Horst Purwin Stefan Lauterbach Gerhard P. Brey Alan B. Woodland Hans-Joachim Kleebe

Transcription

1 DOI /s ORIGINAL PAPER An experimental study of the Fe oxidation states in garnet and clinopyroxene as a function of temperature in the system CaO FeO Fe 2 O 3 MgO Al 2 O 3 SiO 2 : implications for garnet clinopyroxene geothermometry Horst Purwin Stefan Lauterbach Gerhard P. Brey Alan B. Woodland Hans-Joachim Kleebe Received: 1 June 2012 / Accepted: 22 October 2012 Ó Springer-Verlag Berlin Heidelberg 2012 Abstract Samples with eclogitic composition in the system CaO FeO Fe 2 O 3 MgO Al 2 O 3 SiO 2 were produced from various kinds of starting materials held in graphite-lined Pt capsules at a pressure of GPa and temperatures of 800 1,300 C using a piston-cylinder or Belt apparatus. Garnets and clinopyroxenes were characterized by analytical transmission electron microscopy and electron probe microanalysis (EPMA). Fe 3? /RFe ratios determined by electron energy-loss spectroscopy (EELS) decrease in clinopyroxene from 22.2 ± 3.4 % at 800 C to 13.3 ± 5.4 % at 1,300 C, while in garnet, they vary between 10.8 ± 1.5 and 15.4 ± 4.7 %, respectively. Temperature estimates according to Krogh (Contrib Mineral Petrol 99:44 48, 1988) reproduce the experimental temperature to ±60 C without systematic deviations if total iron is used in the calculation. If only the Fe 2? content is used, which was obtained by combining EPMA and EELS results, the experimental temperature is underestimated by 33 C on average at 800 1,200 C and overestimatedby77 C on average at 1,300 C. These systematic deviations can be explained by the temperature-dependent ratio of Fe 2? /RFe in garnet divided by that in clinopyroxene. Communicated by M. W. Schmidt. Electronic supplementary material The online version of this article (doi: /s ) contains supplementary material, which is available to authorized users. H. Purwin (&) S. Lauterbach H.-J. Kleebe Institut für Angewandte Geowissenschaften, Technische Universität Darmstadt, Schnittspahnstr. 9, Darmstadt, Germany purwin@geo.tu-darmstadt.de G. P. Brey A. B. Woodland Institut für Geowissenschaften, Goethe-Universität Frankfurt, Altenhöferallee 1, Frankfurt/Main, Germany Since the difference between the calculated and experimental temperature is relatively small, a Fe 2? -based recalibration of the thermometer appears not to be necessary for the investigated system in the range of pressure, temperature and composition covered by the experiments of this study. Keywords Garnet Clinopyroxene Geothermometry Ferric iron Electron energy-loss spectroscopy Transmission electron microscopy Introduction The garnet clinopyroxene geothermometer is one of the most widely applied methods for obtaining equilibration temperatures of eclogites, garnet-peridotites and other (ultra)basic metamorphic rocks containing garnet and clinopyroxene. It is based on the following Fe 2? Mg exchange reaction: 1=3Mg 3 Al 2 Si 3 O 12 þ CaFeSi 2 O 6 pyrope hedenbergite ¼ 1=3Fe 3 Al 2 Si 3 O 12 almandine þ CaMgSi 2 O 6 diopside : ð1þ If ideal solution is assumed, reaction (1) can be described by the Fe 2? Mg distribution coefficient (Banno 1970), here termed as K D K D ¼ðFe2þ =MgÞ =ðfe 2þ =MgÞ Cpx : ð2þ If all iron in garnet and clinopyroxene is present as Fe 2?, K D is equal to K D which is defined as K D ¼ðRFe=MgÞ =ðrfe=mgþ Cpx ; ð3þ where RFe is the total iron content without distinction between Fe 2? and Fe 3?. The first experimental study by

2 Råheim and Green (1974) showed that K D is very sensitive to temperature and depends to some extent on pressure. Subsequently, further calibrations of K D as a function of temperature, pressure and composition have been proposed (e.g., Ellis and Green 1979; Ganguly 1979; Saxena 1979; Powell 1985; Krogh 1988; Pattison and Newton 1989; Ai 1994; Berman et al. 1995; Ravna 2000; Nakamura 2009). Calcium has the most prominent compositional effect on K D. This was first experimentally proven and quantified by Ellis and Green (1979). They empirically corrected for this non-ideality by a linear dependency on the mole fraction of Ca in garnet expressed as XCa ¼ðCa=ðCa þ Mg þ RFe þ MnÞÞ : ð4þ Instead of a linear expression, Krogh (1988) used a quadratic regression equation to describe and correct for the dependency of K D on X Ca in his recalibration of existing experimental data. This was considered by Brey and Köhler (1990) as improvement over the linear Ca correction of the Ellis and Green (1979) formulation in their evaluation of different thermometers based on experiments on natural lherzolitic compositions (Brey et al. 1990a). Besides Ca, the more recent formulations by Ai (1994), Ravna (2000) and Nakamura (2009) take non-ideal behaviour of Mg on K D into account and the latter two also include the effect of Mn. None of the existing versions of the thermometer consider a correction term for jadeite (NaAlSi 2 O 6 ) component which may be necessary for clinopyroxenes with high jadeite content ([70 mol%, Koons 1984). Several authors evaluated either one or more calibrations of the thermometer on the basis of their own experimental data (e.g., Brey and Köhler 1990; Green and Adam 1991; Nakamura and Hirajima 2005) or on natural samples (e.g., Canil and O Neill 1996) on which another reference thermometer was applied under the assumption it gives the correct temperature. However, from the various evaluations, it can be concluded that there is no general preference of one formulation. At present, the most frequently used formulations are those by Krogh (1988), Powell (1985) and Ravna (2000). Major differences seem to arise from the way how Fe is treated: (1) whether the total iron content (total Fe) in garnet and clinopyroxene is used or (2) whether only Fe 2? is taken into consideration (e.g., Luth and Canil 1993; Canil and O Neill 1996; Li et al. 2005). Depending on how Fe is handled, temperature estimates can differ up to several hundred degrees (e.g., Canil and O Neill 1996; Li et al. 2005). Since the exact redox conditions of the experiments from which the thermometer was calibrated are not known, the accurate temperature estimate of unknown samples may vary generally between temperatures calculated using the total Fe content and those calculated employing only Fe 2? (Luth and Canil 1993). For eclogites with only garnet? clinopyroxene ± quartz, the garnet clinopyroxene thermometer is the only major element method to obtain equilibration temperatures. Thus, it is very important to clarify the necessity for (and the extent of) a correction for Fe 3? by experiments from which the Fe 3? content in the mineral phases has been analysed. We therefore experimentally investigated the effect of the Fe oxidation state in garnet and clinopyroxene on geothermometry in the system CaO FeO Fe 2 O 3 MgO Al 2 O 3 SiO 2 (CFFMAS). Fe oxidation states of eclogitic samples synthesized at different temperatures were determined by transmission electron microscopy (TEM) via electron energy-loss spectroscopy (EELS) combined with compositional data obtained by electron probe microanalysis (EPMA). Experimental procedure Experimental strategy In order to ensure comparability with previous experiments, we used similar experimental set-ups, that is, a graphite capsule sealed into a platinum (Pt) outer capsule. With graphite, Fe loss to the outer Pt capsule is avoided (Falloon et al. 1988) and the oxygen fugacity can be assumed to be at or below the graphite C O equilibrium. Glassy starting materials were chosen since they provide much faster equilibration than a mineral mix of garnets and clinopyroxenes (Råheim and Green 1974). To verify as to whether the results were reproducible, two starting materials with similar main element composition but different Fe 3? /RFe ratios were placed into the inner graphite capsule separated by a graphite disc. For the runs at 800 and 1,200 C, one starting material was a glass with a substantial proportion of Fe 3? and the second a mixture of a CaO MgO Al 2 O 3 SiO 2 glass plus synthetic fayalite. The aim was to approach equilibrium with respect to the oxidation state from two directions. These experiments may be seen as oxidation state reversals. Experimental methods and sample preparation Starting materials Various kinds of starting materials were prepared whose compositions are given in Table 1. Appropriate amounts of reagent-grade SiO 2, MgO, Al 2 O 3,Fe 2 O 3 (fired at 1,000 C) and CaCO 3 (dried at 120 C) were mixed in an agate mortar. Decarbonization was achieved by stepwise heating of the mixture from 700 to 1,000 C and holding this temperature for at least 16 h. The oxides were molten in a Pt crucible (pretreated with iron) at 1,450 C using a 1-atm

