Journal of Petrology | Volume 44 | Number 5 | Pages 867-900 | 2003
© Oxford University Press 2003
Temperatures of Granulite-facies Metamorphism: Constraints from Experimental Phase Equilibria and Thermobarometry Corrected for Retrograde Exchange
1 DEPARTMENT OF GEOLOGY AND GEOPHYSICS, UNIVERSITY OF CALGARY, CALGARY, AB, T2N 1N4, CANADA
2 DEPARTMENT OF EARTH AND ATMOSPHERIC SCIENCES, UNIVERSITY OF ALBERTA, EDMONTON, AB, T6G 2E3, CANADA
3 DEPARTMENT OF GEOLOGY AND EARTH SYSTEM SCIENCE INTERDISCIPLINARY CENTRE, UNIVERSITY OF MARYLAND, COLLEGE PARK, MD 20742, USA
4 DEPARTMENT OF GEOLOGICAL SCIENCES, THE UNIVERSITY OF TEXAS AT AUSTIN, AUSTIN, TX 78701, USA
Telephone: 403-220-3263. Fax: 403-284-0074. E-mail: pattison{at}ucalgary.ca
RECEIVED MAY 29, 2002; ACCEPTED NOVEMBER 18, 2002
| ABSTRACT |
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This study assesses temperatures of formation of common granulites by combining experimental constraints on the PT stability of granulite-facies mineral associations with a garnetorthopyroxene (GrtOpx) thermobarometry scheme based on Al-solubility in Opx, corrected for late FeMg exchange. We applied this scheme to 414 granulites of mafic, intermediate and aluminous bulk compositions. Our findings suggest that granulites are much hotter than traditionally assumed and that the PT conditions of the amphibolitegranulite transition portrayed in current petrology textbooks are significant underestimates by over 100°C. For aluminous and intermediate granulites, mean corrected temperatures based on our method are 890 ± 17 and 841 ± 11°C, respectively (uncertainties reported as 95% confidence limits on the mean), consistent with minimum temperatures for orthopyroxene production by fluid-absent partial melting in these bulk compositions. In contrast, mean temperatures based on GrtOpx FeMg exchange equilibria, using the same thermodynamic data, are 732 ± 22 and 723 ± 11°C, respectively, well below the minimum temperatures for Opx stability. For mafic granulites, the mean corrected temperature using our method is 816 ± 12°C, similar to the mean temperature of 793 ± 13°C from FeMg exchange. Reasons for the differences between the mafic granulites and aluminousintermediate granulites are unclear but may be due to the lower Al concentrations in Opx in the mafic rocks and possible deficiencies in the thermodynamic modelling of these low concentrations. We discuss a number of well-known granulite terrains in the context of our findings, including the Adirondacks, the Acadian granulites of New England, the incipient charnockites of southern India and Sri Lanka, and the Kerala Khondalite Belt. Our findings carry implications for thermotectonic models of granulite formation. A computer program to perform our thermobarometry calculations, RCLC, is available from the Journal of Petrology website at http://www.petrology.oupjournals.org or from the authors at http://www.geo.ucalgary.ca/~pattison/drm_pattison-rclc.htm.
KEY WORDS: granulite-facies metamorphism; thermobarometry; garnet; orthopyroxene
| INTRODUCTION |
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Although thermobarometric studies of granulite terrains have been carried out for more than 30 years, the temperatures reported in many of these studies fundamentally disagree with fluid-absent experimental data delimiting the stability of granulite-facies mineral assemblages. This discrepancy can be attributed to one of two primary causes (e.g. Nair & Chacko, 2002
Resetting of temperatures is related to the diffusional mobility of elements on which conventional granulite thermobarometry is based. Table 1 lists diffusion coefficients and length-scales of diffusion (diffusion penetration distances) for some major elements in common minerals, calculated for 850°C and 10 Ma. The diffusion penetration distances vary over six orders of magnitude in a predictable fashion according to crystal chemical constraints (Dowty, 1980
), and suggest that there is little reason to expect simultaneous closure of elements at any point in a high-grade rock's PT history, let alone at peak PT conditions. Apart from the obvious implications for temperature, variable closure temperature also affects pressure estimates because these depend on the temperature [the feedback effect of Harley (1989)
].
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Many granulite temperature estimates in the literature are based on FeMg fractionation between coexisting phases such as garnet, biotite, cordierite, orthopyroxene and clinopyroxene [Grt, Bt, Crd, Opx, Cpx; abbreviations of Kretz (1983)
Focusing on the primary problem of closure temperature, two important questions are: (1) is the amount of retrograde FeMg exchange below peak granulite conditions generally modest (e.g. <50°C) or substantial (e.g. >100°C)? (2) If it is substantial, what methods can be used to see through its effects to infer peak granulite PT conditions? The first question has been addressed by kinetic modelling studies (e.g. Chakraborty & Ganguly, 1991
; Spear & Florence, 1992
; Ganguly & Tirone, 1999
), but the results have been equivocal owing to uncertainties in the diffusion data and their extrapolation to natural conditions (e.g. Pattison & Bégin, 1994a
, p. 388). The approach in this paper is to use constraints from experimental phase equilibria in concert with a geothermobarometry scheme based on Al-solubility in Opx in equilibrium with garnet, corrected for late FeMg exchange, which we have applied to 414 Grt + Opx + Pl + Qtz-bearing rocks from 62 granulite terrains worldwide. Whereas this combined approach has been used by Harley (1998a
, 1998b
) in his studies of ultra-high-temperature metamorphism, our focus is on the less exotic but more widespread ordinary granulites of common mineralogy. Our results suggest that commonly reported temperatures of granulite-facies metamorphism are significant underestimates, on average by >100°C. We discuss several well-known granulite terrains in the context of our findings, including the Adirondacks, the Acadian metamorphic high of Massachusetts, the incipient charnockites of southern India and Sri Lanka, and the Kerala Khondalite Belt. We then explore the implications of these higher temperatures for thermotectonic processes of granulite formation.
