local origin of high pressure vein material in eclogite...

LOCAL ORIGIN OF HIGH PRESSURE VEIN MATERIAL IN ECLOGITEFACIES ROCKS OF THE ZERMATT-SAAS ZONE, SWITZERLAND

TIMO WIDMER and ALAN BRUCE THOMPSON*Department of Earthsciences, ETH Zurich, CH-8092, Switzerland

ABSTRACT. Prograde dehydration reactions within metabasalts at the blueschist-eclogite facies transition produce kyanite veins, usually with quartz, sometimes withomphacite or chloritoid, of up to several meters length and 20 cm width. Bulk rockanalyses show clear depletion haloes for Al2O3 and SiO2 near the veins. Mass balancecalculations support the suggestion that the vein material must have been derived fromthe immediate surroundings. These veins are interpreted as local segregation phenom-ena and not as fluid dehydration channels of the eo-Alpine subduction zone. Calcula-tions have been performed for a stagnant vein formation model that considers the rateof the dehydration reactions (k) responsible for providing the H2O for Al and Sitransport and the rate of diffusion (D) of these from wall rock to growing vein. Themodel is satisfied for quite a wide range of values for k/D and upper limits on theduration of diffusional vein formation of about 1 Ma are indicated.

introductionVeins of high pressure minerals (notably one or two of kyanite, omphacite, garnet,

glaucophane, chloritoid—commonly with quartz) are often found in eclogite faciesrocks (Philippot and Rumble, 2000). Usually the veins contain high-variance assem-blages, that is, they contain fewer minerals than most eclogite facies rocks.

The object of this work is to clarify how specific veins in the eclogite faciesmetabasaltic rocks of the Zermatt-Saas (ZS)-Zone could have originated at highpressures. In particular we are interested in the extent of fluid motion at the highpressures of the blueschist to eclogite facies transition. In principle there are fourendmember possibilities to consider (Ague, 1994a; fig. 1), two involving external fluidsources (open-system, fig. 1A, B) and two involving local (closed-system) fluid sources(fig. 1C, D):

A. Infiltration of an external fluid from great distance with chemical advection ofdissolved material. Precipitation and dissolution reactions result from chemicaldisequilibrium of the high pressure external fluid with the metabasaltic rockperhaps also enhanced by temperature or pressure gradients.

B. Infiltration can be single pass—involving deeper fluids rising upward or laterally,or multipass—where external fluids are recycled by convection or a pumpingmechanism (Sibson and others, 1975; Fyfe and others, 1978; Etheridge andothers, 1984).

C. Advective material addition from a locally derived fluid. Chemical interactioninduced by pressure gradients—as temperature gradients will be small onoutcrop scale. This may be deformation enhanced (Ague, 1994b, p. 1063).

D. Filling of veins through diffusion processes through a stagnant fluid. Diffusioncaused by chemical potential gradients between vein and enclosing rock (pres-sure solution, reaction kinetics).

To quantify the processes and controlling steps for open versus closed-system veinformation we need to evaluate the relative importance of source terms and transportterms. For the cases of externally derived flowing fluid (A) and (B), the rate of fluidmigration is controlled by permeability or fluid flux through the crystalline rock. For

*Also at Institut fur Mineralogie und Petrographie, University of Zurich

[American Journal of Science, Vol. 301, September, 2001, P. 627–656]

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the case of locally derived fluid, the rate is controlled by permeability for (C) anddiffusion through the matrix for (D). The driving pressure gradients decrease inmagnitude or length scale in the order (A), (B), (C) through (D). The chances ofdiscovering the source regions are highest for (D) and the lowest through to (A). Thesource terms in all cases must describe the controls on fluid flux, which in turnconsiders the rate of devolatilisation. This rate is heat flow controlled on the large scale(A) becoming more sensitive to kinetic control as the length scale gets smaller throughto (D).

There are several examples of open-system fluid infiltration discussed in theliterature, where travelling fluids are deduced to have passed through the local rocks ofinterest (Ferry, 1991, 1994; Oliver, 1996; Skelton and others, 2000). Other studies havesuggested that closed-system fluid behavior was indicated, from low to mediumpressure terrains (Marquer and Burkhard, 1992; Cartwright and others, 1994; Yardleyand Bottrell, 1992) as well as from high pressure blueschist-eclogite terrains (Philippotand Selverstone, 1991; Selverstone and others, 1992; Heinrich, 1986; Becker andothers, 1999). We examine here kyanite 6 quartz veins enclosed in metabasaltic rocks

Fig. 1. Four possibilities for vein filling mechanisms in metamorphic rocks: (A, B) infiltration of anexternal fluid from great distance with chemical advection of dissolved material. Infiltration can besingle-pass (A), or multipass (B); (C) advective material addition from a locally derived fluid; (D) filling ofveins through diffusion processes through a stagnant fluid.

628 T. Widmer and A. B. Thompson—Local origin of high pressure vein material

close to the blueschist/eclogite facies transition from the Pfulwe area of the Zermatt-Saas Zone, Switzerland.

mineralogy of the eclogites and evidence for the PTt-path of metamorphism

The mineral parageneses in the eclogite facies rocks of the Zermatt-Saas zonedefine two facies types. Compositions of coexisting minerals and bulk rock analyses areshown in two CaMgO2/AF2O3/NaAlO2 molar diagrams projected from SiO2 and H2Oin figure 2 (where AF2O3 represents Al2O3 1 Fe2O3).

Most of the “eclogities” of spilitic composition in the first facies type (fig. 2A)contain the paragenesis omphacite 1 paragonite 1 glaucophane 1 garnet 1 epi-dote 1 quartz, which may be considered as being transitional from blueschist toeclogite. It is in this facies type that kyanite is found only in the veins. The transition tothe second facies type (fig. 2B) seems to involve several reactions, which have beengrouped here into the general prograde discontinuous dehydration reaction:

epidote 1 glaucophane 1 paragonite 3

kyanite 1 garnet 1 omphacite 1 quartz 1 H2O (I)

As outlined in app. 1, a phase diagram has been calculated for the compositions ofthe appropriate minerals in the system NCFMASH (Na2O 1 CaO 1 FeO 1 MgO 1Al2O3 1 SiO2) in figure 1A. The activity models and reactions deduced are listed inapp. 2. A likely PTt path has been deduced from subduction zone trajectories(Peacock, 1990; Peacock, Rushmer, and Thompson, 1994) and is consistent withobserved compositional data from Zermatt-Saas samples (for example, XMg isoplethsfor garnet and glaucophane).

vein types in the zermatt-saas zone

Various vein types have been distinguished previously in the Z-S -Zone (Bearth,1967, 1973; Meyer, 1983; Barnicoat and Fry, 1986; Fry and Barnicoat, 1987; Barnicoat,1988; Ganguin, 1988; Muller, 1989, Widmer, 1996). Mineralogical differences permitdistinction between veins formed during the high pressure metamorphism from thoseformed during the later retrograde greenschist facies event.

