American Journal of Science

[American Journal of Science, Vol. 302, June, 2002, P. 465–516]

American Journal of Science JUNE 2002

FIELD MEASUREMENT OF HIGH TEMPERATURE BULK REACTION RATES II: INTERPRETATION OF RESULTS FROM A FIELD SITE NEAR SIMPLON PASS, SWITZERLAND ETHAN F. BAXTER* and DONALD J. DePAOLO University of California, Berkeley, Department of Geology and Geophysics, Berkeley, California 94720 ABSTRACT. Bulk metamorphic reaction rates have been measured using Sr isotopes as tracers of reactive transport processes at a field site near Simplon Pass, Switzerland, employing the technique described in Part I of this study (Baxter and DePaolo, 2002a). The reaction rate, R, inferred, similar to the value first reported in ⴙ1.1 ⴙ5.5 Baxter and DePaolo (2000), is 1.4ⴚ0.4 ⴛ 10ⴚ7 yrⴚ1 (or R៮ ⴝ 7.0ⴚ2.0 ⴛ 10ⴚ9 g/cm2/yr normalized to the geometric surface area of plagioclase) which is several orders of magnitude slower than extrapolations of laboratory data. This rate suggests that attainment of local equilibrium may require 10’s of millions of years, and consequently equilibrium may not be closely approached in dynamic metamorphic systems if significant changes in P-T-X occur over shorter timescales. These data suggest that there is a problem in current extrapolations or applicability of laboratory kinetic data to natural high-temperature systems. Possible reasons for this discrepancy include differences in reactive surface area, reactant supply limited by slow diffusion of major elements, or an armoring effect by which access to grain interiors is limited. On the basis of microchemical patterns in plagioclase, we identify grain boundary migration (GBM) as the rate limiting process for accessing grain interiors, and thus for bulk reaction. Calculation of reaction quotients for six balanced mineral reactions suggests local disequilibrium for garnet with respect to its Ca content. The characteristic equilibrium lengthscales (Le) for Sr and Ca are both about 1 meter. Equilibrium based geochemical tools such as isochron geochronology or geothermobarometry are compromised within a distance Le of the lithologic contact. Bulk Sr diffusivity measured at the field site changes from 10ⴚ9 to 10ⴚ7 m2/yr, suggesting that the characteristics of the intergranular transporting medium (ITM) changed significantly during the early retrograde history of the field site. introduction

Common practice within the field of metamorphic petrology has been to assume the condition of local equilibrium (for example Brady, 1977; Ferry, 1986, 1994; Baumgartner and Rumble, 1988; Bickle and Baker, 1990; Cartwright and Valley, 1991; Bickle and others, 1995, 1997). This assumption is often justified on the basis of available laboratory kinetic data, which suggests reaction rates at high temperatures are very fast (for example Wood and Walther, 1983; Walther and Wood, 1984; also see Baxter and DePaolo, 2002a for further discussion). This assumption persists despite the results of several studies that show that extrapolations of lab data to nature must be made cautiously and only in circumstances where the same mechanisms are known to apply (for example Rubie and Thompson, 1985; Kerrick and others, 1991; Hacker and others, 1992; Luttge and Metz, 1993; Jove and Hacker, 1997; Mosenfelder and Bohlen, *Present Address: California Institute of Technology, Division of Geological and Planetary Sciences, MC 170-25, 1200 E. California Blvd., Pasadena, California, 91125

465

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E. F. Baxter and D. J. DePaolo—Field measurement of high temperature bulk reaction

1997). However, in the last decade, there has been a growing recognition of effects in nature that could be attributable to slower reaction or exchange rates, or to competing rates in high temperature systems (for example Lasaga and Rye, 1993; Barnett and Bowman, 1995; DePaolo and Getty, 1996; Eppel and Abart, 1997; Jove and Hacker, 1997; Skelton and others, 1997; Ague, 1998; Lewis and others, 1998; Abart and Pozzorini, 2000; Baxter and DePaolo, 2000; Ferry, 2000; Lasaga and Luttge, 2001; Waters and Lovegrove, 2002). Part I of this study (Baxter and DePaolo, 2002a), herein referred to simply as “Part I”, describes a technique whereby syn-metamorphic bulk reaction rates may be measured in the field on the basis of systematic Sr isotope measurements. In this paper, we present results of the implementation of this technique at a field site located near Simplon Pass, Switzerland. This analysis was first presented in Baxter and DePaolo (2000). In this paper further details of the data and analysis, refinements in the modeling, and implications of the inferred reaction rate, diffusivities, and other observations are discussed. technique for measuring reaction rates in nature

The technique exploits the potential for isotopic exchange about a lithologic contact where there was, prior to metamorphic processes, a sharp isotopic discontinuity. Dense sampling on both sides of the contact, and 87Sr/86Sr analysis of garnets, plagioclase, and whole rocks are required. Garnets provide information on an initial syn-metamorphic condition and time. Plagioclase and whole rock data provide information on the condition at the end of metamorphic exchange of Sr. Sr isotopes are passive tracers of the bulk rate of dissolution-precipitation reaction in the system – they do not drive reaction. Using coupled equations (eqs 8-10 in Part I) for diffusive transport of Sr through the intergranular transporting medium (ITM) with local exchange of Sr between the bulk solid and ITM, values for R, the local exchange rate between the bulk solid and the ITM (in grams/gram/year), and D*Sr, the total effective bulk diffusivity of Sr in the ITM (in meters2/year), in the system may be inferred. R can be related to the dissolution-precipitation rates of the individual minerals in the rock by: R⫽

冘 R 䡠 M 䡠 CC

Sr,i

i

i

(1)

Sr,bulk

i

where Ri are fractional dissolution rates (mass dissolved/mass of mineral/time) for each mineral, Mi is the mass fraction of the mineral in the rock, CSr,i is the strontium concentration in the mineral, and CSr is the strontium concentration for the bulk rock. D* is defined formally as: D *Sr ⫽

DSr␶ MKSr

(2)

␳s共1 ⫺ ␾兲 is the mass ␳f ␾ ratio of solid to fluid, ␳ is density, ␾ is porosity, and KSr is the equilibrium solid/fluid distribution coefficient for Sr. The reader is referred to Part I of this study for a full description of the technique, governing equations, assumptions and definitions of the parameters involved. where DSr is the diffusivity of Sr in the ITM, ␶ is tortuosity, M ⫽

field site

The field site, SP5, is located south of Simplon Pass, about 100 m west of the Alte Kaserne (Swiss Grid 650175E 115125N; fig. 1). It is structurally situated in the Lebendun Nappe on the west flank of the Lepontine Dome. The Lebendun Nappe is one of several nappe structures in the Alps with protolith deposition of PermianCarboniferous age (Bearth, 1972). The nappe is structurally bound on the top and

rates II: Interpretation of results from a field site near Simplon Pass, Switzerland Monte-Leone Nappe

Gneiss & Schist

Brig Switzerland

Pelitic Schist Garnet Amphibolite

Sim

Marble

plo

np as

Calcareous Schist

s

} }

467

N

Lebendun Nappe Mesozoic Metasediments

S

Quaternary Alluvium Simplon

ad plonpass Ro im Gondo

Site SP5

N

Simplon Li

ne

River

29

Strike and Dip of Folation

SimplonPass Road (covered)

DU

Fault

SWITZERLAND ITALY

D U

5Km

0

meters

250

Site SP5 DU 22 D U

29

Alte Kaserne

D U 26 43

28

22

33

River Traverse

Fig. 1. Geologic map of the field site SP5 near Simplon Pass, Switzerland. Taken from Baxter and others, (2002a).

bottom by younger Mesozoic metasedimentary strata. The Lebendun Nappe here contains three 8-15 meter thick horizons of garnet amphibolite interlayered with pelitic to psammitic metasediments. The protolith was likely deposited in a continental margin sedimentary basin as clay rich sediment (pelite) interlayered with basaltic lava flows (amphibolite) formed during the waning stages of the Hercynian Orogeny. P-T conditions and timing of metamorphism – past work.—Alpine metamorphism in the region reached peak garnet growth conditions (⬃600°C and ⬃8 Kb; Todd and Engi, 1997) at around 29.7⫾4.2 Ma (Vance and O’Nions, 1992). Slow cooling proceeded in the region until the onset of rapid exhumation commenced at about 16 Ma (Mancktelow, 1992; Grasemann and Mancktelow, 1993) in response to embrittlement (Mancktelow, 1992; Axen and others, 2001), the development of the cataclastic Simplon detachment fault (Mancktelow, 1992), and the passage of a complex rolling hinge through the Simplon footwall (Wawrzyniec and others, 2001). 40Ar/39Ar cooling ages from biotites at the field site indicate cooling through 360° ⫾ 30°C at 12.2 ⫾ 0.4 Ma (Baxter and others, 2002a). Additional P-T-t data collected from the field site in this study will be presented below. Rock sample characteristics.—Most samples were taken at the lowermost contact between pelite and amphibolite, just above the road (fig. 2). Sample locations reported are in meters perpendicular to the plane of the pelite-amphibolite contact. The contact between the pelite and amphibolite is quite sharp, easily recognizable and only slightly weathered. Individual sample thickness perpendicular to the bedding was 1.5-6 centimeters. Samples 97 BSP5 L, M, N, P, Q, R, and S were directly adjacent to one another, providing a continuous traverse across the lower contact. Additional samples were collected at the river traverse below the main SP5 site (see figs. 1, 2). Another sample, 98 BSP5 T, was collected about 30 meters along the contact away from the main sample traverse (fig. 2). These samples are all from the same pelite-amphibolite contact.

468


Fig. 2. Photograph of the sampling location, Site SP5, looking NNW. Coarse dashed lines show the approximate position of the pelite-amphibolite contacts. Fine dashed lines show the approximate position of the “vein zone” where exposed. The vein zone is also exposed in the river traverse below and to the left where it is further away from the contact.

Amphibolite mineralogy (figs. 3A, 4) includes (in order of decreasing abundance) amphibole, plagioclase, garnet, sphene, ilmenite, ⫾ biotite, and apatite. The biotite mode decreases from ⬃30 percent at the contact with pelite to zero beyond about 3 meters. Garnet porphyroblasts vary widely in abundance and size, with some as large as 7 millimeters in diameter. These large garnet porphyroblasts are rich in inclusions (⬃12 percent by volume) and display a rotational fabric indicating that the garnets grew syn-deformationally (fig. 4). The garnets in the amphibolite are complexly zoned, especially the largest porphyroblasts (fig. 5). The garnet inclusion population consists of (in order of decreasing abundance) plagioclase, amphibole, epidote, sphene, apatite, and ilmenite. The largest garnets have textures that indicate they have coalesced from many smaller (⬍500 ␮m) garnet nuclei (fig. 5). Garnets are sparser and rarely exceed 500 ␮m in diameter within 10 centimeters of the contact. These smaller garnets have fewer inclusions and display a simple concentric zoning pattern (fig. 6). Plagioclase in the amphibolite is also complexly zoned (fig. 7) Pelite mineralogy (fig. 3B) includes (in order of decreasing abundance) quartz, plagioclase, biotite, muscovite, chlorite, garnet, ⫾ ilmenite, apatite, and zircon. The pelite grades from a quartz-rich (86 percent SiO2) psammite at the contact to a more typical pelite (75 percent SiO2) within ⬃10 cm from the contact. Garnets in the pelite are unusually sparse and small, with maxima in mode (⬃5 percent) and diameter (200 ␮m) found closest to the contact with amphibolite. Garnets decrease in diameter and mode away from the contact, disappearing after several meters. “Vein zone”.—The amphibolite is noticeably different within a zone from about 1.4 to 2.5 meters from the contact with pelite. Most notable is the presence of anomalously abundant, layer-subparallel quartz veins (fig. 8). This zone is also characterized by thin (1-5 cm) lenses of pelite interlayered with the amphibolite, a marked increase in the abundance and size of garnet as compared to the typical amphibolite, and local galena mineralization within the quartz veins. Furthermore this vein zone can be traced laterally sub-parallel to the contact down to the river traverse where it is about 3 meters

rates II: Interpretation of results from a field site near Simplon Pass, Switzerland

469

A garnet

biotite

B

garnet muscovite

chlorite biotite

Fig. 3. (A) Microphotograph of amphibolite from sample 97 BSP5 P in thin section (plane polarized light). Amphibolite consists mainly of amphibole (gray) and plagioclase (white). Some biotite and a few small garnets may also be seen. (B) Microphotograph of pelite from sample 97 BSP5 V in thin section (plane polarized light). Pelite contains mainly quartz and plagioclase (white-gray), as well as biotite, muscovite, chlorite, and a few small roundish garnets. Field of view is about 4 millimeters.

away from the contact, and up to the location of sample 98 BSP5 T, where it is about 30 centimeters from the contact (fig. 2). Though extensive veining as in the vein zone does not exist elsewhere, there are several other randomly dispersed 1-3 centimeters thick pelite lenses within the amphibolite interior. sample preparation

Samples for isotopic analysis were prepared by cutting a fresh 100-300 gram chunk of rock, cleaning in an ultrasonic bath, crushing with a tungsten carbide mortar, and separating two splits: one for whole rock and one for mineral separate analysis. Whole rock samples were powdered using an agate ball-mill. Representative thin sections were also cut from most samples.

