) 365–372www.elsevier.com/locate/lithos

Lithos 97 (2007

The metapelitic garnet–biotite–muscovite–aluminosilicate–quartz(GBMAQ) geobarometer

Chun-Ming Wu a,⁎, Guochun C. Zhao b

a Laboratory of Computational Geodynamics, College of Earth Science, The Graduate University of The Chinese Academy of Sciences,PO Box 4588, Beijing 100049, China

b Department of Earth Sciences, The University of Hong Kong, Pokfulam Road, Hong Kong, China

Received 23 August 2006; accepted 3 January 2007Available online 9 January 2007

Abstract

In this contribution we have empirically calibrated the garnet–biotite–muscovite–aluminosilicate–quartz (GBMAQ) barometerusing low- to medium–high-pressure, mid-grade metapelites. Application of the barometer suggests that the GBMAQ and GASPbarometers show quite similar pressure estimates. Furthermore, metapelites within thermal contact aureole or very limitedgeographic area show no meaningful pressure diversity determined by the GBMAQ and GASP barometers which is the geologicalreality. The random error of the GBMAQ barometer is expected to be around ±0.8 kbar, and this barometer shows no systematicbias with respect to either pressure, or temperature, or AlVI in muscovite, or Fe in biotite, or Fe in garnet. The GBMAQ barometeris thermodynamically consistent with the garnet–biotite geothermometer because they share the same activity models of bothgarnet and biotite. This barometer is especially useful for assemblages with Ca-poor garnet or Ca-poor plagioclase or plagioclase-absent metapelites. Application of this barometer beyond the calibration ranges, i.e., P–T range and chemical ranges of theminerals, is not encouraged.© 2007 Elsevier B.V. All rights reserved.

Keywords: Application; Calibration; GBMAQ; Geobarometer; Metapelite

1. Introduction

The mineral assemblage garnet+biotite+muscovite+quartz±plagioclase±aluminosilicate is common in typi-cal medium-grade metapelites or semipelites. Whenplagioclase and aluminosilicate are present the well-calibrated GASP geobarometer (e.g., Holdaway, 2001)may be applied.However, when plagioclase is present andaluminosilicate is absent the GBPQ geobarometer (Wu

⁎ Corresponding author. Tel.: +86 10 8825 6312; fax: +86 10 88256012.

E-mail address: wucm@gucas.ac.cn (C.-M. Wu).

0024-4937/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.lithos.2007.01.003

et al., 2004a) or GMPQ geobarometer (Wu et al., 2004b;Wu and Zhao, 2006a) may be applied. For TiO2-saturatedrocks the GRIPS geobarometer (e.g., Wu and Zhao,2006b) or the GRAIL geobarometer (e.g., Bohlen et al.,1983; Koziol and Bohlen, 1992) may also be appliedprovided that both rutile and ilmenite coexist with otherminerals. Unfortunately, there is still a shortcoming in thefour geobarometers (GASP, GBPQ, GMPQ andGRIPS) since they are not suitable for assemblages withcalcium-deficient garnet (XCa

grtb0.03) and/or plagioclase(XCa

pl b0.17) (Todd, 1998; Holdaway, 2001; Wu et al.,2004a,b; Wu and Zhao, 2006a,b). In fact, calcium-deficient garnet and/or plagioclase are not uncommon in

366 C.-M. Wu, G.C. Zhao / Lithos 97 (2007) 365–372

metapelites or semipelites. Moreover, in some casesmetapelites are just devoid of plagioclase. All thesesituations limit the application of the GASP, GBPQ,GMPQ and GRIPS geobarometers. On the other hand,plagioclase-free metapelitic assemblage garnet+biotite+muscovite+aluminosilicate+quartz (GBMAQ) constitu-tes a potential geobarometer which in fact has beenempirically calibrated (e.g., Robinson, 1983; Hodges andCrowley, 1985; Holdaway et al., 1988; Aranovich andPodlesskii, 1989;McMullin et al., 1991;Holdaway, 2004)and was first designated MABS (Holdaway et al., 1988)and then SGAM (McMullin et al., 1991). These earliercalibrations either adopted inappropriate activity modelsof the phases, or based on less valid garnet–biotitethermometer and GASP barometer, or used inadequateamounts of samples which to some extent lose generality.Furthermore, the previous workers have seldom studiedthe andalusite-bearing assemblages which limit the use ofthis barometer to low-pressure terrains. Thus theGBMAQ barometer should be refined.

