Three-dimensional quantitative textural analysis of metamorphic rocks using high-resolution computed X-ray tomography: Part II. Application to natural samples

Three-dimensional quantitative textural analysis coupled with numerical modelling has been used to assess the dominant mechanisms governing crystallization of garnet porphyroblasts in rocks from diverse regional metamorphic environments. In every case, spatial dispositions, crystal size distributions, and compositional zoning patterns of porphyroblasts indicate the dominance of diffusion-controlled nucleation and growth mechanisms.
Nine samples from three geological areas were studied: a suite of semi-pelitic rocks from the Picuris Mountains, New Mexico (USA); a suite of mafic samples from the Llano Uplift, Texas (USA); and a kyanite schist from Mica Dam, British Columbia (Canada). The semi-pelitic suite exhibits post-deformational garnet growth, whereas garnet in the mafic suite and in the kyanite schist grew synkinematically in rocks displaying weak and strong penetrative fabrics, respectively.
For each sample, the centres and radii of thousands of garnet crystals were located and measured in three dimensions, using images produced by high-resolution computed X-ray tomography. Statistical measures of the degree of ordering and clustering of nucleation sites, and estimates of crystal isolation for each porphyroblast, were then computed from the measured spatial dispositions. These measures can be reproduced in simple numerical models only by diffusion-controlled nucleation and growth mechanisms. Normalized radius-rate relations computed from compositional zoning patterns in the garnets require thermally accelerated diffusion-controlled growth, providing independent confirmation of the conclusions based on textural analysis. The unexpected similarity of results from all samples indicates that diffusion-controlled nucleation and growth mechanisms may govern porphyroblast crystallization in many metamorphic regimes.     

The effect of metamorphic fluid flow on the nucleation and growth of garnets from Troms, North Norway

A spatial association is observed between the size distribution of garnet porphyroblasts and the size distribution of quartz veins in greenschist facies metapelites from Troms, North Norway. The size distribution of quartz veins reflects the flow regime of metamorphic fluids. The hypothesis that the flow regime of metamorphic fluids is also responsible for the size distribution of garnet crystals was tested by ascribing empirical acceleration parameters to the nucleation and growth rates of garnet crystals.
In regions where fluid flow was interpreted as pervasive', acceleration parameters for nucleation were high, whereas in regions where fluid flow was interpreted as channelled', acceleration parameters for growth were high. Accelerated crystal growth is further implied from the chemical zoning and crystal morphologies of garnets collected near discrete veins.
This spatial association may imply that fluid flow can be instrumental in controlling garnet crystallization. Fluid flow could affect garnet crystallization kinetics by facilitating thermal advection and/or mass transfer. In the study area, rhodochrosite (MnCO₃) veins provide evidence for mass transfer of Mn by fluid flow. An influx of Mn would expand the stability field of garnet to lower temperatures. The resulting thermal overstep could accelerate nucleation and/or growth of garnets.
The corollary of this study is that size distributions and chemical zoning of garnets, or other porphyroblast phases, can be used to study metamorphic fluid flow.     

