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

Amphibole thermodynamics are approximated with the symmetric formalism (regular solution model for within-site non-ideality and a reciprocal solution model for cross-site-terms) in order to formulate improved thermometers for amphibole-plagioclase assemblages. This approximation provides a convenient framework with which to account for composition-dependence of the ideal (mixing-on-sites) equilibrium constants for the equilibria:
 For A and B all possible within-site and cross-site interactions among the species □−K−Na−Ca−Mg−Fe2+−Fe3+−Al−Si on the A, M4, M1, M3, M2 and T1 amphibole crystallographic sites were examined. Of the 36 possible interaction energy terms, application of the symmetric formalism results in a dramatic simplification to eight independent parameters. Plagioclase nonideality is modelled using Darken's quadratic formalism. We have supplemented an experimental data set of 92 amphibole-plagioclase pairs with 215 natural pairs from igneous and metamorphic rocks in which the pressure and temperature of equilibration are well constrained. Regression of the combined dataset yields values for the eight interaction parameters as well as for apparent enthalpy, entropy and volume changes for each reaction. These parameters are used to formulate two new thermometers, which perform well (±40°C) in the range 400–1000°C and 1–15 kbar over a broad range of bulk compositions, including tschermakitic amphiboles from garnet amphibolites which caused problems for the simple thermometer of Blundy and Holland (1990). For silica-saturated rocks both thermometers may be applied: in silica-undersaturated rocks or magmas thermometer B alone can be applied. An improved procedure for estimation of ferric iron in calcic amphiboles is presented in the appendix.

Non-ideal interactions in calcic amphiboles and their bearing on amphibole-plagioclase thermometry

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

This paper provides methods and a description of a Pascal computer program, thermocalc, for various thermodynamic calculations using the thermodynamic dataset presented in earlier papers in this series (Holland & Powell, 1985; Powell & Holland, 1985). The dataset involves uncertainties on the thermodynamic parameters and therefore allows uncertainties to be calculated on results, for example in geothermometry and geobarometry. Recommendations are made for the uncertainties on activities to be used in calculations on rocks, particular emphasis being placed on preventing underestimates of these uncertainties at small mole fractions. Apposite examples of phase diagram and rock calculations are presented with ouput from thermocalc, demonstrating the utility of the program. Of the rock calculations, the most valuable are considered to be those involving simultaneous combination ‘least squares’of calculated conditions for a set of reactions applicable to a rock. This set of reactions involves the independent reactions which can be written between the end-members in the minerals in a rock and in the thermodynamic dataset. In contrast to an approach based on specific geothermometers and geobarometers, this approach maximizes the benefit of having an internally consistent thermodynamic dataset. thermocalc is available in IBM PC and Mac versions, from Roger Powell for A$25 or Tim Holland for £10 per version.

An internally consistent dataset with uncertainties and correlations: 3. Applications to geobarometry, worked examples and a computer program

https://sites.williams.edu/rcox/files/2013/01/MudrockChem.pdf

The influence of sediment recycling and basement composition on evolution of mudrock chemistry in the southwestern United States

The models recognize that ZrSiO4, ZrTiO4,  and TiSiO4, but not ZrO2 or TiO2, are independently variable phase components in zircon. Accordingly, the equilibrium controlling the Zr content of rutile coexisting with zircon is ZrSiO4 = ZrO2 (in rutile) +  SiO2. The equilibrium controlling the Ti content of zircon is either ZrSiO4 + TiO2 = ZrTiO4 + SiO2 or TiO2 + SiO2 = TiSiO4, depending whether Ti substitutes for Si or Zr. The Zr content of rutile thus depends on the activity of SiO2
 $$(a_{\text{SiO}_{2}})$$
 as well as T, and the Ti content of zircon depends on $$a_{\text{SiO}_{2}}$$
  and 
 $$a_{\text{TiO}_{2}}$$
 as well as T. New and published experimental data confirm the predicted increase in the Zr content of rutile with decreasing $$a_{\text{SiO}_{2}},$$
 and unequivocally demonstrate that the Ti content of zircon increases with decreasing $$a_{\text{SiO}_{2}}$$
 . The substitution of Ti in zircon therefore is primarily for Si. Assuming a constant effect of P, unit $$a_{\text{ZrSiO}_{4}},$$
 and that $$a_{\text{ZrO}_{2}}$$
  and $$a_{\text{ZrTiO}_{4}}$$
 are proportional to ppm Zr in rutile and ppm Ti in zircon, [log(ppm Zr-in-rutile) + log
 $$a_{\text{SiO}_{2}}$$
 ] = A1 + B1/T(K) and  [log(ppm Ti-in-zircon) + log
 $$a_{\text{SiO}_{2}}$$
 − log
 $$a_{\text{TiO}_{2}}$$
 ] = A2 + B2/T, where the A and B are constants. The constants were derived from published and new data from experiments with $$a_{\text{SiO}_{2}}$$
 buffered by either quartz or zircon + zirconia, from experiments with $$a_{\text{SiO}_{2}}$$
 defined by the Zr content of rutile, and from well-characterized natural samples. Results are A1 = 7.420 ± 0.105;  B1 = −4,530 ± 111;  A2 = 5.711 ± 0.072;  B2 = −4,800 ± 86 with activity referenced to α-quartz and rutile at P and T of interest. The zircon thermometer may now be applied to rocks without quartz and/or rutile, and the rutile thermometer applied to rocks without quartz, provided that $$a_{\text{SiO}_{2}}$$
  and $$a_{\text{TiO}_{2}}$$
 are estimated. Maximum uncertainties introduced to zircon and rutile thermometry by unconstrained $$a_{\text{SiO}_{2}}$$
  and 
 $$a_{\text{TiO}_{2}}$$
 can be quantitatively assessed and are ≈60 to 70°C at 750°C. A preliminary assessment of the dependence of the two thermometers on P predicts that an uncertainty of ±1 GPa introduces an additional uncertainty at 750°C of ≈50°C for the Ti-in-zircon thermometer and of ≈70 to 80°C for the Zr-in-rutile thermometer.

