur Abschätzung von (^**), also des Unterschiedes im Al-Gehalt auf der 0- undm-Position benützen. Die vorliegende Arbeit untersucht das topologisch idente /-Diagramm auf der Basis der Gestalt des Tetraederverbandes der Alkalifeldspäte. änderungen im Al-Gehalt derT-Position sind mit Änderungen im Kosinus von und korreliert. Während der die cos -änderungen verursachende Al-Gesamtgehalt unmittelbar dem Unterschied im Al-Gehalt derO-undm-Position entspricht, ist der die cos -Änderungen verursachende Al-Gesamtgehalt durch eine komplizierte Funktion ausgedrückt, die aber mit sehr guter Näherung drei Vierteln der Differenz im Al-Gehalt auf denm-und 0-Poisitionen entspricht. Diese quasi-Proportionalität und die Ersetzbarkeit des cos /cos -Diagrammes durch das /-Diagramm bei den Alkalifeldspäten stellen zwei Vereinfachungen bei der Berechnung des Al-Gehaltes dar.

     

Cell parameters of thermally treated anorthite. Al,Si configurations in the average structures of the high temperature calcic plagioclases

Thermal treatments of anorthite carried out at up to 1,547° C show that the unit cell parameter changes as a function of the treatment temperature. The best fit curve found by non-linear least squares analysis is: =91.419-(0.327·10^-6)T ²+(0.199·10^-12)T ⁴-(0.391·10)T ⁶. The results obtained support significant Al,Si disorder (Al0.10, where Al=t ₁(0)-1/3 [t ₁(m)+t ₂(0)+t ₂(m)], Ribbe 1975), in anorthite equilibrated near the melting point and confirm a high temperature series differentiated from the low temperature series for calcic plagioclases in the An₈₅–An₁₀₀ range also. In the plot vs. An-content the high and low temperature curves intersect at An₈₅ composition and progressively diverge in the An₈₅–An₁₀₀ range. The trends of the high and low temperature curves in this range are interpretable on the basis of the degree of Al, Si order in the average structures of calcic plagioclases.     

Relationships among Gibbs free energies and enthalpies of formation of phosphates,oxides and aqueous ions

Two parameters _GO^2– and _HO^2– are defined as the differences between respectively the Gibbs free energies and the enthalpies of formation of an oxide and its corresponding aqueous cation. The Gibbs free energies and enthalpies of formation of phosphates from their consituent oxides are shown to be linear functions of respectively _GO^2– and _HO^2– of their constituent cations.     

Ferric iron in mantle-derived pyroxenes and a new oxybarometer for the mantle

Ferric iron contents of coexisting ortho- and clinopyroxene from spinel lherzolite xenoliths were measured with Mössbauer spectroscopy and found to be significant. In orthopyroxene, the range in Fe³⁺/Fe is from 0.04 to 0.14; in clinopyroxene, the range is from 0.12 to 0.24. Reactions involving coexisting olivine, orthopyroxene, and clinopyroxene, where either the esseneite (CaFe³⁺ AlSiO₆) or the acmite (NaFe³⁺Si₂O₆) component in the clinopyroxene is considered, are used to calculate oxygen fugacities. These oxygen fugacities agree well with those calculated with the olivine-orthopyroxene-spinel oxybarometer. Because these reactions do not involve garnet, spinel, or plagioclase, they may be applied to lherzolites to give internally-consistent oxygen fugacities across the pressure-dependent facies boundaries between plagioclase, spinel, and garnet lherzolite. Another application of this method is to predict the Fe³⁺/Fe in clinopyroxene coexisting with olivine and orthopyroxene given pressure, temperature, , and the compositions of the coexisting phases in either experimental or natural assemblages. At values of equal to those of the synthetic fayalite-magnetite-quartz buffer, for example, 15–35% of the iron in the clinopyroxenes from these xenoliths would be ferric. The simplifying assumption that all Fe is divalent in silicate phases at geologically — reasonable oxygen fugacities must be re-evaluated.     

