Diffusion control of garnet growth, Harpswell Neck, Maine, USA

J. metamorphic Geol., 2001, 19, 179±195 Diffusion control of garnet growth, Harpswell Neck, Maine, USA F. S. SPEAR 1. AND C. G. DANIEL 2 *. 1 Department of Earth and Environmental Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA (spearf@rpi.edu) 2 Department of Geological Sciences, Princeton University, Princeton, NJ, USA ABSTRACT A detailed analysis of chemical zoning in two garnet crystals from Harpswell Neck, Maine, forms the basis of an interpretation of garnet nucleation and growth mechanisms. Garnet apparently nucleates initially on crenulations of mica and chlorite and quickly overgrows the entire crenulation, giving rise to complex twodimensional zoning patterns depending on the orientation of the thin section cut. Contours of Ca zoning cross those of Mn, Fe and Mg, indicating a lack of equilibrium among these major garnet constituents. Zoning of Fe, Mg and Mn is interpreted to re ect equilibrium with the rock matrix, whereas Ca zoning is interpreted to be controlled by diffusive transport between the matrix and the growing crystal. Image analysis reveals that the growth of garnet is more rapid along triple-grain intersections than along double-grain boundaries. Moreover, different minerals are replaced by garnet at different rates. The relative rate of replacement by garnet along double-grain boundaries is ordered as muscovite>chlorite>plagioclase>quartz. Flux calculations reveal that replacement is limited by diffusion of Si along double-grain boundaries to or from the local reaction site. It is concluded that multiple diffusive pathways control the bulk replacement of the rock matrix by garnet, with Si and Al transport being rate limiting in these samples. Key words: diffusion; disequilibrium; garnet; growth; image analysis; kinetics; zoning. INTRODUCTION In recent studies, Daniel & Spear (1998.) and Spear & Daniel (1998.) described garnet zone samples from Harpswell Neck, Maine, that had apparently undergone progressive nucleation and coalescence of multiple nuclei to form single garnet grains as metamorphism proceeded. Furthermore, radius-rate calculations based on garnet zoning maps suggested either interface kinetics or diffusion over short length scales (on the order of crystal diameters or smaller) as the rate-limiting step in garnet growth. Further examination of these samples has provided new insights into garnet nucleation and growth history. In the original papers (Daniel & Spear, 1998.; Spear & Daniel, 1998.), equilibration of Mn was assumed over the area of a thin section, so that the concentration of Mn could be used as a time line in the analysis of progressive nucleation and growth history. Examination of Mn, Fe, Mg and Ca zoning, however, reveals that not all of these elements can be in equilibrium simultaneously. Thus, local bulk composition and/or diffusion is a signi cant in uence on garnet nucleation and growth kinetics. In addition, examination of crystal lattice orientation by electron backscatter diffraction (EBSD) and orientation contrast imaging (OCI) reveals that individual garnet grains are, in general, crystallographically continuous, inconsistent *Present address: Department of Geology, Bucknell University, Lewisburg, PA 17837, USA. with the interpretation that single garnet grains evolved as separate nuclei coalesced (Daniel et al., 1999.; Spear & Daniel, 1999; Daniel et al., unpublished data.). The purpose of this paper is to present a detailed description of the chemical zoning of major and minor elements in garnet from this locality and to evaluate these zoning trends with the aid of phase equilibrium and kinetic considerations. The observed patterns of growth of garnet are discussed and a model based on local diffusive control of garnet growth is presented. GEOLOGICAL SETTING The samples studied (samples 96-1 & 96-2 of Spear & Daniel, 1998.) come from a garnet-grade coastline outcrop of the Jewel Formation on the south-east tip of Harpswell Neck (Hussey, 1988.; Lang & Dunn, 1990.; stop 1 of Grover & Lang, 1995.). The rocks are negrained schists with the assemblage chlorite+biotite+muscovite+ garnet+quartz+plagioclase+ilmenite+graphite (Fig. 1.). Peak metamorphic P±T conditions are estimated at 450±470 uc and 2±3 kbar (Lang & Dunn, 1990.; Grover & Lang, 1995.; Spear & Daniel, 1998.). The P±T path is inferred to be nearly isobaric heating based on the regional low-pressure Buchan-type metamorphism of the terrane, the paragenesis of andalusite to sillimanite and the absence of kyanite. The implications of the inferred P±T path on the interpretations of the garnet zoning are discussed in detail below. A pervasive matrix foliation de ned by muscovite, biotite and chlorite post-dates growth of the garnet cores and produced pressure shadows of quartz in the vicinity of garnet crystals. Inclusions of quartz inside garnet indicate that garnet overgrew a pre-existing foliation now oriented at a high angle to the matrix foliation. The samples from this outcrop are well suited for a study of garnet nucleation and growth. The grade is low, ensuring that post-growth diffusion in garnet is minimal. Although there is moderate variation in bulk composition in the outcrop, individual hand samples are