Controls on porphyroblast size along a regional metamorphic field gradient

Garnet-bearing schists from the Waterville Formation of south-central Maine provide an opportunity to examine the factors governing porphyroblast size over a range of metamorphic grade. Three-dimensional sizes and locations for all garnet porphyroblasts were determined for three samples along the metamorphic field gradient spanning lowest garnet through sillimanite grade, using high-resolution X-ray computed tomography. Comparison of crystal size distributions to previous data sets obtained by stereological methods for the same samples reveals significant differences in mode, mean, and shape of the distributions. Quantitative textural analysis shows that the garnets in each rock crystallized in a diffusion-controlled nucleation and growth regime. In contrast to the typical observation of a correlation between porphyroblast size and position along a metamorphic field gradient, porphyroblast size of the lowest-grade specimen is intermediate between the high- and middle-grade specimens’ sizes. Mean porphyroblast size does not correlate with peak temperatures from garnet-biotite Fe-Mg exchange thermometry, nor is post-crystallization annealing (Ostwald Ripening) required to produce the observed textures, as was previously proposed for these rocks. Robust pseudosection calculations fail to reproduce the observed garnet core compositions for two specimens, suggesting that these calc-pelites experienced metasomatism. For each of these two specimens, Monte Carlo calculations suggest potential pre-metasomatism bulk compositions that replicate garnet core compositions. Pseudosection analyses allow the estimation of the critical temperatures for garnet growth: ∼481, ∼477, and ∼485°C for the lowest-garnet-zone, middle-garnet-zone, and sillimanite-zone specimens, respectively. Porphyroblast size appears to be determined in this case by a combination of the heating rate during garnet crystallization, the critical temperature for the garnet-forming reaction and the kinetics of nucleation. Numerical simulations of thermally accelerated, diffusion-controlled nucleation, and growth for the three samples closely match measured crystal size distributions. These observations and simulations suggest that previous hypotheses linking the garnet size primarily to the temperature at the onset of porphyroblast nucleation can only partially explain the observed textures. Also important in determining porphyroblast size are the heating rate and the distribution of favorable nucleation sites.     

Modeling of zoning patterns in garnet: Thermodynamic and kinetic aspects

Results from the modeling of compositional zoning patterns in garnet porphyroblasts from the medium-grade metapelitic schist of northern Ladoga area are considered. The P-T pseudosections in the model KMnFMASH system were calculated for this purpose using THERMOCALC software (Powell et al., 1998). Particular emphasis is placed upon the effect of garnet growth kinetics on the model zoning profiles for Mn (Gulbin, 2013). They fit the observed profiles if intergranular diffusion-controlled growth is assumed for porphyroblasts. Additionally, a model of metamorphic fractional crystallization is used to characterize the oscillations in both the garnet core and rim. Starting from the assumption that a reservoir, where garnet grows, consists of chlorite, and that this mineral is intensely replaced with biotite and staurolite at the onset of crystallization, a partial release of Mn from the chlorite structure and the concentration of this component in intergranular space is inferred. In terms of the model under consideration, the coefficient of the Mn partition between garnet and reservoir temporarily increases at the early stage of garnet growth, giving rise to the enrichment of the intermediate zone of porphyroblasts in Mn. In addition to the modeling of garnet growth zoning, its subsequent diffusion modification is estimated on the basis of intracrystalline diffusion profile simulation. The reverse zoned, Mn-rich and Mg-poor garnet rims are related to retrograde growth of garnet at the late stage of porphyroblast formation. The data obtained are used to constrain metamorphic evolution and the P-T-t path of staurolite-bearing rocks in the northern domain of the studied area.     

Disequilibrium for Ca during growth of pelitic garnet

Compositional zoning in hundreds of almandine-rich garnets in amphibolite by facies micaceous quartzites from the Picuris Range, north-central New Mexico USA, indicates that although Mn, Mg and Fe achieve chemical equilibrium at hand-sample scale during garnet growth, Ca does not. Instead, Ca concentrations at the surface of growing garnets appear to depend strongly on kinetic factors that govern the local chemical environment, yielding disequilibrium for Ca at scales larger than the region immediately surrounding an individual porphyroblast. Detailed zoning profiles were obtained for 371 garnet crystals in a small volume of a single sample of garnetiferous quartzite, and core analyses were made of 97 additional crystals. Each analysis was made on a section that passed precisely through the morphological centre of the crystal, located by means of 3-D imagery from computed X-ray tomography. The data reveal strong correlations between crystal size and concentrations of Mn, Mg and Fe (but not Ca) in garnet cores; a relationship between crystal size and isolation; rigorous cross-correlations among concentrations of Mn, Mg and Fe (but not Ca); and systematic variations in Ca concentrations as a function of crystal size and core composition that are anomalous in comparison to the behaviour of the other divalent cations. We interpret these observations as the result of thermally accelerated diffusion-controlled garnet growth, in circumstances that promoted rapid intergranular diffusion and thus rock-wide equilibration of Mn, Mg and Fe, but that prevented equilibration at similar scale for Ca because of its more sluggish intergranular diffusion. The anomalous behaviour of Ca is made evident in these garnets by the presence of sharp spikes in Ca concentration, which are demonstrably not a consequence of any simultaneous rock-wide event, such as a change in pressure, temperature, or some other intensive parameter. Instead, Ca concentrations probably reflect the local extent of reaction in the immediate vicinity of each porphyroblast. To the degree that such kinetic factors introduce departures from chemical equilibrium for Ca, thermobarometric estimates that involve grossular contents of pelitic garnet will be in error.     