High Pressure Veins at Mellichen and PfulweSix types of high pressure veins were confirmed cross-cutting blueschist/eclogite

rocks of basaltic (mafic) composition, following the observations of Bearth (1967),Meyer (1983), Ganguin (1988), and Widmer (1996):

1. Quartz-glaucophane-ankerite veins.—This type is particularly common near thepolished rock surfaces beneath the Mellichen glacier. Glaucophane crystals arecentimeter sized (Widmer, 1996, figs. 4.1.3, 4.1.4), as are sometimes ankerite crystals(Widmer, 1996, fig. 4.1.5). Normally such veins are dominated by quartz but cancontain 25 volume percent glaucophane plus ankerite.

2. Quartz-omphacite veins.—Idiomorpic omphacites are found in quartz veins in theeclogites of Mellichen. They are much rarer than the glaucophane-bearing veins.

3. Omphacite veins.—Fractures in omphacite-rich rocks can be filled with pureomphacite. The bladed pyroxenes grow perpendicular to the vein walls. Like thosedescribed by Philippot and Kienast (1989) from the Monviso Ophiolite, these ompha-cites appear also to have formed by a “crack-seal” mechanism (see Ramsay, 1980;Etheridge and others, 1984).

4. Quartz-talc segregation veins.—This association described by Bearth (1967) in theeclogites north of Pfulwe were not found further.

5. Chloritoid-quartz veins.—In the eclogitic outcrops north of Pfulwe, chloritoid-quartz veins are found. The chloritoids are Mg-rich (Bearth, 1963; Ganguin, 1988) and

629in eclogite facies rocks of the Zermatt-Saas Zone, Switzerland

Fig. 2. Eclogite facies mineral paragenesis for various rock types from the Zermatt Saas zone, includingthe kyanite 1 quartz 1 (chloritoid) veins. Mineral and rock analyses (from Ganguin, 1988, and Widmer,1996) are plotted as the molar groupings CaMgO2 (CaO 1 MgO)/AF2O3 (Al2O3 1 Fe2O3)/NaAlO2(Na2O/2 1 Al2O3/2). The two facies types are related by the reaction of glaucophane 1 paragonite in (A) tokyanite 1 omphacite in (B) for assemblages with epidote 1 garnet in projection from quartz and H2O.


are up to 6 cm size. These are sometimes found with kyanite, garnet, epidote, apatite,and rutile (Ganguin, 1988). Bearth (1963) has described talc occurring in such veins(see Widmer, Ganguin, and Thompson, 2000). Often this chloritoid has a retrograderim of paragonite, clinochlore, and magnetite.

6. Kyanite 6 quartz veins.—This vein type has only been found in loose blocks in theeclogitic outcrops north of the Pfulwepass (Bearth, 1967; Ganguin, 1988; Barnicoatand Fry, 1986). Most commonly these veins contain only abundant kyanite (up to 20cm long, fig. 3C), often with interstitial quartz. However, Ganguin (1988) has found inaddition one or more of omphacite, epidote, magnetite, apatite, rutile, and very rarelyankerite. Sometimes kyanite is retrograded to paragonite, suggesting that the requiredNa is supplied from omphacite in the adjacent eclogite at a later stage than veinformation. Commonly omphacite and garnet of the country rocks stand in directcontact with the vein minerals and show no replacement reactions. In thin veinskyanite grows perpendicular from the vein wall into the interior (fig. 3A, B). In thecenters of thick veins, kyanite grows randomly (often slickenslide bladed kyanite growsparallel to the vein walls, fig. 3C) with quartz in the interstices.

None of the six “prograde” vein types exhibits obvious selvages. The wall rocksadjacent to the kyanite 6 quartz veins discussed here show only minor depletion ofparagonite toward the veins.

Retrograde VeinsSeveral generations of retrograde veins outcrop in the upper part of Taschtal

(Bearth, 1967; Ganguin, 1988; Barnicoat, 1988; Muller, 1989; Widmer, 1996). Theseretrograde veins consist mainly of albite and occasionally of prismatic epidote. Themost prominent albite veins in the upper Taschtal are up to 100 m long and 2 m wide.Such veins exhibit very large alteration haloes reflecting conversion to prasinite(albite 1 actinolite 1 epidote 1 chlorite 6 biotite 6 calcite 6 ankerite). In someplaces clots of calcite, sometimes of several cubic meter size, can be found at jogs inveins. All the greenschist minerals from the metabasaltic rocks are also found in suchretrograde veins.

chemistry of the host rocks containing the kyanite 6 quartz veins

Mostly kyanite 6 quartz veins are about 5 cm wide and up to 2 m long. Isolatedveins are the usual case, although sometimes pairs of veins are tens of centimetersapart. Less commonly “en echelon” sets of three veins can be found. Because theschistosity of the eclogites is so weak it is not usually possible to determine anyparticular relationship between vein orientation and schistosity.

Aqueous fluids under high pressures have been suspected to have passed throughthe massive eclogites as a consequence of dehydration reactions and the attendantreduction of porosity due to densification. Brittle behavior permitting vein formationin eclogites contrasts to the highly deformable nearby serpentinite (see Ganguin, 1988;p. 253). As outlined above, high-pressure fluids passing through the eclogite faciesrocks could have transported dissolved materials for the vein minerals. Fluids ofdifferent provenance would show different degrees of fluid-rock interaction with theenclosing eclogites. Samples were selected for chemical analyses with a view todetermining if enrichment or depletion zones exist in the eclogites adjacent to thehigh-pressure kyanite 6 quartz veins.

Sample SelectionFor study of the kyanite 1 quartz veins two loose blocks were intensively sampled

(fig. 4), and a kyanite 1 quartz vein (sample Z69n) was taken from a third block nearby(Block 3). Blocks 1 and 2 lie to the north of the Pfulwepass (map coordinates: 631400/096 500, 3120 m; 631 350/096 550, 3100 m) but have been observed to move


Fig. 3. Photographs of high pressure veins (centimeter divisions numbered on scale) at Pfulwe. (A)Kyanite-quartz veins in eclogite. (B) 20 cm long kyanite crystals in kyanite-quartz vein, Block 1. (C)Kyanite-quartz slickenside, Block 1.


during successive seasons. Samples were obtained by drilling (2.5 cm diam, ;15 cmlong, see fig. 4A). The two blocks were photographed and sketched (fig. 5).

Bulk Rock AnalysesBulk rock analyses were obtained by X-ray fluorescence (XRF). For analysis of

major elements, powdered rock was mixed with lithium tetraborate in the proportion1:5, and the mixture melted at 1150°C in air. For analysis for trace elements, rockpowder was mixed with polyvinyl as a binder. XRF measurements were made on thePhillips PW 1404 at the EMPA in Dubendorf. No measurements were made ofCO2-content or Fe21/Fe31 ratio. The analyses are listed in table 1 (from Widmer,1996, p. 281-286).

