quantitative temperature-time information from retrograde diffusion zoning in garnet: constraints...

J. metamorphic Geol., 1999, 17, 449–461

Quantitative temperature-time information from retrogradediffusion zoning in garnet: constraints for the P–T–t history of theCentral Black Forest, GermanyS. WEYER, 1* J . JARICK 1 AND K. MEZGER 1 , 2

1Max-Planck-Institut fur Chemie, Postfach 3060, D-55020 Mainz, Germany (e-mail: [email protected])2 Institut fur Mineralogie, Universitat Munster, Corrensstr. 24, D-48149 Munster, Germany

ABSTRACT Garnet from a kinzigite, a high-grade gneiss from the central Black Forest (Germany), displays a promi-nent and regular retrograde diffusion zoning in Fe, Mn and particularly Mg. The Mg diffusion profilesare suitable to derive cooling rates using recent datasets for cation diffusion in garnet. This information,together with textural relationships, thermobarometry and thermochronology, is used to constrain thepressure–temperature–time history of the high-grade gneisses. The garnet–biotite thermometer indicatespeak metamorphic temperatures for the garnet cores of 730–810 °C. The temperatures for the outer rimsare 600–650 °C. Garnet–Al2SiO5–plagioclase–quartz (GASP) barometry, garnet–rutile–Al2SiO5–ilmenite(GRAIL) and garnet–rutile–ilmenite–plagioclase–quartz (GRIPS) barometry yield pressures from6–9 kbar. U–Pb ages of monazite of 341±2 Ma date the low-P high-T metamorphism in the centralBlack Forest. A Rb/Sr biotite–whole rock pair defines a cooling age of 321±2 Ma. The two mineral agesyield a cooling rate of about 15±2 °C Ma−1. The petrologic cooling rates, with particular considerationof the fO2 conditions for modelling retrograde diffusion profiles, agree with the geochronological cool-ing rate. The oldest sediments overlying the crystalline basement indicate a minimum cooling rate of10 °C Ma−1.Key words: Black Forest; garnet diffusion modelling; geospeedometry; kinzigites; petrological cooling rate.

(Cygan & Lasaga, 1985; Chakraborty & Ganguly,INTRODUCTION1992; Schwandt et al., 1995; Chakraborty & Rubie,1996). However, application of these garnet diffu-The temperature–time evolution of metamorphic rocks

provides a very important constraint for any model that sion data to real geological situations is rare (e.g.Lindstroem et al., 1991; Spear & Florence, 1992; Florencerelates metamorphism and tectonic processes. In particu-

lar, the cooling rate of metamorphic terranes can provide & Spear, 1995; Spear & Parrish, 1996). In this study, acooling rate is estimated by modelling the diffusionvaluable information on the processes active during the

waning stages of an orogenic cycle (England & profile of garnet from a kinzigite (a high-grade gneiss inthe central Black Forest, Germany), and the results areThompson, 1984; Thompson & England, 1984; Spear,

1993). There are two important methods generally used then compared with the cooling rates obtained fromthermochronology and geological constraints.to obtain cooling rates for metamorphic rocks: thermoch-

ronology and geospeedometry. In thermochronology, The kinzigite samples were collected from the typelocality in the valley of the river ‘kleine Kinzig’ nearminerals with different closure temperatures are dated

(e.g. Mezger, 1990). In geospeedometry, the cooling rate Schenkenzell (Fig. 1). Since the introduction of theterm kinzigite for these rocks, it has been used widely(also called petrological cooling rate) is estimated by

modelling of retrograde chemical diffusion zoning in for rocks with a similar mineral assemblage (Odenwald:Busch et al., 1980; Ivrea zone: Schnetger, 1994).metamorphic minerals, especially in garnet. The theoreti-

cal and experimental aspects of this method were However, the term kinzigite is not unconditionallyrelated to a distinct genesis. In the Ivrea zone (Southernextensively discussed by Dodson (1973, 1986), Lasaga

et al. (1977), Lasaga (1983), Chakraborty & Ganguly Alps. Italy), the kinzigites are restites. In contrast, inthe Odenwald and in the Black Forest, partial melting(1991) and Ehlers et al. (1994). The advantage of

geospeedometry is that it should be possible, at least in plays only a minor role (Busch et al., 1980).principle, to obtain reliable cooling rates even for systemscooling rapidly, which is not possible with thermochron- GEOLOGICAL SETTINGology due to the analytical errors associated with theisotope measurements. The Black Forest is part of the Central Crystalline belt

of the Variscan Orogen (Fig. 1). It consists predomi-Different datasets for the cation diffusion parametersfor garnet have become available over the last few years nantly of high-grade polymetamorphic gneisses,

449© Blackwell Science Inc., 0263-4929/97/$14.00Journal of Metamorphic Geology, Volume 17, Number 1, 1999

450 S. WEYER ET AL .

migmatites, amphibolites, eclogites and S-type granites.The metamorphic grade ranges from lower amphiboliteto granulite facies with some blocks metamorphosedat eclogite facies conditions. Two major metamorphicepisodes can be recognized, an early high-pressurestage followed by a later low-P, high-T overprint.Post-tectonic granites are also a common characteristicof this high-grade metamorphic zone.