3 gas-mixing furnace at the University of Frankfurt. The GEk1b glass was quenched from a melt which was equilibrated in air for 1 h. The melt for the GEk3 glass was equilibrated for 45 min with a CO/CO 2 mixture yielding a log-bar fo 2 between -8.8 and This corresponds to an oxygen fugacity approximately half a log-bar unit above the iron-wustite oxygen buffer. Iron-free Ca Mg Al Si glasses (G1 and G2) were produced at 1,550 C and mixed with synthetic fayalite (syntheses: Fa1 and Fa2) to give a starting material with only Fe 2? (G1Fa1 and G2Fa2). One fragment of each glass was embedded in epoxy and analysed on 10 different spots with a JEOL JXA 8900 RL microprobe with a beam which was defocused to a nominal diameter of 30 lm. The standardization for Ca, Fe, Mg, Al and Si was carried out using the NBS glass K-412 (synthesized and characterized by Marinenko 1982). The results are given in Table 1. The glasses were finely ground in an agate mortar, and a 70-mg aliquot of the glasses GEk1b and GEk3 (corresponding to an absorber thickness of 5 mg Fe/cm 2 ) was used for Mössbauer spectroscopy. Transmission Mössbauer spectra (Fig. 1) were recorded at room temperature on a constant-acceleration Mössbauer spectrometer equipped with a nominal 50 mci 57 Co source in a 6 lm Rh matrix at the University of Frankfurt. Mirror image spectra collected over 512 channels with a velocity range of ±5 mm/s were analysed by the commercially available program NORMOS (written by R.A. Brand, distributed by Wissenschaftliche Elektronik GmbH, Germany). One doublet was assigned to Fe 3?, and two doublets were assigned to Fe 2? different short-range order positions taking into account. Hyperfine parameters are given in Table 2. The glasses GEK1b and GEk3 gave a Fe 3? /RFe ratio of 70.1 and 27.0 %, respectively. The uncertainty in the Fe 3? /RFe ratio of the glasses is estimated to be ±1 %Fe 3? /RFe. The starting materials were stored in a drying oven at 120 C. Sample loading Graphite inner capsules were loaded with approximately 8 10 mg of each of the two different starting materials used for one experiment. For syntheses at temperatures below 1,200 C, water was added in small amounts to the starting materials using a micro-syringe, whereas experiments at C1,200 C were nominally water-free. The two starting materials were separated from each other by a close-fitting graphite disc. Afterwards, the complete graphite capsules were sealed into Pt outer capsules with an outer (inner) diameter of 4.4 (4.0) mm. High-pressure experiments The experiments were carried out in a Belt apparatus at 3.0 GPa and temperatures ranging from 1,000 to 1,300 C. Set-up and calibration of the Belt apparatus with polycrystalline CaF 2 as pressure-transmitting medium are described by Brey et al. (1990b). They estimate an accuracy of ±7 C and ±0.08 GPa. One long-term experiment of about 8 weeks was performed at 800 C in a Boyd- England type piston-cylinder apparatus (Boyd and England 1960) using a pressure cell of polycrystalline CaF 2.No correction was applied for friction loss, and the nominal pressure was taken as the effective pressure acting on the sample (see Köhler and Brey 1990). Pressure and temperature of the piston-cylinder run is estimated to be correct within ±0.1 GPa and ±10 C, respectively. In both apparatus, the temperature was measured by a Type B thermocouple (Pt 94 Rh 6 /Pt 70 Rh 30 ) and controlled using a Jumo Table 1 Composition of starting materials given in wt% GEk1b GEk3 G1 G2 G1Fa1 a G2Fa2 b MgO 8.90(6) 9.41(6) 9.72(8) 12.19(7) Al 2 O (6) 9.35(6) 13.21(22) 11.75(12) CaO 13.06(7) 13.59(8) 19.14(9) 17.93(5) SiO (13) 52.23(21) 58.39(52) 58.57(19) FeO tot 15.87(9) 16.07(17) \D.L. \D.L Total (16) (18) (30) (15) Mg/(Mg? RFe) c Ca/(Ca? Mg? RFe) c Average of 10 EPMA measurements with standard deviation in parentheses in terms of least digits cited, except for G1Fa1 and G2Fa2 which were calculated using the corresponding glass composition and assuming perfect stoichiometry of fayalite a Mixture of glass and synthetic fayalite with 80.7 wt% G1? 19.3 wt% Fa1 b Mixture of glass and synthetic fayalite with 77.2 wt% G2? 22.8 wt% Fa2 c Molar ratio FeO tot = RFe as Fe 2? ; D.L. detection limit