470


~6.5 mm Fig. 4. Rotated garnet in amphibolite sample 97 BSP5 E showing sigmoid inclusion trail pattern. Photo taken in crossed-polarized light.

Garnet (Gr26 Py6 Alm59 Sp9)

Garnet (Gr40 Py2 Alm45 Sp13) epidote: 2.2%

amphibole: 2.9%

sphene: 2.2%

plagioclase: 4.0%

apatite: 0.5%

ilmenite: 0.1%

Fig. 5. Calcium concentration map of a portion of a large garnet porphyroblast from sample 97 BSP5 C. Lighter, brighter color means higher Ca concentration. Note that there are two distinct compositional regimes within the garnet. Note also the abundant inclusions. The scale bar is 100 microns. Relative percent abundance for each inclusion type is shown.


471

Fig. 6. BSE (back scattered electron) images of smaller garnets from the amphibolite, sample 97 BSP5 P, near the contact. These garnets are nearly inclusion free and display a more regular concentric zoning pattern denoted by the dark shadow outlining a more Ca rich and Fe poor core. The unusual star-like pattern appearing in the right garnet is an imaging artifact.

As individual garnet porphyroblasts were too small to separate or analyze individually, bulk garnet mineral separates were collected from each crushed sample. In preparing garnet mineral separates a series of handpicking, magnetic separation, and hydrofluoric acid (HF) partial dissolution steps were undertaken to assure the final solid separate was as pure and inclusion free as possible (see Baxter and others, 2002b for details). Garnets will be used as monitors of the isotopic composition of the local ITM at the time of garnet growth, therefore contamination by inclusions, which may not have the same isotopic composition as garnet, must be avoided. Probe analysis of

Fig. 7. BSE image of an area of abundant plagioclase from the amphibolite, sample 97 BSP5 W within a garnet pressure shadow. The zoning is complex, but in general the darker (Ca poor) regions are representative of older plagioclase while the lighter (higher Ca) are representative of more recent growth. The box defines the region shown in figure 27. Scale bar is 100 microns.

472


Fig. 8. Photo of the vein zone at the river traverse. Note the abundant white quartz veins, and the thin gray pelite lenses. Abundant garnets in much of the vein zone amphibolite are barely visible as gray dots (arrows). The bedding here dips slightly to the right.

several garnet grains after purification shows that the remaining garnet is ⬃99 percent pure, and reproducibility tests (see sample 97 BSP5 E and L in table 1) show that the purification technique yields consistent garnet data where sufficient mass of garnet is available. Given the sparse abundance and small size of the pelitic garnets, efforts to concentrate and purify enough material for reliable analysis of pelitic garnets beyond 30 centimeters from the contact proved impossible. Sample 98 BSP5 D was the furthest sample from the contact where enough garnet could be separated. Replicate analyses revealed a lack of reproducibility, suggesting that the garnets may not have been entirely cleansed of inclusions. The pelite garnets have a very low Sr concentration (about 1 ppm) whereas the amphibolite garnets (which are much more grossular rich) have much higher Sr concentration (about 25 ppm). This difference means that small amounts of contaminant inclusions will greatly effect the pelite garnet 87Sr/86Sr but will have a comparatively small effect on the amphibolite garnets. Sample Dissolution, Separation, and Mass Spectrometry Once prepared and powdered, all samples were fully dissolved in HF, treated with HClO4 to drive off the fluoride, and brought up in 1.5N HCL. A mixed spike was added to an aliquot of each dissolved sample and analyzed on the mass spectrometer for the purposes of determining rough concentrations of Rb, Sr, Sm, Nd, and in some cases, Ca. Aliquots of each sample were spiked for precise determination of concentrations and isotope ratios by isotope dilution. Sample aliquots were loaded into ion-exchange columns in 1.5N HCl for separation of Rb, Sr, and Rare Earth Elements (REE). A secondary fine resin ion-exchange column was used to separate Sm and Nd. The separated samples were dried down for loading onto filaments. Rb samples were loaded onto Re boat filaments with silica gel and phosphoric acid. About 10 ng of Rb was loaded optimally, though for most garnet samples only 1-2 ng was loaded. Sr samples were loaded onto Re flat filaments with a TaO flux to improve ionization. About 100 ng of Sr was loaded optimally. Sm and Nd samples were loaded onto Re flat filaments. About 100 ng of Sm and Nd were loaded optimally. All chemistry and mass spectrometric analyses were carried out at the Center for Isotope Geochemistry at the


473

Table 1A

Whole-Rock Sr isotopic data

Reported errors are 2␴ analytical errors. Reproducibility of the standard was 0.710281 ⫾ 13 (NBS 987) over the duration of the analyses. 87Rb/86Sr errors are ⫾ 0.2% for whole rock samples. Procedural blanks were ⬍1 nanogram for Rb and Sr.

University of California, Berkeley. Sr and Nd isotopic data are presented in tables 1 and 2. Electron Microprobe Analysis Mineral compositions were analyzed with the Cameca electron microprobe at University of California, Berkeley using natural and synthetic standards at 15Kev and a primary beam current of 20 nanoamps. 10 second counting times were used for all elements except for Ca, for which a 20 second count time was used to improve counting statistics. Raw data were corrected with the MAN scheme (Donovan and Tingle, 1996) for major elements and off-peak background correction for trace elements (⬍1 wt percent). The grains analyzed for the four major phases in each thin section are either in contact with each other or within a few 10’s of microns. A summary of representative mineral data is presented in table 3A-D. Mineral end-member activities (also presented in Table 3A-D) are calculated from the following mixing models: Ma¨ der and others (1994) for amphibole, Fuhrman and Lindsley (1988) for plagioclase, McMullin and others (1991) for biotite, and Berman (1990) for garnet.

474

E. F. Baxter and D. J. DePaolo—Field measurement of high temperature bulk reaction Table 1B

Garnet and other mineral Sr isotopic data

Data in italic were early analyses not employing the ultimate preferred garnet preparation method. These were discarded on this basis and due to anomalous Sr isotopic ratios and correlated elevated Rb, and Rb/Sr ratios indicative of contamination by biotite. “hi” and “lo” indicate garnet fractions from the same bulk sample separated on the basis of their slightly differing magnetic susceptibility. Otherwise, all garnet analyses represent bulk separates. 87Rb/86Sr external error is ⫾0.5% for garnet. Blanks and standards are as reported above.


475

Table 2A

Whole-rock Nd isotopic data

All errors reported above are internal analytical 2␴ uncertainties. Nd data was corrected for fractionation using 146Nd/142Nd ⫽ 0.636151. Reproducibility of the standard was .511083 ⫾ 10 for Nd (Ames Metal) over the duration of the analyses. Sm/Nd total external errors are ⫾0.1% for all samples. Blanks are insignificant: ⬍10 pg for Sm and Nd.

Table 4 lists mineral end-member formulas and abbreviations used herein. XRF analysis on select whole rock powders was also performed at the University of California, Berkeley. Table 5 lists whole rock XRF data. conditions of metamorphism

Peak P and T conditions were determined by the TWQ multi-equilibria method of Berman (1991) using the mineral probe analyses and mixing models outlined above. Quartz was considered a pure phase with unit activity. Biotite, which exists only as a trace retrograde phase in the amphibolite far from the contact, was not used in the P-T calculations. Reactions involving only amphibole end-member substitutions were suppressed in the calculations. For zoned minerals, “rim” compositions were used. Samples close to the contact were not used for P-T calculations due to the evidence for thermodynamic disequilibrium among certain phases, which will be discussed later. The resulting peak P-T determination based on 4 independent reactions is 9.1 ⫾ 0.5 kbar and 612° ⫾ 17°C (fig. 9). These values are the average of P-T calculations for five samples far from the contact (samples BSP 5-W, E, A, B, C). The quoted error includes propagation of the standard deviations reported by TWQ. This error is useful

476

E. F. Baxter and D. J. DePaolo—Field measurement of high temperature bulk reaction Table 2B

Garnet and other mineral Nd isotopic data

in quantifying the degree to which the four independent reactions intersected in P-T space and the precision of the estimate. Uncertainties in accuracy, including uncertainties in mixing parameters and thermodynamic data, are surely higher: perhaps ⫾ 30°C and 1 kbar. TWQ geothermobarometry was also done on a single pelite sample where only two independent reactions could be used (Garnet-Biotite Fe-Mg exchange, and Garnet-Biotite-Plagioclase-Muscovite). For muscovite, the mixing model of Chatterjee and Froese (1975) was used. The inferred P-T conditions are 618°C and 8.5 kbar which are similar to the results from the amphibolite data. Though slightly high for the region, our P-T values agree with the reported values of 599°C and 8.15 kbar from near this specific locality reported by Todd and Engi (1997). constraints on the timing of metamorphism – this study

Attempts were made to date the garnets from the field site, but failed due to the adverse effects of reactive transport, poor isochron spread, and REE-rich inclusions in


477

garnet. Therefore the constraints on the timing of garnet growth are limited to the study of Vance and O’Nions (1992) (see above). Plagioclase-WR two point Rb/Sr isochrons for two different samples (BSP 5-E and BSP 5-L) were used to determine the age of plagioclase closure to Sr. The two plagioclase closure ages are 15.8 ⫾ 0.8 Ma and 17.2 ⫾ 0.8 Ma, respectively, yielding a conservative age constraint of 16.5 ⫾ 1.5 Ma. This time may be assigned to a plagioclase closure temperature of 540° ⫾ 60°C as follows. Plagioclase closure temperature is calculated using the closure equation (Dodson, 1973) for a 100 ␮m radius plagioclase sphere, with a cooling rate of 10°C/Ma, and using the diffusion parameters of Cherniak and Watson (1994) for An25 plagioclase. The error reported in the closure temperature calculation includes the uncertainty in the published diffusion parameters. Two biotite-whole rock Rb/Sr isochron ages (10.85 ⫾ .03 Ma and 10.66 ⫾ .02 Ma) were also calculated from samples BSP 5-E and BSP 5-L, respectively. The temperature-time data collected from the field site is summarized in figure 10 and is broadly consistent with other published cooling data from the area (Mancktelow, 1992; Steck and Hunziker, 1994). isotopic data