Origins of yttrium and rare earth element distributions in metamorphic garnet

Highly variable distributions of yttrium and rare earth elements (Y+REEs) are documented in pelitic garnet from the Picuris Mountains, New Mexico, and from Passo del Sole, Switzerland, and in mafic garnet from the Franciscan Complex, California. The wide variety of these Y+REE zoning patterns, and those described previously in other occurrences, imply diverse origins linked to differing degrees of mobility of these elements through the intergranular medium during garnet growth. In the Picuris Mountains, large, early‐nucleating crystals have radial profiles of Y+REE dominated by central peaks and annular maxima, in patterns that vary systematically with atomic number. Superimposed on these features are narrow spikes in HREEs and MREEs, located progressively rimward with decreasing atomic number. In contrast, profiles in small, late‐nucleating crystals contain only broad central maxima for all Y+REEs. In garnet from Passo del Sole, Y+REE zoning varies radically from sample to sample: in some rocks, crystals of all sizes display only central peaks for all Y+REEs; in others, profiles exhibit irregular fluctuations in Y+REE contents that match up with small‐scale patchy zoning in Y and Ca X‐ray maps. In the Franciscan Complex, Y+REE in garnet cores fluctuate unsystematically, but mantles and rims display concentric oscillatory zoning for both major elements and Y+REEs. Our interpretation of the complexity of Y+REE distributions in metamorphic garnet centres on the concept that these distributions vary primarily in response to the length scales over which these elements can equilibrate during garnet growth. Very short length scales of equilibration, due to low intergranular mobility, produce overprint zoning characterized by small‐scale irregularities. Higher but still restricted mobility yields diffusion‐controlled uptake, characterized by patterns of central peaks and annular maxima that vary with atomic number and are strongly influenced by T–t paths during garnet growth. Still greater mobility permits progressively greater, potentially rock‐wide, equilibration with major‐ and accessory‐phase assemblages, leading to mineralogical controls: an unchanging mineral assemblage during garnet growth produces bell‐shaped profiles resembling those produced by Rayleigh fractionation, whereas changes in major‐ and/or accessory‐phase assemblages produce profiles with distinct annuli and sharp discontinuities in concentration. The very high mobility associated with influxes of Y+REE‐bearing fluids can cause these element distributions to be dominated by factors external to the rock, yielding profiles characterized by abrupt shifts or oscillations that are not correlated to changes in mineral assemblages.     

Three-dimensional quantitative textural analysis of metamorphic rocks using high-resolution computed X-ray tomography: Part I. Methods and techniques

Macroscopic textures resulting from different atomic-scale mechanisms for metamorphic crystallization display different degrees of order, clustering, intergrowth and relative isolation of porphyroblasts. Data on the sizes and locations of thousands of crystals in a three-dimensional volume are required to identify reliably the mechanisms governing nucleation and growth of porphyroblasts from these textural features. These data can now be acquired by means of high-resolution computed X-ray tomography. Numerical models that simulate porphyroblast formation governed by either interface-controlled or diffusion-controlled reaction mechanisms indicate that quantitative textural analysis can discriminate between these possibilities. These numerical models also allow a comparison between textures predicted for different crystallization mechanisms and textures measured in natural samples, from which inferences can be drawn concerning the relative importance of these mechanisms in nature. An independent test of the validity of such inferences is possible for porphyroblasts such as garnet that may preserve prograde growth zoning and allow the examination of normalized radius–rate relations.     