180 F. S. SPEAR & C. G. DANIEL Fig. 1. Backscattered electron (BSE) micrograph showing texture of sample 96-1 from Harpswell Neck, SW Maine. Matrix foliation (muscovite+biotite +chlorite+ilmenite) is vertical; inclusion trails in garnet (quartz and ilmenite) de ne an earlier foliation that trends from upper left to lower right (10 o'clock to 4 o'clock). White spots are ilmenite and dark grey are quartz and plagioclase. Quartz pressure shadows resulting from the formation of vertical foliation are visible at the top and bottom of some garnet. White box shows area of X-ray images (Fig. 2.){. relatively homogeneous and the predominant garnet growth reaction is chlorite+quartz=garnet+h 2 O. Plagioclase, ilmenite, biotite and muscovite are also undoubtedly involved in producing garnet, but the modal involvement of these phases is small relative to chlorite. The Mn content in the cores of large garnet is high (X sps =0.45±0.49) and the zoning of Mn is considerable (X sps at the rim 0.20±0.24), providing a considerable range of chemical zoning. The major disadvantages of these samples are that post-growth deformation has reoriented the external foliation and removed the textural environment in which the garnet nucleated and grew, and there are no lower grade samples of the same formation that do not contain garnet with which to compare the garnet-bearing rocks. GARNET ZONING PATTERNS Major element zoning in garnet (Figs 2 & 3.) is similar in both samples examined and similar to that described by Spear & Daniel (1998.). Spessartine is zoned from a maximum of 0.45±0.49 mole fraction to 0.20±0.24 on the rim; almandine from a minimum of 0.46 to 0.67 on the rim; pyrope from a minimum of 0.035 to 0.065 on the rim; and Fe/(Fe+Mg) from a high of 0.93 to 0.91 on the rim. Most importantly, the zoning patterns of Mn, Fe, Mg and Fe/(Fe+Mg) are roughly similar and vary sympathetically or antithetically. In sample 96-1 (Fig. 2.), the highest spessartine occurs in the upper centre of the crystal, and corresponds roughly with the lowest almandine and pyrope. An isolated patch of relatively high spessartine occurs in the lower part of the crystal, again with relatively low values of almandine and pyrope. A band of low spessartine and relatively high almandine and pyrope occurs across the lower centre part of the crystal. In contrast, the zoning of grossular in sample 96-1 (Fig. 2.) is roughly concentric about the garnet centre with low values in the core (X grs =0.055) rising to a high of X grs =0.115 towards the rim and falling to X grs =0.035 at the rim. Sample 96-2 (Fig. 3.) shows nearly constant X grs across the core (X grs =0.045), an annulus of somewhat higher Ca near the rim (X grs =0.063) and lower Ca at the rim (X grs =0.04). Trace element zoning maps were collected to see whether they could reveal insights into the growth evolution of garnet in these {Colour images of all the gures and animation of Figs 14 and 15 are available on the JMG web sites. samples. Concentrations of P, Sc, Cr and Ti are at or below microprobe detectability limits (c. 100 ppm) and maps show no apparent zoning. Zoning of Y in sample 96-1 (Fig. 2f.) reveals slight variations in the interior of garnet that correlate broadly with the zoning of Mn, Fe and Mg. Moreover, Y is observed to increase slightly along the right and top rims of the crystal. Y zoning in the absence of xenotime as a saturating phase for Y has been observed to obey Rayleigh fraction behaviour (Pyle & Spear, 1999.). The similarity between the Y and Mn zoning supports the hypothesis that garnet growth roughly followed the pattern of Mn zoning. Sample 96-2 reveals little Y zoning in the garnet interior (Fig. 3f.) and an annulus located in the same position as the Ca annulus. The signi cance of this annulus in Ca and Y is uncertain, but Pyle & Spear (1999.) attribute Y annuli of similar appearance to a garnet resorption event. It is possible that garnet resorption is also recorded in sample 96-2. Further evidence that the annulus signi es garnet resorption may be seen in the inclusion patterns in sample 96-2. The inclusions in the garnet interior de ne the earlier foliation (trending NE±SW). These inclusion trails stop at the inside edge of the annulus and inclusions are absent from the annulus to the rim suggesting a hiatus in garnet growth near the rim. INTERNAL CRENULATIONS A very important discovery made during the course of this investigation was the observation that, in a number of garnet zoning maps, the pattern of zoning of Fe, Mg and Mn looks very much like small crenulation folds. Examples can be seen in Figs 3 and 4., all from sample 96-2. In each, the orientation of this pattern is consistent with the orientation of quartz inclusions, which are axial planar to the crenulation folds. The crenulation fold was likely a region rich in chlorite and micas. Based on the high Mn contents of the region that de nes the crenulation, this is the place where garnet initially grew, consistent with observations of Bell et al. (1986.) from a variety of rocks of different grades. Williams (1994.) also described the preferential nucleation of garnet on small crenulation hinges.

GARNET GROWTH, HARPSWELL NECK, MAINE, USA 181 Fig. 2. X-ray images showing zoning of (a) almandine (alm), (b) pyrope (prp), (c) spessartine (sps), (d) grossular (grs), (e) Fe/ (Fe+Mg) and (f) yttrium in garnet outlined in Fig. 1., sample 96-1. Alm, prp, sps and Fe/(Fe+Mg) are broadly similar and display elongation in the direction of the earlier foliation (de ned by inclusion trails). Grs zoning is roughly concentric about the geometric centre of the garnet. Bright areas are high concentrations. Numbers are mole fraction of garnet components.

182 F. S. SPEAR & C. G. DANIEL Fig. 3. X-ray images showing zoning of (a) almandine (alm), (b) pyrope (prp), (c) spessartine (sps), (d) grossular (grs), (e) Fe/ (Fe+Mg) and (f) yttrium in garnet from sample 96-2. Alm, prp, sps and Fe/(Fe+Mg) are similar and de ne a pattern roughly in the shape of an `M' fold, rotated 45u clockwise. Grs zoning is relatively at in the core with an annulus near the rim. Yttrium zoning displays an annulus similar to Ca.