The isotopic data are shown in figures 11-14 and tables 1-2. Note the preservation of a 87Sr/86Sr isotopic step in the whole rock profile at the contact. The garnet analyses at ⫺0.15 meters appear to have a lower 87Sr/86Sr value than expected within the profile as compared to the smooth trend formed by the other garnet data near the contact. Further into the amphibolite, the whole rock and garnet samples have generally low 87 Sr/86Sr values reaching a minimum of .7059 in garnet at 5.3 meters, though there is some fluctuation. Data from the upper contact, in contrast to the lower, suggests a more limited extent of Sr bulk diffusion. Garnets near the upper contact were very sparse, so the study was focused on the lower contact. Not shown in figure 11 is a distal pelite whole rock analysis at ⫺4.72 meters. This sample has the highest 87Sr/86Sr measured of .743, and a lower Sr concentration (99 ppm). The vein zone, is characterized by elevated 87Sr/86Sr values in both garnet and whole rock. Sample 98 BSP5 T is actually located about 0.5 meters from the contact, but because it lies within the vein zone, 30 meters along strike, it is plotted within the vein zone in the figures. The Nd isotope data in the amphibolite have constant values right up to the contact. 143Nd/144Nd data in the pelite are more variable, but the 143Nd/144Nd values are much lower in general than those in the amphibolite. A few garnet samples have anomalously elevated 143Nd/144Nd values and may reflect some older inherited signature from included refractory minerals. Most of the garnet samples exhibit slightly lower 147Sm/144Nd than their respective whole rocks, which may indicate contamination by even tiny amounts of included REE-rich minerals such as apatite or epidote. interpretation and modeling of the isotopic data

The measured 87Sr/86Sr variation in the amphibolite, especially within ⬃1 meter of the contact, suggests diffusive exchange with the pelite. Furthermore, the difference between the garnet and WR Sr profiles indicates that the bulk solid matrix 87Sr/86Sr changed after garnet growth due to continuing reactive transport across the contact (in addition to radioactive decay). The contrasting patterns of garnet and whole rock 87 Sr/86Sr suggest local ITM-rock disequilibrium as a result of slow R (that is high Le) similar to the conceptual example shown in figure 7, in Part I of this study. There is no asymmetry that would suggest the existence of significant cross layer advection. However, the elevated 87Sr/86Sr of the vein zone (fig. 11), along with its other petrological characteristics suggest that it is a zone of localized layer sub-parallel fluid advection.

Amphibole compositions


Table 3A

478

Reported data represent the average of 3-5 individual probe analyses.

Biotite compositions

Table 3B

Reported data represent the average of 3-5 individual probe analyses.

(continued)

Table 3A

rates II: Interpretation of results from a field site near Simplon Pass, Switzerland 479

Garnet compositions


Table 3C

480

Table 3C

1—reported data represent the average of the three individual probe analyses with the lowest MnO content, generally near the rim. 2—reported data represent the average of the three individual probe analyses with the highest CaO content, generally near the core, except for V where the core values reported have slightly lower CaO than the rim.

(continued)


Table 3D


Plagioclase compositions

482

Table 3D

1—reported data represent the average of the three individual probe analyses with the highest CaO content, generally near the rim. 2—reported data represent the average of the three individual probe analyses with the lowest CaO content, generally near the core.

(continued)


484

E. F. Baxter and D. J. DePaolo—Field measurement of high temperature bulk reaction Table 4

Mineral end-member formulas and abbreviations

The lack of any significant change in the 143Nd/144Nd value in the amphibolite near the contact (fig. 12) indicates that Nd was essentially immobile during metamorphism and little (if any) cross-layer diffusive exchange of Nd occurred (that is D*Nd ⬍⬍ D*Sr). In this way, the Nd isotopic signature is useful in documenting the extent of heterogeneity prior to metamorphic exchange processes. The data suggest an originally homogeneous amphibolite with a sharp contact. Variations in pelite 143Nd/144Nd suggest that it may have had an isotopically heterogeneous protolith. Sample 98 BSP5 T (“x” symbols, fig. 12) shows a 143Nd/144Nd value intermediate between amphibolite and pelite suggesting some diffusional modification of Nd isotopes or protolith mixing of the thin pelite lens with the surrounding amphibolite. The modeling below uses the data from the lower contact only because there is no evidence of complications due to the presence of advection, and thus the system evolution may be modeled simply as a diffusive process. The isotopic history of the system will be modeled from the time of garnet growth (tinit) to the time of the cessation of metamorphic exchange of Sr (tfinal). The garnet data constrain the initial condition, and the whole-rock data constrain the final solid profile. Sr bulk diffusion occurs via the ITM, at a rate described by the parameter D*Sr. Local Sr isotopic exchange between the bulk solid and the ITM is modeled as a dissolution-precipitation process, operating at a rate, R. Through forward numerical modeling using the


485

Table 5

Whole rock XRF analyses

equations for diffusive-reactive transport (see Part I), values for LeSr, the equilibrium lengthscale defined as Le ⫽ ( D*Sr/R)1/2, and 具Rt典, the total time-integrated amount of reaction, will be derived from the best fit to the field data. Then, with constraints on tinit and tfinal provided by geochronology, direct constraints on R and D*Sr may be calculated. Initial Condition and Time (tinit) for Model Simulation The time of garnet growth, 29.7 ⫾ 4.2 Ma is used as the starting point for numerical simulations, tinit. Each pure garnet analysis preserves the average local ITM isotopic composition for the time interval of garnet growth, probably a few million years. To establish the initial condition, quasi-steady state ITM and solid profiles for initial (tinit ⫽ 29.7 Ma) values of R and D*Sr were constructed such that the ITM 87 Sr/86Sr profile fits the garnet data (see Part I of this study for discussion of the establishment of initial quasi-steady state profiles). The following constraints are imposed on the initial 87Sr/86Sr profile. First, the distal amphibolite value is set to equal the lowest 87Sr/86Sr data point analyzed. This value is from garnet 97 BSP5 B, which indicates the least disturbed amphibolite (.7059). Given the symmetry of the system and the constraint on the initial amphibolite 87Sr/86Sr value, the initial 87 Sr/86Sr profile for the pelite is determined iteratively so as to reproduce the observed inflection point in the data at the contact. In this way, reliance is placed heavily on the less complicated and more complete amphibolite data to constrain the entire initial profile. Initial isotopic heterogeneity and Sr concentration differences in the pelite (fig. 14) may account for the much higher 87Sr/86Sr ratio obtained on the distal pelite far from the contact (at ⫺4.72 m) which was not considered in the modeling. Figure 15A shows the initial quasi-steady state profiles used for the initial values of R (1.4 ⫻ 10⫺7 g/g/yr) and D* (3 ⫻ 10⫺9 m2/yr). The anomalously low garnet data points in the pelite 15 centimeters from the contact have been ignored in the fit. These garnet data are suspect due to the possibility of contamination, lack of reproducibility, and very small size. Numerous model iterations showed that observed garnet (at tinit) and WR (at tfinal) data cannot both be reproduced unless the solid lags the ITM profile at tinit. The initial solid profile which has nearly the maximum allowable deviation from

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E. F. Baxter and D. J. DePaolo—Field measurement of high temperature bulk reaction 12

Pressure (kilobars)

11

10

9

8

7

6 500

550

600

650

700

Temperature (Celsius) Fig. 9. P-T data collected from the field site. White diamonds indicate TWQ multi-equilibria determinations from amphibolite samples described in text. Black diamond is from the pelite sample. The black circle is a published P-T value from nearby (Todd and Engi, 1997).

the final solid profile (that is, it is nearly flat even near the contact) was used so as to ultimately retrieve a maximum possible value of R. The initial solid profiles may not have been as smooth as those shown in figure 15A – particularly in the pelite – but in the absence of more detailed information, the most simple profile shape is assumed. Such second order complexities will not significantly effect the overall result. End of Model Simulation (tfinal) and ⌬t The plagioclase–WR Rb/Sr closure age of 16.5 ⫾ 1.5 Ma represents the end of metamorphic exchange of Sr, tfinal, as plagioclase is the dominant Sr- bearing phase in 700

Temperature (Celsius)

Gt - Sm/Nd 600

Plag - Rb/Sr

500 400

Biot - Ar/Ar

Rb/Sr Musc

Biot - Rb/Sr

300 K/Ar Musc

200

Rb/Sr, K/Ar Biot FT Zircon

100 FT Apatite

0

35

30

25

20

15

10

5

0

Age (Ma) Fig. 10. Temperature-time data from site SP5 (black circles). Also shown are the data of Mancktelow (1992; gray circles) and Steck and Hunziker (1994; diamonds) from nearby localities. Figure taken from Baxter and others, (2002a).


487

0.720

clos e-u p

0.715

ontact er c w lo of

0.710

0.705 -1.2

-0.6

-0.4

-0.2

0.0

0.2

0.4

amphibolite

pelite

upper contact

vein zone

0.715

pelite

Sr/ 86Sr

-0.8

Whole Rock Garnet

0.720

87

-1.0

0.710

0.705 0

5

10

Meters Fig. 11. Sr isotopic data from site SP5. Whole rock data plotted are corrected back to 16.5Ma. Garnet data plotted are corrected back to 29.7Ma. Values for Sample 98 BSP5 T are indicated with an “x”.

the system. That is, once plagioclase is closed to further exchange of Sr, so too is the bulk rock. This time also happens to correspond to the onset of rapid exhumation and cooling of the nappe stack and other structural changes (Mancktelow, 1992; Graseman and Mancktelow, 1993; Wawrzyniec and others, 2001; Axen and others, 2001) as well as an inferred drop in bulk Ar diffusivity within the amphibolite at the field site (Baxter and others, 2002a). Given the values of tinit ⫽ 29.7 Ma and tfinal ⫽ 16.5 Ma discussed above, the total simulation duration, ⌬t, is 13.2 m.y. Model Assumptions The model includes several simplifying assumptions, which are discussed in detail in Part I of this study. The particular assumptions that may be evaluated by the specific characteristics of the field site are reviewed below. No advection.—Neither the data nor the field relations indicate that there was any significant layer-perpendicular advection. The vein zone has been avoided where evidence for layer-parallel flow exists. Layer parallel flow, if present at the contact, will have only a minimal effect (due to the transverse component of dispersivity) on layer perpendicular transport.

488

E. F. Baxter and D. J. DePaolo—Field measurement of high temperature bulk reaction 0.5124

clos e-u

0.5122

p

0.5120

tact con f o

0.5118

0.5116

0.5114

0.5112 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.5124 Whole Rock Garnet

vein zone

0.5118

0.5116

pelite

0.5120

pelite

143

Nd/ 144Nd

0.5122

amphibolite

0.5114 0

5

10

Meters Fig. 12. Nd isotopic data from site SP5. Whole rock data plotted are corrected back to 16.5Ma. Garnet data plotted are corrected back to 29.7Ma.

Constant Rb/Sr.—The 87Rb/86Sr ratio is taken to remain fixed during the simulation. The 87Rb/86Sr profile used is taken directly from the measured values (fig. 13). The anomalous vein zone values are ignored in the modeling. The pattern of Rb and 87 Rb/86Sr about the contact shows that Rb has been transported across the contact at some point during system evolution, but it is unclear when. However, the errors associated with treating the system as having the constant 87Rb/86Sr profile as shown are negligible, especially since the corrections due to decay of 87Rb to 87Sr are small for the young metamorphic age of the Alpine rocks. The Sr concentrations (fig. 14) are also taken to be constant. The shape of the ITM Sr concentration profile, required for modeling, is calculated from the solid Sr concentration data following equation 10 from Part I. All garnets grew during the same time interval.—As the entire system experiences the same metamorphic P-T-t path, bulk composition is the only variable that might influence the relative timing of garnet growth within the outcrop. Thus, this assumption holds for all of the amphibolite garnets and separately for all of the pelite garnets because their bulk compositions, respectively, are very similar. TWQ (Berman, 1991) geothermobarometry of five amphibolite samples and one pelite sample (BSP5 V) indicates that all garnets grew at about the same temperature (fig. 9), and therefore, over the same time interval.


489

4

Rb/Sr (model) Rb/Sr Data

3.5

87

86

Rb/ Sr

3 2.5

n vei ne zo

2 1.5 1 0.5 0 -2

-1

0

1

2

3

4

5

Meters Fig. 13. 87Rb/86Sr whole rock data from site SP5. The dark line shows the linear interpolation of the data used in the model simulations, which ignores the anomalous vein zone data.