Up until now, no experiments have been done tobracket the univariant GBMAQ line in P–T space. Inthis paper, the GBMAQ geobarometer has beenempirically calibrated using natural metapelitic samples(Supplementary Table 1) collated from the literature inwhich the assemblages have been ascertained to be atequilibrium in the P–T range of 530–690 °C and 0.8–9.2 kbar, simultaneously determined by the garnet–biotite geothermometer (Holdaway, 2000) and theGASP geobarometer (Holdaway, 2001), respectively.The P, T and compositional ranges of these samples aresummarized in Table 1.

Through extensive comparative studies, Wu andCheng (2006) concluded that the Holdaway (2000)garnet–biotite geothermometer (Model 6AV) and theHoldaway (2001) GASP geobarometer are the two mostvalid ones among such kinds of geothermobarometers.In the calibration of the GBMAQ geobarometer, thesame activity models of garnet and biotite were adopted

Table 1Natural metapelites in calibrating the GBMAQ barometry summarizedfrom Supplementary Table 1

Al phase P (kbar) T (°C) X AlVImus X Fe

bio X Fegrt

And 0.8–4.1 537–594 0.91–0.97 0.34–0.43 0.65–0.77Sil 2.9–6.7 538–694 0.79–1.00 0.31–0.54 0.54–0.85Ky 4.5–9.2 519–692 0.77–1.00 0.22–0.51 0.51–0.85

Definition of molar fractions of the phasesX i

mus= i/(Fe+Mg+AlVI) i=Fe, Mg, AlVI

X jbio= j/(Fe+Mg+AlVI+Ti) j=Fe, Mg, AlVI, Ti

X kgrt=k/(Fe+Mg+Ca+Mn) k=Fe, Mg, Ca, Mn

as those for the garnet–biotite geothermometer (Hold-away, 2000) and the GASP geobarometer (Holdaway,2001) in order to keep thermodynamic consistencyamong these thermobarometers.

2. Thermodynamic background and calibration

The volumetric change of the fluid-absent, nettransfer GBMAQ reaction is large and thus makes it apotential geobarometer without determining the activityof any metamorphic fluid which is in fact not easy toretrieve. Thermodynamic equilibrium of the modelreaction of the GBMAQ geobarometer

KAl2ðAlSi3ÞO10ðOHÞ2muscovite

þ Fe3Al2Si3O12almandine

¼ KFe3ðAlSi3ÞO10ðOHÞ2annite

þ 2Al2SiO5aluminosilicate

þ SiO2quartz

ð1Þ

may be described as

DG ¼ 0 ¼ DH0−T dDS0 þ P−1ð ÞdDV 0

þ RTlnðX bio

Fe Þ3ðX grt

Fe Þ3ðXmusAlVIÞ2

" #

þ 3RTlngbioFe −3RTlnggrtFe ð2Þ

in which we have made reasonable assumptions: (1)enthalpies, entropies and volumes of the phases involvedwere assumed to be constant in the P–T range of interestand this treatment has been repeatedly ascertained to bevalid in a fairly wideP–T range for solid–solid reactions;(2) muscovite was assumed to be an ideal Fe-Mg-AlVI

ternary solution; and (3) aluminosilicates and quartzwere assumed to be pure phases. We have compareddifferent calibrations including or excluding Cp, α and βof the phases with different activity models of muscovite,and found that they show no appreciable differences.Thus we have excluded Cp, α and β of the phases andadopted an ideal ternary solution model of muscovite incalibrating this barometer.

According to Holdaway (2000, 2001), the excessGibbs free energy of almandine component in garnet isexpressed as

3RTlnggrtFe ¼ FeadTðKÞ þ FebdPðbarsÞ þ Fec ð3Þ

in which Fea, Feb and Fec are polynomials consisting ofthe molar fractions of Fe, Mg, Ca and Mn componentsof garnet and has been given in Wu et al. (2004a).