Modal Mineralogy and Calculated Volume LossesThe rock analyses for Block 1, Profile 2 (table 1, wt percent) were used to compare

calculated modes with observed mineral amounts. The mass loss corresponds to the

Fig. 4. Eclogite blocks containing kyanite-quartz veins. (A) Block 1 showing the location of theboreholes (smallest are 1-inch diam.) perpendicular to the veinwall, at the lower part. (B) Block 2, The veinis the bright region at the right side of the block. The drill machine and its water-tank are shown.


Fig. 5. Sketches of Blocks 1 and 2, showing the Al2O3-depletion haloes determined from chemicalanalyses of samples from the boreholes. (A) The boreholes are located inverted from the photograph offigure 4A. The block shows a thick kyanite-quartz vein at the top (fig. 3A) and a kyanite-quartz slickenside(fig. 3C) at the right. The Al2O3-content of samples away from the veins is measured between 16.3 and 17.1wt percent and decreases systematically toward the veins to 13 to 14 wt percent adjacent to the kyanite-quartzvein. (B) Sketch of Block 2, with a very pronounced Al2O3-depletion halo.


amount of kyanite 6 quartz transported to the veins and is accompanied by a decreasein the amount of paragonite and an apparent increase in the amount of omphacite(inclusions of which in garnet become more jadeitic toward the rim). There are noobvious changes in the amounts of the other minerals (fig. 6).

metamorphic volume changesAl2O3 and SiO2 concentrations (wt percent; fig. 5A, B) show a systematic decrease

in the eclogite toward the kyanite-quartz veins. As it is unlikely that rock volumeremained constant during chemical alteration, the calculation and plotting methodsof Gresens (1967) and Grant (1986) were used to deduce the mass/volume changes.The asymmetric distribution of isopleths in figure 5B emphasises that it is never clearhow well a two-dimensional section represents the three-dimensional distribution.

Gresens-diagram.—By comparing pairs of samples, Gresens (1967) proposed amethod by which the relative volumes of conversion of one to the other could benormalised. An example is shown in figure 5 for the comparison of a vein edge sampleZ69n (taken from the third eclogite block, Block 3; its location is like sample P2, orP11, in Block 1, fig. 5) to the sample Z75 taken far from a vein (fig. 5, which is thuspresumed to be unaltered). Most of the elements plotted on the Gresens diagram (fig.7) show volume factors from 0.84 to 0.88 whereas only Al2O3 and SiO2 show strongapparent volume losses. However, these are exactly the elements that form the kyaniteand quartz in the veins.

Isocon diagram of Grant.—Clearer relationships among mineral analyses can beseen in figure 8 with an isocon diagram of Grant (1986). Here pairs of analyses showgain or loss of an element (oxide) relative to an unaltered reference rock analysis bydivergence from a straight line (Grant’s isocon). The elements lying on the straightline are considered to be immobile. The ratio of two elements with similar mobilityduring metasomatic process will be constant in both protolith and metasomatisedsample (Gresens, 1967; Dipple and others, 1990, p. 650).

For Profile 1 in Block 1 comparison is made (fig. 8A, B, and C) between thechemical composition of altered rock P2 adjacent to the Kya 1 Qtz vein relative to anunaltered reference sample (P5, taken about 25 cm away from the vein), with P3 andP4 lying in between them (fig. 5A). Figure 8D shows a control sample of anotheranalyzed split of sample P59 which is also compared here to P5. The equations for theline fits use the element ratio data given by the open circles, the data for Al2O3 andSiO2 (the squares in fig. 8D) were not used in the line fits.

Furthermore the Al2O3 and SiO2 losses for all strongly altered samples fromBlocks 1 and 2 (fig. 4) show strong correlation (open circles in fig. 9A, see tables 1 and2, expressed as grams per 100 g of unaltered sample P5). The compositions of twokyanite 1 quartz veins (open squares, samples Z69a and P52, SiO2 5 57.22 and 69.17;Al2O3 5 32.31, 27.38; wt percent, respectively) are shown in figure 9B (note that 9A isan inset of 9B). The fit equation in figure 9A includes the analyses for Al2O3 and SiO2.The differences in the vein analyses reflect modal differences of kyanite and quartz,emphasizing their heterogeneous distribution within veins, which unfortunately meansthat further more detailed mass-balancing will be of limited success. Nevertheless thechemical analytical data indicate significant changes in the concentration of severalelements in the wall rocks adjacent to veins (John Ferry, personal communication,December 2000). The chemical analytical data summarized in table 1 present weightpercent for oxides and ppm trace elements for samples indicated in figure 4 for Blocks1 and 2. These data have been normalized to the chemistry of unaltered sample P5 andP53 in table 2. Some general trends are evident, K2O is generally depleted in alteredsamples, as mostly is Na2O, whereas CaO and MgO are generally greater in alteredsamples (relative to unaltered samples P5 and P 53). The considerable heterogeneityindicated by the variability of apparently unaltered samples (for example among P5,


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P6, P7, P8, and P9 from Block 1, and among P53, P31, P64, and P28 from Block 2)reflects mainly the coarse grain size (typically .5 mm). Furthermore, the chemicalchanges do not reflect any major systematic differences in mineralogy in the alteredzones, apart from a decrease in the amount of paragonite toward the veins. Thechemical analyses for altered samples when renormalised to unaltered samples by massloss derived from the isocon diagrams (table 1) do show similar values for mostelements apart from Al2O3 and SiO2. Thus the simple model of loss of mainly Al2O3and SiO2 from unaltered eclogite to vein (with minor loss of Na and K and minor gainof Ca and Mg) is satisfied by the chemical data.

From the slope of the isocon, the mass change can be calculated (table 2) andrelated to volume change by the measured density. For this method, density wasdetermined by pycnometry (Widmer, 1996, p. 256):—

sample Z 75, Eclogite, unaltered 3.05 g/cm3

sample Z69n, Eclogite close to kyanite-quartz vein 3.35 g/cm3.

The isocon diagrams (figs. 8 and 9) show clear losses of Si and Al from samples closertowards the kyanite 1 quartz vein. All other elements define almost a straight lineisocon indicating no significant change for these. The major and trace elementsanalyses (table 1) were multiplied by random factors to spread out their locations inthe isocon diagrams (see Oliver and others, 1998, p. 205). When these data are addedto figure 8, they show that relative to the zero total-mass loss line, in addition to the

Fig. 6. Modal analyses (table 1, wt percent) for samples approaching the kyanite 6 quartz veins (Block 1Profile 2).


small gains of elements Fe, Ca, Mg, Mn, there are slights gains of trace elements (Zn,Ni, Zr, Hf, V) with strong gains of Ba and Pb in the depleted zones (P3, et cetera)relative to the reference rock (P5). Conversely, along with loss of elements Al, Si, K, Na,Ti there are slight losses of the trace elements Yr, Sc, Cr, Sr with strong losses of F andCu in the depleted zones (P3, et cetera) relative to the reference rock (P5).