300

Cs Cf Cs Data

Sr (ppm)

250 200 150 100 50 0 -6

-4

-2

0

2

4

6

Meters Fig. 14. Bulk Sr concentration data at the field site. Shown are the measured whole rock solid Sr concentration (Cs) data and the constant linear interpolation of Cs used in the modeling (thin line). The Sr concentration in the ITM (Cf) (assuming KSr ⫽ 1) is shown for the condition at the end of model simulation. The shape of the Cf profile is calculated from the Cs profile using eq 10 from Part I and is dependant upon the Le of the system.

490


A

0.715

29.7 Ma

87

Sr/ 86Sr

0.720

0.710

Fluid Init Solid Init Garnet 0.705 -0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

5.4

0.4

0.720

B 0.716

16.5 Ma 0.714

87

Sr/ 86Sr

0.718

0.712

Best Fit Fluid Best Fit Solid Whole Rock

0.710 0.708 -1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

Meters Fig. 15. Best fit model simulation for constant R ⫽ 1.4 ⫻ 10⫺7 g/g/yr. A) The initial condition at the time of garnet growth, which fits the garnet data for D*init ⫽ 3 ⫻10⫺9 m2/yr. B) The best fit to the whole rock data at the end of model simulation for D*final ⫽ 5 ⫻ 10⫺7 m2/yr. Figure amended and reprinted with permission from Baxter and DePaolo (2000). Copyright (2000) American Association for the Advancement of Science.

Garnets ceased to exchange Sr with the ITM subsequent to their growth.—Sr diffusivities in garnet are sluggish for the temperature range of these rocks (⬃600°C) (Burton and others, 1995; Ganguly and others, 1998). That fact, and the preservation of major element zoning patterns (figs. 5-6), suggests that the garnet preserved the 87Sr/86Sr from the time of its growth. Modeling Results Sensitivity tests, using both constant and time-varying values for R and D*Sr were conducted using a finite difference Fortran code. R and D* were kept spatially

rates II: Interpretation of results from a field site near Simplon Pass, Switzerland 0.720

Best Fit Solid Whole Rock

“vein zone” 0.715

pelite

amphibolite

87

Sr/ 86Sr

491

0.710

0.705 -1

0

1

2

3

4

5

6

7

Meters Fig. 16. Best fit as in figure 14 shown for the pelite interior. Note that the vein zone whole rock samples are significantly elevated above what would be expected for diffusional exchange with the main pelite alone. Sample 98 BSP5 T, a pelite lens, is marked with an “X”.

constant. The best fit (figs. 15, 16) is obtained for constant R, with 具Rt典 ⫽ 1.85, and LeSr increasing from 15 centimeters at tinit to 1.9 m at tfinal. R and D*Sr are computed from the geochronological constraints, obtaining R ⫽ 1.4 ⫻ 10⫺7 g/g/yr with D*Sr increasing log-linearly from 3.0 ⫻ 10⫺9 to 5.0 ⫻ 10⫺7 m2/yr. These results are nearly identical to those determined if the effects of Sr concentration variations are ignored (Baxter and DePaolo, 2000). Given the baseline pelite (⬃100 ppm) and amphibolite (⬃300 ppm) values far from the contact, there clearly was some diffusional exchange of bulk Sr. The effect of variable Sr concentration accounts for the slight asymmetry in the isotopic profile about the contact. The change in D*Sr (and Le) is required to fit both the steeply sloping initial garnet data and the more gradually sloping final solid data. Note the marked ITM-solid disequilibrium exhibited near the contact by the data and the best-fit model result (fig. 15B). This disequilibrium persists throughout model simulation as the solid is unable to react fast enough to keep up with the fluid. Variations in both R and D* are illustrated in figure 17, and reveal a very robust order of magnitude constraint on R and D*Sr. Considering the conservative errors in the geochronology and assignment of ⌬t, the time-integrated reaction rate, R, existing from near peak garnet-growth conditions (612° ⫾ 17°C), at 29.7 ⫾ 4.2, through early retrograde ⫹1.1 metamorphic conditions (540° ⫾ 60°C), at 16.5 ⫾ 1.5 Ma, is 1.4⫺0.4 ⫻ 10⫺7 g/g/yr. As discussed in Baxter and DePaolo (2000), even without the geochronological data, it is possible to obtain a limit on R from the value of Le alone. Note that the determined values of Le and 具Rt典 are independent of ⌬t. Using the mean value of Le (1.0 m) and the definition of Le, Le ⫽ (D*/R)1/2, gives R ⫽ D*Sr for the field site. R may be estimated by considering a plausible range of estimates of the parameters that define D*Sr (eq 2). Taking a range for porosity (␾ ) of 10⫺5 to 10-3; (Walther and Wood, 1986; Hanson, 1997; Hiraga and others, 2001), for tortuosity (␶) of 0.1 to 1.0 (Brady, 1983), for KSr of 1 to 10 (Kotelnikov and others, 1998), setting DSr to 0.6 m2/yr for aqueous fluid diffusion at 600°C (Oelkers and Helgeson, 1988) and, setting ␳s/␳f to 3, yields a range in D*Sr between 2 ⫻ 10⫺4 and 2 ⫻ 10⫺8 m2/yr. These represent maximum values corresponding to a completely fluid-filled and interconnected ITM. The corre-

492


A

0.720

87

Sr/ 86Sr

0.718 0.716 0.714

R=10 -8 R=1.4x10 -7

0.712 0.710

R=10 -6

0.708 0.706 0.722

B

0.720

87

Sr/ 86Sr

0.718 0.716 0.714

ending D*=5x10 -9 ending D*=5x10-8

0.712

ending D*=5x10 -7

0.710 0.708 0.706 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

Meters Fig. 17. Calculated model profiles of 87Sr/86Sr showing the sensitivity to changes in R. The size of the isotopic step at the contact indicates that R must be ⬃10⫺7 g/g/yr. Figure amended and reprinted with permission from Baxter and DePaolo (2000). Copyright (2000) American Association for the Advancement of Science.

sponding range in R is 2 ⫻ 10⫺4 to 2 ⫻ 10⫺8 yr⫺1, which brackets the inferred value of ⫹1.1 1.4⫺0.4 ⫻ 10⫺7 yr⫺1 derived using the geochronological constraints (fig. 18). Possibility of smaller ⌬t or episodic reaction.—Recent studies (for example Young and Rumble, 1993; van Haren and others, 1996; Graham and others, 1998) have documented the existence of short-lived and/or episodic (103⫺105 yr) reactive-transport events, characterized by interaction with an exotic advecting fluid and enhanced reactivity. Such a scenario is allowable here so long as 具Rt典 ⬇ 1.85 to reproduce the isotopic step at the contact. However, the discussion of LeSr above rules out the possibility that reaction rates were even transiently higher than 2 ⫻ 10⫺4 yr⫺1 (or 10⫺2


493

10 -1 D* range for fluid filled ITM

D* for partially fluid filled ITM

t=1Ka

t=100Ka

10 -5

10 -7

10 -9

.9

=1

Le

10 -11 10 -10

t=13.2Ma

.15

=0

Le

maximum possible D*

R (yr-1)

10 -3

10 -9

10 -8

10 -7

10 -6

10 -5

10 -4

10 -3

D* (m 2 /yr) Fig. 18. Range of R and D* possible given the constraints on Le and 具Rt典 from site SP5. Le at site SP5 ranged from 1.9 meters to 0.15 meters. 具Rt典 was 1.85. The shaded oval labeled (13.2 Ma) would be for the exact values of R and D* associated with a total exchange duration of 13.2 Ma. Shorter total exchange times are shown in ovals labeled “100 Ka” and “1 Ka”. Shorter reaction timescales require very high absolute values of D*, in some cases higher than physically possible (see text). Lower D* is always possible if the ITM is not completely fluid filled. D* for pure grain boundary diffusion is slower than the scale depicted.

yr⫺1 for the minimum Le ⫽ 0.15 m) because D*Sr would need to be implausibly high (see fig. 18). It is also possible that the value of R changed more smoothly from peak to early retrograde time. For example, another best fit was found allowing R to vary log-linearly in time, where Rinit ⫽ 3.3 ⫻ 10⫺7, Rfinal ⫽ 3.3 ⫻ 10⫺8 and D*init ⫽ 5.0 ⫻ 10⫺9, D*final ⫽ 5.0 ⫻ 10⫺7. In this case, most of the reaction happens early on as the reaction rate slows. As it is difficult to constrain if/how R might have fluctuated, the time integrated value (1.4 ⫻ 10⫺7 g/g/yr) is the most useful value of R we can report. But, consider that if R had been as high as 10⫺6 yr⫺1 for 4 m.y. (or 10⫺5 yr⫺1 for 0.4 m.y.) at any time during metamorphism, 具Rt典 from that time alone would be 4, and the step in the solid profile at the contact would have been nearly lost. Although the derived R from this study applies directly only to the time between garnet growth and plagioclase closure, it is unlikely that the prograde R was ever much higher than 10⫺7 g/g/yr. Evidence for Localized Advective Transport and Small Scale Diffusion Figure 16, which illustrates the best fit model results further into the amphibolite, displays anomalously elevated 87Sr/86Sr values in the vein zone above what would be expected from pure diffusional exchange with the pelite across the main contact. Amphibolite whole rocks even further from the contact (between 4 and 7 m) also appear to have slightly high 87Sr/86Sr ratios for the best fit, indicating that some other process may have also affected them. Vein zone advection.—The vein zone has the most evidence of advection within the system: not cross-layer, but layer sub-parallel. Whereas the Sr isotope ratios are anomalously elevated (fig. 16), whole rock Nd isotope ratios and Sm/Nd ratios are the

494


same in the vein zone as in the normal amphibolite (fig. 12). This observation suggests that the differences in 87Sr/86Sr were not original protolith heterogeneities but rather had to have originated during metamorphism. There may have been some small scale diffusional exchange with the few pelite lenses (such as sample 98 BSP5 T), but that cannot account for the local galena mineralized quartz veins or the unusual abundance of garnet and biotite. Most likely, a layer sub-parallel advecting fluid carrying a high 87Sr/86Sr isotopic signature flowed through this zone and deposited the galena and quartz veins, introduced potassium to form the abundant biotite and enhanced the growth of garnet porphyroblasts by the increased fluid content and cation mobility and metasomatic effects related to fluid flow (Ague, 1994). This narrow zone, which can be traced for several tens of meters sub-parallel to the contact, gradually approaches the pelite contact before being obscured by a landslide. This structure suggests that the fluid traveled through the pelite before entering the amphibolite obliquely some ⬃50 m away from the sample traverse in this study. The high 87Sr/86Sr was derived from the pelite, somewhat from small scale diffusion from the pelite lenses locally, but mostly from advection of high 87Sr/86Sr fluid from the pelite beyond the contact. Sample 98 BSP5 T: a crude secondary constraint on R.—Sample 98 BSP5 T may be used to provide an independent constraint on R. Located within the vein zone where it is only 30 centimeters away from the contact, it appears that this pelite lens sample has had its Sr and Nd isotopic signatures shifted towards the surrounding amphibolite values from initial values that were, presumably, similar to the undisturbed pelite (that is, similar to sample BSP 5-V). If we assume that sample 98 BSP5 T initially had a (concentration normalized) 87Sr/86Sr value of .7200, then it has dropped to .7113 by 16.5 Ma due to exchange with the local ITM. Without more detailed sampling both along strike within the vein zone and in the amphibolite immediately adjacent to sample 98 BSP5 T, we cannot constrain exactly what the local ITM 87Sr/86Sr value had evolved to by 16.5 Ma from advective and diffusive exchange. However, garnet data from the sample give 87Sr/86Sr of .7078, which represents the local ITM value at 29.7 ⫾ 4.2 Ma. Crudely then, we can estimate R from sample 98 BSP5 T by assuming the bulk solid has been reacting with a fluid of 87Sr/86Sr ⫽ .7078, and has shifted from .7200 to .7113, 70 percent of the way to equilibrium with the local ITM. Solving the differential equation for isotopic exchange with a fluid of fixed isotopic composition (neglecting radiogenic production) we find: 1 ⫺ e 共⫺R⌬t兲 ⫽ 0.70

(3)

For ⌬t ⫽ 13.2 Ma, we find R ⫽ 0.9 ⫻ 10⫺7 g/g/yr, similar to the value determined by the rigorous contact modeling. Exchange About the Upper Contact Diffusional exchange across the upper contact (fig. 11) seems to have been significantly less than at the lower contact. The upper contact cannot be rigorously modeled without denser sampling and additional baseline data far above the contact. However, in a qualitative sense, the upper contact appears to behave as though it had a much smaller LeSr than the lower contact, perhaps due to a smaller D*Sr. The potassium metasomatism penetrating into the amphibolite from the lower contact is not observed at the upper contact (table 5). In addition Sr isotopic changes observed at the upper contact within the amphibolite (fig. 11) are much smaller than those observed in the lower contact. It is unclear why the upper contact is so different. It is possible that increased porosity or fluid content, perhaps related to the nearby vein zone caused the lower contact to display features indicative of higher D*Sr and, ultimately, permit the opportunity to model and measure R.