Holdaway (2000, Model 6AV)derived the MargulesparametersW FeMg

bio , (W FeAlbio −WMgAl

bio ) and (W FeTibio −WMgTi

bio )responsible for describing the non-ideal mixing proper-

Table 2Regression summary (±2σ) in calibrating the GBMAQ geobarometer

Al phase ΔH 0/ΔV 0 ΔS 0/ΔV 0 WMgAlbio /ΔV 0 WMgTi

bio /ΔV 0 WAlTibio /ΔV 0 1/ΔV 0 r

(bar mol−1) (bar K−1 mol−1) (bar mol−1) (bar mol−1) (bar mol−1) (bar J−1 mol−1)

And 23642.1 31.4192 −261161.5 −1489211.0 −2782295.6 −0.2637 0.911(±8999.7) (±11.4) (±110215.6) (±1884771.6) (±2898941.0) (±0.13)

Sil 7548.7 12.7049 60043.3 338610.9 552294.1 0.2071 0.708(±2066.8) (±2.3) (±22483.7) (±145169.1) (±283605.4) (±0.05)

Ky 11994.5 23.4241 4408.2 410005.4 237639.3 0.0098 0.901(±1136.1) (±1.2) (±12030.8) (±229900.3) (±364607.7) (±0.03)

367C.-M. Wu, G.C. Zhao / Lithos 97 (2007) 365–372

ties of biotite in calibrating the garnet–biotite thermom-eter. Incorporating these parameters to the symmetricquaternary solid solution model of Mukhopadhyay et al.(1993), we have the excess Gibbs free energy of annitecomponent of the Fe-Mg-AlVI-Ti quaternary biotitesolution as:

3RTlngbioFe ¼ W bioMgAldX

bioAl ð1−X bio

Fe −XbioMgÞ

þW bioMgTidX

bioTi ð1−X bio

Fe −XbioMgÞ

−W bioAlTidX

bioAl X

bioTi þ TðKÞð−3:68X bio

Mg

−238:585X bioAl −370:39X

bioTi þ 3:68X bio

Fe XbioMg

þ 238:585X bioFe X

bioAl þ 370:39X bio

Fe XbioTi Þ

þ ð5333:0X bioMg þ 209850:0X bio

Al þ 310990:0X bioTi

−5333:0X bioFe X

bioMg−209850:0X

bioFe X

bioAl

−310990:0X bioFe X

bioTi Þ ð4Þ

in which the W items stand for the unknown Margulesparameters of biotite to be determined.

Inserting Eqs. (3), (4) into Eq. (2) and rearranging theequation, we have obtained the regression model of theGBMAQ barometer as

P barsð Þ ¼ 1−DH0=DV 0� �þ T Kð Þd DS0=DV 0

� �þ W bio

MgAl=DV0

� �X bio

Al X bioFe þ X bio

Mg−1� �

þ W bioMgTi=DV

0� �

X bioTi X bio

Fe þ X bioMg−1

� �þ W bio

AlTi=DV0

� �X bio

Al XbioTi

þ 1=DV 0� �f−RTln ðX bio

Fe Þ3ðX grt

Fe Þ3ðXmusAlVIÞ2

" #

þ TðFeaþ 3:68X bioMg þ 238:585X bio

Al þ 370:39X bioTi

−3:68X bioFe X

bioMg−238:585X

bioFe X

bioAl −370:39X

bioFe X

bioTi Þ

þFebdP barsð Þ þ Fec−5333:0X bioMg−209850:0X

bioAl

−310990:0X bioTi þ 5333:0X bio

Fe XbioMg

þ209850:0X bioFe X

bioAl þ 310990:0X bio

Fe XbioTi g ð5Þ

in which the delta items are unknowns to be determinedthrough non-linear regression.

Substituting the mineral data (Supplementary Table1) to Eq. (5) and thus three sets of over-determined

equations for kyanite-, sillimanite- and andalusite-bearing assemblages have been constructed. Throughnon-linear regression analyses, the unknown thermody-namic parameters in Eq. (5) have been determined andare listed in Table 2. They are ratios of thermodynamicparameters and cannot be directly compared with thosepredicted from any thermodynamic data set. Substitut-ing these parameters (Table 2) into Eq. (5), threebarometer formalisms (Eqs. (6a) (6b) (6c)) wereobtained as

PðAndÞ ¼ f−23641:1þ31:4192T−261161:5X bioAl

� X bioFe þ X bio

Mg−1� �

−1489211:0X bioTi X bio

Fe þ X bioMg−1

� �−2782295:6X bio

Al XbioTi −0:2637

�½−RTln ðX bioFe Þ3

ðX grtFe Þ3ðXmus

AlVIÞ2 !