| RELATIONSHIP BETWEEN THERMOBAROMETRY, PHASE EQUILIBRIA AND aH2O |
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Important first-order constraints on the peak PT conditions of granulites are provided by a large body of experimental data on the PT stability of granulite-facies mineral associations (see below). In the absence of low-aH2O fluid infiltration, the characteristic anhydrous mineralogy of granulites (e.g. Grt, Opx, Cpx, sillimanite) results from supersolidus, vapour-absent dehydration melting reactions that consume muscovite, biotite and/or hornblende and produce a melt phase in addition to the anhydrous minerals (e.g. Brown & Fyfe, 1970
| EXPERIMENTAL CONSTRAINTS ON PT STABILITY OF GRANULITE-FACIES MINERAL ASSOCIATIONS |
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Figure 1 shows experimental and thermodynamically predicted positions of reactions that limit the PT stability of some key granulite-facies mineral assemblages for the three most common bulk compositions, here defined as mafic, intermediate and aluminous. The relevant wet solidi for each composition are also shown. Except at low pressure (<
3 kbar), the reactions occur above the wet solidi and so are dehydration melting reactions. The dehydration melting reactions shown in Fig. 1 were investigated in vapour-absent experiments, simulating conditions in natural (non-infiltrated) granulites in which any free fluid would have been consumed at the wet solidus down-grade of the dehydration melting reactions. The reaction positions shown in Fig. 1 are for the lowest-temperature occurrence of the diagnostic mineral or mineral association (e.g. Opx), and hence provide lower limits on possible PT conditions for rocks containing these minerals. To keep the diagrams legible, experimental brackets have been omitted and lines have been drawn by eye approximately through the midpoints of the limiting experiments of the respective studies. At a given pressure, the typical temperature interval between limiting experiments is 2550°C, so that individual lines should be considered as bands of width ±25°C or so.
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Mafic granulites
Mafic granulites (Fig. 1a) are characterized by Cpx- and/or Hbl-bearing Opx + Pl ± Grt ± Bt ± Kfs ± Qtz mineral assemblages, and are broadly basaltic in composition. The general reaction that first introduces Opx to Hbl + Pl ± Qtz ± Cpx ± Grt-bearing mafic amphibolites below
10 kbar is
![]() | (1) |
10 kbar, an analogous reaction introduces Grt + Cpx without Opx:
![]() | (2) |
Figure 1a shows the experimental constraints on reactions (1) and (2), with reaction (1) being of most interest to this study because it produces Opx. The various experimental studies on reaction (1) are in rather good agreement (850 ± 50°C over the pressure range 310 kbar, with no obvious pressure dependence), even though a fairly wide range of starting mineral compositions is represented [see table 1 of Pattison (2003)
].
Intermediate granulites
Intermediate granulites (Fig. 1b) are characterized by Cpx- and Hbl-free Opx + Pl ± Grt ± Bt ± Kfs ± Qtz mineral assemblages, and are broadly representative of metamorphosed psammites, semipelites and intermediatefelsic igneous rocks in which the major hydrous mineral is biotite. The general reaction that first introduces Opx to these rocks is
![]() | (3) |
800°C at 1 kbar to 900°C at 15 kbar. Vielzeuf & Clemens (1992)
The position of the reaction curve for dry melting of alkali feldspar solid solution + quartz in the NaAlSi3O8KAlSi3O8SiO2 system (Holtz et al., 2001
) is also shown. The position of this curve is a minimum for natural feldspars because addition of Ca results in an up-temperature displacement (e.g. Johannes, 1978
).
Aluminous granulites
Aluminous granulites (Fig. 1c and d) represent metamorphosed pelitic bulk compositions and may contain combinations of the aluminous minerals Grt, Crd, Al2SiO5 (sillimanite, kyanite or andalusite), spinel (Spl), sapphirine (Spr), corundum (Crn) and osumilite (Os), in addition to Opx and/or Bt (e.g. Harley, 1989
, 1998a
). Some workers consider any rock with stable Kfs + Al2SiO5 to be representative of granulite facies. The first appearance of this association is by the general reaction
![]() | (4) |
Comparing the position of reaction (4) in Fig. 1c with reactions (1) and (3) in Fig. 1a and b, the first appearance of Kfs + Al2SiO5 occurs 100150°C below the first appearance of Opx in mafic and intermediate compositions. In regional and contact metamorphic sequences in which the first development of Kfs + Al2SiO5 in metapelites and the first development of Opx in mafic and intermediate composition can both be mapped, the former is invariably significantly down-grade of the latter (e.g. Adirondacks: De Waard, 1969
; Bohlen et al., 1985
; New England: Schumacher et al., 1990a
; Ballachulish: Pattison & Harte, 1991
, 1997
; East Ontario Grenville, Carmichael in Davidson et al., 1990
; Broken Hill: Binns, 1964
).
We therefore prefer to define the amphibolitegranulite transition in metapelites by mineral associations that develop closer (both spatially in the field and, by extension, in pressure and temperature) to the first appearance of Opx in mafic and intermediate compositions, namely, Grt + Crd + Kfs (at pressures below
9 kbar) or Opx + Al2SiO5 (at pressures above
9 kbar). The lowest-grade reactions by which these assemblages develop are, respectively,
![]() | (5) |
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Higher-grade reactions in aluminous granulites involve the minerals or mineral associations sapphirine (Spr), osumilite (Os) and spinel (Spl) + Qtz, with Spr + Qtz indicating particularly high temperatures in excess of 1000°C (e.g. Hensen, 1971
; Harley, 1998a
, 1998b
). Figure 1d shows the estimated positions of some of the key quartz-bearing reactions in the FeMgAl2O3SiO2H2O (FMASH) system and their links to reactions (3), (5) and (6). For simplicity, Qtz-absent equilibria and those involving Os have been omitted, even though these are important in a full evaluation of the phase equilibria of ultra-high-temperature metamorphism (Harley, 1998a
, 1998b
, and references therein). The positions of most of the high-grade FMASH reactions in Fig. 1d are approximate owing to limited and sometimes conflicting experimental data and the strong effect of the water content of cordierite (Harley, 1998a
, 1998b
). In addition, the stability of Spl + Qtz is dependent on Zn content of Spl and on fO2 (Harley, 1998a
, 1998b
). Nevertheless, these mineral associations give useful first-order indications of especially high-grade conditions.
Comparison of experimental data with the amphibolitegranulite transition in textbooks and PT estimates from thermobarometry
Figure 2a compares the positions of the granulite-facies-limiting reactions for mafic, intermediate and aluminous compositions [reactions (1), (3) and (5)] with the amphibolitegranulite boundary from a number of widely used petrology textbooks. The positions of reactions (1), (3) and (5) in Fig. 2 (grey bands) represent the averaged positions from Fig. 1. If the experimental data are accurate simulations of natural granulite-forming reactions, it appears that commonly accepted PT conditions of the amphibolitegranulite transition are significant underestimates, by >100°C. The textbook positions are generally close to reaction (4) (minimum stability of Kfs + Al2SiO5; see Fig. 2a), although whether this is just a coincidence is unknown. Most of the textbooks define the amphibolitegranulite transition by the incoming of Opx in common mafic and intermediate bulk compositions, and place the incoming of Al2SiO5 + Kfs by reaction (4) in the upper amphibolite facies as discussed above.