Characterisation of a garnet population from the Sikkim Himalaya: insights into the rates and mechanisms of porphyroblast crystallisation

The compositional zoning of a garnet population contained within a garnet-grade metapelitic schist from the Lesser Himalayan Sequence of Sikkim (India) provides insight into the rates and kinetic controls of metamorphism, and the extent of chemical equilibration during porphyroblast crystallisation in the sample. Compositional profiles across centrally sectioned garnet crystals representative of the observed crystal size distribution indicate a strong correlation between garnet crystal size and core composition with respect to major end-member components. Systematic steepening of compositional gradients observed from large to small grains is interpreted to reflect a progressive decrease in the growth rate of relatively late-nucleated garnet as a result of an increase in interfacial energies during progressive crystallisation. Numerical simulation of garnet nucleation and growth using an equilibrium approach accounting for chemical fractionation associated with garnet crystallisation reproduces both the observed crystal size distribution and the chemical zoning of the entire garnet population. Simulation of multicomponent intracrystalline diffusion within the population indicates rapid heating along the pressure–temperature path, in excess of 100 \(^{\circ }\)C Myr\(^{-1}\). Radial garnet growth is correspondingly rapid, with minimum rates of 1.4 mm Myr\(^{-1}\). As a consequence of such rapid crystallisation, the sample analysed in this study provides a close to primary record of the integrated history of garnet nucleation and growth. Our model suggests that nucleation of garnet occurred continuously between incipient garnet crystallisation at \(\sim\)520 \(^{\circ }\)C, 4.5 kbar and peak metamorphic conditions at \(\sim\)565 \(^{\circ }\)C, 5.6 kbar. The good fit between the observed and predicted garnet growth zoning suggests that the departure from equilibrium associated with garnet nucleation and growth was negligible, despite the particularly fast rates of metamorphic heating. Consequently, rates of major element diffusion in the intergranular medium during garnet crystallisation are interpreted to have been correspondingly rapid. It is, therefore, possible to simulate the prograde metamorphic history of our sample as a succession of equilibrium states of a chemical system modified by chemical fractionation associated with garnet crystallisation.     

Growth zoning of garnet porphyroblasts: Grain boundary and microtopographic controls

Chemical zoning in the outer few 10s of microns of garnet porphyroblasts has been investigated to assess the scale of chemical equilibrium with matrix minerals in a pelitic schist. Garnet porphyroblasts from the Late Proterozoic amphibolite facies regional metamorphic mica schists from Glen Roy in the Scottish Highlands contain typical prograde growth zoning patterns. Edge compositions have been measured via a combination of analysis of traverses across the planar edges of porphyroblast surfaces coupled to X-ray mapping of small areas within polished thin sections at the immediate edge of the porphyroblasts. These approaches reveal local variation in garnet composition, especially of grossular (Ca) and almandine (Fe) components, with a range at the edge from <7 mol.% grs to >16 mol.% grs, across distances of less than 50 µm. This small-scale patchy compositional zoning is as much variation as the core–rim compositional zoning across the whole of a 3 mm porphyroblast. Ca and Fe heterogeneity occurs on a scale suggesting a combination of inefficient diffusive exchange across grain boundaries during prograde growth and the evolving microtopography of the porphyroblast surface control garnet composition. The latter creates haloes of compositional zoning adjacent to some inclusions, which typically extend from the inclusion towards the porphyroblast edge during further growth. The lack of a consistent equilibrium composition at the garnet edge is also apparent in the internal zoning of the porphyroblast and so processes occurring during entrapment of some mineral inclusions have a profound influence on the overall chemical zoning. Garnet compositions and associated zoning patterns are widely used by petrologists to reconstruct P–T–t paths for crustal rocks. The evidence of extremely localized (10–50 µm scale) equilibrium during growth further undermines these approaches.     

