The thermodynamic properties of 154 mineral end-members, 13 silicate liquid end-members and 22 aqueous fluid species are presented in a revised and updated data set. The use of a temperature-dependent thermal expansion and bulk modulus, and the use of high-pressure equations of state for solids and fluids, allows calculation of mineral–fluid equilibria to 100 kbar pressure or higher. A pressure-dependent Landau model for order–disorder permits extension of disordering transitions to high pressures, and, in particular, allows the alpha–beta quartz transition to be handled more satisfactorily. Several melt end-members have been included to enable calculation of simple phase equilibria and as a first stage in developing melt mixing models in NCKFMASH. The simple aqueous species density model has been extended to enable speciation calculations and mineral solubility determination involving minerals and aqueous species at high temperatures and pressures. The data set has also been improved by incorporation of many new phase equilibrium constraints, calorimetric studies and new measurements of molar volume, thermal expansion and compressibility. This has led to a significant improvement in the level of agreement with the available experimental phase equilibria, and to greater flexibility in calculation of complex mineral equilibria. It is also shown that there is very good agreement between the data set and the most recent available calorimetric data.

An internally consistent thermodynamic data set for phases of petrological interest

This geochemical classification of granitic rocks is based upon three INTRODUCTION variables. These are FeO/(FeO + MgO) = Fe-number [or Although granitoids are the most abundant rock types FeO/(FeO + MgO) = Fe∗], the modified alkali–lime index in the continental crust, no single classification scheme (MALI) (Na2O + K2O – CaO) and the aluminum saturation has achieved widespread use. Part of the problem in index (ASI) [Al/(Ca – 1·67P + Na + K)]. The Fe-number granite classification is that the same mineral assemblage, (or Fe∗) distinguishes ferroan granitoids, which manifest strong iron quartz and feldspars with a variety of ferromagnesian enrichment, from magnesian granitoids, which do not. The ferroan minerals, can be achieved by a number of processes. and magnesian granitoids can further be classified into alkalic, Granitoids can form from differentiation of any hyalkali–calcic, calc-alkalic, and calcic on the basis of the MALI persthene-normative melt and from partial melting of and subdivided on the basis of the ASI into peraluminous, metamany rock types. Furthermore, granitic melts may be luminous or peralkaline. Because alkalic rocks are not likely to be derived solely from crustal components, may form from peraluminous and calcic and calc-alkalic rocks are not likely to be evolved mantle-derived melts, or may be a mixture peralkaline, this classification leads to 16 possible groups of granitic of crustal and mantle-derived melts. Because of this rocks. In this classification most Cordilleran granitoids are magnesian complexity, petrologists have relied upon geochemical and calc-alkalic or calcic; both metaluminous and peraluminous classifications to distinguish between various types of types are present. A-type granitoids are ferroan alkali–calcic, although granitoids. Approximately 20 different schemes have evolved over the past 30 years [see Barbarin (1990, 1999) some are ferroan alkalic. Most are metaluminous although some are for a summary thereof]. Most of these schemes are either peraluminous. Caledonian post-orogenic granites are predominantly genetic or tectonic in nature. This paper is an attempt magnesian alkali–calcic. Those with <70 wt % SiO2 are domto present a non-genetic, non-tectonic geochemical clasinantly metaluminous, whereas more silica-rich varieties are comsification scheme that incorporates the best qualities of monly peraluminous. Peraluminous leucogranites may be either the previous schemes, and to explain the petrologic magnesian or ferroan and have a MALI that ranges from calcic to processes that makes this scheme work. alkalic.

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A geochemical classification for granitic rocks

Knowledge of temperature and pressure, however qualitative, has been central to our views of geology since at least the early 19th century. In 1822, for example, Charles Daubeny presented what may be the very first “Geological Thermometer,” comparing temperatures of various geologic processes (Torrens 2006). Daubeny (1835) may even have been the first to measure the temperature of a lava flow, by laying a thermometer on the top of a flow at Vesuvius—albeit several months following the eruption, after intervening rain (his estimate was 390°F). In any case, pressure ( P ) and temperature ( T ) estimation lie at the heart of fundamental questions: How hot is Earth, and at what rate has the planet cooled. Are volcanoes the products of thermally driven mantle plumes? Where are magmas stored, and how are they transported to the surface—and how do storage and transport relate to plate tectonics? Well-calibrated thermometers and barometers are essential tools if we are to fully appreciate the driving forces and inner workings of volcanic systems.