High temperature,high strain rate deformation in the lower crustal Kalka Intrusion,central Australia

Mafic and ultramafic gneisses (blastomylonites) characterised by a strongly developed planar lenticular foliation-layering are developed in lower crustal (high pressure) cumulates of the stratiform Kalka Intrusion in central Australia. The gneisses occur in two distinct zones, the Numbunja and West Kalka Gneissic Belts, parallel to or at low angles to igneous layering. They developed during and shortly after the final stages of crystallization of the intrusion at temperatures between about 1000 and 1200 ° C, and represent an incipient thrusting deformation probably with associated high strain rates. The most deformed textures in the centre of the belts typically consist of megacrysts of orthopyroxene, clinopyroxene, olivine and plagioclase showing abundant features of extreme ductile flow within a finegrained syntectonically recrystallized matrix of the same material. Mineral elongation, kink band orientation and matrix petrofabrics indicate that the maximum principal elongation and the maximum principal shortening occurred parallel to the lineation and normal to the foliation respectively.Single crystal deformation features (some unique to these rocks) include flow elongation of orthopyroxene and plagioclase (up to at least 400% elongation without recrystallization), kinking of orthopyroxene, clinopyroxene, olivine and plagioclase, production of rare clinoenstatite in orthopyroxene, and an unusual fingerprint texture in clinopyroxene. The occurrence of either flow elongation or kinking of orthopyroxene is dependent on crystal orientation relative to the maximum principal elongation/shortening directions. Detailed analysis shows that the flow orthopyroxenes and possibly the flow plagioclases deformed by simple shear. The results have relevance in studies of possible deformation mechanisms in the upper mantle, and in alpine peridotites.     

Petrology and magnetic properties of the Chiang Khan,Thailand, meteorite

Summary The Chiang Khan meteorite fell on 18th November, 1981 at Chiang Khan, Thailand. It consists of olivine, orthopyroxene, clinopyroxene, Fe-Ni metal, troilite, chromite, plagioclase, glass, and phosphate in order of abundance. Olivine forms barred or porphyritic chondrules, and its composition is uniform (average Fo_80.2), close to the average composition of olivine in equilibrated H chondrites. Orthopyroxene and clinopyroxene also have compositions similar to those in equilibrated H chondrites. Both well-defined chondrules and their broken fragments are present in the recrystallized matrix. Microcrystalline plagioclase and clinopyroxene often occur in the groundmass of chondrules, but clear interstitial plagioclase is absent. Chemical composition of chromite plots in the field of chromites in H chondrites. Chiang Khan meteorite is thus classified as an equilibrated H 5 type chondrite. The equilibrium temperatures estimated by using mineral pairs are as follows: Opx-Cpx 800–900°C; Ol-Chromite 510°C.Water content is 0.24 wt %, and the hydrogen isotopic composition (D) is –89.5In the thermal demagnetization experiment magnetization steadily decreased from 0 to 500°C, whereas the remanent magnetization obtained in the A.C. demagnetization experiment is very unstable, probably owing to the large grain size of the Fe-Ni metal.With 9 Figures     

Feldspathic hornblende and garnet granulites and associated anorthosite pegmatites from Doubtful Sound,Fiordland, New Zealand

Feldspathic hornblende granulites from Doubtful Sound, New Zealand with the assemblage plagioclase+hornblende+clinopyroxene+orthopy-roxene +oxide+apatite are criss-crossed by a network of garnetiferous anorthosite veins and pegmatites. The feldspathic gneiss in contact with anorthosite has a reaction zone containing the assemblage plagioclase +garnet+clinopyroxene+quartz+rutile+apatite. The garnet forms distinctive coronas around clinopyroxene. The origin of these rocks is discussed in the light of mineral and whole rock chemical analyses and published experimental work.It is thought that under conditions leading up to 750 °C, 8 kb load pressure and 5 kb H₂O pressure, partial melting occured in feldspathic hornblende granulites. The melt migrated into extensional fractures and eventually crystallised as anorthosite pegmatites and veins. The gneisses adjacent to the pegmatites from which the melt was extracted changed composition slightly, by the loss of H₂O and Na₂O, so that plagioclase reacted simultaneously with hornblende, orthopyroxene, and oxide to form garnet, clinopyroxene, quartz and rutile.     

X-ray,optical and chemical variation of Potash Feldspar from Loket (Elbogen), Karlovy Vary massif,Czechoslovakia

Summary The studied, perfectly shaped Carlsbad twins from Loket (loc. swimming pool) are orthoclase perthites of low triclinicity (=0.0–0.3); the sodic phase relates to low albite. All phenocrysts having zonal structure contain small areas of triclinic feldspars (=0.6–0.8) independent on the zonality of low triclinicity. This microclinization is believed to be younger than the host orthoclase. The content of microcline within the phenocryst varies from about 10 to 30 percent.