GARNET GROWTH, HARPSWELL NECK, MAINE, USA 183 Fig. 4. X-ray images showing concentrations of Mn in garnet from sample 96-2. Note the regions of high Mn in the garnet interiors, which form a pattern of crenulation folds. Width of each image is 675 mm. Several garnet samples from 96-2, out of the over 30 mapped, reveal similar textures. Recognition of this fold pattern provides an important new interpretation of the patchy zoning of Mn observed in many garnet samples from 96-1 and 96-2, and a resolution to the paradox of how multiple coalesced nuclei could show crystallographic continuity. The new interpretation is based simply on the orientation of the internal crenulation relative to the thin section cut (Fig. 5.). Imagine the garnet in Fig. 3 or 4.being cut into a thin section orientated parallel to the crenulation axis, but normal to the internal foliation. The internal quartz foliation would still be readily visible, but the Mn, Fe and Mg zoning would display two isolated patches separated by the quartz-rich interior, similar to the pattern observed in sample 96-1. The paradox is therefore resolved by recognition that the isolated high-mn zones are connected in the third dimension in the crenulation fold, and coalescence of multiple nuclei is no longer required as an explanation. DISCUSSION The case for equilibrium control of Mn, Fe and Mg and transport control of Ca zoning Observations from chemical zoning Spear & Daniel (1998). assumed that Mn zoning in garnet was produced by growth from a homogeneous matrix under equilibrium conditions on the scale of the thin section, in which case Mn zoning could be used as a proxy for time (a similar assumption was made by Kretz, 1973., 1974., 1993.; Carlson, 1989., 1991.). In both samples examined here, the similarity of Fe, Mg and Mn zoning broadly supports this assumption. However, close inspection of Fig. 2. (sample 96-1) reveals that Mn zoning is not exactly coincident with Fe and INCLUSION SUITES Numerous inclusions are present in garnet from Harpswell Neck and careful examination using backscatter electron imaging and energy dispersive spectroscopy (EDS) for phase identi cation has revealed the presence of quartz, plagioclase, ilmenite, allanite, Ca± Mn epidote (piemontite), Ca±Fe±Mn carbonate, muscovite and margarite. Of these included minerals, only quartz, plagioclase, ilmenite and muscovite have been identi ed in the matrix and it is suggested that the other included minerals were present as matrix phases prior to garnet growth and consumed during initial garnet production. Ilmenite inclusions display variation in Mn concentration depending on their position within garnet. For most ilmenite inclusions, the Mn concentration is broadly consistent with the local Mn concentration in garnet, suggesting an approach to equilibrium between adjacent ilmenite and garnet. Fig. 5. Illustration of the relationship between the internal crenulation fold, which de nes the earliest S1 foliation, the axial plane to the F1 fold, which de nes S2, and the external foliation (S3). It is proposed that garnet with high Mn concentration nucleates on these crenulations. A thin section cut normal to the F1 fold axis will reveal the fold, whereas one cut at 90u to this might reveal only isolated regions of high Mn.

184 F. S. SPEAR & C. G. DANIEL Mg zoning, and is considerably discordant with respect to Ca, which displays broadly concentric zoning. This raises the question of whether Mn zoning is, in fact, a good proxy for time. To illustrate the magnitude of the discrepancy between the contours of Mn and Ca in sample 96-1, contours of Mn concentration were superimposed on the Ca zoning map (Fig. 6.; see Appendix for details). It is clear from an examination of this image that, throughout the growth of this garnet, Mn and Ca could not both have been in equilibrium with the same homogeneous matrix. For example, along the contour X sps =0.35, grossular values vary across nearly its entire range. Only at the very outer margin of the garnet grain (X sps =0.25) does X grs approach uniform composition along a spessartine interval, although the match is still not perfect. Plots of X sps versus X grs (Fig. 7a, c.) reveal that there is a general tendency for X sps to decrease as X grs increases towards the rim (most apparent for sample 96-1) and then for both X sps and X grs to decrease together to the rim. However, for any value of X sps, there exists nearly the entire range of observed values of X grs. Some of this variation is analytical scatter (note 1s error bars), and some of the extreme points are most likely spurious data (mixed analyses). However, the considerable spread in X grs versus X sps, combined with the discordance shown on the contour diagram (Fig. 6.), reveals a lack of equilibrium in one or both of these elements on the scale of the garnet porphyroblast. A similar result is realized in a plot of X sps versus Fe/(Fe+Mg) (Fig. 7b, d.), although the scatter is Fig. 6. X-ray image showing grossular concentrations for garnet illustrated in Figs 1 and 2.with contours of X sps superimposed. Numbers are mole per cent spessartine. Note that the contour for X sps =0.35 crosses the highest and lowest X grs values. not as extreme as observed in the X sps versus X grs plots (Fig. 7a, c.). The bulk of the data clearly indicate a relatively uniform decrease in Fe/Mg with decreasing X sps, consistent with an approach to equilibrium on the scale of the garnet crystal (and perhaps the entire thin section) for these elements. The observations presented in Figs 6 and 7. clearly indicate that not all major cations could have been incorporated into garnet under conditions of local equilibrium with a homogeneous matrix. The question that naturally arises is: were any elements in equilibrium and, if so, which ones? Before attempting to answer this question, it is desirable to de ne what is meant here by the terms `equilibrium control' and `transport control'. The term `equilibrium control' refers to chemical equilibrium being maintained at the rims of all phases at all times. (Clearly, the presence of zoned crystals precludes equilibrium with crystal interiors.) Moreover, within the volume of rock in which equilibrium prevails, the rim compositions of all like phases will be identical. An important consideration is that equilibrium control may occur on different scales for different elements. That is, some elements may exhibit equilibrium in a volume the size of a hand sample, whereas other elements exhibit equilibrium on a scale of only a few centimetres. Irrespective of the length scale, equilibrium control requires that the phase compositions are dictated by the P±T±X phase relations of the system within the volume of equilibration. `Transport control' refers to the situation where there are signi cant gradients in the composition of an element within the volume under consideration, so that the composition of the growing phase (e.g. garnet) is controlled, in part, by the ux of the element. For the reasons listed below, it is hypothesized that the elements Mn, Fe and Mg are in equilibrium throughout the thin section, whereas Ca is transport limited. 1 Zoning systematics. The similar zoning symmetries (Figs 2 & 3.) for Mn, Fe and Mg suggest that these elements are controlled by similar factors, whereas the different zoning symmetry (roughly radially symmetric) for Ca suggests a different control on Ca zoning. It is unlikely that all elements are transport limited, so it remains to be determined whether Fe, Mg and Mn are transport limited or whether Ca is. 2 Zoning patterns. The preservation of a crenulation in the Mn, Fe and Mg zoning of sample 96-2 (Figs 3 & 4.) provides an explanation for the apparently patchy zoning observed in these elements in both samples: garnet initially overgrew mica- and chlorite-rich crenulations. No similar explanation has been found to explain the pattern of Ca zoning. 3 Garnet rim compositions. The rims of all garnet crystals examined in both samples 96-1 and 96-2 (over 100 in total) have the same composition within analytical error. This observation strongly suggests

