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

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

Zircon and rutile are common accessory minerals whose essential structural constituents, Zr, Ti, and Si can replace one another to a limited extent. Here we present the combined results of high pressure–temperature experiments and analyses of natural zircons and rutile crystals that reveal systematic changes with temperature in the uptake of Ti in zircon and Zr in rutile. Detailed calibrations of the temperature dependencies are presented as two geothermometers—Ti content of zircon and Zr content of rutile—that may find wide application in crustal petrology. Synthetic zircons were crystallized in the presence of rutile at 1–2 GPa and 1,025–1,450°C from both silicate melts and hydrothermal solutions, and the resulting crystals were analyzed for Ti by electron microprobe (EMP). To augment and extend the experimental results, zircons hosted by five natural rocks of well-constrained but diverse origin (0.7–3 GPa; 580–1,070°C) were analyzed for Ti, in most cases by ion microprobe (IMP). The combined experimental and natural results define a log-linear dependence of equilibrium Ti content (expressed in ppm by weight) upon reciprocal temperature:

 $$\log ({\text{Ti}}_{{{\text{zircon}}}}) = (6.01 \pm 0.03) - \frac{{5080 \pm 30}}{{T\;(\hbox{K})}}.$$
 In a strategy similar to that used for zircon, rutile crystals were grown in the presence of zircon and quartz (or hydrous silicic melt) at 1–1.4 GPa and 675–1,450°C and analyzed for Zr by EMP. The experimental results were complemented by EMP analyses of rutile grains from six natural rocks of diverse origin spanning 0.35–3 GPa and 470–1,070°C. The concentration of Zr (ppm by weight) in the synthetic and natural rutiles also varies in log-linear fashion with T
 −1:

 $$\log ({\text{Zr}}_{{{\text{rutile}}}}) = (7.36 \pm 0.10) - \frac{{4470 \pm 120}}{{T\;(\hbox{K})}}.$$
 The zircon and rutile calibrations are consistent with one another across both the synthetic and natural samples, and are relatively insensitive to changes in pressure, particularly in the case of Ti in zircon. Applied to natural zircons and rutiles of unknown provenance and/or growth conditions, the thermometers have the potential to return temperatures with an estimated uncertainty of ±10 ° or better in the case of zircon and ±20° or better in the case of rutile over most of the temperature range of interest (∼400–1,000°C). Estimates of relative temperature or changes in temperature (e.g., from zoning profiles in a single mineral grain) made with these thermometers are subject to analytical uncertainty only, which can be better than ±5° depending on Ti or Zr concentration (i.e., temperature), and also upon the analytical instrument (e.g., IMP or EMP) and operating conditions.

Crystallization thermometers for zircon and rutile

The eastern Tonale fault zone: a ‘natural laboratory’ for crystal plastic deformation of quartz over a temperature range from 250 to 700 °C

Mineral equilibria calculations in the system K2O–FeO–MgO–Al2O3–SiO2–H2O–TiO2–Fe2O3 (KFMASHTO) using thermocalc and its internally consistent thermodynamic dataset constrain the effect of TiO2 and Fe2O3 on greenschist and amphibolite facies mineral equilibria in metapelites. The end-member data and activity–composition relationships for biotite and chloritoid, calibrated with natural rock data, and activity–composition data for garnet, calibrated using experimental data, provide new constraints on the effects of TiO2 and Fe2O3 on the stability of these minerals. Thermodynamic models for ilmenite–hematite and magnetite–ulvospinel solid solutions accounting for order–disorder in these phases allow the distribution of TiO2 and Fe2O3 between oxide minerals and silicate minerals to be calculated. The calculations indicate that small to moderate amounts of TiO2 and Fe2O3 in typical metapelitic bulk compositions have little effect on silicate mineral equilibria in metapelites at greenschist to amphibolite facies, compared with those calculated in KFMASH. The addition of large amounts of TiO2 to typical pelitic bulk compositions has little effect on the stability of silicate assemblages; in contrast, rocks rich in Fe2O3 develop a markedly different metamorphic succession from that of common Barrovian sequences. In particular, Fe2O3-rich metapelites show a marked reduction in the stability fields of staurolite and garnet to higher pressures, in comparison to those predicted by KFMASH grids.

The effect of TiO2 and Fe2O3 on metapelitic assemblages at greenschist and amphibolite facies conditions: mineral equilibria calculations in the system K2O-FeO-MgO-Al2O3-SiO2-H2O-TiO2-Fe2O3