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Figure 2b compares the position of reactions (1), (3), (4) and (5) with the array of granulite-facies PT estimates from table 1 of Harley (1989)
| GARNETORTHOPYROXENE Al-SOLUBULITY BASED THERMOBAROMETRY CORRECTED FOR LATE FeMg EXCHANGE |
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We attempt to address the above situation by developing and applying a thermobarometry scheme based on Al-solubility in Opx in equilibrium with Grt that corrects for the effects of late FeMg exchange. Al concentrations in Opx are expected to be preserved from peak granulite conditions because of extremely slow diffusion of Al (e.g. Anovitz, 1991
The rationale and approach of our scheme is not new, having been developed by Fitzsimons & Harley (1994)
and Pattison & Bégin (1994a)
, and refined by Chacko et al. (1996)
. The method reported in this paper is largely the same as reported in Chacko et al. (1996)
. Given knowledge of the pressure, the effects of late FeMg exchange are corrected for by adjusting the FeMg ratios of Grt and Opx to bring the Al-solubility and FeMg exchange equilibria involving the two minerals into agreement (i.e. into internal equilibrium). The above workers found that the corrected Al-solubility temperatures were up to 200°C higher than those based on FeMg exchange. We have refined the approach, using more recent thermodynamic data, and applied it to a large number of granulites worldwide to see if the predicted higher temperatures pertain to granulites in general. A key facet of our approach is the evaluation of the thermobarometry results against the limiting PT conditions of the granulite-facies mineral associations described above. A computer program that performs the calculations, called RCLC (for recalculation), is described below and in Electronic Appendix A. The program and accompanying explanatory notes are available for downloading from the Journal of Petrology website at http://www.petrology.oupjournals.org/.or from the authors at http://www.geo.ucalgary.ca/~pattison/drm_pattison-rclc.htm.
Thermodynamic data
Our thermobarometry scheme uses the TWQ2.02b thermodynamic database, based on the thermodynamic data of Berman & Aranovich (1996)
with modifications to incorporate the experiments of Aranovich & Berman (1997)
on Al-solubility of Opx in equilibrium with Grt in the Fe-end-member system. Use of a single internally consistent database for all phases instead of a range of individually calibrated equilibria (e.g. Harley, 1998a
, 1998b
) eliminates problems of inconsistency between calibrations. The GrtOpx experiments of Lee & Ganguly (1988)
were part of the experimental dataset used by Berman & Aranovich (1996)
in the derivation of the thermodynamic data. As a test of the precision and accuracy of the TWQ2.02b database, GrtOpx Al-solubility temperatures [based on equilibrium (8); see below] were calculated for 64 Grt + Opx-bearing experiments in FeMg ± Ca-bearing systems from three studies (Harley, 1984
; Lee & Ganguly, 1988
; Nair & Chacko, 2002
) (Table 2). Despite the variable quality of some of the experimental Al-solubility data [see discussion in Berman & Aranovich (1996)
and Aranovich & Berman (1997)
], the mean differences between the calculated temperatures and known experimental temperatures are <60°C, and in two of the studies are <35°C (overall mean for 64 samples is 45°C). In all cases, the mean calculated temperatures are lower than the mean experimental temperatures, suggesting that TWQ-based PT results if anything provide slight underestimates.
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Thermodynamic system
The thermodynamic system used in RCLC is summarized in Table 3. The rocks of concern contain the Grt + Opx + Pl + Qtz. Eight end-members in the five-component system CaFeMgAlSi (CFMAS) account for the compositional variability in these phases. The Al-component of Opx is described by the orthocorundum end-member, Al2O3 (Aranovich & Berman, 1997
![]() | (7) |
![]() | (8) |
![]() | (9) |
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Rationale for FeMg correction
Figure 3 shows two diagrams calculated using the TWQ software (Berman, 1991
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In Fig. 3a, the intersection of GrtOpx FeMg exchange equilibrium (7) with the GrtOpxPlQtz barometer expression (9) (point A) represents the conventional PT estimate of the rock (hereafter referred to as the uncorrected FeMg PT estimate). Aranovich & Berman (1997)
RCLC corrects for the effects of late FeMg exchange by adjusting the FeMg ratios of the phases according to mass-balance constraints so that all the equilibria intersect at a point (point C in Fig. 3b). This intersection is hereafter referred to as the corrected FeMgAl PT estimate. The implicit assumption is that this PT point represents the condition of equilibrium before the onset of late FeMg exchange (Fitzsimons & Harley, 1994
; Pattison & Bégin, 1994a
). As is the case with all methods of thermobarometry, this assumption is impossible to prove and may not be correct in all situations (for example, garnet and orthopyroxene may have grown at different times and therefore PT conditions, or may not have equilibrated with respect to Ca and Al). It nevertheless provides a rationale to correct for the obvious and in some cases substantial effects of late FeMg exchange.
The displacement of each equilibrium for the same amount of FeMg change depends on the standard state free energy (mainly enthalpy) change and the effect of the FeMg change on the equilibrium constant. Whereas equilibria (7), (10) and (11) show substantial displacement (compare Fig. 3a and b), equilibria (8) and (9) show more modest displacement. The corrected FeMgAl PT estimate (point C in Fig. 3b) is about 1·4 kbar and 170°C higher than the uncorrected FeMg PT intersection (point A in Fig. 3a), and about 70°C higher than the uncorrected FeAl PT intersection (point B in Fig. 3a).
Calculation method
To bring the equilibria to convergence, FeMg ratios of Grt and Opx are adjusted according to their modal abundance (assuming to begin with that Grt and Opx are the only two FeMg phases in the rock). Implicit in this approach is that intergranular and intragranular transport of Fe and Mg is efficient enough to effect complete FeMg exchange between the two phases. The sequence of steps to achieve convergence is as follows (refer to Fig. 3):
- calculate the PT position of the intersection of equilibria (8) and (9) (uncorrected FeAl PT estimate; point B in Fig. 3a);
- assuming constant bulk-rock composition and using the constraints provided by the modal abundance of Grt and Opx, change their FeMg ratios so that FeMg exchange equilibrium (7) coincides with point B;
- recalculate a new position for the intersection of equilibria (8) and (9) using the new FeMg ratios;
- repeat several times to obtain convergence.