þ TðFeaþ 3:68X bioMg

þ238:585X bioAl þ 370:39X bio

Ti −3:68XbioFe X

bioMg

−238:585X bioFe X

bioAl −370:39X

bioFe X

bioTi Þ

þFec−5333:0X bioMg−209850:0X

bioA1

−310990:0X bioTi þ 5333:0X bio

Fe XbioMg

þ209850:0X bioFe X

bioAl þ 310990:0X bio

Fe XbioTi �g

� 1þ 0:2637Febð Þ ð6aÞ

PðSilÞ ¼ f−7547:7þ12:7049T þ 60043:3X bioAl

� X bioFe þ X bio

Mg−1� �

þ 338610:9X bioTi X bio

Fe þ X bioMg−1

� �þ552294:1X bio

Al XbioTi þ 0:2071

�½−RTln ðX bioFe Þ3

ðX grtFe Þ3ðXmus

AlVIÞ2 !

þ TðFeaþ 3:68X bioMg

þ238:585X bioAl þ 370:39X bio

Ti −3:68XbioFe X

bioMg

−238:585X bioFe X

bioAl −370:39X

bioFe X

bioTi ÞþFec−5333:0X bio

Mg

−209850:0X bioAl −310990:0X

bioTi þ 5333:0X bio

Fe XbioMg

þ209850:0X bioFe X

bioAl þ 310990:0X bio

Fe XbioTi �g

� 1−0:2071Febð Þ ð6bÞ

368 C.-M. Wu, G.C. Zhao / Lithos 97 (2007) 365–372

and

PðKyÞ ¼ f−11993:5þ23:4241T þ 4408:2X bioAl

� X bioFe þ X bio

Mg−1� �

þ 410005:4X bioTi X bio

Fe þ X bioMg−1

� �þ237639:3X bio

Al XbioTi þ 0:0098

�½−RTln ðX bioFe Þ3

ðX grtFe Þ3ðXmus

AlVIÞ2 !

þ TðFeaþ 3:68X bioMg

þ238:585X bioAl þ 370:39X bio

Ti −3:68XbioFe X

bioMg

−238:585X bioFe X

bioAl −370:39X

bioFe X

bioTi Þ

þFec−5333:0X bioMg−209850:0X

bioAl −310990:0X

bioTi

þ5333:0X bioFe X

bioMg þ 209850:0X bio

Fe XbioAl

þ310990:0X bioFe X

bioTi �g

� 1−0:0098Febð Þ ð6cÞfor andalusite-, sillimanite- and kyanite-bearing assem-blages, respectively.

Both the GBMAQ and GASP barometers generallyplace aluminosilicate-bearing calibration samples (Ap-pendix A) into an appropriate aluminosilicate stabilityfield or near the phase transition boundaries (Fig. 1a, b).Furthermore, these two barometers gave identical pres-sures within error of ±1.4 kbar (most within ±1.0 kbar)(Supplementary Table 1; Fig. 1c).

3. Application of the GBMAQ geobarometer

The applicability of the GBMAQ barometer may betested by applying it to metapelites not included incalibrating this barometer.

The Kluane metapelites in the northern Coast Belt ofYukon Territory, experienced a regional metamorphismM1 which is preserved in Ca-rich garnet and Na-richplagioclase cores that were little affected by later events.Later, the intrusion of the Ruby Range Batholith led to acontact metamorphic overprint M2 producing a 5–6 kmwide aureole in which the grade ranges from the garnetzone through the staurolite zone to the cordierite zones(Mezger et al., 2001). The contact aureole is comparablein size (c. 9 km wide) to the regional-scale contact

Fig. 1. P–T plot of the aluminosilicate-bearing pelitic samples(Supplementary Table 1) used in calibrating the GBMAQ barometry.Solid lines represent the aluminosilicate equilibria of Holdaway andMukhopadhyay (1993), whereas the dashed line represents theandalusite = sillimanite equilibrium of Pattison (1992). Temperatureswere determined by the garnet–biotite thermometer (Holdaway, 2000).(a) Pressures determined by the GASP barometer (Holdaway, 2001);(b) pressures determined by the GBMAQ barometer; and (c)comparison between the GASP and GBMAQ geobarometers.

aureoles reported in west central Maine (Holdawayet al., 1988). The mineral isograds are parallel to thecontact of the Ruby Range Batholith and their hot side is

369C.-M. Wu, G.C. Zhao / Lithos 97 (2007) 365–372

consistently towards the intrusive contact, confirmingthat they result from contact metamorphism by theemplacement of the Ruby Range Batholith. Alumino-silicates do not exist in the garnet zone, and muscovitedoes not exist in the cordierite zone, such that theGBMAQ barometer cannot be applied to these twozones. The GASP barometer yielded a pressure rangebetween 3.6 and 4.9 kbar for the staurolite zone(averaged 4.4 kbar). The GBMAQ barometer yieldeda quite similar, constant pressure as that of the GASPbarometer, i.e., 3.7–4.2 kbar (averaged 4.0 kbar) for thestaurolite zone (Supplementary Table 2; Fig. 2a), which

