ALBERT

Notes: Abstract A new thermodynamic formulation of the Fe−Ti oxide geothermometer/oxygen barometer is developed. The method is based upon recently calibrated models for spinel solid solutions in the quinary system (Fe2+, Mg)(Al,Fe3+,Cr)2O4−(Fe2+, Mg)2TiO4 by Sack and Ghiorso, and rhombohedral oxides in the quaternary system (Fe2+,Mg,Mn)TiO3−Fe2O3 (this paper). The formulation is internally consistent with thermodynamic models for (Fe2+,Mg)-olivine and -orthopyroxene solid solutions and end-member thermodynamic properties tabulated by Berman. The constituent expressions account for compositional and temperature dependent cation ordering and reproduce miscibility gap features in all of the component binaries. The calibration does not account for the excess Gibbs energy resulting from compositional and temperature dependent magnetic ordering in either phase. This limits application of the method to assemblages that equilibrated at temperatures above 600° C. Practical implementation of the proposed geothermometer/oxygen barometer requires minimal use of projection algorthms in accommodating compositions of naturally occurring phases. The new formulation is applied to the estimation of temperature and oxygen fugacity in a wide variety of intermediate to silicic volcanic rocks. In combination with previous work on olivine and orthopyroxene thermodynamics, equilibration pressures are computed for a subset of these volcanics that contain the assemblage quartz, oxides and either ferromagnesian silicate. The calculated log10 f O 2-T relations are reflected in coexisting ferromagnesian mineral assemblages. Volcanics with the lowest relative oxygen fugacity (Δlog10 f O 2) are characterized by the assemblage olivine-quartz, those with slightly higher Δ log10 f O 2 s, by the assemblage orthopyroxene-quartz. The sequence proceeds with the necessary phases biotite-feldspar, then hornblende-quartz-clinopyroxene, and finally at the highest Δ log10 f O 2 s, sphene-quartz-clinopyroxene. Quantitative analysis of these trends, utilizing thermodynamic data for the constituent phases, establishes that, in most cases, the T-log10 f O 2value computed from the oxides is consistent with the compositions of coexisting silicate phases, indicating that phenocryst equilibrium was achieved prior to eruption. There is, however, considerable evidence of oxide-silicate disequilibrium in samples collected from more slowly cooled domes and obsidians. In addition, T-log10 f O 2trends from volcanic rocks that contain biotite and orthopyroxene are interpreted to imply a condition of Fe2+−Mg exchange disequilibrium between orthopyroxene and coexisting ferromagnesian silicates and melt. It is suspected that many biotite-feldspar-quartz-orthopyroxene bearing low temperature volcanic rocks inherit orthopyroxene xenocrysts which crystallized earlier in the cooling history of the magma body.

Notes: Abstract A model is proposed for the thermodynamic properties of multicomponent pyroxenes in the composition space defined by the end-member component CaMgSi2O6 and the exchange components Fe(Mg)-1, TiAl2(MgSi2)-1, Fe3+(Al)-1, Fe3+Al(MgSi)-1, and Mg(Ca)-1. It is formulated for the simplifying assumptions that: (1) a molecular mixing type approximation describes changes in the molar configurational entropy associated with the coupled exchange substitutions TiAl2⇔MgSi2, Fe3+Al⇔MgSi, and Al2⇔MgSi (and their ferroan equivalents), and (2) Fe2+ and Mg2+, and Al3+ and Fe3+ display long-range non-convergent ordering between M2 and octahedral M1 sites, and octahedral M1 and tetrahedral sites, respectively. The molar vibrational Gibbs energy is described by a Taylor expansion of second degree in seven linearly independent composition and ordering variables, which is extended to third degree to account for asymmetry in the mixing of Ca and Mg, and Ca and Fe on the M2 site, and is further modified for the assumption that the standard state properties of Ca end-member components of clinopyroxenes are linearly dependent on the coordination number of Ca2+ on the M2 site. The model is shown to be consistent with miscibility gap feaures of pyroxenes in the system CaMgSi2O6−CaTiAl2O6−CaAl2SiO6. In subsequent papers, the model is calibrated for the simplifying assumptions that: (1) all regular-solution-type parameters are constants independent of temperature, (2) Pbca and C2/c end-members have identical heat capacities and coefficients of thermal expansion and compressibility, and (3) the heat capacities and coefficients of thermal expansion and compressibility are zero for all reciprocal reactions relating Pbca and pigeonite or high-calcium pyroxene C2/c endmember components.