Mass balance from host rock to vein.—The Grant isocons (fig. 8) and the Gresensdiagram (fig. 9) both suggest that the vein material gain is close to the mass loss fromthe alteration zone. It should be possible to determine in more detail how much of thevein material is derived locally or externally, from a consideration of a mass balancebetween vein and nearby rock (table 3). If mass ratios of particular elements are similarthen it can be argued (Ague, 1994a) either mass has been conserved, or material hasbeen added/removed also in this proportion.

The analyses presented in table 3 show that the mass loss of the adjacent rock,within about 30 cm, fig. 12), appears to be twice as high as the mass of SiO2 (1413-740)

Fig. 7. Gresens diagram comparing chemical analyses of sample Z69a at the edge of a kyanite-quartzvein from Block 3, with an unaltered reference sample (Z75, fig. 4A). For most components a volume factorbetween 84 to 88 percent results in minimal volume change, implying that the vein-edge sample Z69a has losttotal volume to this amount. Similarly the vein-edge sample Z69a has been depleted by 4–5 g Al2O3 and 7–9 gSiO2 during the vein formation.


and Al2O3 (775-418) in the veins. From the slopes of the isocons (fig. 8) the mass lossesfor individual samples correspond to P2 5 14 percent; P3 5 13 percent; P4 5 5 percent(relative to unaltered sample P5, see table 2). These values suggest therefore that thelocal system is open to these elements and has lost almost half their mass.

The mass lost from a layer of thickness x (cm) within the alteration zone (AZ) canbe obtained from the relationship:

mv 5 O 1l ~Alxr vnl)

where,

mv5 mass loss from the alteration zone (g, Al2O3, or SiO2)nl 5 average mass loss of the first layer of the alteration zone (g/100 g rock)Al 5 area of the alteration zone with average loss of nl (cm2)rv 5 average density of the alteration zone (gcm23)

Fig. 8. Samples of isocon (Grant, 1986) diagrams. (A), (B), (C) Block 1, Profile 1 (fig. 5A, right side).(D) As one test, sample P5 was considered as unaltered rock and a second split of sample P59 was used as acontrol. From the slopes of the isocons the mass losses correspond to (A) P2 5 13 percent; (B) P3 5 10percent; (C) P4 5 5 percent (see tables 2 and 3).


The sample groupings were made according to the 1 percent increments of Al2O3 forBlock 2 as shown in figure 5. Among these groupings the SiO2 content varied morethan 5 percent.

Assuming an average density of 3.0 gcm23 for all rocks gives the masses for SiO2 ingrams, 740 (gain by vein), 1413 (loss from wall rock) (ratio SiO2 5 1.77); for Al2O3, 418(gain by vein), 775 (loss from wall rock) (ratio Al2O3 5 1.82). If the measured densitiesare used (3.05 gcm23 for vein and 3.35 gcm23 for the wall rock) then these valuesbecome 752, 1578, (ratio SiO2 5 2.1), 425, 868, (ratio Al2O3 5 2.02), respectively, table3). Thus according to these figures, from the amount of SiO2 and Al2O3 lost from wallrock, about half goes to make the vein and the other half leaves the local system.

We feel that the heterogeneity resulting from large grain size and the necessarilysmall sample cores introduces sampling but not analytical variability, into the recalcu-lation schemes. There is thus little precision to be gained by additional analyses andrecalculations over and above that done here, so that the present Gresens-plots andGrant-isocons are about the maximum we can attain. In addition, we cannot decide ifdeformation played a role in extraction of excess Al and Si, but clearly an amountappears to have been advected away.

The distribution of other minerals in the veins is extremely irregular, even kyaniteveins without quartz can be found. On the basis of the chemistry we can only say thatNa and K are lost as well as Al and Si from the wall rocks, consistent with the decrease inthe amount of paragonite. Furthermore the heterogeneity of vein mineralogy mightjust as well reflect “lag effects” due to kinetic oversteppings rather than to differentialdiffusive transport from wall to vein. These observations speak for a mechanism ofpredominantly local redistribution of mass with some metasomatic loss of Al2O3 andSiO2 but no indication for advective mass gain.

mechanisms of vein formationFor the origin of many kyanite and quartz veins, flow transport of dissolved Al, Si

by travelling fluids has been proposed (see Kerrick, 1990, p. 325-346). However themass balance data discussed above indicate for the present case that it is not necessaryto invoke the passage of distant infiltrating fluid. If advective fluid transport can be

Fig. 9(A), (B) Comparison of Al2O3- and SiO2-losses for several strongly altered samples from Blocks 1,2, and 3 (open circles: see tables 1, 2, and 3) and for the kyanite-quartz veins (open squares). Note that (A) isan inset of (B). Losses are expressed as grams per 100 g of unaltered sample P5. The correlation betweenAl2O3- and SiO2-loss is evident.


excluded or shown to have played a minor role, then a mechanism of localised masstransfer needs to be developed. A mechanism similar to that proposed to explain theorigin of aluminosilicate segregations within silicate rocks is preferred (Carmichael,1969; Foster, 1977, 1986; Cesare, 1994). A mechanism of “hydrofracturing” has beenproposed by Cesare (1994) to account for andalusite-bearing veins in pelitic hornfelsesin a low pressure tonalite contact aureole. He considers (Cesare, 1994, p. 650) that thematerial for the andalusite-biotite-quartz veins to be derived locally from the pelitichost rocks.

Dehydration of hydrous silicates, particularly white micas, which occurs over alimited P-T interval, induces the opening of a small fissure to accommodate the localvolume increase. This isolated small fissure is maintained at near lithostatic pressure byductile deformation around it where acts it like a large fluid inclusion. Furthermore, atthe high pressures deduced here for the eclogites, a negative volume change for adehydration reaction could result in slightly sub-lithostatically pressured regions towhich further pulses of dehydration fluid will drain. Chemical potential gradients,

Table 2

Recalculated chemical analyses for altered rocks (g per 100 g of unaltered P5, upper row: orP53, lower row). Calculations performed with the mass losses derived from isocon diagrams,

where m represents the derived slopes (from fig. 7).


mainly of alumina, will result in the growth of the aluminosilicate in the veins at theexpense of mica in the wall rocks, even for stagnant fluid.

processes in and around stagnant veins

Localized shearing and elevated pore fluid pressure result in concentration ofhigh pressure fluid. These fluids travelling short distances (,1 m length scale) dissolveAl and Si and transport them along fluctuating pressure gradients through thedehydrating rock matrix. Such a cyclical process of element dissolution duringincreasing fluid pressure and precipitation during falling pressure does not explainwhy only kyanite, and often quartz, and not the whole mineral spectrum of the hostrocks is present in the segregation veins.