A relatively simple petrogenetic grid for partial melting of pelitic rocks in the NCKFMASH system is presented based on the assumption that the only H2O available for melting is through dehydration reactions. The grid includes both discontinuous and continuous Fe-Mg reactions; contours of Fe/(Fe+Mg) for continuous reactions define P-T vectors along which continuous melting will occur. For biotite-bearing assemblages (garnet+biotite + sillimanite + K-feldspar + liquid and garnet + biotite + cordierite + K-feldspar + liquid), Fe/(Fe+Mg) contours have negative slopes and melting will occur with increasing temperature or pressure. For biotite-absent assemblages (garnet + cordierite + sillimanite + K-feldspar + liquid or garnet + cordierite + orthopyroxene + K-feldspar + liquid) Fe/(Fe + Mg) contours have flat slopes and melting will occur only with increasing pressure. The grid predicts that abundant matrix K-feldspar should only be observed if rocks are heated at P   3.8 kbar, and that generation of late biotite + sillimanite replacing garnet, cordierite, or as selvages around leu- cosomes should be common in rocks in which melt is not removed. There is also a predicted field for dehydration melting of staurolite between 5 and 12 kbar. Textures in migmatites from New Hampshire, USA, suggest that prograde dehydration melting reactions are very nearly completely reversible during cooling and crystallization in rocks in which melt is not removed. Therefore, many reaction textures in “low grade” migmatites may represent retrograde rather than prograde reactions.

P -T paths from anatectic pelites

A quantitative petrogenetic grid for pelitic schists in the system KFMASH that includes the phases garnet, chlorite, biotite, chloritoid, cordierite, staurolite, talc, kyanite, andalusite, sillimanite, and pyrophyllite (with quartz, H2O and muscovite or K-feldspar in excess) is presented. The grid is based on thermodynamic data of Berman et al. (1985) and Berman (1988) for endmember KFASH and KMASH equilibria and natural Fe-Mg partitioning for the KFMASH system. Calculation of P-T slopes and the change in Fe/(Fe+Mg) along reactions in the KFMASH system were made using the Gibbs method. In addition, the effect on the grid of MnO and CaO is evaluated quantitatively. The resulting grid is consistent with typical Buchan and Barrovian parageneses at medium to high grades. At low grades, the grid predicts an extensive stability field for the paragenesis chloritoid+biotite which arises because of the unusual facing of the reaction chloritoid+biotite + quartz+H2O = garnet+chlorite+muscovite, which proceeds to the right with increasing T in the KFMASH system. However, the reaction proceeds to the left with increasing T in the MnKFASH system so the assemblage chloritoid + biotite is restricted to bulk compositions with high Fe/(Fe+Mg+Mn). Typical metapelites will therefore contain garnet+chlorite at low grades rather than chloritoid + biotite.

A petrogenetic grid for pelitic schists in the system SiO 2 -Al 2 O 3 -FeO-MgO-K 2 O-H 2 O

On the loss of 40Ar∗ from muscovite during polymetamorphism

The reaction muscovite+cordieritebiotite+Al2SiO5 +quartz+H2O is of considerable importance in the low pressure metamorphism of pelitic rocks: (1) its operation is implied in the widespread assemblage Ms + Crd +And± Sil + Bt + Qtz, a common mineral assemblage in contact aureoles and low pressure regional terranes; (2) it is potentially an important equilibrium for pressure estimation in low pressure assemblages lacking garnet; and (3) it has been used to distinguish between clockwise and anticlockwise P–T paths in low pressure metamorphic settings. Experiments and thermodynamic databases provide conflicting constraints on the slope and position of the reaction, with most thermodynamic databases predicting a positive slope for the reaction. Evidence from mineral assemblages and microtextures from a large number of natural prograde sequences, in particular contact aureoles, is most consistent with a negative slope (andalusite and/or sillimanite occurs upgrade of, and may show evidence for replacement of, cordierite). Mineral compositional trends as a function of grade are variable but taken as a whole are more consistent with a negative slope than a positive slope. Thermodynamic modelling of reaction 1 and associated equilibria results in a low pressure metapelitic petrogenetic grid in the system K2O–FeO–MgO–Al2O3–SiO2–H2O (KFMASH) which satisfies most of the natural and experimental constraints. Contouring of the Fe–Mg divariant interval represented by reaction 1 allows for pressure estimation in garnet-absent andalusite+cordierite-bearing schists and hornfelses. The revised topology of reaction 1 allows for improved analysis of P–T paths from mineral assemblage sequences and microtextures in the same rocks.

Thermodynamic modelling of the reaction muscovite+cordierite→Al2SiO5+biotite+quartz+ H2O: constraints from natural assemblages and implications for the metapelitic petrogenetic grid

for these rocks to about 5008C and 15^16 kbar. These P–T constraints, together with the tectonic fabric of the marbles, suggest that deformation and recrystallization occurred at or near the thermal maximum of metamorphism.

/pdf/glaucophane-bearing-marbles-on-syros-greece-3fne7nfpcq.pdf

John T. Cheney

Papers

P -T paths from anatectic pelites

A petrogenetic grid for pelitic schists in the system SiO 2 -Al 2 O 3 -FeO-MgO-K 2 O-H 2 O

On the loss of 40Ar∗ from muscovite during polymetamorphism

Thermodynamic modelling of the reaction muscovite+cordierite→Al2SiO5+biotite+quartz+ H2O: constraints from natural assemblages and implications for the metapelitic petrogenetic grid

Glaucophane-bearing Marbles on Syros, Greece