Controls on metamorphic equilibration: the importance of intergranular solubilities mediated by fluid composition

A dramatic demonstration of the role of intergranular solubility in promoting chemical equilibration during metamorphism is found in the unusual zoning of garnet in pelitic schist exposed at Harpswell Neck, Maine, USA. Many garnet crystals have irregular, patchy distributions of Mn, Cr, Fe and Mg in their inclusion‐rich interiors, transitioning to smooth, concentric zoning in their inclusion‐poor outer rims; in contrast, zoning of Ca and Y is comparatively smooth and concentric throughout. We re‐assess the disputed origin of these zoning features by examining garnet growth in the context of the thermal and structural history of the rocks, and by evaluating the record of fluid–rock interaction revealed in outcrop‐scale veining and fluid‐inclusion assemblages. The transition in the character of garnet zoning correlates with the onset of a synkinematic, simple‐shear‐dominated phase of garnet growth and with a shift in the composition of the intergranular fluid from CO₂‐rich to H₂O‐rich. Compositional variations in garnet are therefore best explained by a two‐stage growth history in which intergranular diffusive fluxes reflect differences in the concentration of dissolved species in these two contrasting fluids. Interiors of garnet crystals grew in the presence of a CO₂‐rich fluid, in which limited solubility for Mn and Cr (and perhaps Fe and Mg) produced patchy disequilibrium overprint zoning, while appreciable solubility for Ca and Y permitted their rock‐wide equilibration. Rims grew in the presence of an H₂O‐rich fluid, in which high intergranular concentrations for all elements except Cr enabled diffusion over length scales sufficient for rock‐wide equilibration. This striking example of partial chemical equilibrium during reaction and porphyroblast growth implies that thermal effects may commonly be subsidiary in importance to solubilities in the intergranular medium as determinants of length scales for metamorphic equilibration.     

Chromium and manganese zoning in pelitic garnet and kyanite: Spiral,overprint, and oscillatory (?) zoning patterns and the role of growth rate

X‐ray composition maps and quantitative analyses for Mn, Ca and Cr have been made for six pelitic and calc‐pelitic garnet crystals and Al, Fe and Cr analyses maps have been made for two kyanite crystals, from lower and mid/upper amphibolite facies rocks from the Grenville Province of western Labrador, using an electron microprobe analyser and a laser ablation ICP‐MS. Garnet with spiral (‘snowball’) internal fabrics (S_i) has spiral zoning in major elements, implying that growth was concentrated in discrete regions of the crystal at any one time (spiral zoning). Cr zoning is parallel to S_i in low amphibolite facies garnet with both straight and spiral internal fabrics, indicating that the garnet overprinted a fabric defined by Cr‐rich (mica±chlorite±epidote) and Cr‐poor (quartz±plagioclase) layers during growth (overprint zoning) and that Cr was effectively immobile. In contrast, in mid/upper amphibolite facies garnet porphyroblasts lacking S_i, Cr zoning is concentric, implying that Cr diffusion occurred. Cr zoning in kyanite porphyroblasts appears superficially similar to oscillatory zoning, with up to three or four annuli of Cr enrichment and/or depletion present in a single grain. However, the variable width, continuity, Cr concentration and local bifurcation of individual annuli suggest that an origin by overprint zoning may be more likely. The results of this study explain previously observed nonsystematic Cr zoning in garnet and irregular partitioning of Cr between coexisting metamorphic mineral pairs. In addition, this study points to the important role of crystal growth rate in determining the presence or absence of inclusions and the type of zoning exhibited by both major and trace elements. During fast growth, inclusions are preferentially incorporated into the growing porphyroblast and slow diffusing elements such as Cr are effectively immobile, whereas during slow growth, inclusions are not generally included in the porphyroblast and Cr zoning is concentric.     

