SUPPLEMENTARY INFORMATION

Transcription

1 GSA Data Repository 080 Schorn et al., 08, Thermal buffering in the orogenic crust: Geology, SUPPLEMENTARY INFORMATION 3 PHASE DIAGRAM MODELING Phase diagrams are constructed in the eleven-component MnNCKFMASHTO (MnO Na O CaO K O FeO MgO Al O 3 SiO H O TiO O) model system using THERMOCALC v3.45e (Powell and Holland, 988) and an updated version of the dataset ds6 (file tc-ds63.txt, created 05/0/05; Holland and Powell, 0). The activity composition relationships for garnet, orthopyroxene and biotite are those of White et al. (04b), ilmenite hematite is from White et al. (000), C plagioclase and K-feldspar are from Holland and Powell (003) and muscovite is from White et al. (04), but with a reduced G mod value (see notation in Green et al., 06) for the margarite end-member of 5 kj mol from 6.5 kj mol (Palin et al., 06). Augitic clinopyroxene and tonalitic melt are from Green et al. (06). The aluminosilicates, quartz and aqueous fluid (H O) are taken as pure end-member phases. The utilised bulk compositions are listed in Tables DR and DR Enthalpy depends on the amount of material and the absolute values calculated are a function of the bulk composition considered. An arbitrary temperature of 600 ºC has been chosen as common reference point. The subsolidus part of Fig. D F and DR3B has been calculated assuming fluid-saturated conditions; the extensive property of enthalpy implies that the slope of the isotherms is slightly different to the suprasolidus part. It should be noted that the relative spacing between the isotherms remains unvaried compared to the suprasolidus conditions. This indicates that in both the sub- and suprasolidus parts of the diagrams the same increase in enthalpy generally produces the same increment in temperature. Figure DR3 shows the pressure-enthalpy diagrams contoured for temperature for the refractory granite (Fig. DR3A) and the fertile metapelite (Fig. DR3B). Figure DR4 illustrates the relationship between temperature and heating rate in function of variable heat production (S).

2 6 THERMAL MODEL 7 8 The model is based on the formulation that describes the rate of temperature change due to heat input (Stüwe, 007) where S is the volumetric rate of heat production (W m -3 ). Prograde metamorphic reactions consume energy in order to advance (i.e. endothermic). We therefore discriminate between heat that is added (S) from heat that is consumed by the advancing reactions. S is the heat production for which we assume a range of values between 0 µw m -3 (Andreoli et al., 006; Stüwe, 007). ρ is the density (kg m 3 ) and C p is the heat capacity at constant pressure. The values for ρ are calculated along an isobaric heating path at 0.6 GPa assuming a closed system with full melt retention. In this simplest of cases the effect of thermal buffering is likely underestimated as melt retention neglects advective cooling via melt extraction occurring in natural systems. The values for the heat capacity C p are calculated via for a given enthalpy ( H) and temperature interval ( T) on Fig. E, as calculated by THERMOCALC. The modelling yields the enthalpy of reaction at any point in PT space for the given bulk composition. Contrary to the latent heat of fusion (~400 kj kg of granite; Bea, 0) the enthalpy of reaction also considers energy released by the crystallisation of peritectic phases (e.g. feldspars and alumosilicates for the muscovite-breakdown) and represents a more realistic estimate for the energetics involved in the investigated reactions. The values for C p are normalised to the molar weight of the bulk composition of Ague (99), calculated as kg mol -. From () the time parameter dt of thermal buffering is calculated for a given temperature interval via 3 45 From the characteristic time scale of thermal equilibration, given by the relationship

3 ~ (e.g. Stüwe, 007) the critical length scale of thermal equilibration L is estimated using Delta t calculated from (3) and taken as the time scale of thermal equilibration (t eq ). We reformulate (4) to ~ 5 48 where κ is the thermal diffusivity (m s - ) calculated from assuming a constant thermal conductivity k of.5 J s - m - K -. Values for typical crystalline rocks range between J s - m - K - (e.g. Stüwe, 007); this range of values affects our results by ± 5 %, therefore less than an order of magnitude. Homogenous thermal conductivity is assumed for our schematic model. Density and heat capacity are calculated from the modelling The calculated values for the critical length scale (equation 5) for a variable heat production are plotted against temperature (Fig. 3). Fig. 4 illustrates the calculated critical length scale (equation 5, Fig. 4A) and buffering time (equation 4, Fig. 4B) for the investigated reactions as a function of heat production. Supplementary figure DR4 shows the relationship of temperature and rate of temperature increment for the investigated reactions, calculated from equation () REFERENCES CITED Bea, F., 0, The sources of energy for crustal melting and the geochemistry of heat-producing elements: Lithos, v. 53, p Green, E. C. R., White, R. W., Diener, J. F. A., Powell, R., Holland, T. J. B. and Palin, R. M., 06, Activity composition relations for the calculation of partial melting equilibria in metabasic rocks: Journal of Metamorphic Geology, v. 34, p