Fig. 2. Application of the GBMAQ barometer and comparison of the GASequilibria of Holdaway and Mukhopadhyay (1993), whereas the dashed line(a) Metapelites in the outer contact aureole of the Ruby Range Batholith, Canawest central Maine, U.S.A. (Holdaway et al., 1988); (c) metapelites within thand (d) metapelites in the Augusta quadrangle, U.S.A. (Novak and Holdawa

is believed to be the geological reality of the staurolitezone rocks in the thermal contact aureole that metamor-phosed at nearly constant pressure.

Five regional contact metamorphic events (M1–M5)occurred in the Devonian and Carboniferous in westcentral Maine, among which the M3 and M5 are themost important two metamorphic events (Holdawayet al., 1988). These regional contact metamorphic zonescover a large area. Each metamorphic event was closelyassociated with the emplacement of S-type granites,such that the isograd patterns produced in the surround-ing pelitic schists generally follow plutonic outlines.

P and GBMAQ barometers. Solid lines represent the aluminosilicaterepresents the andalusite=sillimanite equilibrium of Pattison (1992).da (Mezger et al., 2001); (b) the regional contact metamorphic zones ine 0.5-km-long exposure at the Hunt Valley Mall, U.S.A. (Lang, 1991);y, 1981).

370 C.-M. Wu, G.C. Zhao / Lithos 97 (2007) 365–372

From north to south, metamorphic grade varies from thechlorite zone to the sillimanite–K–feldspar–muscovitezone, and these zones are designated from low to highgrades as Grades 3, 4, 5, 6 (M3) and Grades 6.5, 7 and8 (M5), respectively (Holdaway et al., 1988). Among thecontact aureole rocks, only Grades 5–8 rocks containaluminosilicates. Holdaway et al. (1988) suggested thatthe M3 metamorphism occurred at 3.1 kbar and the M5metamorphism at 3.8 kbar, but the GASP barometershows no obvious pressure variation more than 0.5 kbarbetween the M3 and M5 metamorphism. Thus these twoepisodes of metamorphism can be regarded to haveoccurred at identical pressure, around 4.8 kbar, withinerror (Supplementary Table 2; Fig. 2b). The GBMAQbarometer yielded similar pressure estimates to that of theGASP barometer (Supplementary Table 2; Fig. 2b) and

Fig. 3. Difference of pressure determination by the GASP and GBMAQ baroand (d) XFe of garnet.

gave an average pressure of c. 4.8 kbar. Furthermore, forthe 10 plagioclase-free samples forwhich pressures cannotbe determined by the GASP barometer, the GBMAQbarometer gave similar pressures, and the average pressurefor these plagioclase-absent rocks is around 4.5 kbar, veryclose to that of the GASP barometer within error.

Lang (1991) studied two metapelitic assemblages, astaurolite assemblage and a staurolite–kyanite assem-blage, which are randomly distributed along a 0.5-km-long exposure at the Hunt Valley Mall, northernBaltimore, Maryland, U.S.A. Of the thirteen samples,six samples contain kyanite whereas the other sevensamples are aluminosilicate-free. Application of thegarnet–biotite thermometer (Holdaway, 2000) andGASP barometer (Holdaway, 2001) to the kyanite-bearing samples yielded uniform metamorphic condi-

meters versus (a) temperature; (b) AlVI in muscovite; (c) XFe of biotite;

371C.-M. Wu, G.C. Zhao / Lithos 97 (2007) 365–372

tions of 568–583 °C and 5.3–5.9 kbar (SupplementaryTable 2; Fig. 2c). Combined with pressure estimates forthe aluminosilicate-free metapelites from the GBPQbarometer (Wu et al., 2004a), it is reasonably assumedthat a uniform pressure of c. 6.0 kbar has been reached.Lang (1991) has attributed the P–T uniformity andmineral assemblage difference of the two differentassemblages to the difference in bulk rock compositionsof these two kinds of rocks. Simultaneously applying thegarnet–biotite thermometer (Holdaway, 2000) and theGBMAQ barometer to the kyanite-bearing metapelites,yielded temperatures of 572–586 °C and pressures of6.3–6.8 kbar, respectively, identical to the GASPpressure within error (Supplementary Table 2; Fig. 2c).