Dependence of reaction kinetics on H2O activity as inferred from rates of intergranular diffusion of aluminium

Quantitative constraints on the accelerative effects of H₂O on the kinetics of metamorphic reactions arise from a comparison of rates of intergranular diffusion of Al in natural systems that are fluid‐saturated, hydrous but fluid‐undersaturated, and nearly anhydrous. Widths of symplectitic reaction coronas around partially resorbed garnet crystals in the contact aureole of the Makhavinekh Lake Pluton, northern Labrador, combined with time–temperature histories from conductive thermal models, yield intergranular diffusivities for Al from ～700–900 °C under nearly anhydrous conditions. Those rates, when extrapolated down temperature, are approximately three orders of magnitude slower than rates derived from re‐analysis of garnet resorption coronas formed under hydrous but fluid‐undersaturated conditions near 575 °C in rocks of the Llano Uplift of central Texas, which are in turn approximately four orders of magnitude slower than rates at comparable temperatures derived from numerical simulations of prograde garnet growth in fluid‐saturated conditions in rocks from the Picuris Range of north‐central New Mexico. Thus, even at constant temperature, rates of intergranular diffusion of Al – and corresponding length scales and timescales of metamorphic reaction and equilibration – may vary by as much as seven orders of magnitude across the range of H₂O activities found in nature.     

Chemical and textural equilibration of garnet during amphibolite facies metamorphism: The influence of coupled dissolution–reprecipitation

Metamorphic equilibration requires chemical communication between minerals and may be inhibited through sluggish volume diffusion and or slow rates of dissolution in a fluid phase. Relatively slow diffusion and the perceived robust nature of chemical growth zoning may preclude garnet porphyroblasts from readily participating in low‐temperature amphibolite facies metamorphic reactions. Garnet is widely assumed to be a reactant in staurolite‐isograd reactions, and the evidence for this has been assessed in the Late Proterozoic Dalradian pelitic schists of the Scottish Highlands. The 3D imaging of garnet porphyroblasts in staurolite‐bearing schists reveals a good crystal shape and little evidence of marginal dissolution; however, there is also lack of evidence for the involvement of either chlorite or chloritoid in the reaction. Staurolite forms directly adjacent to the garnet, and its nucleation is strongly associated with deformation of the muscovite‐rich fabrics around the porphyroblasts. “Cloudy” fluid inclusion‐rich garnet forms in both marginal and internal parts of the garnet porphyroblast and is linked both to the production of staurolite and to the introduction of abundant quartz inclusions within the garnet. Such cloudy garnet typically has a Mg‐rich, Mn‐poor composition and is interpreted to have formed during a coupled dissolution–reprecipitation process, triggered by a local influx of fluid. All garnet in the muscovite‐bearing schists present in this area is potentially reactive, irrespective of the garnet composition, but very few of the schists contain staurolite. The staurolite‐producing reaction appears to be substantially overstepped during the relatively high‐pressure Barrovian regional metamorphism reflecting the limited permeability of the schists in peak metamorphic conditions. Fluid influx and hence reaction progress appear to be strongly controlled by subtle differences in deformation history. The remaining garnet fails to achieve chemical equilibrium during the reaction creating distinctive patchy compositional zoning. Such zoning in metamorphic garnet created during coupled dissolution–reprecipitation reactions may be difficult to recognize in higher grade pelites due to subsequent diffusive re‐equilibration. Fundamental assumptions about metamorphic processes are questioned by the lack of chemical equilibrium during this reaction and the restricted permeability of the regional metamorphic pelitic schists. In addition, the partial loss of prograde chemical and textural information from the garnet porphyroblasts cautions against their routine use as a reliable monitor of metamorphic history. However, the partial re‐equilibration of the porphyroblasts during coupled dissolution–reprecipitation opens possibilities of mapping reaction progress in garnet as a means of assessing fluid access during peak metamorphic conditions.     