Aspects of this mechanism have been considered by Yardley (1975) where thedriving force for the development of quartz-plagioclase veins in pelitic schists isconsidered to be due to chemical potential gradients driven between crystals ofdifferent size and various degrees of internal deformation. In the present case themechanism of formation of the Pfulwe veins cannot be mainly related to these factors,because although kyanite is characteristic of the high-pressure quartz veins it is notfound in the host rocks. Ganguin (1988) had previously suggested that any kyanite inthe enclosing rocks had been retrograded to paragonite. It should also be noted herethat despite the abundance of the suitable bulk compositions by which kyanite could

Table 3

Calculation of the vein mass and the mass loss of Al2O3 and SiO2in the alteration zones for Block 2.


have grown, the rocks of the ZS -Zone only barely reached the conditions of thediscontinuous NCFMASH reaction

Epi 1 Gla 1 Par 3 Kya 1 Gar 1 Omp 1 Qtz 1 H2O (I)

(app. 1, fig. A.1) where the kyanite grew in the veins, and the omphacite (and perhapsgarnet) in the eclogite.

The complex dehydration reaction can be usefully simplified as a breakdownreaction of paragonite:

NaAl3Si3O10~OH!2 3 NaAlSi2O6 ~Jadeite! 1 Al2SiO5 ~kyanite! 1 H2O (IA)

which produces kyanite without quartz and adds jadeite to omphacite. An alternativereaction producing kyanite with quartz can be written with aqueous species:

2*H1 1 2NaAl3Si3O10~OH!2~paragonite! 3

3Al2SiO5 ~kyanite! 1 3SiO2 ~quartz! 1 2*Na1 1 3H2O (IB)

where the symbol * indicates that the exact speciation is not known.The volumetric kyanite/quartz ratio for this reaction is 1.95. As discussed for

Barrovian facies mass transport involving muscovite breakdown (Ague, 1994b, p. 1083),the alkali has probably been transported out of the region now occupied by thekyanite 6 quartz veins at Pfulwe.

chemical potential gradients between veins and eclogitesThe chemical potential of Al2O3 in an aqueous fluid in equilibrium with kyanite 1

quartz (veins) or with paragonite 1 jadeite 1 quartz (simplification for enclosing rocksusing aJad

Omp 5 0.5) has been evaluated. This has been done (fig. 10) as a function oftemperature and pressure using thermodynamic data from Holland and Powell(1990), with the equation of state for H2O from Haar, Gallagher, and Kell (1979) andHolland and Powell (1985). A chemical potential diagram (mAl2O3 2 mSiO2) calcu-lated for 700°C and 25 kb is shown in figure 10B. For both diagrams it was supposedthat quartz was present before reaction I (in fig. A.1) occurred.

Two different equations of state (EOS) for H2O were used in the calculations toinvestigate their divergence when extrapolated to these high pressures. One EOS wasfrom Haar, Gallagher, and Kell (1979, ornamented by open squares in fig. 10A), andthe other a modified Redlich Kwong EOS fit by Holland and Powell (1985, orna-mented by open circles in fig. 10A). For solid phases and reference aqueous species,the Holland and Powell (1990) data set was used. The shaded region in figure 10Acorresponds to the P-T ranges of the blueschist to eclogite reactions (along thededuced subduction path in figure A1, reactions I and 5) considered to be responsiblefor the dehydration fluids involved in the vein formation. The shaded region coincideswith the overlap in the P-T-m relations for the sub-reactions involved in the formationof the kyanite 6 quartz veins.

The solid square in figure 10B shows the m-values (m2 and m4) for the fluid inequilibrium with Par 1 Jad (in Omp) 1 Qtz. The subsequent development iscontrolled by nucleation delays of kyanite in the regions that became veins. Fluids inequilibrium with kyanite lie along the indicated diagonal line in figure 10B. Quartzmay or may not precipitate at the same time as kyanite because some veins contain 80to 100 percent kyanite with interstitial quartz. As noted in table 2 the ratio SiO2/Al2O3in the depleted wall rocks is uniformly about 1.7, close to the weight ratio in kyanite. Sothe m-m path in figure 10 runs from m2-m4 to m1-m3 and then along the kyanitesaturation line to m4-m5 with the formation of quartz interstitial to the kyanite. Adelicate mechanical balance must have occurred between vein opening-rate and


filling-rate by the diffusing components. It is also possible that the interstitial quartzfillings were precipitated only during exhumation. This would depend on the direc-tion of the uplift P-T path relative to the solubility isopleth trajectories for quartz andkyanite (Manning, 1994, 2001).

diffusion resulting from reaction oversteppingReaction (I) is the first reaction along the deduced PT path for the Z-S Zone

eclogite facies metamorphism that generates kyanite. Not all of the product mineralsof reaction (I) will have similar nucleation behavior. The absence of kyanite in the rockmatrix but its growth from the vein walls clearly indicates preferential nucleation there.It has been estimated that dehydration reactions such as (I) must be overstepped by10° to 50°C before reaction progress can be sufficiently fast enough (Ridley andThompson, 1986; Lasaga and Rye, 1993). For this amount of reaction overstepping, apotential difference of up to 3 kJ per mol results between nearby rock and vein (shadedregion in fig. 10A). The fluid in equilibrium with the reactants has a higher mAl2O3value than the fluid in equilibrium with the product phases. This gradient in Al2O3between the reactant phases in the country rocks and the newly produced kyanite plusquartz causes a transport of Al2O3 toward the vein. The process can be simplified (fig.11) in terms of two sub-reactions, one in the country rock,

Fig. 10(A) Chemical potential of Al2O3 in an aqueous fluid in equilibrium with kyanite-quartz (veins) orwith paragonite-jadeite quartz (a simplification for enclosing eclogite, aJad

Omp 5 0.5) as a function oftemperature. With an overstepping of 10 to 50°C a potential difference of up to 3 kJ per mol results betweennearby rock and vein (shaded region). (B) Chemical potential diagram (mAl2O3-mSiO2) calculated at 700°Cand 25 kb, for the subreactions:

Paragonite 5 jadeite 1 SiO2~aq! 1 Al2O3~aq! 1 H2OSiO2~aq! 1 Al2O3~aq! 5 kyanite.

For both diagrams it was supposed that quartz was present before reaction (I in fig. A.1) occurred.Thermodynamic data for minerals and aqueous species from Holland and Powell (1990), equation ofstate for H2O from Haar, Gallagher, and Kell (1979), and Holland and Powell (1985).


paragonite 3 jadeite 1 SiO2~aq! 1 Al2O3~aq! 1 H2O (IC)

and the other in the vein

Al2O3~aq! 1 SiO2~aq! 3 kyanite 1 quartz (ID)

As long as no kyanite nucleates in the country rock the proposed segregationmechanism remains active.