Finally, we applied the GBMAQ barometer to themetapelitic assemblages in the Augusta quadrangle,south-central Maine, U.S.A. (Novak and Holdaway,1981) containing plagioclase although plagioclase wasnot analyzed. This metamorphic terrane underwent aseries of overlapping thermal events among which thefinal metamorphic event was with a heat sourcesupplied by a group of plutons west of the Augustaquadrangle (Novak and Holdaway, 1981). Novak andHoldaway (1981) determined the P–T conditions of thefinal metamorphism to be around 570±40 °C at 3.8±1 kbar by determining the intersections of the garnet–biotite thermometer and two plagioclase-absent, stau-rolite- and fluid-involving equilibria. Simultaneouslyapplying the garnet–biotite thermometer (Holdaway,2000) and the GBMAQ barometer yielded the P–Tconditions of 551–599 °C and 2.6–4.7 kbar (Supple-mentary Table 2), which are consistent with thealuminosilicate stability fields and phase transitionboundary (Fig. 2d).

4. Error consideration

Due to the lack of experimental GBMAQ equilibria,the absolute errors of the GBMAQ barometer cannot beevaluated. However, the close correlation between theGASP and GBMAQ barometers (Fig. 1) suggests that theGBMAQ barometer is in excellent accord with the GASPbarometer within ±1.4 kbar (mostly within ±1.0 kbar) inthe P–T range of 0.8–9.2 kbar and 530–700 °C.

We may anticipate the random error of the GBMAQbarometer through numerical simulation. For ourcollated samples, a T error of ±30 °C may propagateto P errors of ±0.53–0.64 kbar for andalusite-, ±0.60–0.75 kbar for sillimanite- and ±0.71–0.73 kbar forkyanite-bearing metapelites, respectively. An analyticalerror of ±2% for AlVI in muscovite may translate to ±0–0.01 kbar for all the three formalisms. An analytical

error of ±2% for Fe in biotite may translate to ±0–0.03,±0–0.02 and ±0.01–0.06 kbar for the three formula-tions, respectively. Finally, an analytical error of ±2%for Fe in garnet may translate to ±0.03–0.04, ±0.01–0.02 and ±0–0.003 kbar for the three formulations,respectively. Thuswemay infer that the total random errorof the GBMAQ barometer may not exceed c. ±0.8 kbar.

It is found that the pressure difference between theGBMAQ and GASP barometers is independent of eitherpressure (Fig. 1c), or temperature, or octahedral Al inmuscovite, or iron contents in biotite and garnet (Fig. 3),which suggests that this barometer has no systematicbias with respect to these factors.

5. Conclusion

The GBMAQ barometer has been empiricallycalibrated using low- to medium–high-pressure, mid-grade metapelites. This barometer is especially usefulfor assemblages with Ca-deficient garnet and/or Ca-deficient plagioclase, or for plagioclase-free metapelites.This barometer is thermodynamically consistent withthe garnet–biotite geothermometer (Holdaway, 2000)because they share exactly the same activity models ofboth garnet and biotite. The random error of the GBMAQbarometer is expected to be around ±0.8 kbar. Applicationof the barometer to metapelites from different metamor-phic terranes suggests that the GBMAQ and GASPbarometers show quite similar pressure estimates. TheGBMAQ barometer shows no systematic bias withrespect to either pressure, or temperature, or AlVI inmuscovite, or Fe in biotite or Fe in garnet. Application ofthis barometer beyond the calibration ranges, i.e., P–Trange and chemical ranges of the minerals, is notencouraged.

An Excel spreadsheet (Supplementary Table 3) forapplying the GBMAQ geobarometer is deposited at thejournal's website for download. The interested readermay also contact the authors for gaining the spreadsheet.

Acknowledgements

This paper has been greatly improved through criticalreviews by two anonymous referees and the editorialreview by Professor Ian Buick. This research wassupported by the National Natural Science Foundationof China (40472045, 40429001), the Hong KongResearch Grants Council (7055/03P, 7058/04P, 7055/05P), the National Basic Research Program of China(2006CB202201) and The Graduate University of ChineseAcademy of Sciences. This paper is in honour of ProfessorZhendong You (China University of Geosciences).

372 C.-M. Wu, G.C. Zhao / Lithos 97 (2007) 365–372

Appendix A. Supplementary data

Supplementary data associated with this articlecan be found, in the online version, at doi:10.1016/j.lithos.2007.01.003.

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