In rocks that contain FeMg phases in addition to Grt and Opx, such as Crd and Bt, FeMg exchange is assumed to occur amongst all of the phases until Grt and Opx, the slowest FeMg diffusers (Table 1), close to further exchange. Step (2) can therefore be expanded to include Crd and Bt by incorporating their modal abundances into the mass-balance equation, and simultaneously solving for each phases's FeMg ratio so that each of the GrtOpx, GrtBt and GrtCrd FeMg exchange equilibria coincide with point B.
In the situation that the uncorrected FeMg PT estimate is higher than the uncorrected FeAl PT estimate (i.e. the positions of points A and B in Fig. 3a are reversed), the correction scheme works in the same way but results in a downward estimate in temperature. This situation probably indicates mineral compositions that are significantly out of equilibrium, perhaps as a result of the effects of retrograde net-transfer reactions, or of closure of one of Grt or Opx to FeMg exchange and continued exchange of the other with Crd and/or Bt as the rock cooled. We can envisage no situation in which Al would exchange to lower temperatures than FeMg. In these situations, the uncorrected FeAl PT estimates are probably more reliable than the corrected FeMgAl PT estimates.
Effect of varying mineral modes
Table 5 shows effects of varying mineral modes on the corrected FeMgAl PT estimates, using the mineral compositions in Table 4. The effects are rather small, even with extreme variations in modes. Thus, a reasonable PT estimate can be obtained by performing the convergence technique with Grt and Opx alone, regardless of the other FeMg minerals in the rock. Furthermore, the simplifying assumption that the FeMg adjustment can be taken up wholly by either Grt or Opx introduces relatively little error to the final calculated PT conditions [see fig. 17 of Pattison & Bégin (1994) for a graphical demonstration of this point]. These considerations become useful if modes or compositional information on FeMg phases in the rock other than Grt and Opx are lacking. On the other hand, the amount by which each phase changes its FeMg ratio varies significantly according to the mode, becoming most extreme for rocks with unequal modal proportions (Table 5).
Sensitivity of the method
Despite the obvious theoretical advantages of GrtOpx Al-solubility-based thermobarometry, Al concentrations in Opx are typically rather low (112 wt % Al2O3, mostly in the range 15 wt %) and the method is sensitive to small changes in Al concentration. Table 6 shows changes in inferred PT conditions for different Al concentrations in Opx, with all other mineral compositions held constant and the other elements in Opx varied proportionately (the mineral compositions are those listed in Table 4). For ease of comparison with other studies,
in Table 6 is the amount of octahedral Al in Opx assuming a six-oxygen formula [rather than the three-oxygen formula used in Table 3 and reactions (7)
(9)]. For uncorrected FeAl PT estimates, the sensitivity increases as the absolute Al concentration drops, going from
20°C/0·01
at
(
6 wt % Al2O3) to
50°C/0·01
at
(1·3 wt % Al2O3). For the corrected FeMgAl PT estimates, the effects are stronger (
30°C and 60°C, respectively) because of the magnifying effect of the FeMg correction.
The above considerations show that relatively subtle factors become important to PT estimation using GrtOpx Al-solubility methods. These include analytical precision, assumptions about Al partitioning between the tetrahedral and octahedral sites in Opx, and the effects of minor elements such as Na+, Fe3+, Cr3+ and Ti4+.
Droop (1987)
and Carson & Powell (1997)
discussed strategies for assigning Al between the octahedral and tetrahedral sites of Opx and for determining Fe3+ stoichiometrically from microprobe analyses. Regardless of sophistication, no approach can avoid the primary source of error, namely the accuracy and precision of Si and to a lesser degree Fe, Mg and Al. Ignoring initially the issue of Fe3+ and other minor elements, calculating
assuming ideal Tschermak exchange [(Fe,Mg)vi + Siiv = Alvi + Aliv] gives rise to the scheme
(for a six-oxygen Opx formula unit). In our processing of a large body of data from the literature (see below), we have found that this approach results in significantly less scatter and fewer obviously erroneous values than calculating
by the stricter site occupancy scheme
= AlM1 = Altotal (2 Si). With regard to Fe3+, in many cases the magnitude of inferred Fe3+ is similar to or smaller than the combined analytical uncertainty on Si, Fe, Mg and Al, perhaps accounting for the sometimes unpredictable pattern of calculated Fe3+ where there is no independent indication for significant variations in fO2 from oxides or other minerals in the rock. In addition, it is likely that the experimental Opx compositions from which the thermodynamic data were obtained contained at least a small component of Fe3+ that is not accounted for (all Fe is assumed to be Fe2+). Unless there is good evidence to indicate otherwise, we are therefore of the opinion that the dangers of overcorrection are as great as the dangers of undercorrection. Nevertheless, RCLC provides a variety of options for estimating
, including one that takes account of Fe3+ and other minor elements.
For the above reasons and in the interests of uniformity (many studies did not analyse for minor elements and/or assumed all Fe was Fe2+), we have followed Fitzsimons & Harley (1994)
, Aranovich & Berman (1997)
and Berman & Bostock (1997)
in assuming that
= Al/2 (for a six-oxygen formula). This approach provides a maximum estimate for
, which in some cases, particularly high-Al metapelites, may result in an overestimate of calculated temperature (see Appendix A and discussion below on Kerala Khondalite Belt). For low concentrations of Al in Opx (e.g. less than
2 wt % Al2O3), such as in many mafic granulites, the accuracy of the Al analysis may become an issue in itself (see discussion below). We therefore encourage reporting the standards used for Opx analysis along with the weight percent oxides.
Scatter in pressure estimates and the use of RCLC-P
Application of RCLC to a few natural datasets results in widely scattered pressure estimates beyond what is reasonable geologically, suggesting that in some samples the analyzed plagioclase and garnet compositions were substantially out of equilibrium. A modified version of RCLC, termed RCLC-P, allows pressure to be input as a known variable and calculates corrected FeMgAl temperatures by convergence of equilibria (7) and (8) at that pressure [essentially the method of Fitzsimons & Harley (1994)
and Pattison & Bégin (1994a)
]. RCLC-P is also useful if the Grt + Opx-bearing rocks have no plagioclase or the plagioclase compositions were not reported. For example, in estimating the temperatures of the Nain granulites of Berg (1977a
, 1977b
), a pressure of 5 kbar was assumed in the absence of information about Pl composition.
