ALBERT

Notes: Abstract The Big Jim complex is a concentrically zoned ultramafic to felsic plutonic complex which intruded the pelitic Chiwaukum schist. Most of the major plutonic rock types (from websterite through hornblendite, gabbronorite, hornblende gabbro and diorite, to granodiorite) enclose harzburgite and metaperidotite xenoliths similar to foliated metaperidotite lenses included in the Chiwaukum schist. The larger xenoliths preserve tectonite fabrics. All have Mg#'s (mole fraction MgO/(MgO+FeO*)) from 0.90 to 0.89, the same as those of Chiwaukum metaperidotites, and distinctly different from undeformed Big Jim dunite (Mg#'s 0.84 to 0.82) and websterite (0.82 to 0.78). Contact relations indicate widespread, stepwise replacement of harzburgite by pyroxenite, hornblendite, gabbro and diorite. Thermodynamic modelling using an expanded regular solution model for silicate liquids (Ghiorso 1985; Ghiorso and Carmichael 1985) predicts that reaction between olivine (Fo90) and a liquid with the composition of Big Jim diorite +1.5 wt% H2O, at 1,100° C and 3 kb, would produce websterite (Mg#'s 0.75 to 0.81) and dunite (0.79 to 0.82). This process is exothermic and results in a negative change in volume, since it increases total solid mass. Under conditions of decreasing temperature, modelled crystal fractionation with assimilation of olivine reproduces important features of the chemical variation observed in the Big Jim complex where crystal fractionation alone fails. The Big Jim complex has affinities with other ultramafic to felsic plutonic complexes such as the Bear Mountain complex (Snoke et al. 1981, 1982) and the Emigrant Gap complex (James 1971). The latter have wehrlite and clinopyroxenite, rather than websterite, but both have concentric zoning, with olivine-bearing rock types surrounded by successively more felsic pyroxenite, gabbro and diorite. In general, concentrically zoned complexes of this type may form where magma reacts with mantle-derived wall rock or ultramafic cumulates. Assimilation of peridotite in fractionating magma may be important in subduction-related magmatic arcs.

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.

Notes: Abstract Lasaga's (1982) Master Equation for crystal growth is solved for multicomponent systems in situations which allow for coupled diffusion of melt species. The structure of the solution is explored in some detail for the case of a constant diffusion coefficient matrix. Incorporating these results, the growth of plagioclase is modeled in undercooled tholeiitic melts by approximating interface growth rates with (1) a reduced growth rate function and with (2) calculated solid-liquid solution properties obtained from the silicate liquid solution model of Ghiorso et al. (1983; appendix of Ghiorso 1985). For this purpose algorithms are provided for estimating the liquidus temperature or the chemical affinity of a multicomponent solid solution precipitating from a complex melt of specified bulk composition. Compositional trends in initial solids produced by successive degrees of undercooling are opposite to those predicted in the binary system NaAlSi3O8-CaAl2Si2O8. Calculations suggest that the solid phase and interface melt compositions rapidly approach a “steady state” for a given degree of undercooling. Consequently, the overall isothermal growth rate of plagioclase forming from tholeiitic melts appears to be entirely diffusion controlled. In magmatic systems the multicomponent growth equations allow for the formation of oscillatory zoned crystals as a consequence of the “couplingr” between interface reaction kinetics and melt diffusion. The magnitude of this effect is largely dependent upon the asymmetry of the diffusion coefficient matrix. Methods are described to facilitate the calibration of diffusion matrices from experimental data on multicomponent penetration curves. Experimental results (Lesher and Walker 1986) on steady state Soret concentration profiles resulting from thermal diffusion in MORB and andesitic liquids are analyzed using the theory of multicomponent linear irreversible thermodynamics. Under conditions where the entropy production is minimized, a linear relationship is derived between liquid chemical potentials and temperature. This relationship is utilized to evaluate the validity of the solution model of Ghiorso et al. (1983) in melts up to 300° C above their liquidus. The results indicate that configurational entropies are accurately modeled for MORB and andesite bulk compositions. The modeling fails in two four-component systems tested. Equations are derived which allow the calibration of multicomponent regular solution parameters from steady state Soret arrays. An algorithm is demonstrated which permits the calculation of steady state Soret concentration profiles, given an overall bulk melt composition and temperature gradient. This algorithm uses the liquid solution properties of Ghiorso et al. (1983) and constants obtained from the experimental measurements of Lesher and Walker (1986).