GARNET GROWTH, HARPSWELL NECK, MAINE, USA 185 Fig. 7. Plot of X sps versus X grs (a & c) and Fe/(Fe+Mg) (b & d) for the garnet from sample 96-1 (a & b) and 96-2 (c & d). Images were smoothed with a 535 (96-1) or 333 (96-2) averaging kernel with edge recognition (see Appendix). The arrows show the predicted zoning trends for garnet in equilibrium with a homogeneous bulk composition. Solid arrow=isobaric heating path (Path 1, Fig. 9.); broken arrow=clockwise P±T path (Path 2, Fig. 9.). (b) and (d) show several isobaric heating paths for rocks of different bulk Mn and Fe/Mg. Error bars are 1s. that, by the end of garnet growth, local equilibrium for all elements had been established. 4 Correlation of garnet size and core composition. Spear & Daniel (1998.) described the positive correlation of garnet radius (centre cuts) and core Mn concentration as an indication of progressive nucleation. The same observation may be used to rule out gross disequilibrium controlling Mn composition and to support the hypothesis of local equilibrium control. Calcium zoning, on the other hand, displays the same pattern irrespective of garnet size (Fig. 8.). Even the smallest garnet shows a depleted core, an increase towards the rim and a drop off at the rim. If Ca zoning re ected equilibrium growth, then small garnet should have core compositions similar to those of the rims of large garnet, which they do not. This suggests Ca is transport controlled. 5 Trace element zoning. Although Y concentrations are barely within detectability limits of the electron microprobe, Y zoning in the core of sample 96-1 mimics that of Mn (Fig. 2f.). Y zoning in garnet in equilibrium with monazite can be described by Rayleigh fractionation (Pyle & Spear, 1999.), similar to Mn. The similarity of Y and Mn zoning suggests that both are following equilibrium fractionation trends and supports the inference that Mn zoning is equilibrium controlled. 6 Relative diffusion rates. The diffusion of Fe, Mg and Mn in silicates is more rapid than that of Ca (e.g. garnet; Chakraborty & Ganguly, 1992.). Furthermore, estimates by Foster (1981.) of the relative grain boundary transport rates in sillimanite-grade schists reveal Ca transport to be an order of magnitude slower than that of Fe and Mg. Whereas grain boundary diffusion in rocks of the garnet zone has never been measured for these elements, it is likely that the transport of Fe, Mg and Mn is faster than that of Ca, and thus more likely to be equilibrium controlled, whereas Ca is more likely to be transport controlled. 7 Plagioclase inclusion composition. Only one small plagioclase inclusion was found inside the garnet crystal from sample 96-1 and it has a composition of An 4, similar to the plagioclase rim compositions in the matrix. Inasmuch as the matrix plagioclase rims are likely to be in equilibrium with the garnet rim (all garnet rim compositions are the same), the existence of an inclusion of plagioclase of the same composition inside of garnet, where X grs is higher than the rim, suggests a lack of local equilibrium between plagioclase and garnet (e.g. transport control of Ca zoning). 8 Ilmenite compositional variation. Ilmenite inclusions display compositional variation depending on their position within garnet. For most ilmenite inclusions, the Mn concentration is broadly consistent with the

186 F. S. SPEAR & C. G. DANIEL Fig. 8. X-ray maps showing Ca zoning in centre cuts as a function of garnet crystal size. Note that all garnet displays Ca zoning with a low core, increase towards the rim and drop off at the rim, irrespective of size. Sample 96-1. local Mn concentration in garnet, suggesting an approach to local equilibrium between ilmenite and garnet. However, there are some notably Mn-rich ilmenite inclusions that appear to be grossly out of equilibrium. Indeed, in two areas of the garnet, high- Mn ilmenite inclusions are found in close proximity to intermediate-mn ilmenite inclusions, suggesting that disequilibrium dissolution of ilmenite has occurred, at least locally. P±T paths and predicted garnet zoning The local equilibrium model predicts different zoning for garnet grown along different P±T paths. Two possible P±T paths for the Maine samples are shown in Fig. 9. with the predicted garnet zoning for each. In each model shown, the garnet zoning was modelled with the assemblage garnet+chlorite+biotite+muscovite+plagioclase+quartz+h 2 O assuming a homogeneous bulk composition. Model calculations were performed using the program Gibbs following the methods outlined in Spear et al. (1990.). Additional models were run with margarite in the assemblage with qualitatively similar results. Both P±T paths predict Rayleigh depletions in Mn and increases in Fe and Mg, similar to the observed zoning. The isobaric heating path (Path 1) predicts that Ca decreases monotonically from the core to the rim, as dictated by equilibrium with plagioclase and mass balance constraints. The clockwise P±T path, however, predicts increasing Ca from the core towards the rim as pressure increases, then a drop to lower Ca values towards the rim as pressure decreases, which matches the observed Ca zoning in sample 96-1 quite well (Figs 2d & 7a.), but not that in sample 96-2 (Figs 3d & 7c.). A clockwise P±T path also predicts Mn, Fe and Mg zoning similar to that observed. Despite the good match between the Ca zoning predicted along the clockwise P±T path (Path 2) and the observed grossular zoning in sample 96-1, there are several reasons why this is not believed to be the correct path. First, it would be highly unlikely that samples 96-1 and 96-2 followed different P±T paths inasmuch as they were collected only a few metres from each other. and yet, no single clockwise P±T path can be found that matches the Ca zoning in both samples. Second, the regional geological setting of low-pressure, pluton-enhanced metamorphism is more consistent with an isobaric heating path (see also Lang & Dunn, 1990.; g. 3.). Third, the clockwise path enters the kyanite eld, whereas only andalusite and, at higher grades, sillimanite are found in the area. Fourth, the clockwise path predicts no change in plagioclase composition along the loading part of the path, whereas plagioclase in the sample is universally zoned towards more albitic compositions, consistent with the isobaric heating path. Fifth, the clockwise path, although it can explain the Ca zoning in sample 96-1, fails to explain the Ca zoning in 96-2 and also fails to reconcile the patchy zoning observed in Mn, Fe and Mg. An explanation (i.e. Path 2) that forces local equilibrium in Ca by adopting a very speci c P±T path but ignores Mn, Fe and Mg is considered ad hoc. As mentioned above, the transport of Fe, Mg and Mn is likely to be more rapid than that of Ca, and so a P±T