495

0.05

A

0.04

Parg Tsk

0.03 0.02

Mineral End-Member Activity

0.01 0

0.16

B

0.14

Ann Phl

0.12 0.1 0.08 0.06 0.04 0.9

C

0.8

Ab An

0.7 0.6 0.5 0.4 0.3 0.2 0.1

-2

0

2

4

6

8

10

12

Meters Fig. 19. Representative mineral end-member activities for amphibole (A), biotite (B) and plagioclase (C). For plagioclase, rim compositions are shown indicative of latest growth. Mineral end-member abbreviations are listed in table 4. Mineral compositions are fairly homogenous within the amphibolite interior, but show significant variation within 1 meter of the contact. Errors propagated from probe uncertainties are shown or are smaller than the symbols.

evidence for major element transport and disequilibrium

Possible corroborating evidence for reactive transport and disequilibrium in the major elements may be sought by examining patterns in mineral chemistry from several samples throughout the outcrop. Mineral end-member activities (table 3A-D; figs. 19-20) show significant variations within the outcrop, with particularly strong variations within 15 centimeters of the contact. Bulk chemistry also varies towards the contact – most notably Ca and K (fig. 21). But these variations alone do not tell us about the condition of local equilibrium. The mineral activity and bulk chemical variations near the contact likely indicate exchange with the pelite as the amphibolite protolith was probably a chemically homogeneous protolith.

496


A

0.22 0.2

Garnet Mineral End-member Activities

0.18 0.16

Alm

0.14 0.045

B

0.04 0.035 0.03 0.025

Gr

0.02 0.0025

C 0.002

0.0015 Py

0.001

0.0005

-2

0

2

4

6

8

10

12

Meters Fig. 20. Mineral end-member activities for garnet: almandine (A), grossular (B) and pyrope (C). Rim compositions are shown indicative of latest growth. Note the changes towards the contact. Errors propagated from probe uncertainties are shown.

Reaction quotients (Qr) were calculated based on microprobe analysis of minerals for 6 balanced chemical reactions (5 independent) to corroborate the inferences drawn from Sr isotopes about the scale and extent of post-garnet growth reactive transport. For zoned minerals, rim analyses were used. It should be noted that no effort was made to balance these reactions on any specified “reference frame” (in the sense of Brady, 1975), and therefore these particular equations do not describe the stoichiometry driving ITM-mediated diffusional transport of major elements in the system. Rather, Qr calculations will be used only to assess the attainment and extent of local equilibrium. For a given P-T, Qr for any balanced chemical reaction should equal a unique thermodynamically defined Keq (equilibrium constant) for that reaction, regardless of bulk composition, if local equilibrium among phases exists (see Part I for discussion).


497

12

CaO wt%

10

A

8 6 4 2 0

3.0

K2O wt%

2.5 2.0 1.5 1.0 0.5

B

0.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

6.4

Meters Fig. 21. Whole rock XRF data showing CaO wt% (A) and K2O wt% (B). The data show enrichment of K2O and depletion of CaO in the amphibolite near the contact.

The Qr data are shown in table 6 and figure 22. First, note that garnet-absent reactions (open symbols) yield consistent Qr values regardless of location. This observation indicates that the portions of these phases that were analyzed (that is, amphibole, biotite, and plagioclase rims) maintain local equilibrium throughout the outcrop. All six of the reaction Qr’s measured show consistent values beyond 1 meter from the contact, indicating that local equilibrium existed between all phases (including garnet) at those locations. Three Fe-Mg exchange reactions are plotted, two of which involve garnet (fig. 22B). The Fe-Mg reactions involving garnet show some minor variation nearest the contact, but no discernible trend. The grossular garnetbearing reaction (fig. 22C), however, shows a dramatic and systematic shift in Qr within ⬃1 meter of the contact. Note that 1 meter is the average Le for Sr. The Le for Ca should be similar to that for Sr as they are both Group IIa elements. This is a good indication that the garnet, in particular with respect to its Ca content, is not in local equilibrium with the surrounding matrix minerals within about 1 meter of the contact. Two things could account for this apparent disequilibrium: 1) there was local disequilibrium between garnet (and thus the ITM) and the matrix minerals when the garnet

1—representative errors for each Qr calculation include propagation of analytical probe uncertainties

Measured Qr values

Table 6

498 E. F. Baxter and D. J. DePaolo—Field measurement of high temperature bulk reaction


499

A

Reaction Quotient (Qr) Calculated

10

1 Tr + Ab = Ed + 4 SiO2 2 Ab + Tr + Tsk = 2 Parg + 8 SiO2

B 100

10

Ann + Tsk = Phl + FeTsk Py + FeTsk = Alm + Tsk Ann + Py = Phl + Alm

1

10 -6

C

10 -7

10 -8 3 Tr + 12 An = 4 Gr + 2 Py + 12 SiO2 + 3 Tsk

10 -9 0

2

4

6

8

10

12

Meters Fig. 22. Reaction quotients (Qr) for six reactions: (A) plagioclase-amphibole reactions, (B) Fe-Mg exchange reactions, (C) grossular garnet bearing reaction. Non-garnet bearing reactions (open symbols) show flat consistent values throughout the outcrop, whereas garnet-bearing reactions (filled symbols), in particular the grossular bearing reaction (C), show significant variation within ⬃1 meter of the contact. The P-T calculations done for these rocks (see text) used the data from the five samples in the amphibolite interior where local equilibrium prevails.

grew, or 2) the matrix minerals have reacted and experienced open system chemical exchange subsequent to garnet growth. It would also appear from this dataset that Fe and Mg are in equilibrium (or at least closer to it than Ca) between all phases in the system including garnet, and the ITM. This observation implies that the Le for Fe and Mg is significantly shorter than the Le for Ca or Sr (that is, shorter than 1.0 m).

500


A

An (core) An (rim)

0.5 0.4

Mineral End-Member Activity

0.3 0.2 0.1 0 -2

0

2

4

6

0.12

B

0.1 0.08 0.06 0.04 0.02

Gr (core) Gr (rim)

0 -2

0

2

4

6

Meters Fig. 23. Representative core and rim mineral end-member activities for (A) plagioclase (anorthite) and (B) garnet (grossular). The grossular profile shows considerable smoothing near the contact.

Assuming R is similar with respect to all elements (remember, R is weighted towards Ri for the mineral with the highest concentration and mode of the element of interest; eq 1) this observation suggests D*Fe or Mg ⬍ D*Ca or Sr. The key concept is that for a given R, elements which are fast diffusing in chemically heterogeneous systems are more likely to result in local ITM-solid disequilibrium (see Part I; and DePaolo & Getty, 1996). Garnet and plagioclase “core” compositions give further information about the system evolution (fig. 23). The core activities are approximations because the peak P and T (for lack of a better estimate) were used in their determination, but relative patterns should not be compromised. The garnet grossular content (fig. 24B) decreases from core to rim, except in the pelite, where it increases slightly. The changes in garnet composition show that the grossular contents are almost completely smoothed out across the contact. The overall pattern is consistent with bulk diffusive exchange of Ca from the amphibolite to the pelite (fig. 21A).


A

501

Mn, Mg, or Fe Chemical Potential

Fluid Solid

Ca Chemical Potential

2πLe

B

2pLe Solid Fluid

2πLe Fig. 24. Importance of varying equilibration lengthscales (Le) for different major elements with small (A) and large (B) Le. (A) If Fe, Mg, and Mn have small Le, due to slow D*Fe,Mg,Mn, then there will be ITM-rock equilibrium, and hence garnet-matrix equilibrium over wavelengths of heterogeneity greater than 2␲Le with respect to those elements. (B) If Le for Ca is relatively large, due to fast D*Ca, as it appears to be at site SP5, then ITM-rock, and hence garnet-matrix, disequilibrium (indicated by the arrows) will result in a chemically heterogeneous system. See DePaolo and Getty (1996) and Baxter and DePaolo (2000, 2002) for further discussion of the significance of Le in heterogeneous systems. Hexagons are representative garnet compositions mimicking the local ITM.

The plagioclase rims (fig. 23A) display increased anorthite content toward the contact, but do not appear to have smoothed as much as the garnet grossular component did (fig. 23B). This is best explained by continued (but slow) reaction between the matrix minerals like plagioclase and amphibole with perhaps some net consumption of grossular rich garnet accompanied by diffusive exchange of major elements (notably Ca) across the contact after garnet formation. There has clearly been post-garnet growth diffusional transport and reaction at the field site. This is

502


contrary to the common assumption that reactivity and transport are limited after the attainment of peak metamorphism due to a lack of fluid (for example Walther, 1994). Obviously, any attempts to use the grossular content of garnet within 1 meter of the contact to infer, for example, a peak pressure and temperature of equilibrium would fail because the Qr values are not true Keq – the grossular content is not in equilibrium with the other phases. Comparison to another study showing Ca disequilibrium for garnet.—In a study of pelitic schists in a metamorphic environment, Chernoff and Carlson (1997), documented “disequilibrium for Ca at scales larger than the region immediately surrounding” a garnet, and argue that this is due to relatively slow diffusion of Ca relative to Fe, Mg, and Mn which, by contrast, “achieve chemical equilibrium at the hand-sample scale”. At our field site near Simplon Pass, we see local disequilibrium of Ca in garnet with respect to the other phases and infer fast Ca diffusion (and large Le) in the chemically heterogeneous system as the cause – in apparent disagreement with the conclusions of Chernoff and Carlson (1997). As a point of clarification, the disequilibrium referred to by Chernoff and Carslon is not local disequilibrium between phases, but rather an apparent lack of homogeneity with respect to Ca over lengthscales greater than a few millimeters. If the rock was homogeneous with respect to Ca before garnet growth, then the conclusion that Ca heterogeneity has developed during porphyroblast growth due to slow diffusion of Ca to the depleted haloes around garnets is supported. However, figure 24 depicts an alternative explanation. If the rock was heterogeneous with respect to Ca on a scale less than LeCa before garnet growth, then Ca content could be smoothed out in the ITM resulting in local disequilibrium for Ca between the ITM (and garnet) and the other reacting minerals (fig. 24B). Correlated heterogeneities in Mn, Mg, and Fe in the rock could produce varying Mn, Mg, Fe contents of garnets but Ca, if LeCa⬎LeMn,Mg,Fe, would not correlate with Mn, Mg, Fe over short lengthscales (fig. 23). Instead, Ca content would be more similar in contemporaneous garnets located within LeCa of each other in the rock and thus, the Ca “spike” in garnets noted by Chernoff and Carlson (1997) could in fact be a single time marker. This alternative interpretation is contrary to that of Chernoff and Carlson (1997), and in the absence of any corroborating matrix mineral data, it is a less likely explanation than theirs. However, in light of the results of the current study that suggest faster bulk diffusion of Ca than Fe and Mg, this alternative interpretation would reconcile the apparent difference between the two studies. If the relative Le’s and diffusivities of Ca and Mg, Fe, Mn are in fact reversed between our field site and that of Chernoff and Carlson (1997), this itself is interesting and calls for further investigation of the underlying mechanisms responsible for this difference. diffusivity measurements: implications for the nature of the itm