Testing of the method
We analyzed three datasets to test the above method. The first is that of Pattison & Bégin (1994a
), which was concerned with the variation with grain size of the composition of Grt and Opx in two regional granulites from the Minto granulite terrain of northern Quebec. FeMg ratios of core compositions of Grt and Opx show increasing degrees of retrograde exchange as grain size decreases, whereas Al shows little pattern with respect to grain size. Figure 4 shows temperature vs grain size for the uncorrected FeMg, uncorrected FeAl and corrected FeMgAl methods for the two samples. The strong dependence on grain size of the FeMg exchange temperatures is absent from both of the Al-solubility-based methods. In addition, the absolute values of the two Al-solubility methods are in better agreement with the phase equilibrium constraints (estimated from Fig. 1b as 850 ± 25°C at the
7 kbar pressure of the two samples), with the corrected FeMgAl temperatures showing the best agreement for B69E.
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The second dataset comes from the aureole of the Makhavinekh intrusion, Labrador (McFarlane et al., 2003
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The third dataset comes from the ultra-high-temperature rocks of the Napier Complex, Enderby Land, Antarctica (Sheraton et al., 1980
1000°C at 811 kbar (Harley, 1998a| APPLICATION TO GRANULITES |
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Based on the success of the three pilot studies, we applied RCLC to 414 Grt + Opx-bearing rocks from 62 granulite terrains using analyses in the literature, and evaluated the results against the phase equilibrium constraints. An obstacle to applying this analysis to more granulite terrains was the relatively common absence of data on the Al content of Opx, particularly in papers written in the 1970 s and 1980 s, perhaps reflecting the view at that time that FeMg exchange thermometry was all that was needed to estimate peak granulite temperatures. A more subtle factor influencing our results is our lack of control over, and many cases lack of knowledge of, the rationale used in selecting mineral analyses to be used for PT calculations. Different analysis points from the same minerals in the same rock can result in PT estimates that vary by several kilobars in pressure and hundreds of degrees Celsius in temperature (Spear & Florence, 1992
The Appendix lists the terrains, literature references, sample numbers and type of granulite (mafic, intermediate or aluminous) used in the compilation, the last being based on the mineralogical criteria given earlier. Of the 414 granulite samples examined, 80 are aluminous, 201 are intermediate and 133 are mafic. Electronic Appendix B lists key compositional parameters and calculated PT results for each sample using the uncorrected FeMg, uncorrected FeAl and corrected FeMgAl methods, and is available from the Journal of Petrology website or directly from the authors at http://www.geo.ucalgary.ca/~pattison/drm_pattison-research.htm#publications. Table 7 summarizes the results of Electronic Appendix B by listing, for the three types of granulite, the mean, standard deviation, 95% confidence limit on the mean, and range of the compositional parameters and PT estimates. What these statistics actually mean is somewhat unclear, given that the data almost certainly do not represent a Gaussian distribution arising from numerous independent, random perturbations. Systematic perturbations probably cause most of the scatter in the data, most of which result in a lowering of the temperature estimate (see discussion below).
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We caution that the results in Table 7 and related figures below show broad trends only and are influenced by the samples and terrains included in the analysis. For example, the ultra-high-temperature Enderby Land terrain and the high-temperature regional contact aureoles around Nain, Labrador, are represented only by intermediate and aluminous samples. In addition, we cannot apply RCLC to Opx-free Grt + Crd-bearing aluminous granulites or to Grt-free Opx+Cpx-bearing mafic granulites. Nevertheless, we believe that our sample base is broad enough that the general trends are meaningful.
Figure 6a and b shows trends of
vs
, and Mg/(Mg + Fe)opx vs
, grouped according to type of granulite. Compositional clustering in
vs
is obvious, with mafic granulites containing the most Ca-rich Grt and Al-poor Opx, aluminous granulites containing the most Ca-poor Grt and Al-rich Opx, and intermediate granulites in between. There is a gap in Grt composition between approximately
of 0·12 and 0·16, with values above the gap largely restricted to mafic mineral assemblages containing either or both of the calcic mafic phases Hbl and Cpx, and values below the gap restricted to intermediate and aluminous mineral assemblages lacking these phases. With respect to Mg/(Mg + Fe)opx vs
, there is a trend to more Fe-rich compositions in the most Al-poor Opx compositions and a weak trend to higher Mg/(Mg + Fe)opx as Opx becomes more aluminous, similar to that observed experimentally (e.g. Harley, 1984
; Lee & Ganguly, 1988
).
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Figure 7 shows differences in temperature and pressure between the uncorrected FeAl and uncorrected FeMg estimates (points B and A in Fig. 3) and between the corrected FeMgAl and uncorrected FeMg estimates (points C and A in Fig. 3), grouped according to the three compositional types of granulite. Pressure differences between the two sets of estimates are largely the same (Table 7) and so only the difference between corrected FeMgAl and uncorrected FeMg pressures is displayed. The temperature and pressure differences are strongly correlated because of the dependence of the pressure estimate on the temperature.
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Figure 8 illustrates compositional dependence of the results by plotting differences in temperature between the corrected FeMgAl and uncorrected FeMg estimates against
,
and Mg/(Mg + Fe)Grt, grouped according to type of granulites. Figure 9a plots the mean results from Table 7 with respect to the granulite-facies-limiting reactions from Figs 1 and 2.