New thermodynamic models and revised calibrations for the Ti-in-zircon and Zr-in-rutile thermometers

The cation exchange reaction Fe3Al2Si3O12 +KMg3AlSi3O10(OH)2 = Mg3Al2Si3O12+KFe3-AlSi3 O10(OH)2 has been investigated by determining the partitioning of Fe and Mg between synthetic garnet, (Fe, Mg)3Al2Si3O12, and synthetic biotite, K(Fe, Mg)3AlSi3O10(OH)2. Experimental results at 2.07 kbar and 550 °–800 ° C are consistent with In [(Mg/Fe) garnet/(Mg/Fe) biotite] = -2109/T(°K) +0.782. The preferred estimates for Δ¯H and Δ¯S of the exchange reaction are 12,454 cal and 4.662 e.u., respectively. Mixtures of garnet and biotite in which the ratio garnet/biotite=49/1 were used in the cation exchange experiments. Consequently the composition of garnet-biotite pairs could approach equilibrium values in the experiments with minimal change in garnet composition (few tenths of a mole percent). Equilibrium was demonstrated at each temperature by reversal of the exchange reaction. Numerical analysis of the experimental data yields a geothermometer for rocks containing biotite and garnet that are close to binary Fe-Mg compounds.

Experimental calibration of the partitioning of Fe and Mg between biotite and garnet

Review Paper. Mineral evolution

The conditions at which monazite and allanite were produced and destroyed during prograde metamorphism of pelitic rocks were determined in a Buchan and a Barrovian regional terrain and in a contact aureole, all from northern New England, USA. Pelites from the chlorite zone of each area contain monazite that has an inclusion-free core surrounded by a highly irregular, inclusion-rich rim. Textures and 208Pb/232Th dates of these monazites in the Buchan terrain, obtained by ion microprobe, suggest that they are composite grains with detrital cores and very low-grade metamorphic overgrowths. At exactly the biotite isograd in the regional terrains, composite monazite disappears from most rocks and is replaced by euhedral metamorphic allanite. At precisely the andalusite or kyanite isograd in all three areas, allanite, in turn, disappears from most rocks and is replaced by subhedral, chemically unzoned monazite neoblasts. Allanite failed to develop at the biotite isograd in pelites with lower than normal Ca and/or Al contents, and composite monazite survived at higher grades in these rocks with modified texture, chemical composition, and Th–Pb age. Pelites with elevated Ca and/or Al contents retained allanite in the andalusite or kyanite zone. The best estimate of the time of peak metamorphism at the andalusite or kyanite isograd is the mean Th–Pb age of metamorphic monazite neoblasts that have not been affected by retrograde metamorphism: 364.3±3.5 Ma in the Buchan terrain, 352.9±8.9 Ma in the Barrovian terrain, and 403.4±5.9 Ma in the contact aureole. Some metamorphic monazites from the Buchan terrain have ages partially to completely reset during an episode of retrograde metamorphism at 343.1±9.1 Ma. Interpretation of Th–Pb ages of individual composite monazite grains is complicated by the occurrence of subgrain domains of detrital material intergrown with domains of material formed or recrystallized during prograde and retrograde metamorphism.

Prograde destruction and formation of monazite and allanite during contact and regional metamorphism of pelites: petrology and geochronology

Crystal size distributions (CSDs) measured in metamorphic rocks yield quantitative information about crystal nucleation and growth rates, growth times, and the degree of overstepping (ΔT) of reactions during metamorphism. CSDs are described through use of a population density function n=dN/dL, where N is the cumulative number of crystals per unit volume and L is a linear crystal size. Plots of ln (n) vs. L for olivine+pyroxene and magnetite in high-temperature (1000° C) basalt hornfelses from the Isle of Skye define linear arrays, indicating continuous nucleation and growth of crystals during metamorphism. Using the slope and intercept of these linear plots in conjunction with growth rate estimates we infer minimum mineral growth times of less than 100 years at ΔT<10° C, and nucleation rates between 10−4 and 10−1/cm3/s. Garnet and magnetite in regionally metamorphosed pelitic schists from south-central Maine have CSDs which are bell-shaped. We interpret this form to be the result of two processes: 1) initial continuous nucleation and growth of crystals, and 2) later loss of small crystals due to annealing. The large crystals in regional metamorphic rocks retain the original size frequency distribution and may be used to obtain quantitative information on the original conditions of crystal nucleation and growth. The extent of annealing increases with increasing metamorphic grade and could be used to estimate the duration of annealing conditions if the value of a rate constant were known. Finally, the different forms of crystal size distributions directly reflect differences in the thermal histories of regional vs. contact metamorphosed rocks: because contact metamorphism involves high temperatures for short durations, resulting CSDs are linear and unaffected by annealing, similar to those produced by crystallization from a melt; because regional metamorphism involves prolonged cooling from high temperatures, primary linear CSDs are later modified by annealing to bell shapes.

John M. Ferry

Papers

New thermodynamic models and revised calibrations for the Ti-in-zircon and Zr-in-rutile thermometers

Experimental calibration of the partitioning of Fe and Mg between biotite and garnet

Review Paper. Mineral evolution

Prograde destruction and formation of monazite and allanite during contact and regional metamorphism of pelites: petrology and geochronology

Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization