Eclogite thermobarometry: The consistency between conventional thermobarometry and forward phase‐equilibrium modelling

Eclogite thermobarometry is crucial for constraining the depths and temperatures to which oceanic and continental crust subduct. However, obtaining the pressure and temperature (P–T) conditions of eclogites is complex as they commonly display high‐variance mineral assemblages, and the mineral compositions only vary slightly with P–T. In this contribution, we present a comparison between two independent and commonly used thermobarometric approaches for eclogites: conventional thermobarometry and forward phase‐equilibrium modelling. We assess how consistent the thermobarometric calculations are using the garnet–clinopyroxene–phengite barometer and garnet–clinopyroxene thermometer with predictions from forward modelling (i.e. comparing the relative differences between approaches). Our results show that the overall mismatch in methods is typically ±0.2–0.3 GPa and ±29–42°C although differences as large as 80°C and 0.7 GPa are possible for a few narrow ranges of P–T conditions in the forward models. Such mismatch is interpreted as the relative differences among methods, and not as absolute uncertainties or accuracies for either method. For most of the investigated P–T conditions, the relatively minor differences between methods means that the choice in thermobarometric method itself is less important for geological interpretation than careful sample characterization and petrographic interpretation for deriving P–T from eclogites. Although thermobarometry is known to be sensitive to the assumed XFe3+ of a rock (or mineral), the relative differences between methods are not particularly sensitive to the choice of bulk‐rock XFe3+, except at high temperatures (>650°C, amphibole absent) and for very large differences in assumed XFe3+ (0–0.5). We find that the most important difference between approaches is the activity–composition (a–x) relations, as opposed to the end‐member thermodynamic data or other aspects of experimental calibration. When equivalent a–x relations are used in the conventional barometer, P calculations are nearly identical to phase‐equilibrium models (ΔP < 0.1). To further assess the implications of these results for real rocks, we also evaluate common mathematical optimizations of reaction constants used for obtaining the maximum P–T with conventional thermobarometric approaches (e.g. using the highest aGrs2 × aPrp in garnet and Si content in phengite, and the lowest aDi in clinopyroxene). These approaches should be used with caution, because they may not represent the compositions of equilibrium mineral assemblages at eclogite facies conditions and therefore systematically bias P–T calculations. Assuming method accuracy, geological meaningful Pmax at a typical eclogite facies temperature of ~660°C will be obtained by using the greatest aDi, aCel, and aPrp and lowest aGrs and aMs; garnet and clinopyroxene with the lowest Fe2+/Mg ratios may yield geological meaningful Tmax at a typical eclogite facies pressure of 2.5 GPa.

further assess the implications of these results for real rocks, we also evaluate common mathematical optimizations of reaction constants used for obtaining the maximum P-T with conventional thermobarometric approaches (e.g. using the highest aGrs 2 Â aPrp in garnet and Si content in phengite, and the lowest aDi in clinopyroxene).These approaches should be used with caution, because they may not represent the compositions of equilibrium mineral assemblages at eclogite facies conditions and therefore systematically bias P-T calculations.Assuming method accuracy, geological meaningful P max at a typical eclogite facies temperature of $660 C will be obtained by using the greatest aDi, aCel, and aPrp and lowest aGrs and aMs; garnet and clinopyroxene with the lowest Fe 2+ /Mg ratios may yield geological meaningful T max at a typical eclogite facies pressure of 2.5 GPa.
K E Y W O R D S conventional, thermobarometry, eclogite, high pressure, phase-equilibrium modelling, thermobarometry, uncertainty
Accurate forward phase-equilibrium modelling depends on the appropriate choice of sample, determination of a bulk composition (including assessment of mineral fractionation, especially garnet, and the appropriate scale of equilibrium), petrographic interpretation of parageneses, measurement of mineral compositions and the thermodynamic data used for calculation (equation of state, mineral end-member thermodynamic data and activity-composition (a-x) relationships for solid solutions).Accurate conventional thermobarometry depends on similar factors, although the bulk-rock compositions need not be known, and the interpretation of equilibrium mineral composition sets is more crucial.Estimates of P-T may differ between methods because of any (or all) of these variables, thereby influencing geological interpretations.The limitations of method comparisons for natural samples are that differences might be because of a combination of many variables (as described above), and ultimately some decision needs to be made as to which result is best.Given the complexity and impact of this issue, it is worth separating and quantifying the magnitude of uncertainties from individual sources.For example, there have been several recent assessments on how the assumed length scale of equilibrium and associated estimate of the reactive bulk composition influence P-T estimation (Guevara & Caddick, 2016;Lanari & Engi, 2017;Palin et al., 2016).Here, the objective of our work is to assess a single dimension of thermobarometric uncertainty as applied to eclogites.The motivating question for this paper is: If we did everything correctly-choice of sample, appropriate determination of bulk composition, petrographic interpretation, and assessment of equilibrium, and else-how different would mineral composition-based P-T estimates be using common forward-and inversemodelling approaches?
To answer this question, we compare the garnet-clinopyroxene-phengite barometer (calibration of Ravna & Terry, 2004) and garnet-clinopyroxene thermometer (calibration of Ravna, 2000) with forward model predictions using the most recent thermodynamic dataset and a-x relations for modelling phase equilibria of mafic rocks ('ds62';Holland & Powell, 2011;Green et al., 2016) and its predecessor (ds55; Holland & Powell, 1998, updated in 2004).We show that the differences between calculated P-T conditions using both approaches are relatively low for medium-to high-T eclogite facies conditions (>225 C/GPa), meaning that the choice in thermobarometric method itself is less important for geological interpretation than all the other uncertainties related to such methods for most eclogite facies samples.By contrast, differences in results can be high for low-T eclogite (<225 C/GPa): up to ΔT = 80 C and ΔP = 0.7 GPa.We further assess: (a) the effect of X Fe 3+ [X Fe 3+ = Fe 3+ /(Fe 2+ + Fe 3+ )] in the consistency between approaches, (b) the commonly used approaches to obtain peak P-T conditions of eclogites, and (c) the a-x parameters of the considered phases that yield the maximum P-T (P-T max ) conditions.Finally, we put our findings in the context of other uncertainties that affect conventional thermobarometry and forward phase-equilibrium modelling such that more informed decisions can be made in the application of eclogite thermobarometry to real rocks.

| Conventional thermobarometry of eclogites
In this section, we outline the different methodologies used to assess the consistency between the P-T calculations obtained via conventional thermobarometric methods with respect to predictions of forward modelling.
For conventional thermobarometric calculations, we used the calibration of Ravna and Terry (2004) for the garnet-clinopyroxene-phengite barometer and the calibration of Ravna (2000) for the garnet-clinopyroxene thermometer.
The garnet-clinopyroxene-phengite barometer relies on the net transfer reaction among garnet, clinopyroxene and phengite (mineral abbreviations follow Warr, 2021): where the equilibrium constant (K 1 ) of this reaction can be expressed as For the P calculations, we use the activity-composition (a-x) relations considered in the original Ravna and Terry (2004) calibration for garnet (non-ideal mixing model; Ganguly et al., 1996), clinopyroxene (non-ideal mixing model; Holland, 1990) and white mica (ideal mixing model; Holland & Powell, 1998).These a-x relations are given in the Appendix S1.For details of the method, the reader is referred to Ravna and Terry (2004) and Appendix S1.
On the other hand, the garnet-clinopyroxene thermometer (Ravna, 2000) relies on the exchange of Fe 2+ and Mg between garnet and clinopyroxene.The equilibrium Fe 2+ À Mg distribution coefficient (K D ) can be expressed as In addition to the K D , the thermometer uses the garnet's grossular and spessartine contents as well as its Mg# [Mg# = Mg/(Mg + Fe 2+ )].All these compositional parameters are calculated by stoichiometry rather than explicit formulation of end-member activities in an a-x relation.For details of this method, the reader is referred to Ravna (2000), Ravna and Paquin (2003) and Appendix S1.

| Forward phase-equilibrium modelling
Phase equilibria were calculated using Theriak-Domino (de Capitani & Brown, 1987;de Capitani & Petrakakis, 2010) The first set of calculations use the internally consistent thermodynamic dataset ds62 (Holland & Powell, 2011) and the a-x relations for solid-solution phases from Green et al. (2016) and as used in Palin et al. (2016); a second set of calculations were carried out using the ds55 thermodynamic dataset (Holland & Powell, 1998; August update 2004 update) and the a-x relations from Diener and Powell (2012) and as used in Palin and White (2016).
For the comparison, we considered the eclogite facies metamorphism of an oxidized normal mid-ocean ridge basalt (N-MORB).We use the mean N-MORB of Gale et al. (2013).Aqueous fluid was considered pure H 2 O and in excess in the explored P-T window.For initial comparisons, we set the X Fe 3+ to 0.36, which correspond to a value representative of exhumed eclogites (Rebay et al., 2010).The modelled whole-rock composition is given in Table 1.We then determine the sensitivity of the results to this choice of X Fe 3+ , by calculating T-X Fe 3+ and P-X Fe 3+ diagrams as well.

| Comparison methodology
To assess the consistency of the P-T calculations between conventional thermobarometric methods with predictions of forward phase-equilibrium modelling (consistency is used in this paper to refer to how similar P-T conditions are between methods; it is not an assessment of accuracy), we used the following methodology: (a) first, we calculated a P-T phase diagram; (b) second, we extracted the composition of garnet, clinopyroxene and white mica at a given P-T point (refer hereafter as 'reference P and T'); (c) third, we used such compositions to calculate a P using the garnet-clinopyroxene-phengite barometer, and then a value of T using the garnetclinopyroxene thermometer.The barometer and thermometer require a known T and P, respectively, as input.Thus, when P is calculated, we use the reference T as input, and vice versa, when T is calculated, the reference P is used.This was carried out to avoid any inherited dependence between barometric and thermometric calculations.(d) Then, we compared the deviation of the calculated P and T from the reference P and T (i.e. the P-T point where the composition was extracted from the phase-equilibrium diagram), and reported the deviation of the calculated P-T from the reference P-T as ΔP and ΔT; (e) finally, we repeated such procedure along a grid of 2500 P-T points within the explored P-T window (every 5 C and 0.03 GPa).The significance of these comparisons is the difference in the calculated P-T conditions one would obtain from conventional thermobarometers and intersections of mineral compositional isopleths from the phase-equilibrium calculations using the same measured mineral compositions.
The input Fe 2+ and Fe 3+ contents in garnet, omphacite and phengite for conventional thermobarometry were used exactly as calculated by the a-x relations in the phase-equilibrium models (Diener & Powell, 2012;Green et al., 2016;White et al., 2007White et al., , 2014)).In the application of thermobarometry to real rocks, Fe 2+ /Fe 3+ must be estimated from measured mineral compositions, which can lead to additional systematic errors up to ±100 C in the calculated temperatures (Carswell & Zhang, 1999;Proyer et al., 2004;Ravna & Paquin, 2003;Štípsk a & Powell, 2005).
We note that in this work, we are not interpreting the mineral compositions obtained by the forward phaseequilibrium modelling as accurate (or inaccurate) reproduction of the compositions observed in the natural eclogites.Modelled mineral compositions are just used as input (taken as 'knowns') for the conventional thermobarometers.Regardless of how realistic the modelled mineral compositions are, if the conventional thermobarometers and forward phase modelling are relatively consistent, then P-T calculations should be similar (i.e.small ΔP and ΔT).Moreover, we want to note that even if both approaches are somehow consistent, it does not necessarily mean that the obtained P-T calculations are accurate.
In sections and subsections below, we focus on the differences in thermobarometric results, mineral compositions and mineral end-member activities near 2.5 GPa and 660 C.These conditions are the 'mean eclogite facies P-T conditions', which we calculated from P-T conditions of global eclogite facies lithologies reported by Penniston-Dorland et al. (2015); this database include oceanic and continental HP and UHP rocks.

| CONSISTENCY OF CONVENTIONAL THERMOBAROMETRY WITH FORWARD PHASE-EQUILIBRIUM MODELLING
The eclogite facies assemblage, that is, the plagioclasefree garnet + clinopyroxene stability fields, is located at >1.5-1.6 GPa for the investigated temperature range of 550-800 C (Figure 1a).Amphibole is stable through most of the modelled conditions within the lawsonite and epidote stability fields, and becomes unstable at higher P-T (>2.05 GPa and >640 C; Figure 1a).Because of the imposed X Fe 3+ (0.36, Rebay et al., 2010; compared to fresh MORB: 0.10-0.16,Berry et al., 2018;Cottrell & Kelley, 2011;Zhang et al., 2018), epidote-clinozoisite solid solution (referred to as 'epidote' for simplicity) is stable at relatively higher P-T conditions than sometimes considered.At the mean eclogite facies P-T conditions for the modelled rock, that is, 2.5 GPa and 660 C, the mineral assemblages are characterized by garnet + clinopyroxene + epidote + phengite with minor kyanite, rutile and quartz stability field (Figure 1b).

| Pressure comparison
Using the mineral compositions retrieved at different P-T points in the forward model, we obtained the lnK 1 using equation ( 2).The obtained value of lnK 1 (lnK 1 = À2 to À11) is always negative and increases with P in the explored P-T window (Figure 2a).The lnK 1 contours have shallow, positive slopes outside the amphibole stability fields; within the amphibole stability fields, lnK 1 contours have a stronger positive temperature dependence (Figure 2a).The calculated garnet-clinopyroxene-phengite P contours are parallel to lnK 1 , as expected (Figure 2b).For the P-T range investigated, the garnet-clinopyroxenephengite barometer estimates $0.1-0.7 GPa higher P than the mineral compositions in the forward phaseequilibrium modelling.The difference in pressure estimated from the two methods (ΔP) decreases as T increases (Figure 2c).The area with the smallest P deviation is at $2.0 GPa and >650 C, close to the kyanite and amphibole stability boundaries; by contrast, the largest P deviation occurs at low T and P > 2.5 GPa (Figure 2c), where amphibole (near the transition from Na-dominated to Ca-dominated amphibole) and lawsonite are stable.At the average eclogite P-T conditions of 2.5 GPa and 660 C, ΔP is $0.25 GPa (Figure 2c).

| Temperature comparison
We obtained the lnK D using Equation (3) and the mineral compositions retrieved at different P-T points.The value of lnK D is always positive (1.8-2.5) and decreases as T increases (Figure 3a).The lnK D contours have steep, positive slopes but are shallower near the limits of amphibole and kyanite stability (Figure 3a).The calculated garnet-clinopyroxene T are mostly T dependent, as expected (Figure 3b).The highest calculated T (i.e.$850 C) is obtained at the highest T and lowest P part of the diagram, whereas the lowest T is calculated at the highest P and lowest T part (Figure 3b).The pattern of the calculated T contours differs from the lnK D contours as the kyanite and amphibole stability boundaries importantly affect their slope, changing it from positive within the amphibole stability field (no kyanite) and negative in the kyanite stability field (no amphibole).In general, calculated T is lower than predicted at higher P-T and higher than predicted at lower P-T.The largest T deviation (ΔT = À80 C) is where lawsonite is stable without amphibole at HP conditions.The ΔT ranges from À80 to +60 C for the considered P-T window (Figure 3c) but is mostly ≤40 C. The contours of ΔT apparently parallel amphibole stability.At 2.5 GPa and 660 C, ΔT is $ À 45 C (Figure 3c).

| Deviation from the reference P-T conditions
Figure 4a compares the deviation of the calculated P from the reference P from 1.5 to 3.0 GPa at $660 C. The calculated pressure from the garnet-phengiteclinopyroxene barometer is consistently higher than the reference pressure from the phase-equilibrium model (Figure 4a), even considering an uncertainty of ±0.2 GPa, as commonly cited (Cuthbert et al., 2000;Ravna & Terry, 2004;Waters & Martin, 1993).
A comparison between the calculated T and the reference T from 550 to 800 C at $2.5 GPa is shown in Figure 4b.The garnet-clinopyroxene thermometer overestimates the reference T at <570 C and underestimates T at >570 C (Figure 4b); yet all temperatures are within an uncertainty of ±60 C (a commonly cited uncertainty for the thermometer; Ravna, 2000;Ravna & Paquin, 2003;Ravna & Terry, 2004).
We further quantified the mean absolute error (a statistic used to measure differences between methods: Comparison of phase-equilibrium calculations with the garnet-clinopyroxene-phengite barometer (Ravna & Terry, 2004).(a) Calculated reaction equilibrium constant (lnK 1 ) as calculated in Equation 2 in the main text.(b) Calculated pressure using the Ravna and Terry ( 2004) calibration with mineral compositions from the phase-equilibrium calculations (ds62) as inputs.(c) Difference in the calculated pressures from the two methods.The white star in Figure 2c corresponds to the mean eclogite facies conditions (2.5 GPa and 660 C; see Section 2 for details).The largest differences in calculated pressure (>0.5 GPa) occur when two amphiboles and lawsonite are present in the phase-equilibrium calculations.The best agreement is at relatively high P-T, within amphibole-free mineral assemblages.
the mean absolute values of ΔP and ΔT) of the P-T calculations using the conventional thermobarometers and the phase-equilibrium models (Figure 4c and d).For the garnet-clinopyroxene-phengite barometer, we calculated a mean absolute error of ±0.3 GPa and for the garnetclinopyroxene thermometer, a mean absolute error of ±29 C (Figure 4c and d). Figure 4c shows that the garnet-clinopyroxene-phengite barometer systematically overestimates the reference P, whereas ΔT from the garnet-clinopyroxene thermometer was positive or negative in roughly equal numbers of calculations (negative in 57% of the calculations; Figure 4d).

| P-T calculations with ds55
In the subsections above, we described the results using thermodynamic dataset ds62 with their corresponding and recommended a-x relations for solid solution phases (i.e. Green et al., 2016;Holland & Powell, 2011 and references therein).In this section, we present modelling results obtained with the thermodynamic dataset ds55 (Holland & Powell, 1998; August update) and a-x relations from Diener and Powell (2012) and references therein to assess how consistent the predictions from the thermodynamic dataset ds55 are with calculations performed with ds62.
Calculations with ds55 show that the reference P is overestimated by the garnet-clinopyroxene-phengite barometer, including an ±0.2 GPa uncertainty (Cuthbert et al., 2000;Ravna & Terry, 2004;Waters & Martin, 1993) at any given P, except in a narrow P range within 1.65-1.85GPa where P is the same within uncertainty (Figures 5a and S1).This is quite similar to the calculations with ds62 (Figure 4a).The ΔP histogram for ds55 is narrower and shows a normal distribution (Figure 5c); the calculated mean absolute error is ±0.2 GPa (Figure 5c), and this is 31% lower than the mean absolute error from the ds62 calculations (Figure 4c).
The reference T is underestimated by the garnetclinopyroxene thermometer except in a narrow range within 620-640 C, where T is overestimated slightly (Figure 5b).Importantly, at >670 C, ΔT is greater than the estimated ±60 C uncertainty (Ravna, 2000;Ravna & Paquin, 2003;Ravna & Terry, 2004).This contrasts with the ds62 calculations (Figure 4b), where the calculated and reference T are always <60 C. The ΔT histograms for ds55 show a larger ΔT range and is evident that the thermometer tends to underestimate the temperature in more cases than compared to the ds62 calculations (Figures 4d  and 5d).The calculated mean absolute error is ±42 C (Figure 5d); this is 33% higher than the mean absolute error from the ds62 calculations (Figure 4d).

| WHAT CONTROLS THE CALCULATED P -T OF ECLOGITES?
The garnet-clinopyroxene-phengite barometer requires calculation of end-member activities of garnet, omphacite and phengite, as observed from Equation (1), whereas the garnet-clinopyroxene calculations use only the Fe 2+ /Mg ratios in garnet and clinopyroxene as observed from Equation (2).Although the 'successful' application of conventional thermobarometry relies on using phases that are in textural and chemical equilibrium (Essene, 1989;Powell, 1985;Spear, 1995), some studies follow and recommend approaches that are based solely on the reaction constants of thermobarometers.For example, to obtain peak P in eclogites, a common approach is to use the garnet with the highest aGrs 2 Â aPrp and Si content in phengite, and the lowest aDi (Carswell et al., 2000;Cuthbert et al., 2000;Ravna & Terry, 2004).On the other hand, to obtain peak T, it has been suggested to use the garnet with the lowest Fe 2+ /Mg and the omphacite with the highest Fe 2+ /Mg (Carswell et al., 2000;Cuthbert et al., 2000).This combined approach has been suggested to yield the peak P-T conditions reached.Here, we refer to the use of this approach as the 'P-T max approach'.To test such approach, we have calculated the aGrs 2 Â aPrp, aDi and Si content in phengite for the barometer, and the garnet and clinopyroxene Fe 2+ / Mg for the thermometer using the mineral compositions obtained from the phase-equilibrium model (ds62) and a-x relations considered in Ravna and Terry (2004).
Figure 6 shows the P-T behaviour of the activities and compositions used in the P-T max approach for barometric calculations.For instance, the aGrs 2 Â aPrp contours show a negative but relatively flat slopes within the epidote stability field, where the activity product increases with P (Figure 6a).Importantly, the greatest aGrs 2 Â aPrp is not located at high-T but at medium-T conditions.Within the lawsonite stability field, the aGrs 2 Â aPrp contours are steeper and have positive slopes, being more T sensitive (Figure 6a).The contours for aDi of clinopyroxene are relatively flat and P sensitive within the amphibole stability field at low and medium P (Figure 6b).Outside the amphibole and lawsonite stability fields, the aDi contours are steep and T sensitive, with the lowest value occurring at high temperature.The lowest aDi in the amphibole stability field occurs at low F I G U R E 4 Deviation of the calculated P-T from reference P-T conditions using thermodynamic dataset 'ds62' for forward phaseequilibrium modelling.Comparison of calculated versus reference (a) pressure at 660 C using the garnet-clinopyroxene-phengite barometer (Ravna & Terry, 2004) and (b) temperature at 2.5 GPa using the garnet-clinopyroxene thermometer (Ravna, 2000).Histograms and mean absolute error calculations for (c) ΔP and (d) ΔT over the studied P-T range; calc-calculated and ref-reference P-T conditions.
P and shows little temperature dependence (Figure 6b).The Si-in-phengite contours are steep with a positive slope within the amphibole and lawsonite/epidote stability fields and are therefore strongly T sensitive (Figure 6c).Outside the amphibole stability field, the Siin-phengite contours flatten and become more P sensitive; the Si content in phengite increases with P and decreases with T (Figure 6c).
Figure 7 shows the Fe 2+ /Mg partitioning in garnet and clinopyroxene.Garnet Fe 2+ /Mg contours are relatively simple, decreasing with increasing P and T. The temperature sensitivity is lowest in the amphiboleepidote stability field and highest in the amphibolelawsonite stability field.The largest magnitude changes in garnet composition are observed in the lower P and lower T regions of amphibole stability.Outside of the amphibole stability fields, garnet Fe 2+ /Mg changes little.Clinopyroxene Fe 2+ /Mg contours have similar topology to the garnet contours but not identical and exhibit less total magnitude of variation.In the amphibole-epidote stability field, clinopyroxene Fe 2+ /Mg are insensitive to T but decrease notably with increasing P. In the amphibole-lawsonite stability field, there is a strong T sensitivity such that Fe 2+ /Mg decrease with increasing T. At higher P-T, (>2.2 GPa and 650 C), Fe 2+ /Mg increases gently with increasing T.

| A detailed example of a-x behaviour at mean eclogite facies conditions
Figure 8 shows the evolution of the a-x parameters considered in Equations ( 2) and (3) as well as the evolution of the calculated lnK 1 and lnK D as functions of temperature at 2.5 GPa and as functions of pressure at 660 C. For F I G U R E 5 Deviation of the calculated P-T from reference P-T conditions using thermodynamic dataset 'ds55' for forward phaseequilibrium modelling.Comparison of calculated versus reference (a) pressure at 660 C using the garnet-clinopyroxene-phengite barometer (Ravna & Terry, 2004) and (b) temperature at 2.5 GPa using the garnet-clinopyroxene thermometer (Ravna, 2000).Histograms and mean absolute error calculations for (c) ΔP and (d) ΔT over the studied P-T range; calc-calculated and ref-reference P-T conditions.the barometric calculations, aDi, aCel and aPrp increase as P does, and their maximum value corresponds to P max .By contrast, aMs and aGrs decrease as P increases, and their lowest value corresponds to P max (Figure 8a).From all the considered activities, aPrp is the one that changes the most as a function of P, increasing by $1358% of the initial value, followed by aCel, which increases by $243%.As previously shown (Figure 2a), lnK 1 increases with P (Figure 8a).
For the T calculations, garnet Fe 2+ /Mg decreases with increasing T, and the lowest value corresponds to T max (Figure 8b).Clinopyroxene Fe 2+ /Mg decreases from 550 to 650 C and then increases very slightly thereafter.From the considered compositional parameters, garnet Fe 2+ /Mg decreases with T by $78%, whereas the clinopyroxene Fe 2+ /Mg decreases by $43% (although this change is not monotonic); importantly, the lowest clinopyroxene Fe 2+ /Mg is at medium-T and not at the highest T. The calculated lnK D decreases as T increases (Figure 8b).

| EFFECT OF X F E 3 + IN THERMOBAROMETRIC CALCULATIONS
As mentioned in Section 2, the models presented so far use X Fe 3+ = 0.36.In this section, we evaluate the effects of different X Fe 3+ in the consistency between the different thermobarometric methods explored here.For this, we calculated P-X and T-X diagrams, where the x-axis shows different X Fe 3+ values as function of pressure and temperature (Figure 9; phase relations shown in Figure S2).For this example, we only evaluated the thermobarometric approaches using the thermodynamic dataset ds62.The calculated lnK 1 isolines are only weakly sensitive to the system's X Fe 3+ (Figure 9a).For the P and X Fe 3+ range investigated here (at 660 C), the barometer estimates $0.15-0.35GPa higher P than forward modelling (Figure 9b).Generally, the P mismatch increases with the X Fe 3+ of the system, but very large changes in X Fe 3+ are needed to produce geologically meaningful change in the P estimates (≤0.2 GPa change for X Fe 3+ from 0 to 0.5).
The region of smallest P deviation is located $2.2 GPa for all X Fe 3+ ; by contrast, the areas of largest ΔP are at $3.0 and $1.7 GPa and high X Fe 3+ (Figure 9b).The inflection of contours at $2.2 GPa is because of the breakdown of amphibole (Figures 9b and S2).
For the thermometer, the calculated lnK D isolines are not strongly sensitive to the system's X Fe 3+ (Figure 9c).For the explored T and X Fe 3+ range (at 2.5 GPa), the thermometer estimates À20 to À60 C difference between approaches (Figure 9d).The difference in results between methods is insensitive to X Fe

3+
of the rock at T < 640 C, where amphibole is stable (Figures 9d and S2).However, above that temperature and with amphibole breakdown, the T mismatch varies somewhat with the oxidation state of system (Figure 9d).For instance, at 750 C, the T deviations increase from À10 to À60 C over an X Fe 3+ range of 0-0.5.The regions of smallest T mismatch are located in a temperature range from 580 to 600 C through all X Fe 3+ values; by contrast, the largest T mismatch is located at high oxidation states (X Fe 3+ ranges >0.4) at T $ 650 C (Figure 9d).

| DISCUSSION
Our results indicate that for eclogites metamorphosed at >1.5 GPa and $650-800 C (>225 C/GPa), the P-T conditions calculated using conventional thermobarometry will be generally consistent with those estimated from mineral compositions in phase-equilibrium calculations.This suggests that for MT-HT eclogites, conventional thermobarometry and forward phase-equilibrium modelling should not result in significantly different geological interpretations if performed properly.The largest differences in methods occur at HP and low-temperature (LT) conditions (Na-amphibole-lawsonite eclogite: T/ P < 225 C/GPa); however, the P-T conditions of this paragenesis in mafic rocks are well known independently (Tsujimori et al., 2006;Tsujimori & Ernst, 2014) and therefore significant error in geological interpretation unlikely.However, our calculation comparisons assume geologically accurate application of both methods, which is not always straightforward.It is therefore worth considering why the differences in calculated results between the methods exist and how our calculations might inform more rigorous thermobarometry in real rocks.

| On the consistency and discrepancy of eclogite P-T calculations
Discrepancies between P calculated using the Ravna and Terry (2004) barometer with the inferred conditions of the geological setting have been reported previously Behaviour of the a-x parameters as functions of P-T.(a) Pressure-dependence of the end-member activities and lnK 1 at 660 C using the a-x models from Ravna and Terry (2004) and references therein and with mineral compositions from phase-equilibrium calculations as inputs.(b) Temperature-dependence of garnet and clinopyroxene compositions and lnK D at 2.5 GPa using mineral compositions from phase-equilibrium calculations as inputs.(Page et al., 2007).One of the main questions is to what extent the discrepancy in the P-T calculations, as observed in our study, is because of the mathematical formulation of the conventional thermobarometers or because of the different set of a-x relations used in both conventional thermobarometry and forward phaseequilibrium modelling.To answer such question, we present a simple model in Figure 10. Figure 10a shows the reference P-T conditions (the mean eclogite facies conditions; white star in Figure 10) as well as the P-T conditions calculated using conventional thermobarometry with the compositions retrieved from the ds62 and ds55 a-x models and thermodynamic datasets at the reference P-T point (dashed star and triangle in Figure 10a; Table S1).In this example, the temperature is within reasonable agreement between both thermodynamic datasets, and the main discrepancy among the methods is the pressure (Figures 4, 5, and 10a).The fact that both calculations with ds62 and ds55 yield the same P-T conditions but are different than the reference conditions (Figure 10a) suggests that the discrepancy of compositions obtained from ds62 and ds55 models is subordinated compared to that of the a-x relations used for the Ravna and Terry ( 2004) barometer (i.e.Ganguly et al., 1996;Holland, 1990;Holland & Powell, 1998).
To further test the specific cause for the differences, we re-calculated P using the equations of the Ravna and Terry (2004) barometer (solid star/triangle in Figure 10b) but with the end-member activities (extracted from Theriak-Domino) using the ds55 and ds62 a-x models for garnet (White et al., 2007(White et al., , 2014)), clinopyroxene (Diener & Powell, 2012;Green et al., 2016), and white mica (Coggon & Holland, 2002;White et al., 2014), as opposed to the preferred a-x relations used by Ravna and Terry (2004) in their barometer.Here, the mineral compositions and the mathematical formulation of the barometer are the same as in the previous example (Figure 10a), and the only differences are the a-x models.Calculations presented here use thermodynamic dataset 'ds62'.The area where both forward and inverse models yield the most consistent P-T conditions and are less sensitive of the selected X Fe 3+ is within $2.2 GPa and 600-630 C.
We find that ΔP is significantly reduced (Figure 10b) indicating that the differences between the conventional and phase-equilibrium P-T estimates are primarily related to activity calculations rather than any other aspects on the mathematical formulation of the garnetclinopyroxene-phengite barometer.
A comparison of the obtained activities of the garnet, clinopyroxene and phengite end-members using the updated (ds62; Green et al., 2016;White et al., 2014) and older (Ganguly et al., 1996;Holland, 1990;Holland & Powell, 1998) a-x relations indicates that the main discrepancies come from aGrs and aCel (Table S1).For instance, at $2.5 GPa and $660 C (using mineral compositions from ds62 phase equilibria), the Ganguly et al. (1996) aGrs is $0.08 whereas the White et al. (2014) aGrs is $0.03 (Table S1); this is a > 2.5Â difference in aGrs for the exact same input garnet composition.Figure 11 shows a P sensitivity test where lower aGrs yields systematically lower P and higher aCel results in higher P; both activities play a role, but the effect of aGrs in the calculated P is greater.For example, by modifying the aGrs from 0.08 to 0.03 (as from Figure 10 and Table S1) and leaving the other activities the same, the calculated P decreases from 2.8 to 2.4 GPa (ΔP = 0.3 vs ΔP = À0.1).Therefore, as also mentioned above, we interpret that the discrepancies in the calculated P-T conditions are related to the parametrization of a-x relations (cf.Page et al., 2007).For instance, the Ganguly et al. (1996) garnet a-x model is non-ideal with mixing in one site, whereas the White et al. ( 2014) garnet model is a non-F I G U R E 1 0 Differences among P-T calculations at 2.5 GPa and 660 C. (a) Using the mineral compositions predicted by forward phase-equilibrium modelling (both ds62 and ds55) for an average eclogite (2.5 GPa, 660 C), the thermobarometers of Ravna and Terry (2004) and Ravna (2000) yield $2.8 GPa and $625 C. The methods agree relatively well, considering reasonable uncertainties (±60 C: Ravna, 2000;Ravna & Paquin, 2003;Ravna & Terry, 2004;and ±0.2 GPa: Cuthbert et al., 2000;Ravna & Terry, 2004;Waters & Martin, 1993).(b) If the Ravna and Terry (2004) barometer is used with activities calculated from the ds62 and ds55 a-x relations, instead of the a-x relation from Ravna and Terry (2004) and references therein (as in Figure 10a), the differences in pressure between the methods disappear, because the main difference in the results is from the a-x relations, as opposed to the end-member thermodynamic data used for calibration.
F I G U R E 1 1 Sensitivity test of the effects of a Grs and a Cel in the garnet-clinopyroxene-phengite barometer (Ravna & Terry, 2004) at $660 C. The white star indicates the calculated pressure (and ΔP) and a Grs obtained the barometer of Ravna and Terry (2004).The grey star indicates the calculated pressure (and ΔP) and a Grs obtained the a-x relations of White et al. (2014) for the same input mineral composition.The grey line shows the reference pressure (2.5 GPa) from which the mineral compositions were extracted from the phase-equilibrium calculations, and the band represents a ± 0.2 GPa uncertainty associated with the calibration of the barometer (Cuthbert et al., 2000;Ravna & Terry, 2004;Waters & Martin, 1993).
ideal two-site mixing model.Furthermore, Fe 3+ is not considered in the Ganguly et al. (1996) model, whereas in White et al. (2014), Fe 3+ is considered via the 'khoharite' end-member.Other differences between the garnet a-x relations are mainly (but not limited to) their formulation itself, the interaction parameters, among others (for more details on comparisons and limitations of existing garnet solid-solution parameters, the reader is referred to Adams, 2020; see also Appendix S1).It is not possible from this study to say which a-x relations result in more accurate thermobarometry, only to quantify the magnitude of differences among them.Given that neither set of garnet a-x relations was calibrated specifically for the P-T conditions typical of medium-to high-T eclogites (for instance, the Ganguly et al. [1996] a-x relations for garnet were calibrated using a range of pressures at T $ 1000 C, and the White et al. [2014] a-x relations were developed for amphibolite-granulite equilibria), the relative agreement of the results is promising.
Recent studies compared existing thermodynamic datasets and a-x relations to test whether the most recent thermodynamic data indeed yield more realistic results compared to previous datasets (e.g.ds62 vs ds55; Guevara & Caddick, 2016;Lanari & Duesterhoeft, 2019;Starr et al., 2020).Our calculations using phase-equilibrium models with ds62 and ds55 are relatively similar although they show some slight differences (Figures 4,5 and 9).For example, the obtained ΔP and the mean absolute error from ds55 are lower compared to the ones from ds62 (mean absolute errors: ±0.2 GPa in ds55 vs ±0.3 GPa in ds62).Further, the range of ΔP is smaller in ds55 than in ds62 (Figures 3 and 5).Again, we argue that this may be explained by the different garnet a-x relations used for calculations.
The largest difference in our consistency check was found for P at HP-LT conditions using ds62 and their related a-x models (Figure 2b).The region where the largest mismatch occurs is within the lawsonite stability field.We hypothesize that the large mismatch is because of an artefact of how the Ca partitions in different Cabearing phases (lawsonite + amphibole), ultimately affecting the garnet's aGrs.For instance, as explained above, the garnet aGrs are different between ds55 and ds62 (and their related garnet a-x models), resulting in a smaller ΔP in ds55 (Figures 2b and S1).While calculations using ds55 give a better match between both thermometric methods, it does not necessarily mean that such calculations are more geologically sensible.As mentioned above, it is fortuitous that this area of largest mismatch is in the lawsonite stability field, which is well constrained experimentally and therefore less likely to result in substantial geological error in interpretation.
Finally, another plausible explanation that can account for some of the P-T mismatch observed in our work may be related to geochemical processes that can affect the observed mineral compositions of a rock.For example, crucial variables that can affect thermobarometric calculations in natural samples are porphyroblast growth, related compositional modification of system and post-peak diffusion (Lanari & Engi, 2017;Marmo et al., 2002;Zuluaga et al., 2005).Such processes modify the 'true-equilibrium' compositions that the minerals have at a given P-T point.Importantly regarding these points, Ravna (2000) used natural data for calibrating the thermometer; therefore, such thermometric calibration might incorporate uncertainties related to mineral fractionation and/or post-peak compositional modification.If the temperature estimates of these natural samples as used in the thermometer calibration were incorrect, it could result in systematic error in their thermobarometric results.On the other hand, the advantage of using natural data is that it allows for great ranges of T, P and X to be used in thermobarometer calibration than the often-limited experimental data alone.If done properly, this provides more rigorous calibration, with less extrapolation, and therefore more accurate thermobarometry.These problems may also influence some experimental data; it is not guaranteed that experimental products are always in equilibrium.

| Implications for thermobarometry of natural eclogites
The 'P-T max approach' used to obtain P-T max via conventional thermobarometry is commonly used in the eclogite community and has yielded results that are geologically consistent and significant for decades.However, some studies have questioned such approach for eclogites that has undergone garnet and omphacite compositional modification after peak P-T and found that the P-T max conditions do not to represent true peak P-T (e.g.Bukała et al., 2018;Hern andez-Uribe et al., 2018).Based on our results, we argue that the P-T max approach may not be geologically meaningful despite yielding higher calculated P and T values.
The P-T max approach is based on the mathematical maximization of K 1 (for the barometer) and minimization of K D (for the thermometer) to yield the highest possible P-T.However, we find that the mineral compositions corresponding to such an optimization (i.e. the combination of the highest aGrs 2 Â aPrp and Si content in phengite, and the lowest aDi) may be obtained at different P-T conditions, and therefore may not record true geological peak conditions or even an equilibrium mineral assemblage.For example, at 660 C, the greatest aDi, aCel, and aPrp and the lowest aGrs and aMs occur at P max .At 2.5 GPa, the garnet with the lowest Fe 2+ /Mg occurs at T max .The clinopyroxene at T max similarly has Fe 2+ /Mg very close to its lowest value, although it is not the actual lowest value (Figure 8b).Further, clinopyroxene in equilibrium with amphibole will have the lowest Fe 2+ /Mg; thus, in the absence of other petrological information, these parameters might be used to accurately estimate a geological meaningful P-T max (Figures 6-8).Our suggestions are relatively congruent with those proposed previously (Carswell et al., 2000;Cuthbert et al., 2000;Ravna & Terry, 2004), with the exception of Fe 2+ /Mg in clinopyroxene, for which previous studies advocated for using the highest value.While this will result in the calculation of a higher apparent temperature, the lowest Fe 2+ /Mg in clinopyroxene is more likely to have coexisted with the lowest Fe 2+ /Mg in garnet near the metamorphic peak; for both of these minerals, this ratio should generally decrease with P-T (Figure 8b), as also observed in petrological ments (Schmidt & Poli, 1998).
While in this work we did not assess how geologically accurate both conventional thermobarometry and forward phase modelling are, other studies have used both techniques in different set of eclogites to explore the similarity of the approaches in HP-UHP terranes.For example, Wei and Clarke (2011) found that phase-equilibrium modelling and conventional thermobarometry (same set of thermobarometers used here) yield similar P-T conditions for epidote and lawsonite eclogites worldwide; they, however, found that garnet-clinopyroxene-phengite barometer yields more similar results to the phase-equilibrium modelling than the garnet-clinopyroxene thermometer.Furthermore, this similarity between approaches have been also found in eclogites throughout different HP-UHP terranes (e.g.Bukała et al., 2018;Hern andez-Uribe & Palin, 2019a;Klonowska et al., 2016;Ren et al., 2016;Wei et al., 2013).Therefore, if conventional thermobarometry and forward phase-equilibrium modelling are correctly applied to natural eclogites, results should be relatively consistent (see discussion in Section 6.3).
In this work, we also evaluated the influence of X Fe 3+ in the consistency between thermobarometric methods.We find that the area, where both forward and inverse models yield the most consistent P-T conditions and are less sensitive of the selected X Fe 3+ , is $2.2 GPa and 580-600 C (Figure 9).Overall, reduced systems will tend to record the smallest P-T deviation between conventional thermobarometry and forward phase-equilibrium modelling, which is consistent with the generally understood principle that Fe 3+ incorporation into mafic silicates is not as well quantified, thermodynamically, as Fe 2+ .This uncertainty is somewhat compounded for applied thermobarometry, because of the common difficulty in accurately estimating Fe 3+ in rocks and minerals.Importantly, we find that outside amphibole stability, at higher P-T, higher oxidation state of the system will lead to greater P-T mismatch between inverse and forward modelling calculations (Figure 9).We suggest that this is likely because of the greater incorporation of Fe 3+ into amphibole (and also epidote) at lower P-T conditions compared to garnet and clinopyroxene as well as the higher Fe total /Mg in garnet and clinopyroxene at these conditions.This means that both Fe 2+ /Fe 3+ and Fe 2+ /Mg ratios of garnet and clinopyroxene are at their highest, thereby minimizing any systematic errors in the Fe 2+ /Mg thermometers because of Fe 3+ .At higher P-T, the Fe 2+ / Mg ratios of garnet and clinopyroxene are much lower and, for mass balance constraints, the Fe 3+ that was in the amphibole and epidote at lower P-T must be distributed between the garnet and clinopyroxene.This means that garnet and clinopyroxene Fe 2+ /Fe 3+ must also be lower, therefore magnifying any systematic errors in the Fe 2+ / Mg thermometers because of Fe 3+ .These thermodynamic issues are compounded further for thermobarometry of real rocks because of the difficulty of estimating Fe 3+ / Fe 2+ in minerals; when Fe total /Mg in garnet and clinopyroxene is lowest, estimates of Fe 3+ (and therefore Fe 2+ /Mg) will have larger relative uncertainties and any inaccuracy will have a larger effect on the thermometer (Ravna & Terry, 2004).Together with the issue of diffusional modification of Fe 2+ and Mg at HT, this suggests that thermometry of relatively MT amphibole eclogites is likely to have less systematic error related to Fe 3+ estimations.

| On the uncertainties associated with different thermobarometric methods
Random and systematic sources of error affect the calculations and predictions from conventional thermobarometry and forward phase-equilibrium modelling.A detailed discussion is outside the scope of this study, but the reader is referred to other studies that describe and discuss them to different extents (Hern andez-Uribe & Gutiérrez-Aguilar, 2021; Hodges & McKenna, 1987;Kohn & Spear, 1991;Lanari & Duesterhoeft, 2019;Lanari & Engi, 2017;Palin et al., 2016;Powell & Holland, 2008;Yakymchuk, 2017).In our study, we show how consistent the P-T calculations from conventional thermobarometry are with mineral compositions predicted from phaseequilibrium models.Our calculated mean absolute errors for the explored P-T window are ±0.2-0.3GPa and ±29-42 C (Figures 4 and 5).These mean absolute errors can be considerably lower if the same a-x relations are used for both methods (Figure 10b; i.e. when a systematic error between methods is removed).
When compared to other uncertainties affecting both methods applied here, the uncertainties related to the consistency of the conventional thermobarometry with predictions of forward phase modelling (±0.2-0.3GPa and ±29-42 C; Figures 4 and 5) are not as significant as they might appear.For instance, the P mean absolute error is $2-3 times greater than the commonly quoted uncertainty of forward modelling (minimum uncertainty of ±0.1 GPa; Powell & Holland, 2008) and similar to the uncertainty of the garnet-clinopyroxene-phengite barometer that is often reported as ±0.2 GPa (Cuthbert et al., 2000;Ravna & Terry, 2004;Waters & Martin, 1993).The T mean absolute error is lower than the commonly assumed T uncertainty in phase-equilibrium modelling (±50 C; Powell & Holland, 2008), thermometer calibration (±60 C; Ravna, 2000;Ravna & Paquin, 2003;Ravna & Terry, 2004) and the uncertainty related to the calculation of Fe 3+ much as ±100 C; Carswell & Zhang, 1999;Proyer et al., 2004;Ravna & Paquin, 2003;Štípsk a & Powell, 2005).Therefore, we argue that uncertainty related to the difference in thermobarometric methodology (conventional thermobarometry vs forward phase-equilibrium modelling) is minor and subordinate compared to other types of uncertainties.If P-T calculations are performed properly (i.e. in terms of methodology, using consistent thermodynamic datasets and a-x models, etc) in an ideal geological scenario (e.g. with minimal thermal overprinting and redistribution of Fe-Mg), both methods should be comparable for medium and high-T eclogites.Inversely, if large discrepancies between conventional thermobarometry and forward phase-equilibrium modelling of eclogites are found, this might be an indication that either: (1) the minerals in the rock studied do not represent an equilibrium assemblage or (2) one or both methods of thermobarometry might not have been rigorously applied.As such, a comparison of methods in the same sample can be a useful check that the results are reasonable rather than reliance or predetermined preference for just one approach.

| CONCLUSIONS
This contribution addressed the question of how similar the conventional thermobarometry P-T calculations are with predictions from forward phase-equilibrium modelling of HP-UHP eclogites.The discrepancy between both approaches is mainly attributed to the a-x relations used by the methods.Both methods give relatively similar results, but when the same set of a-x relations are used in the garnet-clinopyroxene-phengite barometer, P-T calculations are even more consistent.We find that the calculated P is mainly sensitive to aGrs (and garnet Ca content); as expected, different a-x relations for garnet yield different aGrs and thus affecting the consistency of the P calculations.The P-T estimates obtained with different thermodynamic datasets (ds62 and ds55) and corresponding a-x relations are comparable.We find that, although oxidized systems yield greater P-T mismatch, the influence of X Fe 3+ in thermobarometric calculations less than might be expected, especially for amphibole eclogites.We also find that a geologically meaningful P max (and the temperature corresponding to P max ) is obtained when using the greatest aDi, aCel, and aPrp and lowest aGrs and aMs; geologically meaningful T max is best obtained with the garnet and clinopyroxene with the lowest Fe 2+ /Mg, and the garnet with lowest Grs content.P max and T max need not necessarily be calculated from the same mineral compositions (peak P and peak T need not to coincide), although the chosen clinopyroxene and garnet compositions might often agree using this approach.
An important concluding remark is that the apparent difference between conventional thermobarometry and forward phase-equilibrium modelling (±0.2-0.3GPa and ±29-42 C), especially for MT-HT eclogites, is subordinate and relatively minor compared to the several other uncertainties associated with both methods.Thus, in an ideal scenario, P-T calculations using both methods should yield similar results, and the error associated with the choice of thermobarometric methodology should not be one of the main concerns of HP-UHP petrologists.

F
I G U R E 1 Pressure and temperature (P-T) phase-equilibrium diagram for eclogite facies N-MORB (Gale et al., 2013) with Fe 3+ / Fe total = 0.36 (Rebay et al., 2010).(a) Calculated P-T phase diagram.(b) Summary of the phase evolution along the explore P-T window.The dashed line delineates Na-dominated amphibole (lower T) from Ca-dominated amphibole (higher T).The yellow star indicates the 'mean eclogite facies conditions' (calculated from Penniston-Dorland et al., 2015 database) used in this work for comparing both thermobarometric methods.Error bars are ±0.1 GPa and ±50 C (uncertainties commonly cited for forward phase-equilibrium modelling; Powell & Holland, 2008).1-Cpx Grt Ms Lws Qz Rt H 2 O; 2-Amp Cpx Grt Ep Ms Lws Qz Rt H 2 O; 3-Amp Cpx Grt Ep Ms Ky Qz Rt H 2 O; 4-Amp Cpx Grt Ep Qz Rt H 2 O; 5-Amp Cpx Ep Ms Qz Rt H 2 O (mineral abbreviations follow Warr, 2021).

F
I G U R E 3 Comparison of phase-equilibrium calculations with the garnet-clinopyroxene thermometer(Ravna, 2000).(a) Calculated reaction constant (lnK D ) as in Equation 3 in the text.(b) Calculated temperature using theRavna (2000) calibration with mineral compositions from the phase-equilibrium calculations as inputs.(c) Difference in the calculated temperatures from the two methods.The yellow star in Figure3ccorresponds to the mean eclogite facies conditions (2.5 GPa and 660 C; see Section 2 for details).Contours of ΔT are parallel to amphibole stability, but the methods agree within ≤40 C for most of the calculated P-T space.The largest disagreement (>50 C) occurs in the lawsonite and epidote-and amphibole-free stability fields.

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I G U R E 6 Calculated parameters within the explored P-T window used by the 'P-T max approach' for obtaining P max (see text for details).(a) aGrs 2 Â aPrp, (b) aDi and (c) Si pfu in phengite.Mineral compositions are taken from the phase-equilibrium models, and activities were calculated using the a-x models from Ravna and Terry (2004) and references therein.F I G U R E 7 Calculated mineral Fe 2+ /Mg within the explored P-T window used by the 'P-T max approach' for obtaining T max .(a) Garnet and (b) clinopyroxene.Mineral compositions are taken from the phase-equilibrium models.

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I G U R E 9 Influence of X Fe 3+ on the consistency between conventional and forward phase-equilibrium modelling.P-X diagram showing (a) lnK 1 and (b) ΔP.T-X diagram showing (c) lnK D and (d) ΔT.
Bulk-rock composition used for constructing the phase equilibrium model (normalized wt%).FeO t is total iron expressed as FeO.O = oxygen, which combines with FeO via the equation 2FeO + O = Fe 2 O Note: 3 ; thus, bulk O is identically equal to bulk Fe 2 O 3 , while true bulk FeO is given by FeO t -2 X O. XMg = MgO/(MgO + FeO t ).X Fe 3+ ratios = 2 * O/FeO t and X Mg = MgO/(MgO + FeO).