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Aluminous and intermediate granulites
In aluminous and intermediate granulites, the mean difference between both the uncorrected and corrected Al-solubility-based PT estimates and the uncorrected FeMg PT estimates is substantial: 121 ± 16 and 158 ± 24°C, respectively, for aluminous granulites, and 84 ± 8 and 118 ± 12°C, respectively, for intermediate granulites (uncertainties reported as 95% confidence limits on the mean). These values are of a similar magnitude to those found by Fitzsimons & Harley (1994)
1 kbar higher. Regarding absolute temperatures, for aluminous granulites the mean uncorrected FeMg temperature (732 ± 22°C) is substantially below the minimum stability of Opx (Fig. 1), whereas the uncorrected FeAl and corrected FeMgAl temperatures (890 ± 17 and 854 ± 15°C) are consistent with Opx stability (Fig. 9a). The rather high mean corrected FeMgAl temperature for the aluminous granulites may reflect a combination of sample bias (several samples from ultra-high-temperature localities) and possible temperature overestimation for samples in which there is non-negligible Fe3+. For intermediate granulites, the mean uncorrected FeMg temperature (723 ± 11°C) is substantially below the minimum stability of Opx (Fig. 1), whereas the mean corrected FeMgAl temperature (841 ± 11°C) satisfies this constraint, with the mean uncorrected FeAl temperature (807 ± 10°C) falling in between. We consider that the overall agreement between the Al-solubility-based thermobarometry and the experimental constraints on Opx stability lends support to both approaches, and points to retrograde exchange as the most likely explanation for the discrepancy between the phase equilibria and geothermobarometry discussed in the Introduction. We caution that the PT estimates in Table 7 and Fig. 7 show considerable scatter. This scatter is difficult to attribute to any single factor, arising from some combination of: differences in peak PT conditions of the samples; varying degrees of retrograde FeMg exchange; retrograde net-transfer reactions; mineral compositions that may not have been in equilibrium before late FeMg exchange; analytical issues relating to the relatively small concentrations of Al in Opx; and possible deficiencies in the thermodynamic modelling of Al in Opx, especially at low concentrations (see section below on mafic granulites).
Figure 8a shows that temperature differences between the corrected FeMgAl and uncorrected FeMg estimates are positively correlated with
. This correlation is probably due to the fact that, for a given pressure, higher Opx Al contents indicate higher temperatures. The higher the peak temperature is above the closure temperature for FeMg exchange, the greater the expected difference between the calculated Al-solubility and FeMg exchange temperatures. This explanation probably also accounts for the greater spread in corrected FeMgAl temperatures compared with uncorrected FeAl temperatures, especially at higher absolute temperature (compare Fig. 7a and b, and 7d and e, respectively). Figure 8b shows a negative correlation between the above temperature differences and
, probably a secondary effect owing to the fact that
decreases as
increases (Fig. 6a). Figure 8c shows that there is no significant dependence of temperature difference on Mg/(Mg + Fe)Grt.
The mean difference between the corrected FeMgAl and uncorrected FeAl temperatures (points B and C in Fig. 3) is 45 ± 9 and 34 ± 4°C for aluminous and intermediate granulites, respectively (see Table 1). It could be argued that this difference is so small as to be immaterial, supporting Aranovich & Berman's (1997)
cautionary view of applying recorrection schemes. Our view is that if demonstrable and systematic errors can be corrected for it is worth while to do so, especially when in a number of cases the difference becomes significant (e.g. Enderby Land examples given above). About 10% of the aluminous and intermediate samples have uncorrected FeMg temperatures that are higher than the uncorrected FeAl temperatures. As discussed above, we consider the uncorrected FeAl PT estimates to be more reliable for these samples.
Mafic granulites
In mafic granulites, the mean corrected FeMgAl estimate (816 ± 12°C) is lower than in the intermediate and aluminous granulites but is still in agreement within error with the phase equilibrium constraints (Fig. 9a). In contrast, the mean uncorrected FeMg exchange estimate (793 ± 13°C) is considerably higher than in the intermediate and aluminous granulites. The higher mean pressure for the mafic granulites (
10 kbar) compared with the intermediate and aluminous granulites (68 kbar) is a result of the fact that garnet is a stable phase in mafic granulites only at relatively high pressure (e.g. Pattison, 2003
).
The temperature difference between the corrected FeMgAl estimate and the uncorrected FeMg exchange estimate (23 ± 16°C) is so small as to be insignificant (Table 7). Just under half of the mafic samples show FeMg temperatures that are higher than Al-solubility-based temperatures (Fig. 7gi). Figures 6 and 8a and b show that these results correspond to the generally low
in the more Ca-rich mafic samples.
The reasons for these patterns are unclear. Assuming that FeMg always closes at lower temperature than Al, the most likely explanations are: (1) FeMg diffusion is slower in Ca-rich garnets than in Ca-poor garnets, resulting in a smaller temperature gap between closure of FeMg and Al; (2) the rocks experienced retrograde net-transfer reactions (Spear & Florence, 1992
), leading to spuriously high FeMg temperatures; (3) the parts of the Grt and Opx analyzed were not in equilibrium before late FeMg exchange; (4) some of the analytical data for the generally low Al concentrations in Opx in these rocks are in error (too low); (5) the thermodynamic model for Al solubility in Opx loses accuracy at low
. Although slower FeMg diffusion may account for the higher mean FeMg exchange temperatures, it does not account for the many samples showing FeMg temperatures that are higher than Al-solubility temperatures. Analytical inaccuracy seems unlikely as a general explanation because in studies in which several samples were analyzed using the same procedure (e.g. Adirondack Highlands, Furua Complex: Appendix and Electronic Appendix B), some samples indicate Al-solubility temperatures higher than FeMg temperatures whereas others show the opposite. We see no reason why retrograde net-transfer reactions should be more prevalent in mafic granulites than in aluminous and intermediate granulites. We therefore think that thermodynamic inaccuracy is the most likely single explanation, perhaps augmented in some cases by selection of analysis points on minerals that were not in equilibrium and/or analytical errors. Additional experimental data and attendant thermodynamic modelling bearing on this question are needed.
Comparison with other refractory methods of thermobarometry
The results obtained with our GrtOpx Al-solubility method are comparable with those obtained with other thermobarometry methods based on refractory cation systems, such as reintegrated feldspar thermometry [Kroll et al. (1993)
and references therein] and reintegrated FeTi-oxideolivinepyroxene thermometry (Frost & Lindsley, 1992
; Lindsley & Frost, 1992
). For example, reintegrated compositions of mesoperthitic alkali feldspar grains in sample 45-84 from the Kerala Khondalite Belt of south India (Chacko et al., 1987
) indicate a temperature of 975°C [feldspar model of Fuhrman & Lindsley (1988)
] compared with uncorrected FeMg and corrected FeMgAl temperatures of 821 and 926°C, respectively, for the same sample. Mean corrected FeMgAl temperatures from the Enderby Land granulites (
950°C; see above) are similar to temperatures calculated from reintegrated mesoperthitic feldspars [9501050°C, using the analyses of Ellis et al. (1980)
and Sandiford (1985)
and the feldspar model of Fuhrman & Lindsley (1988)
], both of which show good agreement with the ultra-high temperatures (>950°C) indicated by metamorphic pigeonite (Sandiford & Powell, 1986
) and the Spr + Qtz mineral assemblages. Unfortunately, exsolution features in feldspars and pyroxenes are easily destroyed during later deformation (e.g. Frost & Chacko, 1989
), and are therefore considerably less widespread in granulite terrains than GrtOpx assemblages.