The modeling results also show that D*Sr must change from 3 ⫻ 10⫺9 to 5 ⫻ 10⫺7 from peak to early retrograde conditions at Simplon Pass. This result is surprising if we consider only that, in general, there is a positive correlation of temperature with ionic diffusivity, D. However, recalling the definition of D* (eq 2) we obtain the following relation D* ⬀ D␶␾/K

(4)

While a decrease in T could decrease D and increase K, ␶ and ␾ could at the same time increase, and dominate the net change in D*. Indeed, this scenario would appear the only plausible explanation for increasing D* with decreasing T. Such an increase in porosity and/or tortuosity correction factor could arise as the system becomes more brittle as temperatures cool enhancing microfracturing and facilitating transport, so long as enough fluid remained in the system. Fluid inclusion data from Wawrzyniec


503

and others (1999) show that fluid did persist locally until temperatures were below 500°C. Figure 18 shows that the ITM must have been at least partially fluid filled to account for the significant post-peak transport of Sr (and Ca) observed. The important conclusion is that D*Sr was certainly fast enough from peak metamorphism through early retrograde time to accommodate a significant amount of accelerating diffusive transfer such that a completely dry system can be precluded. It is possible, however, that after 16.5 Ma, the time of plagioclase closure to Sr and the time of the onset of rapid cooling and exhumation (Mancktelow, 1992), the system did in fact go dry, imposing severe limitations on bulk diffusivity. In fact, independent Ar isotopic data from biotites collected about the same lithologic contact suggest a major drop in Ar bulk diffusivity within the amphibolite after about 16 Ma (Baxter and others, 2002a). discussion

It is difficult to directly compare the bulk reaction rates we derived in nature to those derived in the lab, because effects such as reactive surface area, the functional dependence on ⌬G, variable reaction mechanisms, and the form of the rate law must be accounted for. Such comparisons must begin by recalling the definition of the reaction rate, R, that we have measured here, which is discussed in detail in Part I of this study. R is the fractional rate of Sr exchange between the bulk solid and the ITM mediated by dissolution and precipitation of the bulk solid. Equation 1 shows that, for the Simplon Pass rocks, the R we infer is biased towards the reaction rate of plagioclase, because it is the dominant Sr-bearing phase (Sr concentrations in plagioclase are 10 to 100 times greater than the other major minerals, see table 1). Taking plagioclase as the rate limiting mineral for bulk Sr exchange, we can calculate the reactive surface area of plagioclase in the rock, and normalize our bulk reaction rate to that surface area (Lasaga, 1998). The average mode (by volume) of plagioclase in the amphibolite (determined by point count) is 20 percent. Taking a representative average grain radius of 100 microns, yields a reactive surface area of 20 cm2/g. Thus, the surface area ⫹5.5 ៮ measured at Simplon Pass is R៮ ⫽ 7.0⫺2.0 normalized reaction rate, R, ⫻ 10⫺9 g/cm2/yr. Next, we must estimate the overall ⌬G that characterized the field site and drove net reaction progress. The overall ⌬G in the system is related to the overstep (or understep) in T as the system heats and cools. However, we can expect that the overall ⌬G at the field site is also enhanced by the significant bulk chemical (X) change near the contact. We can calculate a minimum overall ⌬G for the field site by modeling the steady state temperature overstep between the actual temperature, T, and the temperature reflected by the bulk mineral assemblage, Tmin, as follows: dT min ⫽ R 共T ⫺ Tmin兲 dt

(5)

⫹1.1 ⫻ 10⫺7 yr⫺1, an overstep of at least 70° ⫾ Given the reaction rate observed, 1.4⫺0.4 30°C (or 5600 ⫾ 2400 J, assuming 80 J/degree of overstepping of a typical reaction; Walther & Wood, 1984) would be expected (assuming an average dT/dt of 10°C/Myr) as the system reacts slowly and fails to equilibrate with the changing temperature, as well as pressure and composition. Not surprisingly, this overstep is much larger than that predicted by Walther & Wood (1984) on the basis of their much faster reaction rates, but it is consistent with the recent theoretical predictions of Lasaga and Luttge (2001).

Comparison to Rnet Predicted by Lab-Based Kinetic Data Figure 25 shows one way to visualize the comparison between the natural reaction rate measured at Simplon Pass to net rates of reaction, Rnet, as predicted by laboratory

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Fig. 25. Comparison of laboratory derived rate constants, k (right column), extrapolations of those data to the natural conditions of Site SP5 (gray arrows and gray shaded bars in left column), and the actual natural reaction rate data derived in this study (box labeled “B & D”). Laboratory rate constants are normalized to the surface area of the rate-limiting mineral (see Part I for details). Rate laws used are shown in the legend. The dark gray boxes at the top of each bar represent extrapolations for ⌬G ⫽ 5600 ⫾ 2400 J, representative of the field site and those outlined are appropriate for direct comparison to B & D. The XCO2 ⫽ 0.6 data of Heinrich and others, (1989) is not representative of the fluid composition at Simplon Pass (see text). Gradational shading in the lower portion of the bars represents extrapolations for lower ⌬G ranging down to 80 J. Question marked arrows depict the need to reassess the extrapolations (and/or relevance) of lab-based kinetic data to yield reasonably accurate predictions of natural reaction kinetics.

based kinetic data. Surface area normalized rate constants from the various lab studies are extrapolated to the natural conditions of the field site using the rate laws for each study, with T ⫽ 600°C, s ⫽ 20 cm2/g, and ⌬G ⫽ 5600 ⫾ 2400 J (fig. 25; dark gray boxes). Also shown are extrapolations using smaller ⌬G ranging down to 80 J representative of the ⬃1°C reaction overstep suggested by Walther and Wood (1984, 1986). Insofar as these lab-based data are assumed to be representative of high


505

temperature reaction rates in general (which they frequently are: Wood & Walther, 1983; Walther & Wood, 1984; Walther, 1996; Valley and others, 1997; Ague, 1998; Ague and Rye, 1999; Lasaga and others, 2000, 2001; Gillis and others, 2001; Widmer and Thompson, 2001), it is clear from figure 25 that the rates predicted from extrapolations of lab data are many orders of magnitude too fast when compared to the actual reaction rate we have measured in nature. An obvious question is why the natural reaction rate we have measured is so much slower than the laboratory-based predictions. A similar discrepancy has already been noted for low temperature weathering rates (Velbel, 1993; White and Brantley, 1995). If we accept that both the bulk reaction rate data from this study and the lab-based rate constants accurately represent the natural and laboratory systems they measured, respectively, then the question ultimately surrounds the extrapolation itself (question marks in fig. 25) including the issue of whether the same mechanisms apply in the lab and nature. With the field-based kinetic ground truth provided by this study, we now know better where the extrapolations should point, and we can work towards evaluating and adjusting them accordingly. In the sections that follow, we investigate several of the possible parameters and mechanisms that may (or may not) account for this discrepancy. Importance of ⌬G.—Strictly speaking, our reaction rate, R, serves only as a maximum value for Rnet as isotopic exchange responds to the gross forward, Rf (and backward, Rb) dissolution-precipitation rates (that is, R⬇Rf; see Part I). For petrological applications, Rnet describes the net rate of progress of the overall reaction, and is determined by rate laws such as those shown in figure 25, which include a functional dependence on ⌬G (that is, the overall chemical affinity) for the reaction. In general, R net ⫽ R f ⫺ R b

(6)

and transition state theory (see Lasaga, 1998) dictates that that Rnet may be related to Rf by, R net ⫽ 1 ⫺ e⫺⌬G/᏾T Rf

(7)

A ⌬G of 5600 ⫾ 2400 J means that our R overestimates Rnet for the overall reaction by less than a factor of two (eq 7). For a ⌬G of 5600 ⫾ 2400 J, the difference between the actual Rnet in nature and the lab based-predictions of Rnet shown (excluding Heinrich and others, 1989: XCO2 ⫽ 0.6; see below) is at least 5 orders of magnitude (fig. 25). It is true that using a smaller ⌬G in the extrapolations shown in figure 25 would lead to slower predicted Rnet. But, not only are such small ⌬G’s unlikely given the growing disequilibrium at the field site, but smaller ⌬G would also mean that our R itself overestimates Rnet by that much more as well (eq 7). So, differences in ⌬G (even for non-linear rate laws) cannot account for the large discrepancy between the natural and lab-based predictions of Rnet. That is not to say that our R is not itself affected by the overall system ⌬G. Transition state theory dictates that the driving potential for Rf (and hence, R) is the free energy difference between reactants (or products) and the activated complex (Lasaga, 1998), but this clearly is related to the overall ⌬G (consider eqs 6 and 7). Furthermore, studies have shown that the rate, R, of pure isotopic exchange via bulk dissolution-precipitation may itself be enhanced by increased ⌬G of the overall reaction (for example Beck and others, 1992; Cole and Chakraborty, 2001). Importance of the rate law.—Besides the dependence on ⌬G, more complex rate laws have been proposed including the effects of other factors such as evolving dissolution stepwaves (Lasaga and Lutttge, 2001) or inhibition and catalyzing effects (Ganor and

506


Lasaga, 1998). Also, the rate constant, k, may itself be a function of pH or other fluid compositional parameters (see Aagard and Helgeson, 1982; Lasaga, 1998; Wood and Walther, 1983; Heinrich and others, 1989; Lasaga and Luttge, 2001). As these parameters vary significantly between the lab and natural environments, extrapolations may be effected. For example, the experiments of Heinrich and others (1989) for fluid with XCO2 ⫽ 0.6 show a significantly slower reaction rate than with XCO2 ⫽ 0.1 (fig. 25). Although this fluid compositional effect on reaction kinetics should be noted, this effect cannot account for the slow rates at the field site where fluid inclusion studies in nearby rocks suggest XCO2 ranging from 0.02-0.12 at T⬎500 conditions (Wawrzyniec and others, 1999). Importance of the reactive surface area.—Many studies have discussed the importance of the reactive surface area in extrapolating lab data to natural systems (see Helgeson and others, 1984; Lasaga and Luttge, 2001; Brantley and Mellott, 2000; Gautier and others, 2001). Some studies have shown that much less than 100 percent of the total geometric surface area is actually reactive (Helgeson and others, 1984; Knauss and Wollery, 1988). The rationale for such small reactive surface areas is microscale observations of mineral surfaces which indicate that only small portions of a surface are actually engaged at any one time in the reaction process (Helgeson and others, 1984; Knauss and Wollery, 1988; Teng and others, 2000). Activated sites on the mineral surface indicated by etch pits suggest that reaction is limited to those sites where defects in the mineral structure promotes breakdown of the mineral (for example Lasaga, 1998; Helgeson and others, 1984; Lasaga and Luttge, 2001). As long as there are no differences between the ratio of reactive surface area (sr) to geometric surface area (s) for various systems and minerals, all rates may be normalized to the geometric surface area with no loss of consistency. At Simplon Pass, the discrepancy between the natural and laboratory-based kinetic data could be reconciled solely on this basis if the ratio sr/s in nature were four (or more) orders of magnitude smaller than in lab experiments. Such a difference in sr/s seems at first glance extreme. However, if the ITM immediately surrounding a reacting mineral is not entirely wetted in nature (as it often is in fluid rich powder experiments), and if wetting is required for rapid reaction, then reaction may be limited to those portions of the mineral surface that are wetted. Estimates of fluid wetting in metamorphic rocks (which vary strongly with porosity and wetting angle) suggest that sr/s could range from 0.3 and 0.0003 for porosities between 10⫺3 and 10⫺5 and dihedral angles between 30° and 180° (fig. 4 of Skelton and others, 1997), and thus could potentially be significant in the discrepancy between lab-derived and natural reaction rates. However, laboratory kinetic studies using both powders and solid rock samples (Luttge and Metz, 1993) yielded similar rates suggesting this effect may not be more than an order of magnitude. Another possibility for differences in reactive surface area is the type of reaction(s) that dominates the overall reactivity of the system. In many laboratory studies, designed to study dissolution, phase transition, or discontinuous net-transfer reactions, the reactions by definition involve a wholesale breakdown of one phase (or several phases) and growth of a new phase(s). Such reactions thus constantly generate new surface area and allow ready access to those grain interiors which otherwise might be armored from reaction (see below). Reactions at Simplon Pass may involve continuous transfer among solid-solutions of the various minerals. In this case, the matrix phases may remain stable and the approach to equilibrium is accommodated largely by changes in the composition of the minerals, not the mode. Therefore, the reactive surface area remains roughly constant because few if any of the minerals are being consumed. As a consequence, systems dominated by discontinuous net-transfer reactions might have a greater evolved reactive surface area than systems that may be dominated by continuous net-transfer reactions involving solid solutions.