The Black Forest can be subdivided into threeNE-trending tectono-metamorphic zones, which, fromthe north to the south, are the Saxothuringian Belt,the Central Gneiss Complex, and the Southern Gneissand Granite Complex (Fig. 1). The Central GneissComplex represents the largest of the polymetamorphicbasement units. It consists predominantly of bandedbiotite–plagioclase paragneisses with a chemicalcomposition suggestive of a greywacke–shale prot-olith, and also includes tonalitic orthogneisses(Wimmenauer, 1984). Numerous small intercalationsof eclogites and granulite facies gneisses are indicativeof high-P and medium-P events. The entire CentralGneiss Complex was overprinted by a late low-P,high-T metamorphism (Wimmenauer, 1986; Stengeret al., 1989). Migmatization in the monotonous gneissesis widespread and is related to the last metamorphicoverprint (Flottmann & Kleinschmidt, 1989).

The P–T –t evolution of the basement of the BlackForest is rather poorly constrained. A pre-Variscanage (520±15 Ma, U–Pb on zircon) was interpreted byTodt & Busch (1981) as the intrusion age of tonaliticprotoliths (orthogneisses). Hofmann & Kohler (1973)interpreted Rb–Sr ages of 450–480 Ma, calculated frombest-fit lines for migmatite whole-rock samples, as theage of migmatite formation. High-pressure metamor-phism has recently been dated at 334–337 Ma bySm–Nd isochrons on garnet, clinopyroxene and whole-rock samples from eclogites (Kalt et al., 1994a). The(last) migmatization and low-P, high-T metamorphismwhich overprinted the eclogites was dated by Kaltet al. (1994b) at 336–330 Ma (U–Pb on monazite frommigmatites and monotonous gneisses, and Rb–Sr thin-slab dating of migmatites). Thus, the currently avail-able geochronological data cannot be used for a cleartemporal distinction of the high-P and the low-P, high-T stage. If the Sm–Nd mineral–whole rock isochronsfrom the eclogites date the high-pressure event (Kaltet al., 1994a), then the transition from the high-Pregime to the low-P, high-T regime must havehappened within a few million years. This interpret-ation is likely if the Sm–Nd system in garnet has ahigh blocking temperature (Cohen et al., 1988).However, if the blocking temperature is only around650 °C (Mezger et al., 1992), then the Sm–Nd system

Fig. 1. Simplified geological map of the Black Forest showingthe main basement units (CGC, Central Gneiss Complex) andthe location of the Kinzigite (samples). The inset shows theBlack Forest within the Variscan massifs of central Europe.

DIFFUSION MODELLING OF METAMORPHIC GARNET 451

dates the time of low-P, high-T overprint and the time inclusions of ilmenite (20–100 mm), some massive rutile,quartz and very small oriented needles which mightof eclogite formation is still unconstrained.

Cooling ages between 330 and 320 Ma from Kalt be rutile or sillimanite. The needles are too small formicroprobe analysis. In some inclusions there areet al. (1994a; Rb–Sr on biotite–whole rock) imply

rapid cooling and exhumation of the basement of the transitions from rutile to ilmenite.The garnet rims have inclusions of quartz, biotite orBlack Forest. Syn- and post-tectonic granites intruded

between 340 and 310 Ma (Brewer & Lippolt, 1974; feldspar. Along the rims garnet is mostly resorbed andreplaced by biotite and/or cordierite. Since cordieriteTodt, 1976) and at least parts of the orogenic belt were

exposed at the surface by 270–260 Ma as indicated by is never observed as an inclusion in garnet, it is likelythat it formed due to decreasing pressure at thethe presence of undeformed and unmetamorphosed

sediments (Upper Rotliegendes) discordantly overlying expense of garnet. Decreasing temperature probablyled to new biotite growth at the expense of garnet.the high-grade basement.Another possible source of retrograde biotite andcordierite growth is from the reaction of garnet with

ANALYTICAL TECHNIQUESsmall amounts of liquid. Textural and chemical evi-dence indicates that the production of retrogradeMajor element analyses were obtained for garnet,

biotite, plagioclase and ilmenite using two electron biotite and cordierite occurred close to the thermalpeak.microprobes (Cameca Camebax and Jeol JXA

8900 RL) at the Institut fur Geowissenschaften at the Microprobe analyses (Table 1) show a very distinctretrograde diffusion zoning in Fe, Mg and Mn of theJohannes-Gutenberg Universitat Mainz. The analytical

conditions for the JEOL probe were: accelerating outer 200–300 mm of the garnet. As shown in Fig. 2,the zoning is parallel to the garnet rim and must havevoltage 15.0 kV, beam current 10 nA and beam diam-

eter 2 mm (defocused). With the Cameca probe, all been generated subsequent to the last episode ofretrograde biotite growth at the expense of garnet. Inminerals except plagioclase (defocused, 5 mm) were

measured with a focused beam, the beam current was addition there is no change in the diffusion profile asa function of the juxtaposed mineral. The zoning12 nA and the accelerating voltage 15 kV. Standards

for the calibration included orthoclase (K), wollastonite profiles for Mg are very prominent and regular andthe Mg content decreases towards the garnet rim by(Ca, Si), MnTiO3 (Mn, Ti), albite (Na), corundum

(Al ), hematite (Fe) and Cr2O3 (Cr). Most of the about 30%. The Mn profiles are very steep and Mnincreases towards the rim by a factor of three (Fig. 3).analytical data used for thermobarometry was obtained

on the Cameca microprobe. The line profiles used for The cores are completely homogeneous in theseelements, but not in Ca. At the garnet rims there is nodiffusion and cooling rate modelling as well as the

compositional maps were obtained with the JEOL evidence for diffusion zoning of Ca. The Ca zoning iscut off by the newly formed garnet rim duringmicroprobe. The compositional maps given in Fig. 2

are semi-quantitative analyses and were obtained over retrograde formation of biotite and this must haveoccurred prior to the development of the diffusionan area of 1.5×1.5 mm of a garnet with 500×500

points (resolution 3 mm) and with an integration time zoning in Fe, Mg and Mn.Diffusivity for Fe, Mg, Mn and Ca varies in garnet,of 100 ms per point.