4 Fig. 1 Room temperature Mössbauer spectra of the starting glasses GEk1b (a) and GEk3 (b) showing two doublets corresponding to Fe 2? (grey and light grey) and one doublet assigned to Fe 3? (shaded by lines). Full circles and a black line correspond to the measured and the calculated spectrum, respectively. The corresponding hyperfine parameters are given in Table 2 Table 2 Mössbauer parameters of the starting glasses GEk1b and GEk3 obtained at room temperature dtron 304 controller. The experiments were quenched by switching off the electric power. All experiments were conducted in devices at the University of Frankfurt. Run conditions and phases obtained are given in Table 3. Sample preparation GEk1b GEk3 Fe 2? (1) CS (mm/s) QS (mm/s) FWHM (mm/s) A(%) Fe 2? (2) CS (mm/s) QS (mm/s) FWHM (mm/s) A (%) Fe 3? CS (mm/s) QS (mm/s) FWHM (mm/s) A (%) CS centre shift, QS quadrupole splitting, FWHM full width at half maximum, A area After the run, each capsule was cut into several 150 to 300 lm thick slices using a Well diamond wire saw Model 4240 equipped with a 130 lm diamond wire. One slice was embedded in epoxy and polished for EPM analysis, and another one was prepared for TEM: the two samples from each run were cut out of the surrounding graphite and treated separately. After grinding to lm thickness, the samples were polished on both sides and glued onto 3-mm-sized Mo grids. Electron transparency was obtained by conventional Ar ion milling under an incidence angle of 12 at an accelerating voltage of 5 kv (followed by 3 kv for 5 min to remove the amorphous surface layer) using a Gatan Dual Ion Mill Model 600. Analytical methods Electron energy-loss spectroscopy and energy-dispersive X-ray spectroscopy (EDS) were performed at 120 kv on a FEI CM12 transmission electron microscope equipped with a LaB 6 cathode at the Technische Universität Darmstadt. The instrumentation allowed the analysis of coexisting garnets and clinopyroxenes within\500 nm of their shared grain boundaries, where equilibration within the run period can be assumed. EELS spectra were taken from garnets and clinopyroxenes on the thinnest parts of the wedge-shaped sample using a Gatan PEELS 666 parallel electron spectrometer fitted to the microscope. Energy resolution was ev for an undersaturated filament, visible as full width at half maximum (FWHM) of the zero-loss peak in the energyloss spectrum. The Fe L 2,3 electron energy-loss near-edge structure (ELNES) was recorded at an energy dispersion of 0.1 ev/channel in TEM diffraction mode with a camera length L = 110 mm, an illumination semi-angle a = 2.6 mrad and a 2 mm PEELS entrance aperture yielding a collection semi-angle of b = 7.0 mrad. Spot sizes were approximately nm and measuring times 5 to 15 s integration time per read-out. To improve the peak/background ratio, a series of 8 12 spectra on each measurement spot was taken and added up. After correcting the spectra for dark current and channel-to-channel gain variations, the spectra were energy-calibrated using the Fe L 3 maximum, which is for predominantly Fe 2? - and Fe 3? -bearing silicate minerals located at and ev, respectively (Garvie et al. 1994). Background intensity was subtracted by fitting an inverse power law in the range of ev and extrapolating this function to higher energy losses. Ideal single-scattering spectra of clinopyroxene and garnet were obtained by applying the Fourier-Ratio technique (e.g., Egerton 1996). Afterwards, the Fe 3? /RFe ratios were

5 Table 3 Run conditions Run T ( C) P (GPa) Run duration H 2 O (wt%) Starting material Sample Run products HPE10 1, h GEk1b HPE10-1b Cpx,, Qz, glass GEK3 HPE10-3 Cpx,, Qz, glass HPE06 1, h GEk1b HPE06-1b Cpx,, Qz GEk3 HPE06-3 Cpx,, Qz HPE16 1, h GEK3 HPE16-3 Cpx,, Qz G1Fa1 HPE16-G1Fa1 Cpx,, Qz, scheelite a HPE14 1, h 2.4 GEk1b HPE14-1b Cpx,, Qz GEk3 HPE14-3 Cpx,, Qz HPE17 1, h 45 min b 3.2 GEk3 HPE17-3 Cpx,, Qz G1Fa1 HPE17-G1Fa1 Fa, Cpx,, Qz, W-bearing phases a HPE ,358 h 3.5 GEK3 HPE21-3 Cpx,, Qz G2Fa2 HPE21-G2Fa2 Cpx,, Qz Cpx clinopyroxene, garnet, Qz quartz, Fa fayalite a Identified by EDS on the electron microprobe b Terminated by cooling water failure calculated according to the method of van Aken et al. (1998) using an empirically calibrated universal curve. The absolute error of this method is ±5 %Fe 3? /RFe for Fe 3? / RFe \40 % (van Aken et al. 1998). All phases measured were verified by EDS using an EDAX Genesis 2000 system also attached to the microscope. The chemical composition of garnets and clinopyroxenes was analysed with a JEOL JXA 8900 RL electron microprobe at the University of Frankfurt operating at an accelerating voltage of 15 kv and a beam current of 20 na where the beam was focused on the surface of the sample. Peak and background intensity was measured with an integration time of 30 s for Si, Al, Mg and Ca. For Fe, the integration time on the peak and on the background was 40 s. Wollastonite (Ca? Si), Al 2 O 3 (Al), olivine (Mg) and synthetic fayalite (Fe) were used as standards. Detection limits (3r) for Si, Mg, Al and Fe (expressed in their oxides) were below 300 wt-ppm SiO 2, MgO, Al 2 O 3 and CaO, respectively. The detection limit for Fe was below 400 wtppm FeO tot. Prior to analyses, overview back-scattered electron (BSE) images were taken of the run products characterizing texture, grain sizes and homogeneity of the mineral phases. Experiments, analytical strategy, evaluation of analyses and results General description of run products Run products are garnet, clinopyroxene and quartz (Fig. 2a d). In addition, glass was found in samples HPE10-1b and HPE10-3 near the contact to the graphite liner. Scheelite was observed in HPE16-G1Fa1, while additional W-bearing phases were found in sample HPE17- G1Fa1. Since unreacted fayalite and almost Fe-free garnets and clinopyroxenes were also found in HPE17-G1Fa1, this sample was not further considered. Probably, tungsten carbide particles, broken off from a tungsten carbide piston used for crushing the synthetic fayalite Fa1, are the source for tungsten in the samples HPE16-G1Fa1 and HPE17- G1Fa1. At temperatures C1,200 C, grain sizes are lm using the starting glass GEk1b (Fig. 2a), 5 25 lm with GEk3 (Fig. 2b) and \5 lm using G1Fa1. The garnets grown from GEk1b contain several inclusions of quartz and clinopyroxene (Fig. 2a), whereas the garnets from the more reduced starting materials GEk3 (Fig. 2b) and G1Fa1 have only few and very small inclusions. Quartz and clinopyroxene do not show any inclusions. At temperatures \1,200 C, the garnets are characterized by numerous inclusions of all coexisting phases, while at 1,100 C, they are overgrown by up to *100-lm-sized clinopyroxenes (Fig. 2c). At 800 C, larger-sized garnets are embedded in a fine-grained matrix of quartz, clinopyroxene and smaller garnets with grain sizes below 3 5 lm (Fig. 2d). BSE images do not indicate zonation of either garnets or clinopyroxenes, except for Fe-richer quenched clinopyroxene rims in melt containing samples at 1,300 C. Iron oxidation states determined by EELS Figure 3a is a TEM bright field (BF) image of sample HPE06-3 showing a typical garnet clinopyroxene grain boundary and the regions examined by EELS and EDS. For one selected garnet clinopyroxene pair, the corresponding