This chapter presents methods to estimate the P-T conditions of volcanic and other igneous processes. The coverage includes a review of existing geothermometers and geobarometers, and a presentation of approximately 30 new models, including a new plagioclase-liquid hygrometer. Our emphasis is on experimentally calibrated “thermobarometers,” based on analytic expressions using P or T as dependent variables. For numerical reasons (touched on below) such expressions will always provide the most accurate means of P-T estimation, and are also most easily employed. Analytical expressions also allow error to be ascertained; in the absence of estimates of error, P-T estimates are nearly meaningless. This chapter is intended to complement the chapters by Anderson et al. (2008), who cover granitic systems, and by Blundy and Cashman (2008) and Hansteen and Klugel (2008), who consider additional methods …

Thermometers and Barometers for Volcanic Systems

https://www.perplex.ethz.ch/papers/connolly_epsl_05.pdf

Computation of phase equilibria by linear programming: A tool for geodynamic modeling and its application to subduction zone decarbonation

The thermodynamic properties of 254 end-members, including 210 mineral end-members, 18 silicate liquid end-members and 26 aqueous fluid species are presented in a revised and updated internally consistent thermodynamic data set. The PVT properties of the data set phases are now based on a modified Tait equation of state (EOS) for the solids and the Pitzer & Sterner (1995) equation for gaseous components. Thermal expansion and compressibility are linked within the modified Tait EOS (TEOS) by a thermal pressure formulation using an Einstein temperature to model the temperature dependence of both the thermal expansion and bulk modulus in a consistent way. The new EOS has led to improved fitting of the phase equilibrium experiments. Many new end-members have been added, including several deep mantle phases and, for the first time, sulphur-bearing minerals. Silicate liquid end-members are in good agreement with both phase equilibrium experiments and measured heat of melting. The new dataset considerably enhances the capabilities for thermodynamic calculation on rocks, melts and aqueous fluids under crustal to deep mantle conditions. Implementations are already available in thermocalc to take advantage of the new data set and its methodologies, as illustrated by example calculations on sapphirine-bearing equilibria, sulphur-bearing equilibria and calculations to 300 kbar and 2000 °C to extend to lower mantle conditions.