The techniques for the Rb–Sr and U–Pb analyses because of their non-ideal behaviour. An additionalcomplication is that the diffusion behaviour of anare described in Moller et al. (1998) and Mezger &

Cosca (1999). element depends not only on the charge and ionicradius of the element itself but also on the chemicalcomposition of the host garnet (Chakraborty &

PETROLOGY AND MINERAL CHEMISTRYGanguly, 1991). The zoning of Ca in the garnet coresof the kinzigite is strong evidence that its diffusion rateThe kinzigite occurs as small intercalations with diffuse

contacts to the surrounding biotite–plagioclase– in garnet from pelitic rocks is much slower than thediffusion rate of Fe, Mg and Mn. During metamor-cordierite paragneisses (Brauhauser & Sauer, 1911;

Busch et al., 1980). The mineral paragenesis is phism, Fe, Mg and Mn were completely homogenized,but the peak temperature was not high enough togarnet + biotite + plagioclase + quartz + cordierite

(pinite). K-feldspar is absent. Accessory phases include homogenize the Ca content, so that at least part of theoriginal growth zoning of Ca is still preserved. Thegraphite ± zircon ± monazite ± ilmenite ± rutile ±

sillimanite. The kinzigite has a slightly banded fabric truncation of the Ca zoning pattern in Fig. 2 can beused to estimate the amount of garnet that reacted towith large porphyroblastic garnet (up to 5 mm) and

plagioclase (up to 7 mm). biotite during the early stages of the retrogradeP–T path.

Retrograde diffusion zoning with increase in Fe,Garnet typically appears as subhedral porphyroblastswith abundant inclusions. In many garnets there are Fe/(Fe+Mg) and Mn, and decrease in Mg from core

to rim is common in garnet from high-grade rockstwo clearly distinguishable zones that seem to representtwo different growth stages. The cores have abundant (Spear & Florence, 1992; Robinson, 1991). Robinson


Fig. 2. Garnet element map (garnet ks 2.2-2): The outer 200 mm of the garnet shows retrograde diffusion zoning in Fe, Mg and Mnbut not in Ca. Part of the original growth zoning of Ca is still preserved. (a) Fe: red inclusions in garnet are ilmenite; (b) Mg: redphase inside and outside garnet is biotite, green phase outside garnet is chlorite; (c) Mn; (d) Ca: red phase is plagioclase.

(1991) suggested that a net transfer reaction was the same homogeneous composition and the highestFe/(Fe+Mg). Some biotite inclusions in plagioclaseresponsible for the Mn zoning. The Mn of the resorbed

garnet could equilibrate with the new physical garnet have slightly lower Fe/(Fe+Mg) than the matrixbiotite, and it is likely that this is the only biotite inrim in the presence of a fluid, but if cooling was rapid,

there would be insufficient time to homogenize Mn equilibrium with the garnet cores. Biotite is generallycompletely unzoned but it is possible that the matrixin the entire garnet. This mechanism for Mn increase

due to resorption is important for garnet because the biotite increased its Fe/(Fe+Mg) slightly during retro-grade metamorphism because of the garnet resorp-concentration of Mn is negligible in other Fe–Mg

minerals such as biotite. tion. The biotite inclusions in garnet have the lowestFe/(Fe+Mg) because they had no contact with the

Biotite forms 0.1–1 mm large xenocrysts that com-matrix biotite and re-equilibrated with garnet during

monly surround the garnet and plagioclase porphyrob-retrograde metamorphism. The composition of this

lasts in the kinzigite. There are two petrographicallybiotite varies only slightly with size and the inclusions

distinguishable biotite generations in the kinzigite. Theare generally too small to develop diffusion zoning of

older one is preserved only as inclusions in garnet ormore than a few micrometres in the surrounding garnet.

plagioclase porphyroblasts. The matrix biotite haspartially formed by garnet resorption and re-equili- Plagioclase occurs as large porphyroblasts as well as

fine grains in the matrix and is generally highlybrated with garnet during retrograde metamorphism.Most of the matrix biotite shows some chloritization. sericitized. Inclusions are less abundant in plagioclase

than in garnet. The most common inclusions areMicroprobe analyses reveal three chemically dis-tinguishable biotites: matrix biotite, inclusions in quartz and biotite with some garnet and very rare

sillimanite. Some plagioclase has very fine orthoclaseplagioclase and inclusions in garnet (Table 1). Thematrix biotite and the biotite rims around garnet have exsolutions. Plagioclase has a strong and blotchy


Table 1. Microprobe analyses of garnet, biotite and feldspar.

Garnet Biotite Plagioclase

ks2.2–1 ks2.2–1 ks2.3–1 ks 2.3–1 ks2.2 ks2.2 ks2.3 ks2.3–1 ks2.2 ks2.3–1

Core Rim Core Rim Incl. in PL Matrix Matrix Incl. in Grt Matrix Matrix Incl. in Grt