Our model so far has linked diffusion of SiO2(aq) with that of Al2O3(aq) withoutany separate explanation for the diffusion of SiO2(aq). As long as quartz is present inthe wall rock as well as the vein there is no gradient in mSiO2. From thin-section

Fig. 11. Sketch of chemical processes involved in vein formation. The kyanite-forming discontinuousreaction (reaction I, fig. A.1, app. 3) is considered as two sub-reactions (Ia) in the enclosing spilitic eclogite,which releases Al2O3 and SiO2 to the fluid, and (Ib) in the vein, which causes these dissolved species toprecipitate as kyanite 1 quartz. The arrows are intended to show the direction of intergranular diffusion, themiddle panel shows the initial conditions before diffusion, and the lower panel shows a schematic mAl2O3profile at some time into the diffusion history.


observations it appears that the quartz in the wall rocks grew late and even possiblyafter the filling of the vein quartz. Otherwise, explanations would need to involvedifferent surface energies between minerals in the vein and the wallrock (due to grainsize, population of inclusions, or deformed crystals, for example, Yardley, 1986; Lasagaand Rye, 1993).

Little can be said about the speciation of Al in H2O in the high-pressure veinforming fluid in the ZS-Zone. Alkali-Al-Si complexes (Anderson et al., 1987; Stalder etal., 2000) cannot be excluded although the veins contain no or little Na or K-minerals(mica and albite are found in retrograde veins). Increasing solubility of Al in H2O isexpected with increasing pressure (Kerrick, 1990, after Schneider and Eggler, 1986;Baumgartner and Eugster, 1988; Manning, 2001). High pressures should increase thediffusional mobility of Al in intercrystalline metamorphic fluids (Carmichael, 1969;Fisher, 1978; Manning, 2001).

advective diffusive transport modellingChemical diffusion profiles can be related and predicted from diffusion coeffi-

cients and reaction rates with the help of error functions (Crank, 1975; Baumgartnerand Rumble, 1988; Lassey and Blattner, 1988; Blattner and Lassey, 1989; Abart andSperb, 1997; Eppel and Abart, 1997). These quantities can be related to mass transportproperties determined from the mass released by chemical reactions compared todiffusional masses in metasomatic processes (see app. 3). For the case of stagnantdiffusion fluid advection is not considered (fig. 12), and thus the relevant quantity toevaluate is the dimensionless second Damkohler number (DaII 5 kL2/D). For this weneed to obtain likely values for the effective mineral/fluid chemical exchange rateconstant (k) and the mass diffusion coefficients for Al2O3 and SiO2(D).

Fig. 12. Al2O3 and SiO2 mass changes measured in the samples for Profile 1 in Block 1 (fig. 5A) relativeto 100 g of unaltered P5. Sample P2 does not lie on the calculated trend because reaction (I) is at completionnearest to the vein. The remaining Al2O3 is found in omphacite, garnet, and unconsumed reactant minerals.


Lasaga and Rye (1993, p. 381-397) have determined rate constants from variousexperimental studies. For common dehydration and combined dehydration-decarbon-ation reactions they deduce values for their effective rate constant keff, similar to thesimplest form used here, of 0.085 to 50.04 yr21 (2.7 3 1029 to 1.6 3 1026 s21). Rateconstants show greater variation when temperature extrapolations are included (La-saga and others, 2000). We have used values of k 5 2 3 1027 to 2 3 1028 s21 for thecalculations illustrated in figure 13. For values for D, the mass diffusion coefficientsthrough the wall rocks, a range of 0.031 to 0.31 m2yr21 5 1029 to 1028m2s21 has beensuggested by Lasaga and Rye (1993, p. 382), Joesten (1991), and Eppel and Abart(1997, p. 722). We have used values of D 5 1029 to 10210 m2s21 for the calculationsillustrated in figure 13.

Several different ways are required to estimate time scales for the vein formation.A very fast estimate for the duration of hydrofracture due to dehydration reactions hasbeen obtained by Nishiyama (1989) to be from normally about 10 yrs (3 3 108 s) to amaximum of 200 yrs (6 3 109 s). Lasaga and Rye (1993, p. 376) suggest that the time toreach steady state (tst) for devolatilisation transformations can be approximated bytst 5 2/keff which for the above values of keff(2.7 3 1029 to 1.6 3 1026s21), times of 109

to 106s are obtained. The rate of subduction for the P-T path shown in figure A.1 is 2.25cm yr21, and the times of overstepping reaction I can then be obtained as 8 3 105 yrs(2.4 3 1013 s) for DT 5 100°C, 8 3 105 yrs (2.4 3 1012 s) for DT 5 10°C, to 8 3 103 yrs(2.4 3 1011 s) for DT 5 1°C. We have used a median value of ta 5 2 3 1011 s (6.3 3 103

yrs) in calculations illustrated in figure 13.The recent solubility work for kyanite in H2O by Manning (2001) gives mAl

(700°C, 10 kbar) 5 6 3 1023 mol/kg H2O, which for r 5 1000 kgm23, results in mAl 56 molm23 5 6 3 1026 molcm23. We have used a median value of Dc 5 1024 to 1025

molcm23 in calculations illustrated in figure 13.Porosity varies during devolatilization reactions because of the interaction be-

tween pore fluid pressure and matrix compaction. For the negative volume changesdeduced here there should be no pore pressure inflation, so that the values of porosity,f 5 0.01 (51 percent) used here may indeed be too high for rocks undergoingblueschist/eclogite facies dehydration. As discussed below the effect of changingporosity (f) can be examined (fig. 13B) by changing the values of the rate constant (k)because of the product grouping f. k in eq. A.4.

The compositional data for Al2O3 and SiO2 plotted against distance from the vein(fig. 12) have been used to evaluate the range of possible diffusional parameters fromeq A4 in app. 1. The calculations illustrated in figure 13 used fixed values for porosity,f 5 0.01 (51 percent), and Al2O3 concentration difference, Dc 5 1025 mol cm23, toshow the range of diffusion coefficients (fig. 13A), and reaction rate constants (fig.13B), which are consistent with the compositional data profiles and the assumedmodel. Ranges of D 5 1029 to 10210 m2s21, k 5 2 3 1027 to 2 3 1028 s21, and DaII ofabout 8 (for L 5 0.2 m) result (figs. 12 and 13).

To relate SiO2(aq) diffusion to Al2O3(aq) diffusion it was assumed that

q ~SiO2! 5 Kq~Al2O3! 5 Kk$cR~Al2O3! 2 cF~Al2O3!% (I)

where q (SiO2) 5 production rate of SiO2q(Al2O3) 5 production rate of Al2O3

K 5 proportionality constant for reaction stoichiometry.cR(Al2O3) 5 concentration of Al2O3(aq) in equilibrium with reactant phases

(mol cm23)cF(Al2O3) 5 concentration of Al2O3(aq) in the fluid

k 5 dehydration reaction rate.


Fig. 13. Evaluation of mass advection for Profile 1, using the measured Al2O3-contents from figures 5Aand 11 fitted with eq (A.4) from app. 3. In (A), the diffusion coefficient (D) is varied with fixed reaction-rateconstant, k 5 2 3 1027 s21; in (B) k varies with fixed D 5 10210 m2s21.

In contrast to the values for D and k, the Damkohler number II (DaII) is independent of the chosenvalues for porosity (f), concentration gradient (Dc), and duration (ta). It can be seen that the measurementsare best satisfied with values of DaII 5 8, and k 5 1.5 3 1028 s21.