507

Diffusion versus surface controlled kinetics.—Whether the bulk reaction rate is limited by surface reaction processes or by supply of reactants, via diffusion, to the reacting surface has been a major theme in geochemical kinetics (for example Lasaga, 1998). Unfortunately, our data and observations provide no direct evidence that would serve to support or refute either possibility. The relevant information would be constraints on the diffusivity of each major element in the system (that is Si, Al, Mg, Fe, Ca, Na, et cetera), which could be done by comparing Le for each. From our data, we know that both Ca and Sr are relatively fast diffusing within the ITM compared to the local bulk reaction rate (Le ⬃1 m). Therefore, the diffusivity of Ca or Sr to the reacting surface is not rate limiting for the bulk reaction. If all of the major elements had similarly fast diffusivities (and large Le) we could safely conclude that supply to the reacting site was not rate limiting. However, major element data suggests that Le for Fe and Mg might be shorter than for Ca. Furthermore, Si and Al may be even less mobile, and the supply of those elements to the reacting surface may in fact limit the bulk reaction rate. Bickle (1992) and Skelton and others (1997, 2000) have advocated an apparent bulk reaction rate limited by the rate of slow diffusion away from channels or cracks of rapid transport. In this scenario, local fluid-mineral equilibrium is maintained, but the bulk rock exchange rate (for volume-averaged bulk rock samples larger than the crack spacing) is limited by the slow diffusion in to the wallrocks surrounding such cracks. The following equation (after Bickle, 1992; Skelton and others, 1997) shows an approximate relation between the bulk reaction rate, R, and diffusive transport away from cracks if that is the limiting factor: R⫽

␳sD*␾2␲2 4␳fB2␾1

(8)

where ␾1 is the porosity in the cracks, ␾2 is the porosity of the wallrock, and B is the crack spacing. Using this equation with R ⫽ 10⫺7 and D*Sr ⫽ 10⫺7 (appropriate for the field site) would result in a crack half spacing of 3 to 30 centimeters (for a porosity contrast (␾2/␾1) in the range 10⫺4 to 10⫺2). However, this crack spacing is too large to be consistent with the observed smooth diffusive profile in 87Sr/86Sr from continuous 1.5-4.0 centimeters thick sampling density near the contact, so diffusion limited reaction is unlikely at the field site. Solid-state diffusion as a reaction mechanism.—The inferred value of R approaches a rate that could be accounted for by volume diffusion of Sr alone. Direct comparison of a dissolution-precipitation exchange mechanism and a volume diffusion exchange mechanism is difficult due to the non-linear nature of diffusional exchange. For our purposes, a close comparison can be made by considering the effect of dissolutionprecipitation versus diffusion in a simple closed system computational experiment. Consider a solid consisting of spherical grains of radius a, with an initial 87Sr/86Sr ratio of C0, in an ITM of initial and constant 87Sr/86Sr ratio of C1. If we allow dissolutionprecipitation to proceed for 具Rt典 ⫽ 1.85, representative of the field site, we find that the bulk solid in this case will have proceeded 84.3 percent toward the equilibrium 87 Sr/86Sr value of the ITM. Using the equations for diffusional exchange with spherical grains from Crank (1975), we find that the same amount of bulk solid-ITM exchange 13.4Ds t ⫽ 1.85. Essentially, diffusional exchange (84.3 percent) is achieved when a2 scales with dissolution-reprecipitation exchange, over an 具Rt典 of 1.85 by,

冓

冔

R⬇

13.4Ds a2

(9)

508


Effective Bulk Reaction Rate in yr-1

10-3

10-5

Reaction Rate, R, at Site SP5

10-7

10

mm 0.1 = r , Sr m .5m r=0 Sr,

-9

10-11

10-13

m .1m =0 r , -Na mm Ca 0.5 , r= a -N Ca

10-15 400

450

500

550

600

650

700

Temperature (Celsius) Fig. 26. Comparison of reaction rates for dissolution-precipitation mechanism (measured at site SP5) with reaction rates by diffusional exchange mechanism of Sr and Ca-Na interdiffusion. While Sr diffusion would be sufficient to account for the bulk reaction rate measured at site SP5, Ca-Na interdiffusion rates are far too slow to account for observed changes in Ca-Na content of plagioclase. As discussed in the text, diffusional reaction rate is calculated by R ⫽ 13.4D/a2 for 84.3% equilibration as at site SP5. For Sr, the diffusional parameters of Cherniak and Watson (1994) are used for an average plagioclase of An25 composition. The diffusional parameters used for Ca-Al/Na-Si interdiffusion are from Yund (1986).

Figure 26 shows a comparison of the bulk dissolution-precipitation reaction rate measured at site SP5 with equivalent rates, calculated as above, for a purely diffusional exchange mechanism for both Sr chemical diffusion and Ca-Na interdiffusion. Figure 26 suggests that, for the range of grain radii observed in the site SP5 rocks, a diffusional exchange mechanism could account for nearly all of the observed exchange of Sr isotopes in the amphibolite. However, Ca-Na interdiffusion in plagioclase is much slower. As discussed above, there is evidence that both Sr isotopes as well as major element plagioclase composition (that is Ca, Na content) have changed significantly during the time interval under consideration. Plagioclase zoning patterns (figs. 27, 28) document these changes, but suggest that they cannot be explained by simple diffusional exchange between plagioclase and the ITM in grain boundaries. Therefore, a solely diffusional exchange mechanism is not sufficient to account for all of the chemical changes observed and dissolution-precipitation exchange must still have dominated the overall bulk reaction rate at site SP5. Armoring effect and the equilibrium skeleton.—As discussed above, the R we infer is biased towards the reaction rate of plagioclase. Individual plagioclase grains are complexly zoned in terms of their bulk chemical composition, (fig. 7), suggesting that some portions of plagioclase grains are closer to equilibrium with the ITM than other portions. Plagioclase exteriors that are directly or closely in contact with the ITM may react relatively rapidly, but act as an armor for ITM exchange with the grain interior. Broadly similar armoring effects have been proposed and discussed in several other studies (for example Helgeson and others, 1984, and references therein; Luttge and Metz, 1991; Zheng and others, 1999) where the armor may range from an “amorphous crystalline precipitate” to a different mineral phase altogether.


509

amph. sphene

quartz

amph.

100 µm Fig. 27. Location of probe traverse across plagioclase grains in sample 97 BSP5 W (solid arrow). These grains are also pictured in the box in figure 7. The solid curve indicates the current position of a grain boundary. The dashed curve shows the inferred past position of the same grain boundary which has since migrated to its present position, sweeping through the region shown by the dashed arrow. The image is an x-ray scan of calcium concentration, brighter, lighter colors indicate higher calcium. Other matrix minerals are as indicated.

An extreme case is where the ITM reacts quickly and remains in perfect equilibrium with the grain exteriors of all plagioclase grains, but not with plagioclase grain interiors. We can imagine such a system as an interconnected network, or skeleton, of equilibrium. As the model equations assume dissolution and precipitation of the average composition of the mineral (see Part I and Richter and DePaolo, 1987), such intra-mineral variations in reaction rate are not directly accounted for. However, this scenario may be envisioned by treating the plagioclase interiors and the plagioclase exteriors as two separate minerals, each with its own effective reaction rate, Ri. Therefore, the rate limiting factor in the bulk reaction rate we have measured is the ability for plagioclase grain interiors to be accessed by penetrating the armor by some means. Two mechanisms are candidates for accessing grain interiors: volume diffusion, which, as we have shown, is too slow for major elements, or grain boundary migration (GBM). Grain boundary migration (GBM).—A detailed electron microprobe traverse was conducted across the interface between two plagioclase grains (figs. 27, 28). The geometry of the grain boundaries and intra-grain chemical variations are compelling. About the present grain boundary itself, there is a large asymmetric step in plagioclase major element composition (An percent). Obviously only one (if either) of these two compositions which borders the ITM could possibly be in equilibrium with the ITM. The compositional variations do not appear to be exsolution features, and no peristerite gap that spans these compositions has been reported (Janney and Wenk, 1999). On the basis of core-rim relationships observed in 13 thin sections of amphibolite, the most recent equilibrium composition of the plagioclase is the highest An percent abutting the grain boundary on the left side (fig. 28). The pattern of the data may be explained if that grain boundary had migrated from left to right, leaving in its wake the ever-changing most recent equilibrium An percent plagioclase and consuming the older grain interior compositions in the process. GBM is itself a dissolutionprecipitation phenomenon, whereby plagioclase on one side of the grain boundary is

510

E. F. Baxter and D. J. DePaolo—Field measurement of high temperature bulk reaction 26

A

24

An%

22 20

impinging grain boundary

18

unreacted grain interior

16 14 12 1000

B

900

Sr (ppm)

800 700 600 500 400 300 0

20

40

60

80

100

120

140

microns Fig. 28. Probe traverse data across plagioclase grains in figure 27 for anorthite% (A) and Sr concentration (B). Note the asymmetric discontinuities at the present grain boundary (solid line). The second smaller discontinuity (dashed line) is interpreted to be the location of another former grain boundary that has since migrated to the left. As the grain boundaries migrate, consuming the plagioclase compositions into which they move, they leave in their wake new equilibrium compositions of plagioclase which, in this case, have higher An% and Sr content. Sr error bars show precision of microprobe analysis (for 100 nA beam current and 30 second count time used). Solid line in (B) is a 3-point moving average.

dissolved, its components transported through, and equilibrated with, the ITM, and finally the new equilibrium composition precipitated on the other side of the migrating grain boundary. Figure 7 shows other plagioclase grain boundaries with similar chemical discontinuities indicative of grain boundary migration. Grain boundary migration has already been recognized in the lab as a means of effectively promoting chemical reaction of plagioclase interiors (Yund and Tullis, 1991). These observations indicate that grain boundary migration (GBM) is the key mechanism for accessing plagioclase interiors and allowing reaction with the ITM to occur. Therefore, the rate and amount of GBM will be the rate limiting process in the overall bulk reaction rate, R. The reaction rate of the plagioclase interiors, Ri, may be related to the velocity of GBM, vGB, by: R i ⫽ vGB 䡠 AGB 䡠 ␳sr/␳s

(10)

where AGB is the total surface area of plagioclase grain boundaries (expressed as area of grain boundary per volume of rock), ␳sr is the density of the reacted plagioclase and ␳s