SiO2 38.45 37.49 38.92 37.88 36.36 36.14 36.54 36.72 60.56 60.70 58.61

Al2O3 21.53 21.04 21.64 21.14 15.98 16.13 16.20 17.67 25.08 25.24 26.41

FeO 28.49 31.39 27.41 31.49 15.31 16.34 16.67 12.02 0.03 0.13 0.17

MnO 1.03 2.58 0.96 2.56 0.07 0.05 0.06 0.06 – – –

Na2O – – – – 0.35 0.37 0.40 0.31 7.01 7.18 6.50

K2O – – – – 9.01 8.99 8.92 9.12 0.20 0.44 0.08

MgO 8.21 5.67 8.41 5.17 12.96 12.48 12.72 14.58 – – –

CaO 1.73 1.35 1.89 1.30 0.00 0.00 0.01 0.03 7.13 6.23 7.97

TiO2 0.03 0.09 0.04 0.03 4.48 3.58 3.52 4.20 – – –

Total 99.47 99.61 99.27 99.57 94.52 94.08 95.04 94.71 100.01 99.92 99.74

Normalized to 24 O

Si 6.00 5.97 6.05 6.03 5.48 5.50 5.50 5.42 2.69 2.70 2.62

Al 4.00 3.95 3.96 3.97 2.84 2.84 2.88 3.08 1.31 1.32 1.39

Fe 3.72 4.18 3.56 4.19 1.93 1.93 2.10 1.48 0.00 0.00 0.01

Mn 0.14 0.35 0.13 0.35 0.00 0.00 0.00 0.00 – – –

Na – – – – 0.10 0.10 0.12 0.09 0.60 0.62 0.57

K – – – – 1.73 1.73 1.71 1.72 0.01 0.03 0.00

Mg 1.90 1.35 1.95 1.23 2.91 2.91 2.86 3.21 – – –

Ca 0.29 0.23 0.32 0.22 0.00 0.00 0.00 0.00 0.34 0.30 0.40

Ti 0.00 0.00 0.00 0.00 0.51 0.51 0.40 0.47 – – –

OH – – – 4.00 4.00 4.00 4.00 – – –

Total 16.05 16.03 15.96 15.98 19.51 19.53 19.58 19.48 4.96 4.96 5.00

FM 0.66 0.76 0.65 0.77 0.40 0.40 0.42 0.32

alm 0.61 0.69 0.60 0.70

pyp 0.31 0.22 0.33 0.21

sps 0.02 0.06 0.02 0.06

grs 0.05 0.04 0.05 0.04

ab 0.63 0.66 0.58

or 0.01 0.03 0.00

an 0.36 0.32 0.41

compositional variation, with An contents rangingMETAMORPHIC CONDITIONS

from 25–40 mol%, and on average about 35 mol% An(Table 1). Even inclusions in garnet have the same The garnet–biotite thermometer and the barometers

GASP (3anorthite=grossular+2kyanite+quartz),range in An content. Diffusion of Ca in plagioclase isslower than in garnet (Spear, 1993) because of slow GRAIL (3ilmenite+sillimanite+quartz=almandine+

3rutile) and GRIPS (garnet (grs1alm2)+2rutile=kinetics of the coupled substitution Al+Ca=Si+Nawhich allows preservation of zoning profiles even 2ilmenite+anorthite+quartz) were used to estimate

the P–T conditions for the equilibration of theunder granulite facies conditions.kinzigites. For the garnet–biotite thermometer, thecalibration of Perchuk & Lavrent’eva (1983),Cordierite is completely pinitized in all kinzigite

samples, and it was not possible to obtain a chemical Kleemann & Reinhardt (1994) and Patino-Douce et al.(1993) were used. Pressures were determined with theanalysis. In some cases, the outlines of the subhedral

cordierite pseudomorphs are still preserved. Cordierite calibrations of Koziol & Newton (1988), Bohlen et al.(1983) and Bohlen & Liotta (1986) for the GASP,consumed garnet from the rim as well as biotite and

never occurs as inclusion in garnet. Thus cordierite GRAIL and GRIPS reaction, respectively. The press-ures and temperatures were calculated with themay not have been stable during garnet growth.program ‘Thermobarometry’ 2.0 of Kohn & Spear(1996; ftp://harold.geo.rpi.edu/pub/spear).Ilmenite and very rare rutile occur exclusively in garnet

cores. The inclusions are oval and 10–100 mm in size.Some grains are partly ilmenite and partly rutile Temperature estimatesindicating a reaction from rutile to ilmenite. Ilmenitecomposition is constant, in spite of some alteration The temperature for the peak of metamorphism is an

essential parameter in the diffusion calculations thatalong grain boundaries, which led to the transformationof ilmenite to pseudorutile. Some rare thick solitary follow and was calculated at 7 kbar (see pressure

estimates below). The various thermometers yield aneedles in garnet were identified as rutile, but it is notcertain whether the abundant very fine (width <1 mm) wide temperature range for the metamorphic peak

conditions (Fig. 4). The reliabilities of any of theseoriented needles are also rutile or possibly sillimanite.


Fig. 4. P–T diagram showing the metamorphic conditions ofthe kinzigite. (a) GRAIL, (b) GRIPS and (c) GASP give garnetcore pressures; (d) GASP gives the garnet rim pressure whichcorresponds to the peak metamorphic temperature. (1)Perchuk & Lavrent’eva (1983), (2) Kleemann & Reinhardt(1994) and (3) (Patino-Douce et al., 1993) give peaktemperatures. Dotted lines (4) give the closure temperature ofthe three thermometers. Dashed lines: Al2SiO5 phase diagramof Hemingway et al. (1991). Grey area: estimated P–T field forthe temperature peak.

rim composition are almost identical using all threecalibrations of the garnet–biotite thermometer. Theclosure temperatures were determined in two differentways: (1) using the garnet rim (5 mm from the physicalrim) and the adjacent biotite (TC1), and (2) using ahost garnet and biotite inclusions (TC2 ).

In the first case, reequilibration during coolinghappens nearly exclusively by the change of the garnetrim composition, while in the second case it isdominated by a change in the biotite composition. TheFig. 3. Garnet zoning profile (garnet ks2.11-1). Fe and Mg

zoning (a) and Ca and Mn zoning (b) is presented from core to two closure temperatures are in good agreement,rim. The zoning of Fe, Mg and Mn is generated by diffusion. indicating that the diffusive exchange seems to haveThe original growth zoning is at least partially preserved in the progressed similarly to temperatures of 600–650 °CCa pattern.