This leads to a relationship between SiO2 and Al2O3 diffusion equations

]u]t

5 D]2u]x2 1 k~cR 2 cF! (II)

u 5 concentration of SiO2 in fluid (mol/cm3)cF 5 concentration of Al2O3 in fluid (eq I).

The solution to this relationship can be calculated analytically (app. 3). Figures 12 and13 show these relationships for linked mass transfer of SiO2 and Al2O3 from vein intowall-rock and the fit for DaII of 8 (see also, for example, Eppel and Abart, 1997, figs. 3and 4).

We have made several sets of calculations using ranges of parameter sets for thediffusion equations presented in app. 3. It is very useful here to examine the productand quotient groupings of k, D, t and f in these equations. The combinations k/D, D.t,k.t, f.k are evident. Thus the indicated values used in the calculations in figure 13 canbe rescaled appropriately to see the parameter ranges possible to obtain the illustratedcurves. For example, the effect of changing porosity (f) can be examined (fig. 13B) bychanging the values of the rate constant (k) because of the product grouping f.k in eq.A.4. The results of numerical tests with a large range of parameter choices arepresented in app. 4.

other high pressure veins

This investigation suggests that the development of kyanite 6 quartz veins reflectslocal segregation phenomena involving locally derived fluid. The H2O-rich fluid isderived from internal dehydration reactions, and physical reorganization of porosity isresponsible for the localization of fluid segregations. Mass transport to the veins occursby intergranular diffusion. These chemical potential gradients result from presence ofkyanite 6 quartz in the veins and the reactants (mainly paragonite) in the enclosingrocks.

In other high pressure veins large rutile crystals cannot be easily explained byhigh Ti solubility in H2O. Ti complexes with CO2 and Cl (Wiegand and Seward,1997) and these fluid species are found in some fluid inclusions (Widmer, 1996,p. 195). The relative roles of unusual complexing compared to a diffusive transportmechanism for Ti like that discussed for Al needs to be investigated further.Furthermore Mg chloritoid occurs with quartz in veins in the ZS-Zone, rarely in therock matrix.

conclusions

The material for kyanite and quartz in the veins in eclogite facies rocks at Pfulweappears to have been derived locally, and does not require the advection of largeamounts of external fluid into the eclogite during high-pressure metamorphism. Thisview is supported by the scarcity of these veins. Mass transfer is driven from enclosingrock to growing vein by gradients in Al2O3 and SiO2 through a stagnant pore fluid. Theveins could have first formed in low stress regimes to accommodate H2O-rich fluidsreleased from blueschist to eclogite dehydration localized by regimes of brittle failure.Mass transfer occurs as long as kyanite grows in the veins and not in the enclosingrocks. Consistent with this it appears that quartz in the matrix of the enclosing rocksgrew after the formation of quartz in the vein.

Such a diffusional origin for kyanite 6 quartz veins is significant because thismechanism circumvents the need to discover even more enhanced solubility mecha-nisms for the “immobile” element Al in H2O than suggested by the recent high-pressure (to 10 kbar) solubility measurements by Manning (2001).


acknowledgmentsThanks to Rainer Abart, Nick Oliver, and John Ferry for reviews, to Jay Ague for

helpful editing, to Peter Nievergelt for translating the figures, to Ursula Stidwill forproof reading, to the SNF at the ETH for financial support.

Appendix 1

Calculated mineral equilibria and deduced PT pathThe phase diagram shown in figure A.1 was calculated in the system NCFMASH using the program

FRENDLY (Connolly, 1990) with thermodynamic data from Holland and Powell (1990) for the mineralskyanite (Kya), garnet (Gar), epidote (Epi), glaucophane (Gla), omphacite (Omp), paragonite (Par), Quartz

Fig. A.1. P-T path obtained by comparing observed mineral assemblages and compositions with a phasediagram calculated in the system NCFMASH, using the data contained in app. 1 and 2.


(Qtz), lawsonite (Law), and for H2O from Haar, Gallagher, and Kell (1979) and Holland and Powell (1985).The activity coefficients from Evans (1990) are listed in app. 2, with the reaction coefficients for thenumbered reactions. Calculated isopleths for XMg in garnet and in glaucophane are shown by dashed anddotted lines, respectively. Chlorite reactions have not been shown in figure A.1. These calculated results aresimilar to results from recent experimental studies (Schmidt and Poli, 1998).

Also shown in figure A.1 is a P-T path for subduction and exhumation of the ZS-Zone (Widmer, 1996,fig. 3.1.9), a hypothetical extrapolated subduction P-T path from the model of Peacock (1990, Peacock andothers (1994) with positions of subducted samples after 2.2 and 3.0 Ma.

appendix 2

Minerals considered and the compositions and activities used in calculatingthe mineral reaction coefficients

The following endmember mineral compositions were used:

Garnet (Gar) (Fe, Mg)2.4Ca0.6Al2Si3O12Glaucophane (Gla) Na2(Fe, Mg)3(Al)2Si8O22(OH)2Lawsonite (Law) CaAl2Si2O7(OH)2 z H2OOmphacite (Omp) CaNa(Fe, Mg)AlSi4O12Epidote, Clinozoisite (Epi) Ca2Al3Si3O12(OH)Paragonite (Par) NaAl3Si3O10(OH)2Quartz (Qtz) SiO2

these tabulated reaction coefficients in CASH, NCMASH, and NCMASH were ob-tained:

CASH System1 [Gar, Par, Gla, Omp] Law 5 0.25 Kya 1 0.5 Epi 1 0.25 Qtz 1 1.75 H2ONCMASH or NCFASH2 [Law, Kya] 84 Epi 1 95 Gla 5 129 Omp 1 65 Gar 1 61 Par 1 118 Qtz 1 76 H2O3 [Gla, Law] 7.25 Qtz 1 4.5 Epi 1 5 Gar 1 12 Par 5 12 Omp 1 23.75 Kya 1 14.25 H2O4 [Epi, Law] 10 Gar 1 18 Par 1 16 Qtz 5 6 Gla 1 6 Omp 1 28 Kya 1 12 H2O5 [Par, Law] 2.7 Epi 1 2.4 Gla 5 1 Gar 1 9.6 Omp 1 3.05 Kya 1 2.05 Qtz 1 3.75 H2ONCFMASHI [Law] Gla 1 Par 1 Epi 5 Kya 1 Omp 1 Gar 1 Qtz 1 H2O (variable stoichiometry)IV [Kya] Gla 1 Epi 1 Par 1 Qtz 1 H2O 5 Omp 1 Law 1 Gar (variable stoichiometry)

The coefficients in the two NCFMASH reactions (I and IV) in figure A.1 are not specified along theunivariant curves.

The following models for activity coefficients (from Evans, 1990) were used:

aPyrope 5 ~XMg!3, aAlmandine 5 ~1 2 XMg!

3, XMg 5Mg

Mg 1 Fe

aGlaucophane 5 ~XNaM4!2 z ~XAl!