Notes: Abstract A thermodynamic model for the Gibbs free energy of igneous pyroxenes with the general formula [Na, Ca, Fe2+, Mg]M2[Fe2+, Mg, Ti, Al, Fe3+]M1[Al, Fe3+, Si]TetSiO6 is calibrated from experimentally determined compositions of coexisting pyroxene and silicate melt. The model is based upon the general formulation, and relies upon the calibration of the “quadrilateral” subsystem, previously published by the present authors. The calibration database of pyroxene-liquid equilibria spans a broad spectrum of temperature, pressure and oxygen fugacity conditions, ranging from 1000°–1600°C, 0.001–30 kbar and iron-wüstite to air. Chemical potentials of endmember pyroxene components as well as exchange potentials between pyroxenes and coexisting liquids are defined utilizing the present authors' thermodynamic melt model. Model parameters are extracted from these relations by regression analysis. The resulting model and derivative endmember properties are internally consistent with an existing standard state thermodynamic database. The success of the model and its applicability to igneous petrogenesis are demonstrated by comparing calculated and experimentally determined liquidus compositions, temperatures and symmetry states for pyroxenes crystallizing from a variety of silicate melts, ranging in composition from tholeiites and angrites through rhyolites to potash ankaratrites.

Notes: Abstract Activity/composition relations are presented for high-structural state feldspars whose bulk compositions lie within the ternary system NaAlSi3O8 CaAl2Si2O8-KAlSi3O8. The expressions are parameterized from the data for coexisting feldspars of Seck (1971a) using an asymmetric regular solution approximation for the excess Gibbs free energy of mixing and an Al-avoidance model for the configurational entropy of solution. The solution properties of the plagioclase and alkali-feldspar binaries have been made to conform to the recent work of Thompson and Hovis (1979) and Newton et al. (1980). Using the proposed model the ternary feldspar solvus is extrapolated in temperature (up to 1,500° C) and pressure (up to 5kbars). A new two-feldspar geothermometer is presented which provides somewhat more reasonable estimates of crystallization temperatures than the equations and graphs of Stornier (1975), Powell and Powell (1977), Brown and Parsons (1981) and Haselton et al. (1983). In conjunction, some criteria are suggested for establishing the existence of “equilibrium” tie-lines between coexisting ternary feldspars in rhyolites and trachytes. Calculated values of the activity of KAlSi3O8 in plagioclase are examined in some detail. These compare favorably with independent estimates obtained from experimentally grown plagioclases precipitating at liquidus temperatures from igneous rocks of widely varying alkali contents.

Notes: Abstract Estimates of the oxygen fugacity of the source regions of martian shergottites are obtained from coexisting Fe-Ti oxides and from Fe3+/Fe2+ ratios in pyroxenes. These estimates are one to four log10 units lower than previously reported values, and indicate that the shergottite source region has an oxidation state about two or three orders of magnitude below the quartz-fayalite-magnetite (QFM) oxygen reference buffer. An approximation of the major element composition of the shergottite source region is obtained utilizing the MELTS petrologic modeling software. A bulk composition of the shergottite source region is derived, which is consistent with the generation of sher-gottites upon 3% partial melting at 10 kbar. This composition is decidedly less enriched in Na2O and FeOTot than previous estimates. When compared to the bulk composition of the terrestrial mantle, the source region of the shergottites is lower in CaO, Al2O3, Na2O and TiO2, and higher in MgO.

Notes: Abstract Numerical examples of the approach described in Part I of this series (Ghiorso, 1985) are presented in this paper. These examples include the calculation of the compositions and proportions of liquid and solid phases produced during (1) the equilibrium crystallization of a basaltic andesite at 1 bar, (2) the fractional crystallization of an olivine tholeiite at 1 bar and elevated pressures, (3) the fractional and equilibrium crystallization of an olivine boninite at 1 bar, and (4) the (a) isothermal and (b) isenthalpic assimilation of olivine (Fo90) into a liquid/solid assemblage of quartz dioritic composition at ∼1,125° C and 3 kbars. The numerical results on the crystallization of the basaltic andesite are verified by comparison with experimental data while those calculations performed using olivine tholeiitic and olivine boninitic compositions are favorably compared against whole rock and mineral analytical data and petrographic and field observations. In each of the examples presented, the heat effects associated with the modelled process are calculated (e.g. heat of crystallization, heat of assimilation), and free energies of crystallization are examined as a function of the degree of mineral supersaturation. The former quantities are on the order of 173 cal/grm for the cooling and fractional crystallization of an olivine tholeiite to a rhyolitic residuum (corresponding to a 400° C temperature interval). The latter represents an important petrological parameter, in that it quantifies the driving force for the rate of crystal growth and rate of nucleation in magmatic systems. Calculated free energies of crystallization are small (on the order of hundreds of calories per mole per 25° C of undercooling) which indicates that the kinetics of crystallization in magmatic systems are affinity controlled. Melt oxygen fugacity and the degree of oxygen metasomatism play a major role in controlling the fractionation trends produced from crystallizing basaltic liquids. Calculations suggest that in order to generate a silica rich residuum and the characteristic iron enrichment trend during the fractional crystallization of a tholeiitic basalt, the magma must crystallize esentially along $$f_{{\text{O}}_{\text{2}} } $$ buffer. This buffered state can be maintained by exchange of oxygen (via hydrogen diffusion) between the magma and the surrounding country rocks or by magmatic oxidation-reduction equilibria. Additional calculations indicate the possibility that oxygen exchange may be unnecessary if the magma contains sufficient sulfur to maintain the system along an S2/SO2 oxygen buffer during the initial stages of crystallization.