(Fig. 4)The calculation of closure temperatures is very

accurate, because Fe and Mg equilibrated in garnetcalculated temperatures were evaluated by relatingthem to petrological constraints based on the complete and biotite by diffusion during retrograde metamor-

phism. The determination of peak metamorphic tem-mineral assemblages in the kinzigite. The paragenesis,including the absence of staurolite, indicates a peak perature is more difficult, because it is not certain

whether biotite corresponding to peak metamorphictemperature of at least 700 °C, while homogenizationof Fe and Mg by diffusion of 2–5 mm garnet requires composition is still preserved. The most likely peak

biotites are inclusions in feldspar that have a slightlya minimum temperature of 700–750 °C (derived afterSpear, 1989). According to Chakraborty & Ganguly lower Fe/(Fe+Mg) than matrix biotite. If the Fe–Mg

exchange reaction operated, the matrix biotite should(1991), to homogenize Mn in garnet of 2 mm diameterrequires a thermal event lasting 100 Myr at 650 °C, have the lower Fe/(Fe+Mg). However, because of the

production of new biotite at the expense of garnet, thewhich is an unrealistically long time, or 1 Myr at800 °C. For garnet that has experienced 800 °C or matrix biotite became more Fe-rich (1–2 mol%). Thus

the matrix biotite would yield a higher peak metamor-more, Ca growth zoning has never been observed(Tuccillo et al., 1990; Martignole & Pouget, 1993). phic temperature with the garnet cores.Thus the expected peak metamorphic temperature isbetween 700 and 800 °C. Pressure estimates

This temperature estimate is confirmed using theabove mentioned thermometers which give a peak Pressures determined with the equilibria GASP,

GRAIL and GRIPS are 6.5–9 kbar. The pressuresmetamorphic temperature range of 730–810 °C (Fig. 4).The closure temperatures estimated with the garnet estimated with GASP can be separated into garnet


core and garnet rim pressures. The garnet core about 1 log unit below the upper stability curve forgraphite. This constrains log fO2 to about −17, if thepressures were determined with matrix feldspar and

with feldspar inclusions in garnet and give about H2O activity was maximum. This estimate is in goodagreement with the results based on the reaction8 kbar in both cases, with no systematic differences.

The garnet rim pressures determined with matrix 2Fe2Oilm3 +4TiOrtl2 =4FeTiOilm3 +O2 (Zhao et al., 1996)which yields values for log fO2 ranging from −16plagioclase are about 1 kbar lower, because of the

lower Ca content at the garnet rim. Since the zoning to −18.of Ca in garnet is not a diffusion zoning, the garnetrim seems to have grown during a pressure decrease, GEOCHRONOLOGICAL CONSTRAINTSincreasing temperature or during a second growthstage with a lower pressure. It is unlikely that this A thermochronological cooling rate can be derived

from the U–Pb ages of monazite combined with Rb–Srgarnet rim grew under retrograde temperature con-ditions since resorption has occurred near peak biotite–whole rock ages. With a closure temperature

of about 700 °C (Copeland et al., 1988), the U–Pbmetamorphic temperatures. Thus the pressures esti-mated for the garnet rim seem to fit with the peak monazite ages correspond to the metamorphic peak

conditions that were attained close to 341±2 Matemperature. Since ilmenite and rutile occur only asinclusion in the garnet cores, GRAIL and GRIPS can (Table 2; Fig. 5). The Rb–Sr biotite–whole rock system

(Table 3) gives an age of 321±2 Ma and correspondsonly be used to calculate garnet core pressures. Thepressures calculated with GRAIL are even lower than to the closure temperature of about 400 °C (e.g. Wagner

et al., 1977). This age is similar to the Rb–Sr agesthe rim pressures calculated with GASP. But usingGRAIL is questionable because the almandine compo- obtained by Kalt et al. (1994b) in other parts of the

Black Forest. The Rb–Sr age of 282 Ma obtained fornent of the garnet cores is reset in Fe during high-temperature metamorphism, such that the equilibrium sample ks2.5 is most likely the result of resetting due

to fluid infiltration that also affected some of thewith ilmenite might be destroyed. Even the GASPgarnet core pressures present only minimum values, kinzigites. This young age is identical to the age of

late hydrothermal veins obtained by Glodny (1997)because Ca may also be partially reset.The petrographic differences between garnet core from a location within a few hundred metres of the

kinzigite outcrop. Using the oldest and most likelyand rim indicate two different growth stages. Theoccurrence of rutile only in garnet cores is interpreted least affected mica age and the U–Pb ages for monazite

combined with the peak metamorphic temperatures,as an indication of a high-pressure stage, possibly thestage that led to the formation of eclogites in central the cooling rate has to be about 15±3 °C Ma−1.Black Forest. However, it is not possible to decidewhether the high-P event (growth of garnet cores) and

MODELLING RETROGRADE DIFFUSIONthe low-P high-T event (growth of garnet rims) are

PROFILES IN GARNETrelated to the same metamorphic cycle (clockwise P–Tpath) or whether the garnet cores are relics from an

Thermodynamic constraints and dataset usedearlier metamorphism.