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Röntgenographische, optische und chemische Variation der Kalifeldspäte von Loket (Elbogen), Karlovy Vary (Karlsbad)-Massiv, Tschechoslowakei

Zusammenfassung Die untersuchten, ideal ausgebildeten Karlsbad-Zwillinge von Loket (Lokalität Badeanstalt) sind Orthoklas-Perthite kleiner Triklinität (=0,0–0,3); die Natronfeldspat-Phase entspricht Albit. Alle Phänokristalle mit Zonarbau enthalten unabhängig von der schwachen zonaren Triklinität kleine Bereicho von triklinem Feldspat (=0,6–0,8). Diese Mikroklinisierung ist anscheinend jünger als der umschließende Orthoklas. Der Mikroklingehalt der Phänokristalle schwankt von ungefähr 10 bis zu 30%.

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Oxygen isotope geochemistry of hydrothermally-altered synmetamorphic granitic rocks from South-Central Maine,USA

Hydrothermally-altered mesozonal synmetamorphic granitic rocks from Maine have whole-rock ¹⁸O (SMOW) values 10.7 to 13.8. Constituent quartz, feldspar, and muscovite have ¹⁸O in the range 12.4 to 15.2, 10.0 to 13.2, and 11.1 to 12.0, respectively. Mean values of _Q–F ( ¹⁸O_quartz– ¹⁸O_feldspar)=2.4 and _Q–M ( ¹⁸O_quartz– ¹⁸O_muscovite)=3.3 are remarkably uniform (standard deviations of both are 0.2). Measured _Q–F and _Q–M values demonstrate that the isotopic compositions of the minerals are altered from primary magmatic ¹⁸O values but that the minerals closely approached oxygen isotope exchange equilibrium at subsolidus temperatures. Analyzed muscovites have D (SMOW) values in the range –65 to –82.Feldspars in the granitic rocks are mineralogically altered to either (a) muscovite+calcite, (b) muscovite+calcite+epidote, (c) muscovite+epidote, or (d) muscovite only. A consistent relation exists between the assemblage of secondary minerals and the oxygen isotope composition of whole rocks, quartz, and feldspar. Rocks with assemblage (a) have whole-rock ¹⁸O>12.1 and contain quartz and feldspar with ¹⁸O>13.8 and >11.4, respectively. Rocks with assemblages (b), (c), and (d) have whole-rock ¹⁸O<11.4 and contain quartz and feldspar with ¹⁸O< 13.1 and <11.0, respectively. The correlation suggests that the mineralogical alteration of the rocks was closely coupled to their isotopic alteration.Three mineral thermometers in altered granite suggest that the hydrothermal event occurred in the temperature range 400°–150° C, 100°–150° C below the peak metamorphic temperature inferred for country rocks immediately adjacent to the plutons. Calculations of mineral-fluid equilibria indicate that samples with assemblage (a) coexisted during the event with CO₂-H₂O fluids of and ¹⁸O=10.8 to 12.2 while samples with assemblages (b), (c), or (d) coexisted with fluids of and ¹⁸O=9.4 to 10.1. Compositional variations of the hydrothermal fluids were highly correlated: fluids enriched in CO₂ were also enriched in ¹⁸O. Because CO₂ was added to the granites during hydrothermal alteration and because fluids enriched in CO₂ were enriched in ¹⁸O, some or all of the variation in ¹⁸O of altered granites may have been caused by addition of ¹⁸O to the rocks during the hydrothermal event. The source of both the CO₂ and ¹⁸O could have been high-¹⁸O metasedimentary country rocks. The inferred change in isotopic composition of the granites is consistent with depletion of the metacarbonate rocks in ¹⁸O close to the plutons and with large volumes of fluid that were inferred from petrologic data to have infiltrated the metacarbonate rocks during metamorphism.A close approach of minerals to oxygen isotope exchange equilibrium in altered mesozonal rocks from Maine is in marked contrast to hydrothermally-altered epizonal granites whose mineral commonly show large departures from oxygen isotope exchange equilibrium. The difference in oxygen isotope systematics between altered epizonal granites and altered mesozonal granites closely parallels a differences between their mineralogical systematics. Both differences demonstrate the important control that depth exerts on the products of hydrothermal alteration. Deeper hydrothermal events occur at higher temperature and are longer-lived. Minerals and fluid have sufficient time to closely approach both isotope exchange and heterogeneous chemical equilibrium. Shallower hydrothermal events occur at lower temperatures and are shorter-lived. Generally there is insufficient time for fluid to closely approach equilibrium with all minerals.     