Our results are also comparable with those calculated with the oxygen isotope thermometry method of Farquhar et al. (1993)
, which corrects for the effects of retrograde isotope exchange. In applying this scheme to the high-temperature Enderby Land granulites and Spl + Qtz-bearing Taltson granulites (Chacko et al., 1994
; Berman & Bostock, 1997
; Grover et al., 1997
), Farquhar et al. (1996)
retrieved oxygen isotope temperatures >900°C that are consistent with the mineral assemblage stabilities.
Strategies for effective use of the method
The scatter of PT results using our method calls into question the reliability of any individual PT estimate, and suggests that to be confident of a PT estimate for a given area, many samples need to be analyzed. We also advocate element (X-ray) mapping of minerals before analysis points for thermobarometric calculations are selected so that zoning patterns can be interpreted and compositions that are obviously out of equilibrium can be avoided (see Pattison & Bégin, 1994a
; Kohn & Spear, 2000
). Even with X-ray maps, non-central sectioning of Opx grains is an important factor to consider, given the generally small corerim variation in Al content of individual Opx grains (typically
12 wt %) and the strong temperature dependence on these small changes. An unanswered question of fundamental importance to the use of Al solubility-based thermobarometry is the nature and controls of zoning of Al in Opx (e.g. McFarlane et al., 2003
).
| IMPLICATIONS FOR PT CONDITIONS OF GRANULITE-FACIES METAMORPHISM |
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The central conclusion of our study is that a significant number of thermobarometry-based temperature estimates for granulites over the past 30 years are too low and are therefore misleading. Many of these estimates are inconsistent with the stability of the mineral assemblages in the rock. A higher temperature for the amphibolitegranulite transition compared with traditional estimates (Fig. 2a) spreads out the PT range of the upper amphibolite facies. Concomitantly, it reduces the PT interval between ordinary granulite-facies metamorphism and ultra-high-temperature metamorphism (Harley, 1998a
In many cases it could be argued that thermobarometry, including our method, provides little additional temperature information beyond what the mineral assemblages indicate. Where our method of thermobarometry may be most useful is for bulk compositions that maintain the same mineral assemblage over large ranges of elevated P and T, such as in the 8001000°C range for intermediate and mafic bulk compositions (e.g. Fig. 1).
| PT ESTIMATES OF GRANULITE TERRAINS |
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Table 8 provides a summary of mean PT results for 24 terrains with six or more samples. The uncorrected FeMg PT estimates and corrected FeMgAl PT estimates are plotted in Fig. 9b with respect to the granulite-facies-limiting reactions from Figs 1 and 2. In terrains in which the corrected FeMgAl PT estimates are lower than the uncorrected FeAl PT estimates (e.g. Adirondack Highlands), we have plotted the corrected FeMgAl PT estimates to maintain consistency, even though we favour the higher estimates.
In some of the terrains, such as the Kerala Khondalite Belt and the Nilgiri Hills, the mean PT estimates are to some degree meaningless because of significant PT variations across the region from which the samples were collected. The main purpose of Fig. 9b is to show that the corrected FeMgAl PT estimates largely fall in or close to the granulite-facies stability field, in contrast to the uncorrected FeMg PT estimates which typically fall well below the granulite-facies stability field. Terrains in which a significant proportion of the sample suite consists of mafic granulites tend to show the lowest PT estimates [e.g. the Nilgiri Hills datasets of Raith et al. (1990)
and Srikantappa et al. (1992)
], and may be unreliable for the reasons discussed above. Some well-known granulite terrains are discussed separately below.
Adirondacks
The Precambrian rocks of the Adirondack region of upper New York State (Fig. 10a) comprise one of the best-known granulite-facies terrains in the world. In their summary papers on the granulite-facies metamorphism of the Adirondacks, Bohlen et al. (1985)
and Valley et al. (1990)
presented a pattern of isotherms based on a variety of geothermobarometers that they considered to represent peak or near-peak PT conditions. Kitchen & Valley (1995)
modified the distribution of isotherms in the NW part of the Adirondacks (Fig. 10b). Valley et al. (1990)
concluded that the granulite-facies metamorphism was largely driven by the magmatic processes of intrusion and partial melting, based on low calculated values of aH2O, abundance of migmatitic features associated with the granulite mineral assemblages, and absence of evidence for large-scale fluid infiltration.
|
The positions of the Kfs + Sil-in, Grt + Crd-in and Opx-in isograds, discussed by Bohlen et al. (1985)
Three possible explanations are: (1) the peak PT conditions have been significantly underestimated, especially in the vicinity of the isograds, as a result of retrograde cation exchange from peak conditions; (2) the isotherms record a later cryptic, broadly amphibolite-grade, metamorphic event that reset some element systematics but did not modify the peak mineral assemblages; (3) low-aH2O fluid infiltration has been widespread. Locally variable aH2O in the absence of fluid infiltration is not a tenable explanation if the peak mineral assemblages were developed by partial melting because aH2O is internally buffered by the mineral + melt assemblage. We accept the evidence of Valley et al. (1990)
against widespread fluid infiltration and therefore favour an explanation involving PT underestimation as a result of either retrograde exchange from peak conditions or the effects of a cryptic, lower-grade overprint.
An independent indication of higher peak temperatures in the Adirondack Lowlands in the vicinity of the isograds comes from a recalculated FeMgAl solubility temperature of 820°C for the one Grt + Opx-bearing sample (RS-34) reported by Edwards & Essene (1988)
. In the Adirondack Highlands, several recent studies have suggested peak temperatures higher than
850°C, including those by Spear & Markussen (1997)
and Alcock & Muller (1999)
. A puzzling aspect of the Adirondacks results in Table 8 is the higher mean temperature from FeMg exchange than from the Al-solubility-based methods, which may be due to some or all of the factors discussed above for mafic granulites in general.