6 Fig. 2 Back-scattered electron images of typical synthetic eclogite samples showing phase assemblages consisting of garnet (light grey), clinopyroxene (dark grey) and quartz (dark) for a sample HPE06-1b, b sample HPE06-3, c sample HPE14-1b and d sample HPE21-3. Samples HPE06-1b and HPE14-1b originated from the higher EELS and EDS spectra are shown in Fig. 3b, c, respectively. In the EELS spectra (Fig. 3b), two significant features can be observed, the Fe L 3 -edge and the Fe L 2 -edge. Both edges exhibit parts which arise either due to Fe 2? or Fe 3?. The quantification of van Aken et al. (1998) using a modified L 2 /L 3 white line intensity ratio yields in this example 21.1 ± 5.0 % Fe 3? /RFe for clinopyroxene and 16.3 ± 5.0 % Fe 3? /RFe for garnet. Because of the very similar mass-thickness contrast of clinopyroxene and garnet (Fig. 3a), they cannot be readily distinguished in a BF image. However, a differentiation can be made by their EDS spectra (compare spectrum 1 with spectrum 2 in Fig. 3c). The aim of the EELS investigations was to determine in each sample the iron oxidation state of garnet clinopyroxene pairs with a common grain boundary as the ones shown in Fig. 3a. This was not always possible since common grain boundaries were rare in the electron-transparent regions, which are in Ar ion milled TEM foils relatively small compared to the large grain sizes (of up to *100 lm) of the experimental phases. However, for each oxidized starting glass GEk1b (70.1 % Fe 3? /RFe), whereas samples HPE06-3 and HPE21-3 crystallized from the less oxidized starting glass GEk3 (27.0 % Fe 3? /RFe). Texture and grain sizes vary with the oxidation state of iron in the starting materials (compare a and b) and with temperature (compare a and c; b and d). Note the different scales temperature, at least one garnet clinopyroxene pair measurement could be obtained. In addition, individual grains of garnet and clinopyroxene were analysed within each sample. The raw Fe 3? /RFe ratios for clinopyroxene vary between 8.5 and 26.8 % in the temperature range of this study (Online Resource 1). They are plotted as a function of temperature in Fig. 4a. In cases where both samples from one run could be analysed, the results from GEk1b/ G2Fa2 and GEK3 overlap. This, however, does not represent a reversal determination of the Fe 3? /RFe ratios, since both starting materials approach equilibrium from the same direction. Equilibrium is approached from two directions at 800 and 1,200 C with the starting materials G2Fa2/G1Fa1 (0 % Fe 3? /RFe) and GEk3 (27 % Fe 3? / RFe), and the equilibrium value is probably bracketed. The overlap of the bracket at 800 C lies between 18.8 and 25.5 % Fe 3? /RFe. There is a small gap between 16.5 and 18.8 % Fe 3? /RFe for the 1,200 C experiment. The ranges of the bracket and gap coincide with Fe 3? /RFe ratios measured in clinopyroxenes near garnet clinopyroxene

7 Fig. 3 a TEM BF image of a typical garnet clinopyroxene grain boundary in sample HPE06-3. The regions examined by EELS and EDS are marked by white circles. Variations in contrast arise from interactions between the electron beam and either the sample geometry generating bending contours and thickness fringes or a defect in the centre of the clinopyroxene but they do not indicate chemical heterogeneity. For a selected garnet clinopyroxene pair which is marked by the numbers 1 (clinopyroxene) and 2 (garnet), the corresponding EELS and EDS spectra are shown in b and c, respectively. EELS spectra are treated as described by van Aken et al. (1998) to determine the Fe 3? / RFe ratio from a modified L 2 /L 3 white line intensity ratio. The Fe 3? /RFe ratios obtained by using the universal curve of van Aken et al. (1998) include an absolute error of 5 % grain boundaries (Fig. 4b), and these values are taken as equilibrium values. The Fe 3? /RFe ratios in garnet (Online Resource 2) vary between 8.0 and 21.9 % over the experimental temperature range (Fig. 4c). Brackets can be established between 9.3 and 12.2 % Fe 3? /RFe for 800 C and between 11.4 and 15.6 % Fe 3? /RFe for 1,200 C. The comparison of the bracketed data (Fig. 4c) with the Fe 3? /RFe ratios obtained near garnet clinopyroxene grain boundaries (Fig. 4d) yield identical results within the analytical error for garnets like for clinopyroxenes. This verifies that EELS measurements in the vicinity (B500 nm) of a garnet clinopyroxene grain boundary correspond to equilibrium values with respect to the iron oxidation state in both phases. Therefore, the averages of these measurements (with the standard deviation as the uncertainty) and, where available, the mid-points of the bracket / gap are taken as the equilibrium values with half of the width of the bracket / gap as the uncertainty. The results are listed in Table 4 and plotted as a function of temperature in Fig. 5: the Fe 3? /RFe ratios in clinopyroxene decrease from 22.2 ± 3.4 % at 800 C to 13.3 ± 5.4 % at 1,300 C and these in garnet vary between 10.8 ± 1.5 and 15.4 ± 4.7 %. While Fe 3? /RFe ratios in garnet appear to be constant in the range of 800 1,000 C, they show a slight increase from 1,100 to 1,300 C. At all temperatures, the iron oxidation state in garnet is lower than in clinopyroxene except for 1,300 C, where it is within error the same. Chemical composition analysed by EPMA Electron probe micro-analysis encountered two problems: the first one is that garnet analyses in samples produced at 800 C show unusual high sums ranging between 102 and 103 wt%. However, cations per formula unit (cpfu) on a 12-oxygen basis indicate acceptable stoichiometry, that is, Si close to 3.00 cpfu and cation totals close to The reason for the high sums is probably due to the interaction between the electron beam and a small polishing relief of the sample which results from the different polishing behaviour of the phases caused by their difference in hardness. Small garnet grains next to clinopyroxene may have a higher relief and therefore show an edge effect. Absorption path lengths for some characteristic X-rays may differ from that expected by matrix correction, thus leading to an overestimation of some