An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids

Ternary-feldspar modeling and thermometry

A solution model has been developed for coexisting magnetite-ulvcispinel and hematiteilmenite solid solutions and applied to the Buddington-Lindsley (1964) geothermometer and oxygen barometer. The model is based on results from the hydrothermal experiments of Lindsley (550-1000"C), gas-mixing experiments of Katsura et al. (1976) and Webster and Bright (1961) (1000-1200'C), and new hydrothermal experiments performed by Spencer and Lindsley (1978) using the Co-CoO bufer. The model assumes (1) ilmenite"" behaves as a binary asymmetric Margules solution; (2) titanomagnetite behaves as a binary asymmetric Margules solution below Sfi)"C and as an ideal binary solution above 800"C; (3) configurational entropy terms can be approximated by a molecular mixing model for magnetites, and by Rumble's (1977) model B (disorder of Fe3+) for (R3) ilmenites; (4) only ordered (R3) ilmenite solutions are present. The free energy of the exchange reaction Fe3O4 + FeTiO3 : Fe2O3 * Fe2TiOa and the excess parameters for each solution were solved by least-squares fit of the experimental data. The model has successfully reproduced experimental data in the temperature-fo, range 600-1300'C, bounded (approximately) by the nickel-nickel oxide and wtistitemagnetite buffer curves. The model predicts a consolute point for Mt-Usp of -550"C at -Usp 32 Mt 68. No attempt was made to estimate mathematically the Hem-Ilm two-phase field. Uncertainties in T andf6, are approximately 40-80"C and 0.5-1.0 log units/e, (2o) assuming -rlVo uncerlainties in Usp,. and llm.. compositions. Introduction Since the introduction of the Mt""Jlm". (for list of abbreviations see Table l) geothermometer-oxybarometer, most workers have utilized the graph of Lindsley (1963; Buddington and Lindsley, 1964, Fig. 5) to determine the temperature and oxygen fugacity of magnetite-ilmenite pairs. This graph has a number of drawbacks: (l) It involved interpolation between data obtained at a limited number of oxygen buffers, and this interpolation was largely intuitive; (2) for many Mt.,-Ilm,. pairs-especially those from volcanic rocks-it is necessary to extrapolate the curves to higher temperatures or to higher oxygen fugacities, or both; and (3) the treatment of "minor constituents" such as Mn, Mg, Al, Cr, and V is necessarily arbitrary. Ideally one would like to know the effects of such constituents on the activities of Fe2O3 and FeTiO3 in llm"" and of Fe3Oa and Fe2TiOa in Mt".. An adequate solution model would eliminate these limitations-although additional experimental data would still be needed to assess quantitatively the effects of the minor constituents. We present here a solution model for coexisting Mt., and Ilm.r, based on a least-squares fit of thermodynamic parameters to experimental data obtained at 550 to 1200"C. We also include results from a new series of experiments on pure Fe-Ti oxides done using the Co-CoO oxygen buffer, which has improved our understanding of the phase relations between Mt." and Ilm"" by permitting us to experiment in a region of ?-/6, space previously inaccessible to well-calibrated oxygen buffer assemblages. In the discussion that follows it is assumed that the Mt"" and Ilm." are pure binary Fe-Ti oxides; no minor constituents are considered. 0003-0M)uE I /l I l2-1 I 89$02.00 l lE9

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A solution model for coexisting iron–titanium oxides

Developpement d'un modele pour la coexistence ilmenite ss -magnetite ss , fonde sur des donnees experimentales nouvelles et existant deja pour les oxydes Fe-Ti et utilisant une programmation lineaire qui est egalement coherente de facon interne avec les donnees disponibles sur l'echange Fe-Mg dans olivine ss -ilmenite ss et olivine ss -magnetite ss et sur l'echange Fe-Mn dans ilmenite ss -grenat ss

Internally consistent solution models for Fe-Mg-Mn-Ti oxides; Fe-Ti oxides

A systematic study of the crystal structure of titanomagnetites was undertaken to characterize the effects of composition and quenching temperature on the cation distribution. Powder specimens ranging in composition from pure magnetite to a slightly nonstoichiometric ulvrispinel were synthesized at temperatures between 930 and 1350'C. Several specimens quenched from 1350'C were later annealed at 800"C for up to 95 days. Unit-cell parameters were determined by X-ray diffraction, and saturation magnetization values were measured at room temperature on a vibrating sample magnetometer. The oxygen coordinate, thermal parameters, and sublattice magnetizations were determined from neutron difraction data using profile refinement techniques. No significant diferences were found in the unit-cell parameters or magnetization resulting from different synthesis temperatures or annealing, and no change was observed in the oxygen positional parameters following annealing. Ti occupies only octahedral sites in all specimens. Temperature factors increase markedly with Ti content, indicating static positional disorder due to mixing of Fe and Ti on octahedral sites. Values of the saturation magnetization and individual sublattice magnetic moments are consistent with the cation distribution model of Akimoto and do not support models that propose a quenchable, temperature-dependent Fe2*-Fe3* distribution. Diffuse scattering in the neutron diffraction patterns suggests the presence of short-range order, possibly involving octahedral cations, but no long-range order inconsistent with space group Fd3m was found. Systematic trends in the oxygen position and unit-cell parameter as a function of composition may be influenced bv octahedral cation interactions.

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Donald H. Lindsley

Papers

Ternary-feldspar modeling and thermometry

A solution model for coexisting iron–titanium oxides

Internally consistent solution models for Fe-Mg-Mn-Ti oxides; Fe-Ti oxides

Crystal structure and cation distribution in titanomagnetites (Fe (sub 3-x) Ti x O 4 )

Equilibria among Fe-Ti oxides, pyroxenes, olivine, and quartz : Part II. Application