Garnet polycrystals and the significance of clustered crystallization

Polycrystalline garnets are common in metamorphic rocks and may form as a result of close spacing of nuclei (if clustering is early) or impingement of larger grains (if clustering occurs later in the growth history). The timing of clustering relative to garnet growth is relevant to understanding the formation and evolution of porphyroblasts and evaluating the significance (if any) of clustering. Electron backscattered diffraction (EBSD) analysis of garnet-bearing metamorphic rocks reveals the presence of polycrystalline garnet in nine localities examined in this study: the northern Appalachians (Vermont, Maine, New York, USA); North American Cordillera (North Cascades Range, Washington; Snake Range, Nevada, USA); western Rocky Mountains (British Columbia, Canada); southern Menderes Massif (Turkey); Santander Massif (Colombia); and the Sanandaj–Sirjan zone (Hamadan, Iran). In some samples, polycrystals comprise ~20–30% of garnets analyzed, and chemical and textural evidence suggests that early coalescence of garnet polycrystals is common. Some early-coalescing polycrystals exhibit growth zoning that is concentric about the geometric center of the polycrystal. In thin section, these garnets may be undetectable as polycrystals based on morphology or zoning. In some polycrystals, zoning is unrelated to the location of internal grain boundaries; in others, Fe–Mn–Mg zoning has a different pattern than that of Ca; zoning patterns may vary on the scale of a single thin section. In addition, some polycrystals are characterized by high-angle misorientation boundaries that may be in special (non-random) orientations, an observation that indicates that these polycrystals are not random clusters of grains. The presence of internal grain boundaries may affect diffusion pathways and length scales, and may facilitate communication of porphyroblast interiors with matrix phases, thereby influencing reaction history of the rock and the composition/zoning of garnet.     

Development of garnet porphyroblasts by multiple nucleation,coalescence and boundary misorientation‐driven rotations

Two types of garnet porphyroblast occur in the Schneeberg Complex of the Italian Alps. Type 1 porphyroblasts form ellipsoidal pods with a centre consisting of unstrained quartz, decussate mica and small garnet grains, and a margin containing large garnet grains. Orientation contrast imaging using the scanning electron microscope shows that the larger marginal garnet grains comprise a number of orientation subdomains. Individual garnet grains without subdomains are small (< 50 µm), faceted and idioblastic, and have simple zoning profiles with Ca‐rich cores and Ca‐poor rims. Subdomains of larger garnet grains are similar in size to the individual, small garnet grains. Type 2 porphyroblasts comprise only ellipsoidal garnet, with small subdomains in the centre and larger subdomains at the margin. Each subdomain has its own Ca high, Ca dropping towards subdomain boundaries. Garnet grains, with or without subdomains, all have the same Ca‐poor composition at rims in contact with other minerals. The compositional zonation patterns are best explained by simultaneous, multiple nucleation, followed by growth and amalgamation of individual garnet grains. The range of individual garnet and garnet subdomain sizes can be explained by a faster growth rate at the porphyroblast margin than in the centre. The difference between Type 1 and Type 2 porphyroblasts is probably related to the growth rate differential across the porphyroblast. Electron backscatter diffraction shows that small, individual garnet grains are randomly oriented. Large marginal garnet grains and subdomain‐bearing garnet grains have a strong preferred orientation, clustering around a single garnet orientation. Misorientations across subdomain boundaries are small and misorientation axes are randomly oriented with respect to crystallographic orientations. The only explanation that fits the observational data is that individual garnet grains rotated towards coincident orientations once they came into contact with each other. This process was driven by the reduction of subdomain boundary energy associated with misorientation loss. Rotation of garnet grains was accommodated by diffusion in the subdomain boundary and diffusional creep and rigid body rotation of other minerals (quartz and mica) around the garnet. An analytical model, in which the kinetics of garnet rotation are controlled by the rheology of surrounding quartz, suggests that, at the conditions of metamorphism, the rotation required to give a strong preferred orientation can occur on a similar time‐scale to that of porphyroblast growth.     