GARNET GROWTH, HARPSWELL NECK, MAINE, USA 187 Fig. 9. (a) Two alternative P±T paths for prograde metamorphism of schists of Harpswell Neck, Maine. Al 2 SiO 5 triple point after Holdaway (1971.). (b) Calculated zoning along isobaric heating path (Path 1). (c) Calculated zoning along clockwise P±T path (Path 2). Both zoning pro les calculated using the Gibbs method (Spear et al., 1990.) and garnet core composition as reference values. path constrained by calculation of local equilibrium between plagioclase and garnet but that requires transport control of Fe, Mg and Mn zoning is not reasonable. Whereas this last argument is indirect, together all the arguments suggest that the zoning cannot be reconciled by the choice of P±T path. For the remainder of this paper, an isobaric heating path will be assumed. A better time line for garnet growth The preceding discussion argues for local equilibrium control on the Fe, Mg and Mn composition of garnet, but diffusion control of the Ca composition. However, it is also argued that the matrix was not homogeneous, but varied locally in Fe, Mg and Mn (e.g. Fig. 6.). In this case, isopleths of Mn are not time lines because it is possible that two parts of the garnet with different Mn, Fe and Mg concentrations could have grown simultaneously, yet each region could still be in equilibrium with the local bulk composition. The compositional control on the growth of garnet in the system SiO 2 ± Al 2 O 3 ±MgO±FeO±MnO±K 2 O±H 2 O (MnKFMASH) is illustrated on a pair of phase diagrams (Fig. 10.). Tielines on each isothermal, isobaric diagram (i.e. Fig. 10a, b.) illustrate the compositions of coexisting garnet and chlorite in equilibrium at the indicated conditions. For example, at 450 uc, 3 kbar, garnet crystals with X sps ranging from approximately 0.15 to 1.0 may coexist with chlorite with Fe/(Fe+Mg) ranging from 1.0 to 0.0. Note that there is also a correlation between the Fe/(Fe+Mg) of garnet and X sps, with higher X sps requiring lower Fe/(Fe+Mg). Although both the spessartine content and Fe/ (Fe+Mg) may vary with the local bulk composition, a compositional parameter that is dependent only on the temperature of crystallization is the projection point of the garnet phase boundary onto the Fe±Mg (Mn-free) axis (Fig. 10c.). Note that this parameter has units of Fe/(Fe+Mg), but is not equivalent to the Fe/ (Fe+Mg) of the spot analysis. Grossular behaves in a similar fashion, such that there is a unique projection point that will vary monotonically with temperature irrespective of the bulk composition. If the compositions of coexisting chlorite, biotite and plagioclase and the P±T are assumed, the projection point can be found following a procedure described as a `thermodynamic projection' (Spear, 1988.). The method involves solving the Jacobean transformation matrix for the assumed equilibrium assemblage; for this application, the required partial derivatives are (hx alm / hx sps ) T,P,Xgrs and (hx alm /hx grs ) T,P,Xsps. The partial derivatives are multiplied by the desired changes in grossular and spessartine (DX sps and DX grs ) to obtain the dependent change in X alm (equivalent to Fe/ (Fe+Mg) at X sps =X grs =0). As described by Spear (1988.), the method is applied incrementally with the Jacobean recalculated after each incremental change in spessartine and grossular. In the present application, the partial derivatives are assumed to be constant, and the projected composition of garnet (i.e. X alm ) is calculated by multiplying the partial derivatives by X sps and X grs (Fig. 11.). This procedure was applied to the images in Figs 2 and 3.(see Appendix) and a new image was generated that represents the projected composition (intercept or `b' values) of every pixel (Fig. 12.). This image may be taken to represent a time sequence of garnet growth insofar as it may be assumed that garnet grew in local equilibrium within a region of variable bulk composition. That is, contour lines on this image are inferred to represent time lines. Comparison of Fig. 12.with Figs 2 and 3. reveals that the general pattern of zoning is similar to that observed in spessartine and almandine, indicating simply that the zoning of these elements dominates the garnet zoning pattern. Also, note the