8 Fig. 4 Measured Fe 3? /RFe ratios plotted as a function of experimental temperature (T exp ) for a all analyses in clinopyroxene, b analyses in clinopyroxene near garnet clinopyroxene grain boundaries, c all analyses in garnet and d analyses in garnet near garnet clinopyroxene grain boundaries. The brackets and gaps established from reversal experiments at 800 and 1,200 C in a for clinopyroxene and in c for garnet are shown in b and in d for comparison: within the error, a good agreement between analyses performed near garnet clinopyroxene grain boundaries and the bracketed Fe 3? /RFe ratios determined by reversal experiments is observable for both, clinopyroxene and garnet elements. However, this effect is small as indicated by the correct stoichiometry. Since only the stoichiometry is relevant for geothermometry, these analyses were accepted but normalized to 100 wt% to achieve comparability with the analyses from other samples. A serious problem in the analysis of the samples produced at 800 1,100 C and sample HPE16-G1Fa1 is the small grain sizes and/or the numerous inclusions in garnet which led to mixed analyses through the excitation volume of the electron beam. We used CaO versus Al 2 O 3 plots to distinguish between mixed and clean analyses by the compositional vectors towards the endmember compositions. ThisisshownforsampleHPE14-3inFig.6 where the endpoints correspond to clean compositions of quartz (0 wt% Al 2 O 3, 0 wt% CaO), clinopyroxene (highest CaO content, low Al 2 O 3 content) and garnet (highest Al 2 O 3 content, low CaO content). Only those garnet and clinopyroxene analyses which plot at or very close to the corresponding end-points were accepted. These selected compositions are consistent with the results from higher temperatures, as can be seen in Fig. 7a, b, which are diagrams of the molar ratios X Mg = Mg/ (Mg? RFe) and X Ca = Ca/(Ca? Mg? RFe), respectively, plotted against temperature (note that the compositionally different starting materials have to be considered individually). In Fig. 7a, it is apparent that (I) X Cpx Mg decreases and X Mg increases with temperature for the starting material GEk3, (II) X Cpx Mg and X Mg are lower for GEk1b and G1Fa1 at each temperature, in agreement with the lower Mg/(Mg? RFe) ratios of these starting materials (Table 1), and (III) at 800 C, X Cpx Mg differs slightly between the starting materials GEk3 and G2Fa2 despite their almost identical bulk compositions (Table 1). Complete equilibrium may not have been achieved at 800 C in one or both starting materials despite the long run duration of about 8 weeks and the addition of water (see discussion below).

9 Table 4 Experimental results Sample HPE10-1b HPE10-3 HPE06-1b HPE06-3 HPE16-G1Fa1 T ( C), P (GPa) 1,300, 3.0 1,300, 3.0 1,200, 3.0 1,200, 3.0 1,200, 3.0 Starting material GEK1b GEK3 GEK1b GEK3 G1Fa1 Phase (n) (11) Cpx(25) (13) Cpx(17) (7) Cpx(5) (6) Cpx(9) (1) Cpx(1) MgO 8.79(17) 12.26(16) 9.28(15) 12.26(12) 7.86(8) 12.06(4) 8.19(12) 12.42(10) 5.52(4) 10.66(5) Al 2 O (7) 4.79(6) 22.11(13) 4.89(7) 21.60(13) 2.62(5) 21.80(12) 2.90(3) 20.85(7) 3.31(3) CaO 8.20(11) 17.17(10) 8.20(13) 17.65(11) 8.12(8) 18.86(11) 8.40(10) 19.20(7) 11.06(5) 20.95(8) SiO (12) 51.18(14) 40.24(8) 51.26(18) 39.87(13) 51.89(22) 39.76(25) 52.05(23) 39.94(9) 51.71(10) FeO tot 22.02(26) 14.88(16) 21.22(12) 14.19(10) 23.27(11) 14.58(4) 22.49(18) 13.58(10) 23.64(8) 14.11(6) Total (18) (16) (25) (29) (19) (31) (15) (23) cpfu a Mg 0.985(18) 0.686(8) 1.038(15) 0.685(5) 0.891(7) 0.679(1) 0.927(13) 0.696(5) Al 1.952(5) 0.212(3) 1.955(8) 0.216(3) 1.936(10) 0.117(2) 1.950(10) 0.128(2) Ca 0.661(9) 0.690(4) 0.659(11) 0.708(5) 0.662(7) 0.763(5) 0.683(9) 0.773(4) Si 3.020(8) 1.920(2) 3.019(6) 1.919(2) 3.032(9) 1.961(2) 3.019(14) 1.956(4) RFe 1.385(17) 0.467(5) 1.331(7) 0.444(4) 1.480(7) 0.461(1) 1.428(13) 0.427(4) Total 8.004(6) 3.974(2) 8.003(4) 3.973(2) 8.001(5) 3.981(2) 8.006(11) 3.980(3) Fe 3? /RFe c 15.4 ± ± ± ± ± ± ± ± ± ± 1.6 K D 2.06 ± ± ± ± ± 0.03 K D 2.01 ± ± ± ± ± 0.11 X Ca ± ± ± ± ± X Ca ± ± ± ± ± T calc (total Fe) d ( C) 1,310 1,343 1,193 1,188 1,143 T calc (Fe 2? ) d ( C) 1,360 1,394 1,188 1,182 1,140 Sample HPE14-1b HPE14-3 HPE17-3 HPE21-3 HPE21-G2Fa2 T ( C), P (GPa) 1,100, 3.0 1,100, 3.0 1,000, , , 2.5 Starting material GEK1b GEK3 GEK3 GEk3 G2Fa2 Phase (n) (1) Cpx(6) (3) Cpx(7) (2) Cpx(3) (1) b Cpx(2) (3) b Cpx(1) MgO 6.90(4) 11.90(5) 7.74(3) 12.40(5) 7.40(8) 12.98(13) 6.47(4) 14.49(22) 5.86(15) 13.12(6) Al 2 O (7) 2.26(9) 21.07(28) 2.25(8) 21.61(18) 1.67(13) 20.90(7) 0.66(1) 21.26(27) 1.30(2) CaO 8.70(5) 19.40(3) 8.38(12) 20.03(10) 8.41(10) 21.19(9) 7.22(4) 22.11(0) 7.82(34) 21.85(8) SiO (9) 52.48(5) 40.35(52) 52.85(31) 39.42(20) 52.81(14) 39.13(9) 53.07(4) 39.02(20) 53.38(10) FeO tot 24.32(8) 14.71(13) 23.64(20) 13.18(17) 24.27(11) 11.99(7) 26.27(9) 10.20(7) 26.05(62) 11.84(6) Total (13) (26) (29) (11) (7) (18)