4 Holland, T. J. B. and Powell, R., 003, Activity composition relations for phases in petrological calculations: an asymmetric multicomponent formulation: Contributions to Mineralogy and Petrology, v. 45, p Holland, T. J. B. and Powell, R., 0, An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids: Journal of Metamorphic Geology, v. 9, p Powell, R. and Holland, T. J. B., 988, An internally consistent thermodynamic dataset with uncertainties and correlations: 3. Application, methods, worked examples and a computer program: Journal of Metamorphic Geology, v. 6, p Stüwe, K., 007, Geodynamics of the Lithosphere, Springer Verlag, Berlin, Germany. White, R. W., Powell, R. and Johnson, T. E., 04, The effect of Mn on mineral stability in metapelites revisited: new a x relations for manganese-bearing minerals: Journal of Metamorphic Geology, v. 3, p White, R. W., Powell, R., Holland, T. J. B. and Worley, B. A., 000, The effect of TiO and Fe O 3 on metapelitic assemblages at greenschist and amphibolite facies conditions: mineral equilibria calculations in the system K O FeO MgO Al O 3 SiO H O TiO Fe O 3 : Journal of Metamorphic Geology, v. 8, p White, R. W., Powell, R., Holland, T. J. B., Johnson, T. E. and Green, E. C. R., 04b, New mineral activity composition relations for thermodynamic calculations in metapelitic systems: Journal of Metamorphic Geology, v. 3, p

5 FIGURE CAPTIONS Figure DR. Results of modelling calculations, pressure enthalpy phase equilibrium diagrams contoured for temperature. A: Average granite. B: Average metapelite. A and D: Enthalpy depends on the amount of material and the absolute values calculated are a function of the bulk composition considered. An arbitrary temperature of 600 ºC has been chosen as common reference point (see text). Mineral abbreviations: bi biotite, cd cordierite, cpx clinopyroxene, g garnet, melt granitic melt, Melt tonalitic melt, ilm ilmenite, ksp K-feldspar, ky kyanite, mt magnetite, mu muscovite, opx orthopyroxene, pl plagioclase, q quartz, ru rutile, sill sillimanite, sp spinel Figure DR. Relationship between temperature and rate of temperature increment during thermal buffering in function of external heat production (S) at 0.6 GPa. The colored shading indicates the location of reaction () and (), respectively. 00 5

6 (A) granite g cpx bi solidus + q + ksp + ilm + mt g cpx opx Melt Fig. DR C 700 C Pressure (GPa) g cpx opx bi 800 C cpx opx Melt 900 C 000 C 0.4 cpx Melt 0.3 cpx opx bi opx Melt Melt Pressure (GPa) Enthalpy (kj.mol - ) (B) metapelite C + q + pl + ilm + melt g bi cd ksp mt 8 cd mt [q] Enthalpy (kj.mol - ) 700 C wet solidus 750 C g bi sill mu pl ilm q melt g bi sill mu pl ilm mt q melt 3 bi sill ksp pl ilm mt q melt 4 bi cd ksp pl ilm mt q melt H O 5 bi cd ksp pl ilm mt q melt 6 bi cd ksp pl ilm mt melt 7 g opx bi cd ksp pl ilm mt melt 8 g opx cd ksp pl ilm mt melt g bi ky mu 800 C 850 C g bi sill ksp mt g bi sill mu ksp mt ky sill g bi cd sill ksp mt g bi sill ksp g cd sill ksp mt g cd ksp mt 900 C 6 g cd ksp mt [q] 950 C g sill ksp C 9 opx cd ksp pl ilm mt melt 0 opx cd pl ilm mt melt cd pl ilm mt melt g cd pl ilm mt melt 3 g cd sp pl ilm mt melt 4 g cd sp ksp pl ilm mt melt 5 g cd sill ksp pl ilm mt melt 6 g cd sill ksp pl ilm q melt

7 Temperature ( C) S (µw.m -3 ) Fig. DR Rate of temperature increment (K.my - )

8 TABLE DR. BULK-ROCK COMPOSITIONS (WT% OXIDES) Lithology SiO TiO Al O 3 Fe O 3 FeO MnO MgO CaO Na O K O P O 5 Fe 3+ /Fe + avg. A-type granite* avg. amphibolite-facies metapelite *Whalen et al Ague, 99. TABLE DR. BULK-ROCK COMPOSITIONS EMPLOYED IN PHASE EQUILIBRIA MODELLING (MOL% OXIDES). SEE TABLE DR FOR ORIGINAL DATA Lithology H O SiO Al O 3 CaO* MgO FeO K O Na O TiO MnO O avg. A-type granite avg. amphibolite-facies metapelite *corrected in proportion to the P O 5 -content to account for CaO accomodated in apatite. Whalen et al Ague, 99.