188 F. S. SPEAR & C. G. DANIEL Fig. 10. Calculated Fe±Mg±Mn phase diagrams in the system MnKFMASH projected from quartz, muscovite, H 2 O and biotite. (a) Conditions of the garnet core. (b) Conditions of the garnet rim. Dot indicates highest X sps composition of garnet in core (a) and core±rim zoning (b). (c) Diagram depicting the evolution of garnet Fe±Mg±Mn compositions as a function of increasing grade. Note that even though the absolute values of Fe, Mg and Mn in garnet in equilibrium with chlorite at a xed P±T are a function of bulk composition, the intercept on the Fe±Mg axis is a monotonic function of temperature. similarity with Y zoning (Fig. 2f.). Most importantly, it is clear that the projection scheme does not result in a pattern that is concentric about the garnet core as observed in grossular zoning (Fig. 2d.). Therefore, it is concluded that garnet did not grow concentrically, as might be suggested by examining the Ca zoning alone, but grew in the time sequence indicated by the pattern in Fig. 12. `Threshold' tool in NIH Image such that all pixels with a value greater than a chosen value are rendered in the same colour (in this case grey). Insofar as the time line projection re ects sequential garnet growth, the image reveals the shape of the garnet at a point in its growth history. Clearly visible in Fig. 13.are isolated bits of garnet outboard from the main garnet mass. Daniel & Spear Garnet nucleation and growth model The improved time line image (Fig. 12.) can be used to examine the geometry of garnet growth through time. As discussed earlier, garnet apparently nucleated on micas and chlorite, and often on crenulation folds (cf. Bell et al., 1986.). Once garnet nucleated in a particular mica+chlorite domain location, growth apparently occurred fairly easily along the mica+chlorite domain, replacing the phyllosilicates with high-mn garnet. This can readily be seen in the examples in which garnet outlines crenulation folds (e.g. Figs 4 & 12b.). In Fig. 12(a.), it is inferred that the two patches of high- Mn garnet at the top and bottom of the crystal are connected in the third dimension. Following growth along the mica+chlorite domain, garnet continued growing into the quartz domain. In general, there are two types of grain intersection in a three-dimensional crystal aggregate: triple-grain intersections and double-grain intersections. These may be grains of similar material, such as two or three quartz grains, or dissimilar material, such as a garnet±quartz grain boundary. Garnet growth occurred along both of these types of grain intersection, and there is evidence that growth was more rapid along triple-grain intersections. Figure 13.is a projected `time line' image of a small part of the garnet interior that has been enhanced to reveal the amount of garnet that has already grown at a point in time. Figure 13.and the subsequent two images (Figs 14 & 15.) were created using the Fig. 11. Transformation of garnet composition space (alm± prp±sps±grs) into Cartesian coordinates. At xed P±T, the composition of garnet in equilibrium with chlorite (+quartz+muscovite+h 2 O+plagioclase+biotite) is approximately described by a plane. The intercept (b) is a monotonic function of grade. This intercept is not known, but can be calculated from the measured composition of garnet, provided the slopes (hx alm /hx sps ) P,T,Xgrs and (hx alm / hx grs ) P,T,Xsps are known. Note that although the Ca content of the garnet core is believed to be diffusion controlled rather than controlled by equilibrium with plagioclase, there is still a unique phase plane that de nes the accessible garnet composition at every P±T.

GARNET GROWTH, HARPSWELL NECK, MAINE, USA 189 (1998.) and Spear & Daniel (1998.) interpreted these as being distinct garnet nuclei, but the EBSD and OCI data rule out this possibility. These apparent nuclei are here interpreted as the intersection of triple-grain boundaries containing garnet (i.e. in roughly the shape of a tube) with the plane of the thin section. Of particular note is the proximity of these nuclei to quartz inclusions, which appear black in Fig. 13. The quartz inclusions are bounded by present-day grain boundaries (quartz± garnet), and must have also been grain boundaries at the time of garnet growth at these locations. From this observation, it is inferred that garnet growth in the quartz domain proceeded most rapidly along these triple-grain intersections, which, presumably, are pathways of more rapid material transport. Further evidence supporting the growth of garnet along grain intersections is presented in Figs 14 and 15., which illustrate the sequence of garnet evolution resulting in `mineral capture' (formation of a mineral inclusion). It is clear from these series that garnet grew most rapidly along triple-grain boundaries (e.g. a1, a2, b1, b2), then along double-grain boundaries (e.g. c3, f3) until a crystal was surrounded. Further replacement of the mineral by garnet continued until, presumably, the mineral was isolated from the matrix on all sides. Of particular note is the appearance of isolated islands of garnet near the garnet rim (i.e. relic triple-grain intersections; a1 and a2 in Fig. 15a.), indicating that rapid growth along triple-grain intersections occurs throughout the growth history. Images showing similar features during garnet growth were presented by Spear & Daniel (1998.). Ca zoning It remains to explain the origin of the roughly concentric Ca zoning (i.e. Figs 2d & 3d.) in light of the inference that garnet has not grown radially. Local equilibrium with plagioclase during garnet growth Fig. 12. Processed X-ray images showing the temporal evolution of garnet (intercept value `b' of Fig. 11.) calculated using the Jacobean partial derivatives (Appendix). Assumes local equilibrium with quartz, muscovite, H 2 O, biotite, chlorite, and the chemical potential of Ca de ned by the local diffusion gradient, referred to as the `time line' image. (a) Sample 96-1. (b) Sample 96-2. Fig. 13. Portion of `time line' image of Fig. 12(a.) (white box in Fig. 12a.). Dark grey areas highlight regions with Mn greater than an arbitrary threshold value to illustrate the pattern of apparent nucleation using Mn as a time line. Note the abundance of isolated apparent nuclei (arrows) that occur outboard of the main garnet crystal (upper right) and the proximity of these apparent nuclei to quartz grains (black). Length of base of image is 160 mm.