Garnet is the most suitable mineral in high-grademetamorphic rocks to derive quantitative tempera-

fO2

conditionsture–time information from retrograde diffusionzoning. In many metapelites (including the kinzigite),It is necessary to estimate the fO2 conditions of the

kinzigite because this parameter controls volume the main exchange partner of garnet is biotite. Thevolume diffusion in garnet is much slower than volumediffusion in garnet. During metamorphism, fO2 in the

kinzigite was controlled by the presence of graphite. diffusion in biotite and intergranular diffusion, whichcan be considered as infinitely fast to a first approxi-At 750 °C and Pfluid=8 kbar, the upper stability limit

of graphite in the C–O–H system is at log fO2=−16 mation. Even in dry rocks, volume diffusion in biotiteis about 10 times faster than in garnet (Florence &(Ohmoto & Kerrick, 1977). In the presence of graphite,

the H2O activity in a fluid phase is always <1, because Spear, 1995). Thus the exchange reaction betweengarnet and biotite is controlled by the volume diffusionCO2 is present. At these metamorphic conditions, the

maximum H2O activity is 0.85 (Ohmoto & Kerrick, rate in garnet. Because of its slow diffusion kinetics,garnet often develops a retrograde diffusion zoning in1977). The presence of a fluid with H2O is very likely

during most parts of retrograde metamorphism as Fe, Mg and Mn along the rim, and this profile can beused to estimate the cooling rate.indicated by the growth of H2O-bearing phases during

retrogression (formation of biotite from garnet resorp- Fick’s second law describes the relation between thechange in concentration with time and the curvaturetion during high-grade metamorphism; chloritization

of biotite, sericitization of plagioclase and pinitization of the concentration profile with distance (x)of cordierite at lower temperatures). In the diagramlog fO2 versus T (Ohmoto & Kerrick, 1977), the curve dC

dt=D

∂2C∂x2

(1)of the maximum H2O activity is parallel and just


Table 2. U–Pb analytical data.

Ratio Age (Myr)

Sample 206Pb/204Pb1) 208Pb/206Pb2) 207Pb/206Pb2) 206Pb/238U2) 207Pb/235U2) 206Pb/238U 207Pb/235U 207Pb/206Pb

ks2.2–1 1888 5.5439 0.053182 (53) 0.05495 (16) 0.4029 (13) 343 342 337 (2)

ks2.2–2 6192 3.6454 0.053099 (49) 0.05422 (9) 0.3970 (7) 345 344 333 (2)

ks2.5–1 342.7 2.1960 0.052968 (195) 0.05469 (9) 0.3994 (16) 340 339 327 (7)

ks2.5–2 853.1 3.7848 0.053208 (77) 0.05490 (14) 0.4028 (12) 343 341 338 (3)

ks2.5–3 2067 3.5188 0.053211 (55) 0.05457 (9) 0.4004 (8) 345 344 338 (2)

1) Measured ratio corrected for fractionation.

2) Corrected for fractionation. Blank and common Pb using the isotope composition of plagioclase from sample ks2.2: 206Pb/204Pb=18.542 (18); 208Pb/204Pb=38.339 (38); 207Pb/204Pb=15.611 (16).

ignored. These considerations apply only for constanttemperature. Diffusion zoning in garnet, however,develops while the temperature changes during retro-grade metamorphism. Thus the equilibrium constantKD changes with time

ln K (t)=ln K0−DH0sRT0

t (Lasaga, 1983) (4)

where DH0 is the enthalpy of exchange reaction, T 0 isthe peak metamorphic temperature, K0 is the equilib-rium constant for the peak temperature T 0, and s isthe cooling rate. The parameters necessary to obtain acooling rate s by modelling a diffusion profile in garnetare DGrt0 , QGrt, DHexchange, T 0, the concentration (c0) ofthe species at the time T 0 and the radius (x) of thegarnet. All diffusion profiles are modelled using thecomputer code from Kohler et al. (1991) with a finitedifference approximation (step size=5 mm). A constant

Fig. 5. Concordia diagram for monazite from samples ks2.2 cooling rate was assumed for the calculations, definedand ks2.5: (1) ks2.2-1; (2) ks2.2-2; (3) ks2.5-1; (4) ks2.5-2; by T (t)=T 0−at (see Lasaga, 1983 or Dodson, 1973(5) ks2.5-3.

for details).For estimation of the cooling rate, the Mg diffusion

The diffusion coefficient D depends on the intensive profiles were modelled. Magnesium has the mostparameters P and T . However, in the context of this regular diffusion profile and the most experimentalstudy, the possible pressure ranges would have a datasets for diffusion in garnet are available for Mg.negligible effect and the relationship is described by an DH0 for the Fe–Mg exchange reaction between garnetArrhenius equation of the form and biotite is well known (17.6 kJ: Ferry & Spear,

1978).ln D

T=ln D0−

Q

RT(2) There are some important assumptions and require-

ments that have to be met to model a retrogradewhere Q is the activation energy for diffusion. The diffusion profile and derive quantitative tempera-Fe–Mg exchange with biotite can be described with ture–time information.the equilibrium constant 1 No other garnet reaction acted contemporaneously

with the Fe–Mg exchange by diffusion, and thus thedevelopment of the diffusion profile was not modifiedKD=

(Fe/Mg)Grt(Fe/Mg)Bt

(3)by changes in the garnet volume. This is the mostcritical point for modelling any metamorphic garnet.Cordierite is a minor phase compared to biotite, soSeveral diffusion profiles were determined for garnetthat the effect of exchange with cordierite can befrom the kinzigite and there is no discernible differencebetween obviously strongly resorbed and nearly unre-Table 3. Rb–Sr analytical data.sorbed garnet. Thus garnet resorption operated prior

Sample Rb (ppm) Sr (ppm) 87Rb/86Sr 87Sr/86Sr Age (Myr) to the onset of the development of the diffusion profile;nevertheless, the most unresorbed garnet was selectedks2.2 Whole rock 127.9 313.5 1.1818 0.71427 321±2