2 z ~XMg!3, XNa

M4 5 1, XAl 5AlVI

AlVI 1 Fe31 5 1

aFerroglaucophane 5 ~XNaM4!2 z ~XAl!

2 z ~1 2 XMg!3

aGrossular 5 ~XCa!3 5 0.008, XCa 5

CaCa 1 Mg 1 Fe

5 0.2

aJadeite 5 XNaM2 z XAl

M1 z 2 5 0.5, XNaM2 5 0.5, XAl

M1 5 0.5

aDiopside 5 XCaM2 z XMg

M1 z g 5 0.875, g 5 3.5, XCaM2 5 0.5, XMg

M1 5 0.5,

aLawsonite 5 1, aH2O 5 1, aParagonite 5 1, aKyanite 5 1, aEpidote 5 1


Appendix 3

Mathematical formulation of chemical diffusion combined with a kinetically controlledmetamorphic reaction

Chemical transport fronts propagate by fluid advection moderated by (1) molecular diffusion, (2)hydrodynamic dispersion, (3) mineral/fluid chemical exchange. The relative contributions to chemicaltransport, normalized to some scaling length L, can be evaluated with two dimensionless ratios (Abart andSperb, 1997). The chemical Peclet number, PeC 5 nL/D, relates the contribution by fluid advection tochemical diffusion/dispersion. The first Damkohler number (DaI) relates the mineral/fluid exchange rateto the advective contribution (DaI 5 kL/n). These dimensionless numbers may be combined to give thesecond Damkohler number (DaII 5 kL2/D 5 PeC.DaI 5 (nL/D).(kL/n). The DaII is used for the case wherethere is no advection but where the chemical transport is moderated by the rates of reaction kinetics formineral/fluid chemical exchange and molecular diffusion over a characteristic distance (Damkohler, 1936).

If the sub-reaction

epidote 1 glaucophane 1 paragonite 3 garnet 1 omphacite 1 H2O 1 SiO2~aq! 1 Al2O3~aq! (IE)

or in the simplified form,

paragonite 3 jadeite 1 SiO2~aq! 1 Al2O3~aq! 1 H2O (IC)

occurs fast enough then the vein fluid is always in equilibrium with kyanite and quartz. Thus the subreaction

Al2O3~aq! 1 SiO2~aq! 3 kyanite 1 quartz (ID)

and hence the diffusion of Al, are rate limiting for the whole dehydration-reaction/segregation/vein-forming process. We assume for simplicity that the reaction rate for (IC or ID) is linearly dependent uponthe difference in the Al-concentration in the fluid (cF, in equilibrium with kyanite and quartz) and the fluidin equilibrium with the reactant phase (cR).

For first order kinetics (linear kinetics of Lasaga and Rye, 1993)

q 5 k z ~cR 2 cF! (A.1)

where q is the reaction rate and k is the rate constant. For no advective component (dispersion 5 n.]c/]x 50), the differential equation of diffusion for a simple one-dimensional case (fig. 12 for Block 1) may beapproximated by

]c]t

5 D]2c]x2 1 k~cR 2 cF! (A.2)

for the initial and boundary conditions

c~x 5 0! 5 cF

c~x 3 `! 5 cR

c~t 5 0, x . 0! 5 cR

The differential equation can be solved analytically (Crank, 1975)

c 5 Dc 2 Dc z 512

z expS2x z ÎkDDzerfcS x

2zÎDt2ÎktD

112

z expSx z ÎkDDzerfcS x

2zÎDt1ÎktD 6 (A.3)

With this analytical solution it is possible to calculate the remaining amount of Al2O3 in the enclosing rock(MAl) after a particular duration (ta) of the diffusion.

MAl 5 MAl° 2f z mAl2O3

r rock.k.Dc.5

12

z expS2x z ÎkDD E

0

ta

erfcS x

2 z ÎDt2ÎktD]t

112

z expSx z ÎkDD E

0

ta

erfcS x

2zÎDt1ÎktD]t 6 (A.4)


where rrock 5 rock density (gcm23)k 5 reaction rate constant (s21)D 5 diffusion rate (cm2s21)c 5 concentration Al in fluid (mol cm23)

cR 5 equilibrium concentration of Al2O3 (aq) with reactant phases (mol cm23)cF 5 actual concentration of Al2O3 (aq) in the fluid phase

MAl 5 Mass (g) of Al2O3 per 100 g altered rockMAl° 5 Mass (g) of Al2O3 in 100 g unaltered rock

f 5 porosity (pore volume per rock volume)mAl2O3 5 molecular wt of Al2O3 (101 g mol21)

ta 5 duration of the process (diffusion and reaction)Dc 5 cR 2 cF

x 5 direction of diffusion, x 5 0 at the vein contactL 5 characteristic diffusion length (taken as L 5 20 cm)

DaII 5 DamkohlernumberII 5 kL2/D (s21m2)/m2s21)—(dimensionless mass relating the amount ofmaterial released by chemical reaction related to the amount of material transported bydiffusion).

kL2/D can be related to the term x=k/D in eq A.3 and A.4, for L 5 x 5 20 cm.

Appendix 4

Parameter choices and numerical testsA large range of parameter choices will produce the curves shown in figure 13. Although the curves

illustrated are generated for particular choices of values for f, Dc, and ta, the DaII numbers corresponding tothese choices can be expressed independently of them and in terms of the ratio k/D multiplied by L2. Forthe characteristic length of diffusion of L 5 20 cm (L2 5 0.04 m2), a DaII value of 8 is certainly acceptablefrom figures 12 and 13. These values gives a ratio DaII/L2 5 200 5 k/D, which is satisfied by 2 3 1027/1029,2 3 1026/1028, 2 3 1027/10210, etc. Other results are not easy to deduce from the form of the eqs (A.3) and(A.4). For example a rough idea of using lower values for porosity can be made by increasing k by one orderof magnitude because of the grouping k.f. But because k also occurs in both groupings x=k/D and =ktwithin the curved brackets of eq (A.4), this is no accurate solution.

Many numerical tests were made using two criteria, the slope of the chemical gradient within thecharacteristic length, L 5 20 cm, and the concentration at the constant plateau into the unaltered rock. Weexamine in particular the results for decreasing the porosity to 0.1 percent (f 5 0.001). The whole range ofparameter combinations mentioned above for varying f, k, t and D, for f 5 0.001 and Dc 5 1025 mol cm23,produces acceptable results to fit the slope of the chemical gradient at L , 20 cm. One especially interestingresult provides an upper time limit range to the diffusion process, for example, if the diffusion times areprogressively increased by orders of magnitude (for example, from 2 3 1012 to 2 3 1013 s) thenconcentration at the constant plateau steadily drops below the observed value. A similar result to this isobtained by lowering the value of the dehydration rate constant, k, indicating that the effect of changing k inboth groupings x=k/D and =kt within the curved brackets of eq (A.4) has the opposite effect to changing itin the grouping f.k.

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