190 F. S. SPEAR & C. G. DANIEL Fig. 14. Sequence of `time line' images with thresholding applied (dark grey) to illustrate phenomenon of `mineral capture', in this case a crystal of muscovite (see Fig. 12.for location). Each pixel=131 mm; width of each image=100 mm. Numbered letters (e.g. a1, a2, etc.) are spots referred to in the caption. (a) Initial conditions. Two crystals are indicated by arrows: a1=muscovite and a2=quartz. (b) Two apparent nuclei (b1 & b2) appear slightly outboard of main garnet crystal. These are interpreted as representing the intersection of garnet tubules with the plane of the section and are not isolated nuclei. (c) The two apparent nuclei are connected to the main garnet mass (c1 & c2). In addition, garnet begins to encroach around the margins of the muscovite crystal (c3 & c4). (d) Garnet continues to encroach around the muscovite (d1 & d2) and new bits of garnet appear along what appears to be a relic grain boundary (d3). (e) Garnet growth continues along relic grain boundaries (e1 & e2). Point e3 is a relic triple-grain intersection. (f) The quartz crystal is completely ringed by garnet (f1) and a second `phantom' crystal nearly so (f2) as garnet grows along double-grain boundary from f3. The non-garnet material at f1 and f2 was probably quartz at this time. (g) Quartz and muscovite are replaced by garnet at g1, g2 and g3 and elsewhere. (h) The muscovite crystal is completely isolated from the matrix in this two-dimensional slice (h1), although probably not in the third dimension inasmuch as further replacement by garnet occurs in (i) (e.g. i1). along an isobaric heating path predicts Ca zoning that is monotonically decreasing (Figs 7a, c & 9b.). However, Fig. 6.demonstrates that Ca concentrations were not uniform along Mn contours, indicating that Ca zoning cannot be controlled by local equilibrium with plagioclase and a kinetic model must be pursued. The proposed model for Ca zoning calls for the supply of Ca to be controlled by diffusion over a length scale of roughly the radius of the nal garnet crystal. In this model, the initial local supply of Ca (from dispersed plagioclase and other Ca-bearing phases) is depleted during the initial growth of garnet over the phyllosilicate domain (Fig. 16a, b.). Once this local source of Ca is gone, Ca is supplied by breakdown of the anorthite component of plagioclase in the matrix and transport along grain boundaries. The part of the garnet crystal closest to the Ca source receives the highest supply of Ca and crystallizes with the highest grossular concentration, whereas the core crystallizes with the lowest grossular concentration (Fig. 16c.). The white line in Fig. 17(a.) outlines the highest grossular portion of the garnet, which represents the limit of the Ca depletion zone in this crystal. This model appears to be consistent with simple mass

GARNET GROWTH, HARPSWELL NECK, MAINE, USA 191 Fig. 15. Garnet growth pattern and partial quartz capture at garnet rim (see Fig. 12.for location). Each pixel=131 mm; width of each image=170 mm. (a) Garnet (dark grey) appears outboard from main garnet mass (a1, a2) presumably along triple-grain intersections. (b) Garnet continues to replace the matrix by lling in double-grain boundaries (b1, b2) and isolating some matrix minerals (b2). (c) Garnet has replaced most of the partially included minerals; grain at c1 remains but is replaced by garnet eventually. balance calculations. Consider a restricted volume of rock with an initial mode of plagioclase of composition X an =0.33 (the composition of the core of matrix plagioclase). If all of the plagioclase in this volume is consumed in the production of initial garnet, then the relationship between the amount and composition of garnet and plagioclase is given by: X grs /X an =[(Moles pl /3)/Moles grt ]={[(Mode pl / V pl )/3]/ (Mode grt / V grt )} Using the values X an =0.33 and X grs =0.11, the production of 5% modal garnet will consume 3±4% modal plagioclase, which is consistent with the observed 3±5% modal plagioclase in sample 96-1. Of course, if plagioclase was not evenly distributed in the rock prior to garnet nucleation, then plagioclase depletion could have occurred with even less garnet growth. During initial plagioclase depletion, the Al and Si from the breakdown of plagioclase are used in the production of garnet, whereas the Na is required to diffuse away from the growing crystal into the matrix, where it precipitates as the albite component on existing plagioclase, consistent with the observed zoning towards more albitic plagioclase in the matrix. A single plagioclase inclusion observed within garnet has a composition X an =0.04, consistent with the depletion of the anorthite component during the growth of garnet. The initial X grs in garnet before the development of the plagioclase depletion zone was likely 0.11 (the maximum X grs in the garnet) (Fig. 17a.). It is signi cant that there exist numerous, small, isolated regions in the garnet interior that have high Ca concentrations (Fig. 17b.). Some of these high-ca spots are garnet with X grs approaching 0.11 (accurate quantitative analysis is impossible owing to their small size), whereas others are Ca±Al phases such as epidote and margarite. In some locations, it appears that the highgrossular garnet spots occur in the general regions where the earliest garnet forms but, in other locations in the garnet interior, high-grossular garnet spots appear in later formed garnet. The Ca±Al silicates included in the garnet interior most likely represent relic matrix phases that were trapped in the garnet interior owing to incomplete dissolution. The high X grs Fig. 16. Illustration of Ca gradients during garnet growth. (a) Initial conditions showing approximately 4% modal plagioclase (hexagons represent An 33 plagioclase). Broken line outlines size of nal garnet crystal. (b) Initial growth of garnet results in consumption of all plagioclase in the garnet interior producing garnet of composition X grs =0.05 for 10% garnet growth. (c) Once plagioclase is consumed, a concentration gradient in Ca is set up between the matrix, where Ca concentration is controlled by plagioclase equilibria, and the garnet interior. Note that in such a gradient, garnet of different grossular content can grow simultaneously and the highest grossular garnet will be nearest the matrix.

192 F. S. SPEAR & C. G. DANIEL in garnet in the vicinity of these inclusions supports the interpretation of transport control of Ca. Growth of the garnet interior by diffusion of elements from the matrix continued until all existing transport avenues (i.e. garnet±mineral grain boundaries) were sealed off. At this point, garnet could only grow outwards from the rim, although the process of `mineral capture' was still active (e.g. Fig. 15.). Once garnet growth had transferred to the rim outward, all elements zoned more or less concentrically, consistent with diffusion control of nutrients from the matrix to the growing garnet. Local reaction and mass ux The observations presented herein suggest that local growth of garnet was diffusion controlled along triplegrain and double-grain boundaries, presumably with different diffusivities. It is likely that not all elements diffuse at the same rate and, insofar as the `time line' projection provides an accurate measure of the growth history of garnet, it is possible to place some constraints on the relative rates of replacement of different minerals by garnet and, thereby, on the relative uxes of different elements. Measurement of the rate at which garnet replaces other minerals is accomplished directly on the `time line' image (Fig. 12.) as shown in Fig. 18. The change in projected composition and the distance over which the composition change occurs are measured from the image and the rate of change calculated as: replacement rate=ddistance/dcomposition Relative replacement rates were measured for quartz, muscovite, chlorite and plagioclase from the observed chemical zoning in garnet around inclusions of these minerals (Table 1., column 2). It is possible to convert these measurements into crude estimates of the absolute replacement rates in the following manner. Fig. 17. (a) X grs X-ray map of sample 96-1. Line is drawn around highest Ca concentration, which is interpreted to represent limit of Ca diffusion pro le. Box shows location of (b). (b) Enlargement of a portion of (a) showing spots with high X grs (0.10±0.13) that occur throughout the garnet core. Bulk of garnet core has X grs =0.05±0.06. These spots may represent high diffusivity pathways along which Ca-rich phases precipitated. Fig. 18. Illustration of the measurement of the replacement rate of muscovite by garnet. The difference in the composition of the end pixels along a traverse across the garnet±muscovite interface is divided by the distance of the traverse to yield Ddistance/Dmole fraction. Inasmuch as Dmole fraction is a proxy for time, this method can be used to compare the rates of replacement of different minerals by garnet.