Biotite 217.9 5.930 111.42 1.21804 for this study. As shown in Fig. 3, the zoning profilesks2.5 Whole rock 101.4 320.4 0.9157 0.71299 282±2 for Fe, Mg and Mn are parallel to the rims of the

Biotite 101.8 10.15 29.358 0.82725garnet independent of the neighbouring mineral. Thus


it is assumed that the effect of resorption can be modify the diffusivity of an ion according to therelationshipneglected. In addition, the effect of net transfer reaction

must be much smaller for Mg than for Mn. Assumingall the Mn zoning of the garnet rims (Fig. 3b) is due

log D(P,T , fO2)#log D(P,T ,f ∞O2 )+1

6AlogfO2f ∞O2

Bto resorption of garnet and back diffusion of Mninto the remaining garnet, this results in a maximum (5)amount of garnet dissolution of 30 vol%. This dis-solution can account for a maximum increase in the This relationship was first described for olivine by

Buening & Buseck (1973). The fO2 conditions ofpyrope component at the garnet rim of 1–2 mol%. Inthis case, the estimated cooling rates are slightly too the kinzigite corresponds to a graphite–O2-buffered

system, since abundant graphite is present in thehigh because a maximum of 10% of the diffusionprofile is due to possible garnet dissolution during assemblage.

Chakraborty & Rubie (1996) undertook experimentsretrogression.2 DBt&DGrt, so that the diffusion rate is controlled by at 750–850 °C with natural garnet and a constant fO2

of 10−17.5 to determine Mg tracer diffusion coefficients.volume diffusion in garnet. The fact that the zoningprofile is always well developed, even if minerals other They compared their results with high P–T data

(Chakraborty & Ganguly, 1992; Chakraborty & Rubie,than biotite are in contact with garnet, is evidence thatintragranular diffusion is much faster than volume 1996) and found that there is no change in diffusion

mechanism from extrinsic to intrinsic between 750 anddiffusion in garnet. The regular diffusion zoningimplies that the exchange between garnet and matrix 1450 °C. The fO2 of 10−17.5 is similar to the C–O

buffer at the temperature of 750–850 °C. Thus thebiotite was aided by the presence of a fluid(Robinson, 1991). conditions during peak metamorphism of the kinzigite

were similar to the experimental conditions of3 The biotite composition is approximately constantduring the development of the diffusion profile, so that Chakraborty & Rubie (1996) at low temperatures. In

addition, the garnet composition of the kinzigite isthe closure temperature is only a function of theposition in the garnet. This seems to be the case since very similar to the samples used in the experiments of

Chakraborty & Rubie (1996), so that a compositionalthe modal amount of biotite is at least twice as highas the modal amount of garnet and there is no evidence effect on diffusivity can be excluded.

Schwandt et al. (1995) also determined self-diffusionfor a late biotite formation after closure temperaturefor exchange with garnet is reached. (see Ehlers et al., coefficients for natural garnet at similar temperatures

(800–1000 °C) and fO2 slightly lower than defined by1994). In addition, the amount of garnet exchangingwith the biotite is only a small fraction of the total the quartz+fayalite+magnetite (QFM) buffer. Thus

their fO2 was lower than that in the experiments ofmodal garnet.4 Only the zoning profiles of garnet grains that are Cygan & Lasaga (1985), but higher than in the

experiments of Chakraborty & Ganguly (1992) andcut close to their centre in the thin section are usefulfor cooling rate estimation (see Ehlers et al., 1994). Chakraborty & Rubie (1996). Their garnet had similar

pyrope-rich composition as used by Cygan & LasagaAlthough several zoning profiles of large garnet weredetermined, only the steepest profiles are most likely (1985) for their experiments.to represent a cut near the garnet centre and thus givethe real cooling rate.

ResultsFor modelling of the garnet diffusion profiles, the

experimental cation diffusion data from Cygan & All the diffusion data used for modelling the curvesshown in Fig. 6(a)–(e) are given in Table 4. DiffusionLasaga (1985), Chakraborty & Ganguly (1992),

Schwandt et al. (1995) and Chakraborty & Rubie profiles were modelled using the four datasets describedabove and using different cooling rates and peak(1996) were used. Cygan & Lasaga (1985) experimen-

tally determined self-diffusion coefficients of Mg in temperatures of 750 and 800 °C (Fig. 6a–e). Thediagrams also include the measured Mg diffusionpyrope garnet at temperatures of 750–900 °C and fO2

corresponding to the HM (hematite–magnetite) buffer. profiles of garnet ks2.3/1. All diffusion profiles weremodelled with a DH0 of 17.6 kJ mol−1 for the Fe–MgChakraborty & Ganguly (1992) conducted their experi-

ments at high temperatures (15–40 kbar and 1100– exchange reaction between garnet and biotite (Ferry& Spear, 1978). The curvature of the natural Mg1300 °C) and with a natural almandine–spessartine

pair. They determined the tracer-diffusion coefficients profiles is in excellent agreement with the modelleddiffusion profiles. The diffusion profiles in Fig. 6(a)–(c)D*

Tfor Fe, Mg and Mn from multi-component diffusion

profiles. The diffusion couples were encased in graphite were modelled with the estimated peak metamorphictemperature of 750 °C. The different datasets yieldcapsules, so that the fO2 conditions were defined

by the graphite–O2 buffer. For temperature changes cooling rates between 3 and <100 °C Ma−1.A cooling rate of 3 °C Ma−1 is obtained with thealong an fO2 buffer, the diffusion rate changes due

to the changes in temperature as well as fO2. dataset of Chakraborty & Ganguly (1992); coolingrates only slightly slower than 10 °C Ma−1 areAfter Chakraborty & Ganguly (1991), fO2 will


Fig. 6. (a)–(e) Mg diffusion profiles modelled for different cooling rates with different starting temperatures and differentexperimental diffusion parameters. (2) The measured garnet zoning profiles of sample ks 2.3-1.