Subsolidus orthopyroxene-clinopyroxene systematics in the system CaO-MgO-SiO2 to 60 kb: a re-evaluation of the regular solution model

On the basis of an increased set of experimental data, covering the miscibility gap between orthopyroxene and clinopyroxene from 2 to 60 kb with a temperature range of 850–1,500° C, we present a new version of a regular solution model. The model with two independent regular solutions for opx and cpx is capable of reproducing experimental data in the system CaO-MgO-SiO₂ over a large range of temperatures and pressures. It is qualitatively in agreement with observed stability regions for an Fe-free low-Ca pyroxene, termed pigeonite. The model is constrained by and thus consistent with calorimetric measurements on pyroxenes. The simple form of equations provides a good starting point for the development of more reliable thermometers based on the miscibility gap.Abbrevations Used in the Text cpx clinopyroxene - di diopside, CaMgSi₂O₆ - en enstatite, Mg₂Si₂O₆ - pig pigeonite - opx orthopyroxene - H (i) molar enthalpy difference (of reaction i) - S (i) molar entropy difference of reaction (i) - V (i) molar volume difference of reaction (i) - X[i]j mole fraction of i in phase j     

NaSi⇌CaAl exchange equilibrium between plagioclase and amphibole

The exchange equilibrium between plagioclase and amphibole, 2 albite+tschermakite=2 anorthite+glaucophane, has been calibrated empirically using data from natural amphibolites. The partition coefficient, K _D, for the exchange reaction is (X _an/X _ab)_plag ·(Na, M4/Ca, M4)_amph.. Partitioning is systematic between plagioclase and amphibole in suites collected from single exposures, but the solid solutions are highly non-ideal: values of In K _D range from –3.0 at X _an=0.30 to –1.0 at X _an=0.90 in samples from a single roadcut. Changes in both K _D and the topology of the ternary reciprocal exchange diagram occur with increasing metamorphic grade. Temperature dependence of In K _D is moderate with ¯H35 to 47 kcal at X _an=0.25; pressure dependence is small with ¯V –0.24 cal/bar. Usefulness of this exchange equilibrium as a geothermometer is restricted by uncertainties in the calculation of the amphibole formula from a microprobe analysis, especially with regard to Na, M4 in amphibole, to approximately ±50 ° C.     

The enthalpy of fusion of anorthite

The high-temperature enthalpies of liquid and glassy CaAl₂Si₂O₈ were measured by drop calorimetry using a diphenyl ether drop calorimeter. These data are combined with published values of the high-temperature enthalpy of crystalline anorthite and the enthalpy of vitrification of anorthite to obtain the enthalpy of fusion of anorthite. Analysis of the data yields the following preferred values (enthalpy in kcal/mol, uncertainty limits correspond to two standard deviations):enthalpy of vitrification at 985 K, _v H _{v 985}=18.6±0.6; enthalpy of the liquid at 1,830 K, H ₁₈₃₀ ^l ₃₀₀ ^g =130.4±1.2; enthalpy of the glass at 985 K, H ₉₈₅ ^g -H ₃₀₀ ^g =46.7±0.4; enthalpy of crystalline anorthite between 985 and 1,830 K, H ₁₈₃₀ ^c -H ₉₈₅ ^c =69.9±1.4; calculated enthalpy of fusion of anorthite at 1,830 K, _f H ₁₈₃₀= 32.4±2.1.The average heat capacity of supercooled liquid CaAl₂Si₂O₈ between the glass transition (T _g 1,086 K) and the melting point (T _f7=1,830 K) is 102 ± 2 cal/mol/K. The large difference between the enthalpy of fusion and the enthalpy of vitrification for the minerals anorthite and diopside is emphasized. The practice of assuming _fH _vH should be discontinued for silicate compounds for which T _f T _g.     

Gibbs energy of aluminous minerals

The discrepancy between the tabulated Gibbs Energies of Formation for Al₂SiO₅ and corundum relative to muscovite and kaolinite is considered to lie principally with the latter two minerals. New values for heat of formation of gibbsite [Gbs] will affect the tabulated H _f ⁰ , G _f(298,1) ⁰ for the other aluminous minerals which are referred to gibbsite as calorimetric aluminum reference. Gibbs Energy Difference Functions, calculated from phase equilibria in the system CaO-Al₂O₃-SiO₂-(H₂O-CO₂), can be used to estimate consistent H _f ⁰ , G _f(298,1) ⁰ values for aluminous minerals. A self consistent data set is presented referred to G _f(298,1) ⁰ [Corundum]=–378.08 kcal mol^–1. Two independent values for G _f(298,1) ⁰ [Anorthite]=–961.52 and –960.29 kcal, from a recalculation of the H _f ⁰ [Anor] based upon the revised H _f(298,1) ⁰ [Gbs]=–309.325 kcal mol^–1 and from measurement of silica activity on the anorthite-saturated part of the CaO-Al₂O₃-SiO₂ liquidus, respectively, are considered to show the magnitude of the discrepancy and are used in the calculations.