511

is the average density of the bulk plagioclase (in general, ␳sr ⫽ ␳s). On this basis a very crude estimate of vGB is possible if we assume the bulk reaction rate, R ⫽ 1.4 ⫻ 10⫺7 g/g/yr, to be limited entirely by plagioclase GBM. Approximating plagioclase grains as cubes with 100 micron edges, AGB for pure plagioclase portions of the rock would be 30,003 m2/m3, which yields vGB ⫽ 4.7 ⫻ 10⫺12 m/yr, or, 4.7 ⫻ 10⫺6 ␮m/yr. In 13.2 Ma, the time interval for the exchange processes measured at the field site, a single plagioclase grain boundary should have migrated 62 ␮m, which is about the distance the grain boundary pictured in figure 27 appears to have migrated. In laboratory settings, in particular for smaller grain sizes or fluid rich systems, GBM will probably not be a rate limiting process, and therefore, reaction rates from the lab will be fundamentally different. GBM may be driven not only by chemical potential energy, but also by strain energy stored in the form of dense dislocation tangles in older, more strongly deformed portions of a mineral (Stunitz, 1998). GBM accommodated dislocation creep strain will tend to promote GBM towards older mineral portions, consuming high dislocation density material (Poirier, 1985; Yund and Tullis, 1991; Stunitz, 1998) the same direction of GBM that we infer from our samples. The possibility of a mechanistic link between strain and reaction in this context is worthy of consideration (Baxter, ms, 2000; Baxter and DePaolo, 2002b). Conclusions

Modeling of Sr isotopic data about a lithologic contact near Simplon Pass, Switzerland using the method described in Part I of this study (Baxter and DePaolo, ⫹1.1 2002a) yields a bulk reaction rate of 1.4⫺0.4 ⫻ 10⫺7 g/g/r. This rate is biased towards the reaction rate of plagioclase, the dominant Sr bearing mineral in the rocks. The reaction rate normalized to the geometric surface area of the rate limiting mineral, ⫹5.5 plagioclase, is R៮ ⫽ 7.0⫺2.0 ⫻ 10⫺9 g/cm2/yr. Grain scale chemical patterns indicate that plagioclase grain boundary migration is likely the rate limiting process. Even given the errors inherent in working from a complex natural system, it is clear that the bulk reaction rate in nature is many orders of magnitude slower than the predictions of laboratory based data. Where Wood and Walther (1983) suggested reaction timescales of hundreds to thousands of years, our natural measurement suggests a ⬃10 million year (⬃107 yr) reactive timescale. This discrepancy must be due to fundamental differences between the conditions of the lab and nature, resulting in inaccurate extrapolations. Differences in reactive surface area, and differences in the rate limiting mechanisms (that is, grain boundary migration in nature) are important contributors to this discrepancy. In light of these observations, modified lab and field experiments, as well as refinements to the theory, may be undertaken to reach a complete understanding of reaction rates and processes that may be applied to nature. Significance to Geochemical and Petrological Techniques The reaction timescale of about 107 years, and evidence for significant post-peak reactivity and transport suggests that mineral assemblages and chemistry may lag the P-T-X conditions of the system. To obtain proper ages and to understand metamorphic processes these effects must be accounted for in the sampling, analysis and interpretation of metamorphic rocks. The garnet-WR isotopic disequilibrium and Keq variations displayed within ⬃1 meter of the contact will have adverse effects on isotope dating and geothermobarometry, respectively, if not avoided or accounted for. For example, garnet-WR Rb/Sr ages calculated from samples within one meter of the contact yield precise – but grossly inaccurate - ages ranging from 141 Ma to – 80 Ma, neither consistent with each other or geological reality. Furthermore, studies relying on chemical and isotopic zoning in garnet, and the local equilibrium assumption to determine growth and strain rates (for example Christensen and others, 1989, 1994;

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Vance and O’Nions, 1990, 1992), and P-T-t histories (Spear and Selverstone, 1983) would be similarly compromised for samples within one meter of the contact at the field site. Pressures and temperatures calculated from mineral compositions within one meter of the contact using the TWQ multi-equilibria method are up to ⬃2 kbar and ⬃60°C too low as compared to the P-T determinations from the equilibrium amphibolite interior. P-T estimates based only on grossular bearing reactions would be even more skewed. Whole rock isotopic studies designed to constrain the amount and direction of chemical transfer via fluid flow or fluid mediated diffusion will underestimate results because they ignore the sluggish kinetics of fluid-rock exchange. Similarly, fluid-flux estimates made on the basis of reaction–progress monitoring (for example Ferry, 1986) will underestimate the flux. Studies of diffusion metasomatism (for example Brady, 1977; Frisch and Helgeson, 1984; Joesten, 1977), which also rely on the assumption of local equilibrium, would be affected by slow reaction kinetics, though the final mineralogical zoning patterns could still be produced (Lasaga and Rye, 1993). Although this reaction rate data highlights the need for careful evaluation of equilibrium based analysis in metamorphic systems, it is not our intent to discourage any use of such techniques. Rather, in light of the importance and magnitude of natural reaction kinetics, we can emphasize ways in which both equilibrium and kinetic based treatments may be used to gain even more information about evolving geologic systems. Perhaps the most important concept is the Le of the system for a given element of interest. We can still interpret rocks by understanding the lengthscales within which disequilibrium in heterogeneous systems might be expected (Le), avoiding these areas for equilibrium-based applications, or accounting for the kinetic effects in our models, as has been done, for example, in this study or in Lasaga and Rye (1993), to determine more accurate material fluxes and reaction rates. Sample collection is, as always, a crucial aspect of geochemical and petrological study. Care should always be taken to document the location of any heterogeneities of lengthscale less than the Le such as lithologic contacts, layers, or veins relative to the sample location. The R៮ from Simplon Pass may be applied in other natural high temperature systems following the guidelines in Part I of this study. If natural systems are indeed characterized by large ⌬G (due to slow reaction) as at our field site, then the most direct, and accurate, usage of R៮ from this study for natural metamorphic reaction kinetics in general is: R net ⱕ R៮ 䡠 s

(11)

៮ overestimates Rnet by less than a factor of two (eq 7). A more rigorous rate law Here, R䡠s (for example, the rate laws in fig. 25) with the added uncertainty of the functional dependence of both Rnet and R៮ on ⌬G is probably not necessary or helpful for natural applications until more data is available. It should be emphasized that the reaction rate measured at this field site obviously does not necessarily apply to every (or any!) other geological environment as conditions, mineralogy, and mechanisms may vary. For example, some field based arguments suggest that contact metamorphic environments may actually evolve over timescales of 1000’s to 10,000’s of years implying much faster reaction rates than those documented at Simplon Pass (for example Joesten, 1983; Cook and others, 1997; Ferry and others, 2001). Some other existing studies of Sr isotopic transport across lithologic contacts (for example Bickle and Chapman, 1990; Bickle and others, 1995; Bickle and others, 1997) do not appear to clearly preserve an isotopic step, and consequent disequilibrium. If indeed no isotopic step exists, then 具Rt典 for those sites must be greater than at our field site, but without constraints on initial conditions and time scales, it is


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impossible to tell whether that difference is due to longer t or faster R. The technique employed in this study (Part I, Baxter and DePaolo, 2002a), or techniques broadly similar to it, may be used to extract more quantitative constraints on natural bulk reaction rates from other geologic environments to determine the degree of variability of these rates in nature and begin to understand the controlling factors. Until then, the result from Simplon Pass may be used as a rough guide for natural metamorphic reaction kinetics in general. acknowledgments

This research was supported by NSF Grant EAR-9805218 awarded to Donald J. DePaolo. Support for Ethan F. Baxter from a Geochemistry Postdoctoral Fellowship at Caltech, where much of this manuscript was written, is also greatly appreciated. We thank Andreas Lu¨ttge and David Jenkins for valuable reviews and discussions. References Aagaard, P., and Helgeson, H. C., 1982, Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions. I. Theoretical considerations: American Journal of Science, v. 282, p. 237-285. Abart, R., and Pozzorini, D., 2000, Implications of kinetically controlled mineral-fluid exchange on the geometry of stable-isotope fronts: European Journal of Mineralogy, v. 12, p. 1069-1082. Ague, J. J., 1994, Mass transfer during Barrovian metamorphism of pelites, south central Connecticut. II: Channelized fluid flow and the growth of staurolite and kyanite: American Journal of Science, v. 294, p. 1061-1134. –––––– 1998, Simple models of coupled fluid infiltration and redox reactions in the crust: Contributions to Mineralogy and Petrology, v. 132, p. 180-197. Axen, G. J., Selverstone, J., and Wawrzyniec, T., 2001, High-temperature embrittlement of extensional Alpine mylonite zones in the midcrustal ductile-brittle transition: Journal of Geophyical Research, v. 106, p. 4337-4348. Barnett, D. E., and Bowman, J. R., 1995, Coupled mass transport and kinetically limited isotope exchange: applications and exchange mechanisms: Geology, v. 23, p. 255-228. Baumgartner, L. P., and Rumble, D., 1988, Transport of stable isotopes: I: Development of a kinetic continuum theory for stable isotope transport: Contributions to Mineralogy and Petrology, v. 98, p. 417-430. Baxter, E. F., ms, 2000, Field measurement and implications of reaction rates and chemical diffusivities in regional metamorphic systems, Ph.D. thesis, University of California, Berkeley, California. Baxter, E. F., and DePaolo, D. J., 2000, Field Measurement of Slow Metamorphic Reaction Rates at Temperatures of 500° to 600°C: Science, v. 288, p. 1411-1414. Baxter, E. F., and DePaolo, D. J., 2002a, Field Measurement of High Temperature Bulk Reaction Rates I: Theory and Technique: American Journal of Science, v. 302, p. 442-464. –––––– 2002b, Can Metamorphic Reactions Proceed Faster than Bulk Strain?: Davos, Switzerland, 12th Annual V. M. Goldschmidt Conference. Baxter, E. F., DePaolo, D. J., and Renne, P. R., 2002a, Spatially Correlated Anomalous 40Ar/39Ar “Age” Variations in Biotites About a Lithologic Contact near Simplon Pass, Switzerland: A Mechanistic Explanation for Excess Ar: Geochimica et Cosmochimia Acta, in press. Baxter, E. F., Ague, J. J., and DePaolo, D. J., 2002b, Prograde Temperature-Time Evolution in the Barrovian Type-Locality Constrained by Sm/Nd Garnet Ages from Glen Clova, Scotland: Journal of the Geological Society, London, v. 159, p. 71-82. Bearth, P., 1972, Simplon Sheet, Geologisher Atlas der Schweiz, 1:25000, 61. Beck, J. W., Berndt, M. E., and Seyfried, W. E., 1992, Application of isotope doping techniques to evaluation of reaction kinetics and fluid/mineral distribution coefficients: an experimental study of calcite at elevated temperatures and pressures: Chemical Geology, v. 97, p. 125-144. Berman, R. G., 1990, Mixing properties of Ca-Mg-Fe-Mn garnets: American Mineralogist, v. 75, p. 328-344. –––––– 1991, Thermobarometry using multi-equilibrium calculations: a new technique, with petrological applications: Canadian Mineralogist, v. 29, p. 833-855. Bickle, M. J., 1992, Transport mechanisms by fluid-flow in metamorphic rocks: oxygen and strontium decoupling in the Trois Seigneurs Massif- a consequence of kinetic dispersion?: American Journal of Science, v. 292, p. 289-316. Bickle, M. J., and Baker, J., 1990, Advective-diffusive transport of isotopic fronts: an example from Naxos, Greece: Earth and Planetary Science Letters, v. 97, p. 78-93. Bickle, M. J., and Chapman, H. J., 1990, Strontium and oxygen isotope decoupling in the Hercynian Trois Seigneurs Massif, Pyrenees: evidence for fluid circulation in a brittle regime: Contributions to Mineralogy and Petrology, v. 104, p. 332-347. Bickle, M. J., Chapman, H. J., Wickham, S. M., and Peters, M. T., 1995, Strontium and oxygen isotope profiles across marble-silicate contacts, Lizzies Basin, East Humboldt Range, Nevada: constraints on metamor-

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