Table 4. Diffusion data used for modelling. grade diffusion affect the garnet core composition.A higher cooling rate affects only the garnet rim

Dataset Diffusion coefficient Activation energy

(D0 ) (cm2 s−1 ) (Q) (kJ) composition.The data of Cygan & Lasaga (1985) yield unreason-

Chakraborty & Ganguly (1992) 1.1×10−3 284.5ably fast cooling rates even for the lower limit of theChakraborty & Rubie (1996) 1.82×10−6 226

Cygan & Lasaga (1985) 9.8×10−5 239 estimated peak temperature. However, with the pro-Schwandt et al. (1995) 1×10−4 294 posed fO2 correction of Chakraborty & Ganguly

(1991), the diffusion data of Cygan & Lasaga (1985)become very similar to the values of Chakraborty &Rubie (1996) and yield cooling rates of 3–10 °C Ma−1with 750 °C as a starting temperature. The diffusionobtained with the dataset of Chakraborty & Rubie

(1996). The cooling rates determined with the data of Schwandt et al. (1995) cannot be adaptedeasily and yield unrealistic results when applied to theChakraborty & Rubie (1996) data are higher because

they were calculated with a constant fO2, rather than kinzigites.a temperature-dependent fO2 of the C–O buffer(Chakraborty & Ganguly, 1992). Oxygen fugacity of

CONCLUSIONSthe dataset of Chakraborty & Rubie (1996) is onlyabout 1.5 log units higher than the C-O buffer for Modelling of retrograde diffusion profiles in garnet

can produce meaningful results that are in agreementpeak metamorphic conditions (750 °C). However,during retrograde metamorphism, DT,fO

2

of the buff- with thermochronological constraints. The best esti-mate for the cooling rate of the kinzigite is aboutered system used in the experiments of Chakraborty

& Ganguly (1992) decreases more rapidly than for a 15 °C Ma−1 for the samples used in this study whenthe petrological results are combined with the therm-constant fO2 (Chakraborty & Rubie, 1996). Thus

diffusion becomes slower during retrograde metamor- ochronological results. However, the choice of adequatediffusion data is essential, since the spread of coolingphism than it would be under constant fO2. The

dataset of Cygan & Lasaga (1985) gives a much higher rates estimated with different datasets is enormous.For pelitic high-grade rocks, the data of Chakrabortycooling rate of almost 100 °C Ma−1, which is also

much higher than the geochronological cooling rate. & Ganguly (1992) and Chakraborty & Rubie (1996)are likely to give the best results, since the garnet usedFor a peak temperature of 800 °C, the cooling rate

would be still higher. in their experiments is similar to natural ones and thefO2 of the experiments was controlled. Oxygen fugacityModelling with the diffusion data of Chakraborty

& Ganguly (1992) for the peak metamorphic tempera- seems to be important and diffusion data must beadapted if fO2 of the samples is different fromture of 800 °C gives a cooling rate of about

15–20 °C Ma−1, which is in excellent agreement with experimental conditions. For samples with higher fO2,close to the HM buffer, the experimental data ofthe geochronological cooling rate (Fig. 6d). The data

of Chakraborty & Rubie (1996) give a slightly faster Cygan & Lasaga (1985) might be more suitable.Garnet in the kinzigite of the Black Forest has well-cooling rate of 30–50 °C Ma−1 for this starting

temperature. In contrast, modelling with the dataset developed retrograde diffusion profiles 200–300 mmwide that can be used to test the experimentallyof Schwandt et al. (1995) gives an unrealistically low

rate of 0.3 °C Ma−1, even for 800 °C as starting determined diffusion data. Uncertainties exist in theinput parameters for modelling, particularly in thetemperature (Fig. 6e).assumption that net transfer reactions did not affectthe zoning profile significantly. This assumption can

Discussionbe somewhat problematic for metamorphic rocks ingeneral, but seems to be justified in this specific case.The datasets for Mg diffusion in garnet of Chakraborty

& Ganguly (1992) and Chakraborty & Rubie (1996) As shown in this study, the choice of experimentaldiffusion data and adjustment of the data to theyield the most reasonable cooling rates for the

kinzigites from the Black Forest. Assuming a peak appropriate physico-chemical conditions duringmetamorphism can result in geologically reasonabletemperature of 750–800 °C results in cooling rates of

3–50 °C Ma−1. The diffusion data of Chakraborty & cooling rates. Thus, based on the observations madehere on the kinzigites from the Black Forest, it shouldGanguly (1992) are considered to be the best for these

samples, because they determined DT,fO2

with buffered be possible to obtain reliable cooling rates in otherfavourable situations. However, more testing is neededfO2 and thus very similar conditions to those of the

kinzigites. Using these diffusion data, the best agree- to evaluate the experimental data in more naturalsettings.ment with geochronological results is achieved with a

peak temperature of 800 °C. The modelled profiles also Differences between a thermochronological and apetrological cooling rate may exist because the tem-show that the garnet cores should have preserved their

peak metamorphic composition. Only with an unrealis- perature range over which the cooling rate wasdetermined with the two methods is different. Thetic low cooling rate of <3 °C Ma−1 does the retro-


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quantitative temperature-time information from retrograde diffusion zoning in garnet: constraints...

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