10 Table 4 continued Sample HPE14-1b HPE14-3 HPE17-3 HPE21-3 HPE21-G2Fa2 T ( C), P (GPa) 1,100, 3.0 1,100, 3.0 1,000, , , 2.5 Starting material GEK1b GEK3 GEK3 GEk3 G2Fa2 Phase (n) (1) Cpx(6) (3) Cpx(7) (2) Cpx(3) (1) b Cpx(2) (3) b Cpx(1) cpfu a Mg (2) 0.875(6) 0.691(4) 0.841(9) 0.723(6) (10) 0.678(17) Al (4) 1.883(28) 0.099(4) 1.942(18) 0.073(6) (0) 1.946(22) Ca (2) 0.681(11) 0.801(5) 0.687(9) 0.848(5) (2) 0.651(27) Si (2) 3.060(29) 1.974(6) 3.006(11) 1.973(3) (2) 3.030(17) RFe (4) 1.499(16) 0.412(5) 1.547(5) 0.374(2) (3) 1.692(44) Total (1) 7.998(16) 3.977(5) 8.023(2) 3.991(1) (3) 7.997(6) Fe 3? /RFe c 11.2 ± ± ± ± ± ± ± ± ± ± 3.4 K D 2.85 ± ± ± ± ± 0.18 K D 3.20 ± ± ± ± ± 0.33 X Ca ± ± ± ± ± X Ca ± ± ± ± ± T calc (total Fe) d ( C) 1,125 1, T calc (Fe 2? ) d ( C) 1,084 1, Values in parentheses correspond to the standard deviation (in terms of least digits cited) of n EPMA measurements, except for n = 1 where the 1r-error of the counting statistics is given Molar ratios: K D = (RFe/Mg) /(RFe/Mg) Cpx, K D = (Fe2? /Mg) /(Fe 2? /Mg) Cpx, X Ca a = (Ca/(Ca? Mg? RFe)), X Ca = (Ca/(Ca? Mg? Fe2? )) Cations per formula unit (cpfu) calculated on the basis of 12 O-atoms and 6 O-atoms for garnet and clinopyroxene, respectively, with RFe taken as Fe 2? b c d Normalized to 100 wt% Equilibrium oxidation states obtained by the method described in the text on the basis of oxidation states determined by EELS after van Aken et al. (1998) Estimates of equilibration temperatures using the calibration by Krogh (1988)

11 Fig. 5 Equilibrium Fe oxidation states obtained for clinopyroxene (Cpx) and garnet () shown as a function of experimental temperature (T exp ). Data points at 800 and 1,200 C correspond to the mid-points of the brackets / gaps in Fig. 4a, c for clinopyroxene and garnet, respectively, with half of the width of a bracket / gap as the uncertainty. At all other temperatures, the equilibrium oxidation states correspond to the averaged Fe 3? /RFe ratios measured near garnet clinopyroxene grain boundaries and the uncertainty is related to the standard deviation. Solid lines fitted by eye indicate the variations of the Fe oxidation states upon temperature The following systematic trends are observable in Fig. 7b: (I) at constant bulk composition, X Cpx Ca decreases with increasing temperature. (II) X Ca is practically independent of temperature in agreement with earlier findings in an eclogitic system (Råheim and Green 1974) and the system CaO MgO Al 2 O 3 SiO 2 (CMAS) with coexisting orthopyroxene, Fig. 7 Plots of the molar ratios X Mg (a) and X Ca (b) versus experimental temperature (T exp ) for clinopyroxene (Cpx) and garnet (). Each symbol indicates an analysis Fig. 6 CaO versus Al 2 O 3 plot of EPMA raw data of sample HPE14-3. This figure illustrates the method used to discriminate mixed analyses. Only analyses with the highest CaO and low Al 2 O 3 content and analyses with the highest Al 2 O 3 and low CaO content were accepted as clean clinopyroxene (Cpx) and garnet () compositions, respectively (grey circles). All other data points (black squares) correspond to mixed analyses of garnet clinopyroxene, garnet/ clinopyroxene quartz(qz) or garnet clinopyroxene quartz and were discarded clinopyroxene and garnet (e.g., Brey et al. 1986). (III) The starting material G1Fa1 with a significantly higher Ca/ (Ca? Mg? RFe) ratio of *0.42 compared to the other starting materials used at 1,200 C with a ratio of 0.35 also yields Ca-richer clinopyroxenes and garnets. Where several analyses were available, a tight clustering of the compositional parameters illustrated in Fig. 7a, b can be observed for each sample, indicating good homogeneity. Consequently, the averages of clinopyroxene and garnet analyses were used to calculate the distribution coefficients K D and KD as well as X Ca (Eqs. 3, 2, 4) and XCa ; the latter being defined as XCa ¼ðCa=ðCa þ Mg þ Fe 2þ ÞÞ : ð5þ and X Ca The Fe 2? concentrations used to determine KD were obtained by combining the Fe 3? /RFe ratios with compositional data according to