Acadian metamorphic high
One of the classic prograde amphibolitegranulite transitions is represented by the Acadian metamorphic high in central Massachusetts. The higher-grade parts consist of the following zones, defined by mineral assemblages in pelitic compositions: Zone IIIMs + Sil zone; Zone IVMs + Sil + Kfs zone; Zone VKfs + Sil zone; Zone VIGrt + Crd + Sil + Kfs zone (Schumacher et al., 1990a
). Within Zone VI, Opx + Cpx + Pl assemblages occur in metabasites. The Zone IIIIV transition reaction corresponds approximately to reaction (4), the Zone VVI transition reaction corresponds approximately to reaction (5), and the development of metabasic Opx + Cpx + Pl assemblages in Zone VI implies PT conditions above reaction (1). Schumacher et al. (1990a
, fig. 9.9) provided the following approximate temperature boundaries between the zones, based on GrtBt FeMg exchange thermometry assuming a pressure of 6 kbar: IIIIV, 640°C; IVV, 670°C; VVI, 690°C. Thomson (2001)
estimated peak temperatures of 700750°C for Grt + Crd-bearing metapelitic granulites in Zone VI. Whereas Schumacher et al.'s Zone IIIIV estimate is in reasonable agreement with the minimum stability of Kfs + Sil at 6 kbar (
680°C), the Zone VVI estimate is >50°C below the minimum stability of Grt + Crd in metapelites [reaction (5)] and >100°C below the minimum stability of Opx + Cpx + Pl in metabasites [reaction (1)] (Fig. 9). Lack of reported Grt + Opx-bearing assemblages in Zone VI does not permit estimation of peak temperatures by our recorrection method.
Incipient charnockites of southern India and Sri Lanka
The incipient charnockite localities of southern India and Sri Lanka are characterized by the development of green-weathering, Opx-bearing assemblages in discrete planar and linear networks within white, grey and pink Opx-free gneisses (e.g. Janardhan et al., 1982
). These localities were the focus of intense interest in the 1980 s and early 1990 s because their formation was ascribed to channelled infiltration of low-aH2O (carbonic) fluids (e.g. Newton et al., 1980
; Janardhan et al., 1982
; Hansen et al., 1987
; Perchuk et al., 2000
), leading to a debate over the relative importance of infiltration-driven carbonic metamorphism vs thermally driven partial melting in the generation of granulites.
We have applied RCLC to 18 incipient charnockite localities in the literature (six of the seven KarnatakaTamil Nadu samples in the Appendix, eliminating one outlier, and samples 83-123, 4-10a, 121-166, 141-201, M-4, 23, 25, K18-6a, K18-17, 147-214, TN3-1 and TN21-4 from the Kerala Khondalite Belt). Two of the samples are mafic granulites with the rest being intermediate granulites. The mean and 95% confidence limit on the mean of the temperature estimates is 827 ± 18°C for a pressure range of 68 kbar, not significantly different from the equivalent values for all intermediate granulites (841 ± 11°C; Table 7). Even though low-aH2O fluid infiltration appears to have triggered the production of Opx in these localities, the amount by which aH2O in the fluid was lower than ambient values in the host gneisses might have been rather modest if the host gneisses were close to a temperature where they would produce Opx by closed-system dehydration melting.
This observation supports the suggestion of Frost & Frost (1987)
and Clemens (1992)
that intrusion and degassing of maficcharnockitic magmas, partial melting and local low-aH2O fluid infiltration are expected to be intimately related processes in granulite formation, and may occur in close proximity to one another in individual terrains rather than occurring as terrain-scale end-members. The southern Indian incipient charnockites may therefore represent sporadically developed, slightly lower-temperature, fluid-triggered granulite fronts that develop locally a little down-grade of the main expanse of granulite, the latter controlled largely by magmatic and partial melting processes. A counter-argument to the generality of this inference comes from the experimental study by Nair & Chacko (2002)
on dehydration melting of the host gneisses to some of the southern India incipient charnockite localities. As is typical of many of the south Indian localities, the gneisses contain biotite with high Ti and F contents. The gneisses did not undergo fluid-absent melting until temperatures in excess of 900°C (at P
6 kbar) were reached. For these localities, mean temperatures of
830°C from RCLC are well below the temperatures necessary for fluid-absent melting, suggesting that aH2O in the infiltrating fluid was significantly lower than in the host gneisses.
Kerala Khondalite Belt
The Kerala Khondalite Belt (KKB) of southern India (Fig. 11) is an example of a terrain in which the results of GrtOpx Al-solubility-based PT estimation resulted in a complete reinterpretation of the PT regime and associated thermotectonic evolution (Chacko et al., 1996
). Earlier studies based on FeMg exchange methods (e.g. Chacko et al., 1987
) suggested a rather uniform PT regime across the belt of 56 kbar and 700800°C (Fig. 11a). Recalculation of the same samples using RCLC reveals a sharp contrast between a lower PT (
800850°C, 6 kbar) central zone with numerous incipient charnockite localities, a northern marginal zone where extreme PT conditions (>950°C, 910 kbar) are found, and a southern marginal zone where less extreme but still elevated temperatures of 850950°C are found (Fig. 11b). Calculated temperatures taking account of stoichiometrically determined Fe3+ in Opx are on average 44°C lower for the whole sample suite but reveal the same regional pattern (Fig. 11c). The elevated temperatures in the marginal zones were attributed by Chacko et al. (1996)
to the intrusion of igneous charnockite in the massifs to the north and south of the KKB. Nandakumar & Harley (2000)
came to similar conclusions based on an independent set of samples.
|
The >950°C temperatures of the northern zone can be confirmed in a limited number of samples with exsolved feldspars. In the southern zone, Braun et al. (1996)
| THERMOTECTONIC MODELLING OF GRANULITES |
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The indication that most ordinary granulites form at considerably higher temperature than previously assumed carries significant implications for thermotectonic models of granulite formation. In granulites that show isobaric cooling paths and that may have formed along anti-clockwise PT paths, the heat source for the metamorphism is usually ascribed to mafic magmatic underplating (e.g. Bohlen, 1987
2030 km depth) by this means (England & Thompson, 1984
850°C and above (Fig. 1 and Table 8), much higher heat flow and heat generation parameters, or preferential incorporation of high heat-producing material at mid- to lower-crustal levels (Patiño-Douce et al., 1990| Supplementary Data |
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Supplementary data for this paper are available on Journal of Petrology online.
| APPENDIX: LOCALITIES, SAMPLES AND REFERENCES |
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| ACKNOWLEDGEMENTS |
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This research was supported by NSERC Discovery Grants 0037233 to D.R.M.P. and 0046751 to T.C. We thank Ron Frost, Simon Harley and Frank Spear for their reviews. D.R.M.P. thanks Jason Krauss, Ron Voordouw and Connie Sullivan for helping to compile data from the literature.
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, uncorrected FeMg method; , corrected FeMgAl method. Reactions are numbered as in the text and 