GARNET GROWTH, HARPSWELL NECK, MAINE, USA 193 Table 1. Rates of replacement of quartz, muscovite, chlorite and plagioclase by garnet. mm (mole fraction) x1a. mm uc x1b. mm Myr x1c. Quartz 20 0.05 5 Muscovite 110 0.27 27 Chlorite 56 0.14 14 Plagioclase 66 0.16 16 a Measured rate from image. b Assumes a temperature derivative of dx/dt=x2.46310 x03 X uc x1. c Assumes a heating rate of 100 uc Myr x1. The rate of change of the garnet `time line' compositional parameter with respect to temperature is calculated using the Gibbs method to be x 2.5310 x03 (mole fraction uc x1 ) (Table 1., column 3). Assuming a heating rate of 100 uc Myr x1 (an estimate for the heating rate in a regional contact environment), the measured replacement rates can be converted to absolute replacement rates (Table 1., column 4). These values must be considered highly uncertain because the measurement of the replacement rate is subject to large errors. Nevertheless, they indicate that quartz is the most dif cult mineral for garnet to replace and muscovite the easiest, consistent with the observed patterns of mineral capture and identities of inclusions in garnet. It should be noted that the absolute replacement rates (Table 1., column 4) are quite small, on the order of mm Myr x1, which is much too small to account for the growth of the entire garnet, which is nearly 1 mm in diameter. These replacement rates are only valid on a very local scale where garnet is replacing another mineral along a double-grain boundary. The reaction stoichiometry along each mineral± garnet interface can be balanced by conserving oxygen (Table 2.). Conservation of oxygen yields similar results to balancing reactions based on conservation of volume, and is based on the assumption that mineral replacement occurs primarily by diffusion of cations along the double-grain boundary. It is signi cant to note that, balanced this way, replacement of micas (muscovite and biotite) by garnet requires no ux of Si and replacement of plagioclase and chlorite requires no ux of Al, whereas replacement of quartz requires uxes of both Al and Si (Table 2.). Multiplication of the replacement rates by the Table 2. Stoichiometric reaction coef cients for selected mineral replacement by garnet assuming conservation of oxygen. Si Al Fe+Mg+Mn Ca K Na H Grt 6Qtz x3 2 2.85 0.15 0 0 0 = 1 Ab x1.5 0.5 2.85 0.15 0 x1.5 0 = 1 An 0 x1 2.85 x1.35 0 0 0 = 1 1.5 An33 x1 0 2.85 x0.35 0 x1 0 = 1 Ms 0 x1 2.85 0.15 x1 0 x2 = 1 Bt 0 1 x0.15 0.15 x1 0 x2 = 1 Chl 1.34 0 x0.15 0.15 0 0 x5.33 = 1 Positive coef cients indicate material added to the reaction site; negative coef cients indicate material removed. Table 3. Relative uxes of Si, Al and Fe+Mg+Mn consistent with the observed replacement of quartz, muscovite, chlorite and plagioclase (An 33 ) by garnet. Si Al Fe+Mg+Mn Qtz x60 40 57 Ms 0 x110 315 Chl 75 0 x8 An33 x66 0 188 Positive uxes indicate addition of material, negative uxes indicate removal. reaction stoichiometries (Table 3.) provides an estimate of the relative uxes of cations to, or from the reaction site for the replacement of each mineral. If the replacement reaction is not limited by the ux of a particular cation, then the calculated ux is dictated entirely by the reaction stoichiometry and can take a wide range of values. For example, the ux of Fe+Mg+Mn varies from eight (for replacement of chlorite) to 315 (for replacement of muscovite) and this is interpreted as signifying that the ux of these cations is not rate limiting. It is remarkable that the ux of Si for the replacement of quartz, chlorite and plagioclase is nearly identical (muscovite replacement does not require addition or removal of Si). The similarity of Si uxes is interpreted to signify that Si diffusion is rate limiting in these replacement reactions. Inasmuch as Si has the highest eld strength of the elements considered, this result is consistent with the general result that high eld strength elements have low diffusivities. At sites where muscovite replacement occurs, it is likely that Al ux is rate limiting, although the present analysis does not provide any direct constraint. Although not included in the present analysis, ilmenite replacement also appears to be very slow, consistent with Ti removal as rate limiting in some reaction sites. CONCLUSIONS The results of this study indicate that nucleation and initial growth of garnet occurred preferentially in mica domains. It is not clear why nucleation should have preferred mica crenulations rather than micas located elsewhere in the sample, but Bell et al. (1986.) argued for porphyroblasts in crenulations because elsewhere in the rock the strain is suf ciently high that mineral dissolution occurs. Alternatively, it is possible that the bent phyllosilicates in the crenulations were sites of high strain, which contributed to the energy required for nucleation (see Williams, 1994. for similar arguments). In either case, studies that examine the spatial distribution of porphyroblasts in a sample may, in fact, be examining the distribution of crenulations or other heterogeneities within the rock, rather than any property intrinsic to garnet growth kinetics (e.g. Carlson, 1989., 1991.; Denison & Carlson, 1997.; Daniel & Spear, 1999.). The supply of Ca to garnet growth sites was apparently limited by diffusion over length scales on