Notes: Abstract A thermodynamic solution model is developed for minerals whose compositions lie in the two binary systems Mg2SiO4-Fe2SiO4 and Mg2Si2O6-Fe2Si2O6. The formulation makes explicit provision for nonconvergent ordering of Fe2+ and Mg2+ between M1 and M2 sites in orthopyroxenes and non-zero Gibbs energies of reciprocal ordering reactions in both olivine and orthopyroxene. The calibration is consistent with (1) constraints provided by available experimental and natural data on the Fe-Mg exchange reaction between olivine and orthopyroxene ± quartz, (2) site occupancy data on orthopyroxenes including both crystallographic refinements and Mössbauer spectroscopy, (3) enthalpy of solution data on olivines and orthopyroxenes and enthalpy of disordering data on orthopyroxene, (4) available data on the temperature and ordering dependence of the excess volume of orthopyroxene solid solutions, and (5) direct activity-composition determinations of orthopyroxene and olivine solid solutions at elevated temperatures. Our analysis suggests that the entropies of the exchange [Mg(M2)Fe(M1)⇔Fe(M2)Mg(M1)] and reciprocal ordering reactions [Mg(M2)Mg(M1)+ Fe(M2)Fe(M1)⇔Fe(M2)Mg(M1)+Mg(M2)Fe(M1)] cannot differ significantly (± 1 cal/K) from zero over the temperature range of calibration (400°–1300° C). Consideration of the mixing properties of olivine-orthopyroxene solid solutions places tight constraints on the standard state thermodynamic quantities describing Fe-Mg exchange reactions involving olivine, orthopyroxene, pyralspite garnets, aluminate spinels, ferrite spinels and biotite. These constraints are entirely consistent with the standard state properties for the phasesα-quartz,β-quartz, orthoenstatite, clinoenstatite, protoenstatite, fayalite, ferrosilite and forsterite which were deduced by Berman (1988) from an independent analysis of phase equilibria and calorimetric data. In conjunction with these standard state properties, the solution model presented in this paper provides a means of evaluating an internally consistent set of Gibbs energies of mineral solid solutions in the system Mg2SiO4-Fe2SiO4-SiO2 over the temperature range 0–1300° C and pressure interval 0.001–50 kbars. As a consequence of our analysis, we find that the excess Gibbs energies associated with mixing of Fe and Mg in (Fe, Mg)2SiO4 olivines, (Fe, Mg)3Al2Si3O12 garnets, (Fe, Mg)Al2O4 and (Fe, Mg)Fe2O4 spinels, and K(Mg, Fe)3AlSi3O10(OH)2 biotites may be satisfactory described, on a macroscopic basis, with symmetric regular solution type parameters having values of 4.86±0.12 (olivine), 3.85±0.09 (garnet), 1.96±0.13 (spinel), and 3.21±0.29 kcals/gfw (biotite). Applications of the proposed solution model demonstrate the sensitivity of petrologic modeling to activity-composition relations of olivine-orthopyroxene solutions. We explore the consequences of estimating the activity of silica in melts forming in the mantle and we develop a graphical geothermometer/geobarometer for metamorphic assemblages of olivine+orthopyroxene+quartz. Quantitative evaluation of these results suggests that accurate and realistic estimates of silica activity in melts derived from mantle source regions,P-T paths of metamorphism and other intensive variables of petrologic interest await further refinements involving the addition of “trace” elements (Al3+ and Fe3+) to the thermodynamic formulation for orthopyroxenes.

Notes: Abstract Thermodynamic and mathematical relations are presented to facilitate the description of an algorithm for the calculation of chemical mass transfer in magmatic systems. This algorithm extends the silicate liquid solution model of Ghiorso et al. (1983) to allow for the quantitative modelling of natural magmatic processes such as crystal fractionation, equilibrium crystallization, magma mixing and solid-phase assimilation. The algorithm incorporates a new method for determining the saturation surface of a non-ideal multicomponent solid-solution crystallizing from a melt. It utilizes a mathematical programming (optimization) approach to determine the stable heterogeneous (solids+liquid) equilibrium phase assemblage at a particular temperature and pressure in magmatic systems both closed and open to oxygen. Closed system equilibria are computed by direct minimization of the Gibbs free energy of the system. Open system equilibria are determined by minimization of the Korzhinskii potential (Thompson 1970), where oxygen is treated as a perfectly mobile component. Magmatic systems undergoing chemical mass transfer processes are modelled in a series of discrete steps in temperature, pressure or bulk composition, with each step characterized by heterogeneous solid-liquid equilibrium. A numerical implementation of the algorithm has been developed (in the form of a FORTRAN 77 computer program) and calculations demonstrating its utility are provided in an accompanying paper (Ghiorso and Carmichael 1985).