12 Fe 2þ ¼ð100 Fe 3þ =RFeÞRFe; where the Fe 3? /RFe ratio is given in %, and Fe corresponds to the molar total iron content determined by EPMA. Experimental results including chemical composition, equilibrium oxidation states, thermometric variables and calculated equilibration temperatures are listed in Table 4. K D values obtained at a particular temperature from different starting materials with similar Ca content agree within the stated errors, except for the run at 800 C. In this case, the distribution coefficients differ by about 11 % which may be attributable to uncertainties in the equilibrium values for the clinopyroxenes as stated above. For thermometric purposes, sufficiently enough equilibration can also be assumed for the samples HPE21-3 and HPE21- G2Fa2: this is indicated by temperature estimates (using total Fe) reproducing the experimental temperature for all samples within ±60 C (see below), which is suggested to be the error of garnet clinopyroxene Fe Mg geothermometry (Ravna and Terry 2004). At 1,200 C, the Ca-richer starting material G1Fa1 gives a higher K D of 3.24, as compared to the Ca-poorer starting materials GEk1b and GEk3 with K D s of 2.45 and 2.51, respectively, consistent with previous results on the influence of Ca on the Fe Mg distribution coefficient (e.g., Ellis and Green 1979). At constant bulk composition (e.g., GEk3 or GEk1b), the KD and K D values are identical within error at 1,300 C. They increasingly deviate from a 1:1 relationship with decreasing temperature, with KD systematically becoming higher than corresponding K D values (Fig. 8). XCa is higher than X Ca and is related to the latter by the following equation, which is obtained in a XCa versus X Ca plot by linear regression through the origin (Fig. 9): XCa ¼ð1:062 0:003ÞXCa ; R2 ¼ 0:997 ð7þ Calculated equilibration temperatures ð6þ Since the influence of Mg on Fe Mg distribution between garnet and clinopyroxene is suggested to have only a minor effect for 0.17 \ X Mg \ 0.54 (Krogh 1988) and all samples in this study exhibit values of X Mg within this range (Fig. 7a), the Mg effect on K D can be neglected. We therefore used Krogh s (1988) calibration, which is given by T calc ¼ 6; 173ðX Ca Þ2 þ 6; 731XCa þ 1; 879 þ 100 P ln K D þ 1: ; ð8þ where T calc is the temperature estimate in C, P is the pressure in GPa, and X Ca and K D are defined according to Eqs. (4) and (3), respectively. If only Fe 2? is considered, the equation changes to Fig. 8 Comparison of K D and K D values. Error bars correspond to propagated uncertainties Fig. 9 X Ca T calc ¼ plotted as a function of X Ca. Error bars indicate propagated uncertainties. The solid line corresponds to a linear regression forced through the origin. The stated uncertainty corresponds to the standard error. Symbols are as in Fig. 8 6; 173ðX Ca Þ2 þ 6; 731XCa þ 1; 879 þ 100 P ln KD þ 1: ; ð9þ with the variables as in Eq. (8) and XCa and KD in Eqs. (5) and (2). Temperature estimates with Eq. (8) reproduce the experimental temperatures within ±60 C without systematic deviations (Fig. 10a). If Fe 2? is used, that is, Eq. (9) is applied, the experimental temperature is systematically underestimated in the range of 800 1,200 C by an average of 33 C and overestimated at 1,300 C by an average of 77 C (Fig. 10b).

13 Since the thermometers were always calibrated using lnk D and X Ca according to Eq. (8), it is apparent that the systematic deviations are related to the differences between ln KD and lnk D, and XCa and X Ca. It is, however, not straightforward to predict the influence of measured Fe 2? on temperature estimates, since ln KD and X Ca are not independent from each other. They are both based on the Fe 2? concentrations in garnet, and they correlate differently with temperature, that is, ln KD is inversely proportional and XCa is by a quadratic term proportional to temperature. Within the investigated temperature range, the difference between XCa and X Ca is constant and positive, and a constant temperature overestimate is implied. Hence, the observed underestimation of the experimental temperatures between 800 and 1,200 C must be mainly due to the difference between ln KD and lnk D. Since ln KD may be defined as 0 1 Fe 2þ =RFe RFe ln KD ¼ ln B Mg Cpx A ð10þ Fe 2þ =RFe RFe Mg Fig. 10 Difference between temperature estimate (T calc ) and experimental temperature (T exp ) shown as a function of experimental temperature using total Fe (a) and Fe 2? (b). All temperature estimates were obtained by applying the calibration of Krogh (1988). Symbols are as in Fig. 8 Discussion Estimation of equilibration temperature using total Fe and Fe 2? in the system CFFMAS Use of total Fe in geothermometry The very good reproduction of our experimental temperatures by the use of total Fe is not surprising, because our experimental procedures, especially with the use of internal graphite containers, are very similar to earlier experiments on which Krogh s (1988) calibration was based. It merely indicates that the oxidation state of Fe in our and in earlier experiments was the same. Use of Fe 2? in geothermometry The experimental temperatures are systematically underestimated with this thermometer at T B 1,200 C and overestimated at 1,300 C when only the measured Fe 2? is used in the calculations. Why do these systematic deviations exist and why are they relatively small, despite the significantly high Fe 3? /RFe ratios measured in the experimental garnets and clinopyroxenes? which can be rewritten as! ln KD ¼ ln ðfe2þ =RFeÞ ðfe 2þ =RFe) Cpx þ ln K D ; ð11þ it is obvious that the difference between ln KD and lnk D corresponds to the natural logarithm of the Fe 2? /RFe ratio in garnet divided by the Fe 2? /RFe ratio in clinopyroxene, which we define for easier further use as lnb. Lnb can be obtained by the measured Fe 3? /RFe ratios as follows! ln b ¼ ln KD ln K ðfe 2þ =RFeÞ D ¼ ln ðfe 2þ =RFeÞ Cpx! 100 ðfe 3þ =RFeÞ ¼ ln 100 ðfe 3þ =RFeÞ Cpx ; ð12þ where Fe 2? /RFe and Fe 3? /RFe ratios are both given in %. This relationship between the Fe 3? /RFe ratios and the difference of both distribution coefficients has been similarly expressed for the garnet orthopyroxene thermometer by Nimis and Grütter (2010). Because for a garnet clinopyroxene thermometer, the temperature is inversely proportional to lnk D, it is evident that temperature calculations using Fe 2? are as follows: a. overestimates if lnb \ 0, because ln KD \ lnk D b. accurate if lnb = 0, because ln KD = lnk D c. underestimates if lnb [ 0, because ln KD [ lnk D. Values of lnb computed from equilibrium oxidation states in garnet and clinopyroxene (Table 4) according to Eq. (12) are plotted as a function of 1/T in Fig. 11. Lnb can

14 be fitted as a function of x = 10,000/T (T in K) by using a sigmoidal Boltzmann function: A B ln b ¼ þ B; ð13þ 1 þ e ðx x 0Þ=dx with A = , B = , x 0 = and dx = (R 2 = ). At 800 1,200 C, lnb is positive which explains the observed underestimation of the experimental temperatures in this range. At 1,300 C, lnb has a negative value which corresponds to the overestimation at this temperature. It can also be seen that lnb is constant between 800 and 1,100 C and decreases from 1,100 C onwards. The decrease in lnb is a result of the substantially decreasing Fe 3? /RFe ratios in clinopyroxene, while in garnet, the oxidation state only increases slightly with temperature (Fig. 5). In the investigated temperature range, the oxidation state in garnet (85 89 % Fe 2? /RFe) is only slightly different to that in clinopyroxene (76 87 % Fe 2? /RFe) which means that the (Fe 2? /RFe) /(Fe 2? /RFe) Cpx ratios are close to unity, resulting in lnb values close to zero. As a consequence of this partially compensating effect of oxidation state ratios in garnet versus clinopyroxene on ln KD ; the difference between ln KD and lnk D is relatively small. Hence, temperature estimates using Fe 2? are within ±50 C identical to the ones using total Fe (Table 4) and reproduce all experimental temperatures within ±100 C (Fig. 10b) despite the mentioned systematic deviations. Comparison of ln K D versus 1/T and lnk D versus 1/T plots: implications for garnet clinopyroxene geothermometry in the system CFFMAS Figure 12 demonstrates that lnb is not linearly dependent on 1/T. Due to the fact that in all previous works, a linear Fig. 11 Values of lnb shown as a function of inverse temperature. Error bars indicate propagated uncertainties. The solid line corresponds to a sigmoidal fit (R 2 = , fitting parameters are given in the text) used to clarify the variation of lnb with temperature correlation between lnk D and 1/T has been observed, ln K D most probably has to show a nonlinear dependence on 1/T. To verify this conclusion, lnk D versus 1/T and ln K D versus 1/T plots are established according to the following procedure: 1. K D values from Table 4 are normalized, where necessary, to a pressure of 3.0 GPa by using the pressure correction given in Ellis and Green (1979). 2. lnk D (P = 3.0 GPa) values are then normalized to X Ca = by using Eq. (10) of Krogh (1988). 3. If more than one data point at the same temperature is available, lnk D (P = 3.0 GPa, X Ca = 0.200) values are averaged, and plotted as a function of inverse temperature. 4. KD values from Table 4 are treated in the same way as described above. However, to allow a direct comparison, ln KD has to be normalized to a value of XCa = 0.212, which corresponds to X Ca = according to Eq. 7). The plots of averaged lnk D (P = 3.0 GPa, X Ca = 0.200) and ln KD (P = 3.0 GPa, X Ca = 0.212) versus 1/T are shown in Fig. 12: lnk D clearly plots on a straight line where linear regression yields ln K D ð3:0 GPa; XCa ¼ 0:200Þ ð3; Þ ¼ ð1:555 T 0:110Þ; R 2 ¼ 0:995; ð14þ where the temperature T is given in K and the stated uncertainty corresponds to the standard error. Our fit is in good agreement with the one by Krogh (1988) (Fig. 12), again indicating good consistency between our experiments and the ones from which the calibration of Krogh (1988) has been established. Comparing ln KD with lnk D, one can observe that the former is consistently higher than the latter in the range of 800 1,100 C. From 1,100 to 1,300 C, a decrease of ln KD relative to lnk D can be seen, yielding a lower value for ln KD than for lnk D at 1,300 C. According to Eqs. (11) and (12), ln KD can be described as a function of 1/T (T given in K) by adding Eqs. (13) and (14) to give ln KD ð3:0 GPa; X Ca ¼ 0:212Þ 0:2054 3; 504 ¼ þ 1 þ eð10;000=t 6:7051Þ=0:2715 T 1:4193: ð15þ From Fig. 12, it is evident that ln KD is, at least in the range of 1,100 1,300 C, not linearly dependent on

15 of XCa of 0.21 B X Ca B 0.32 [corresponding to a range of X Ca of 0.20 B X Ca B 0.30 according to Eq. (7)] and an oxygen fugacity similar to that imposed by the graphite capsule. This is supported by the fact that our temperature estimates using Fe 2? are within ±50 C identical to the ones using total Fe. General implications for garnet clinopyroxene geothermometry Fig. 12 Averaged lnk D (P = 3.0 GPa, X Ca = 0.200) and ln KD (P = 3.0 GPa, X Ca = 0.212) plotted as a function of inverse temperature, where K D and KD correspond to the (RFe/Mg) /(RFe/ Mg) Cpx and (Fe 2? /Mg) /(Fe 2? /Mg) Cpx ratio, respectively. Data at 800 C are corrected for pressure using the correction given in Ellis and Green (1979). Before averaging, values of lnk D and ln KD were normalized to X Ca = and a corresponding XCa = 0.212, respectively, according to Krogh (1988). The linear fit of lnk D (P = 3.0 GPa, X Ca = 0.200) on 1/T by Krogh (1988) is shown for comparison. The fitting parameters for lnk D (this study) and ln KD (linear and nonlinear) on 1/T are given in the text 1/T. The reason for this deviation is not clear. A detailed crystal-chemical consideration of the clinopyroxenes and garnets of this study, especially with respect to Fe 3? incorporation, could give the answer but is beyond the aim of this paper. Since the deviation from ideal behaviour is only pronounced at 1,300 C and appears to be negligible at 1,100 1,200 C, the relationship between ln KD and 1/T may be approximated by a linear fit in the range of 800 1,200 C (Fig. 12) with Eq. (16): ln KD ð3:0 GPa; X Ca ¼ 0:212; 1; 073 K T 1; 473 KÞ ð3; Þ ¼ ð1:583 T 0:052Þ; R 2 ¼ 0:999; ð16þ which is within the standard errors in agreement with Eq. (15) Theoretically, Eq. (15) or for the temperature range 800 1,200 C also Eq. (16) might be combined with the effect of pressure and Ca on ln KD to give a thermometer which is solely based on Fe 2?. However, since the temperature estimates according to Krogh (1988) using Fe 2? only exhibit a small, averaged systematic error of -33 C at temperatures between 800 and 1,200 C, and?77 C at 1,300 C, it becomes apparent that a recalibration of the thermometer in the system CFFMAS considering Fe 2? is not explicitly necessary for 800 1,300 C, *3 GPa, a compositional range In contrast to the experiments in CFFMAS of this study, natural samples may show large differences in temperature estimates depending on how Fe is treated as mentioned in the introduction. The important question is as follows: when is the equilibration temperature of a sample accurately determined, overestimated or underestimated? Use of total Fe in geothermometry For the Fe 2? Mg olivine clinopyroxene thermometer of Brey and Köhler (1990), Luth and Canil (1993) predicted that the equilibration temperature is accurate if the Fe 3? / RFe ratios in the sample and in the phases used to calibrate the thermometer are similar. If this is not the case, the estimate will exhibit an error which will be a function of the difference between the Fe 3? /RFe ratios in the pyroxenes of the experiments relative to those in the specimens under consideration (Luth and Canil 1993). In garnet clinopyroxene thermometry, this is more complicated since not only clinopyroxene but also garnet may exhibit significant Fe 3? /RFe ratios. In the following section, we derive the conditions at which the thermometer will work accurately or will yield a systematic error: The correlation between lnk D using total Fe and ln K D considering Fe 2? is given by combining and rearranging Eqs. (11) and (12), defined for the sample by ln K D ðsampleþ ¼ln KD ðsampleþ ln bðsampleþ; ð17þ and for the experimental charges by ln K D ðexp.þ ¼ln KD ðexp.þ ln bðexp.þ: ð18þ Since the application of the thermometer requires per se that for the same pressure, temperature and Ca content, ln KD in the experiment and in the sample are identical expressed as ln KD ðexp.þ ¼ln K DðsampleÞ for P; T; X Ca ðexp.þ ¼ P; T; XCa ðsampleþ; Equations (17) and (18) can be combined to ð19þ