Variations in rates of nucleation and growth of biotite porphyroblasts

Differences in rates of nucleation and diffusion‐limited growth for biotite porphyroblasts in adjacent centimetre‐scale layers of a garnet‐biotite schist from the Picuris Mountains of New Mexico are revealed by variations in crystal size and abundance between two layers with strong compositional similarity. Relationships between fabrics recorded by inclusion patterns in biotite and garnet porphyroblasts are interpreted to reflect garnet growth following biotite growth, without substantial alteration of the biotite sizes. Sizes and locations of biotite crystals, obtained via high‐resolution X‐ray computed tomography, document that of the two adjacent layers, one has a larger mean crystal volume (9.5 × 10^?4v. 2.4 × 10^?4 cm³), fewer biotite crystals per unit volume (232 v. 576 crystals cm^?3), and a higher volume fraction of biotite (23%v. 14%). The two layers have similar mineral assemblages and mineral chemistry. Both layers show evidence for diffusional control of nucleation and growth. Pseudosection analysis suggests that the large‐biotite layer began to crystallize biotite at a temperature ～67 °C greater than the small‐biotite layer. Diffusion rates differed between layers, because of their different temperature ranges of crystallization, but this effect can be quantified. The bulk compositional difference between the layers, manifested in different modal amounts of biotite, has an effect on the biotite sizes that is also quantifiable and insufficient to account for the difference in biotite size. After these other possible causes of variation in crystal sizes have been eliminated, variability in nucleation and diffusion rates remain as the dominant factors responsible for the difference in porphyroblastic textures. Numerical simulations suggest that relative to the small‐biotite layer, the large‐biotite layer experienced elevated diffusion rates because of the higher crystallization temperature, as well as increased nucleation rates in order to achieve the observed size and number density of crystals. The simulations can replicate the observed textures only by invoking unreasonably large values for the thermal dependence of nucleation rates (activation energies), strongly suggesting that the observed textural differences arise from variations between layers in the abundance and energetics of potential nucleation sites.     

Strain rates from snowball garnet

Spiral inclusion trails in garnet porphyroblasts are likely to have formed due to simultaneous growth and rotation of the crystals, during syn‐metamorphic deformation. Thus, they contain information on the strain rate of the rock. Strain rates may be interpreted from such inclusion trails if two functions are known: (1) The relationship between rotation rate and shear strain rate; (2) the growth rate of the crystal. We have investigated details of both functions using a garnetiferous mica schist from the eastern European Alps as an example. The rotation rate of garnet porphyroblasts was determined using finite element modelling of the geometrical arrangement of the crystals in the rock. The growth rate of the porphyroblasts was determined by using the major and trace element distributions in garnet crystals, thermodynamic pseudosections and information on the grain size distribution. For the largest porphyroblast size fraction (size L=12 mm) we constrain a growth interval between 540 and 590 °C during the prograde evolution of the rock. Assuming a reasonable heating rate and using the angular geometry of the spiral inclusion trails we are able to suggest that the mean strain rate during crystal growth was of the order of =6.6 × 10^?14 s^?1. These estimates are consistent with independent estimates for the strain rates during the evolution of this part of the Alpine orogen.     

Ostwald ripening of garnet in high P/T metamorphic rocks

This paper presents a theoretical formulation of Ostwald ripening of garnet and discusses the importance of the process during high pressure and low temperature (high P/T) metamorphism. The growth rate of garnet due to Ostwald ripening is formulated for the system consisting of minerals and an intergranular medium. Crystal size distribution (CSD) of garnets are examined and compared with the theoretical distribution for Ostwald ripening. Two types of CSDs are recognized. One is consistent with the theoretical prediction of size distribution while the other is wider than the theoretical distribution. The former CSD applies to samples in which garnets show homogeneous spatial distributions. The latter CSD applies to samples in which garnets show heterogeneous spatial distributions such as in clusters or layers. These relations suggest that the heterogeneity of spatial distributions results in a heterogeneity of concentration of garnet, causing the wide distributions. The mean diameter (dg) has a large variation in samples having narrow distributions. Ostwald ripening explains well the similar patterns of CSD in these samples with different dg because of a scaling law. Compositional profiles of garnets with different size are consistent with Ostwald ripening rather than nucleation and growth kinetics. This suggests that the CSDs result from Ostwald ripening. Magnitude of heating rate will determine which mechanism controls CSD. Nucleation and growth kinetics are dominant when heating rate is large. On the other hand, Ostwald ripening is dominant when heating rate is small. CSDs of garnets in high P/T metamorphic rocks are consistent with the latter case.     

Porphyroblast crystallization kinetics: the role of the nutrient production rate

The mechanisms that govern porphyroblast crystallization are investigated by comparing quantitative textural data with predictions from different crystallization models. Such numerical models use kinetic formulations of the main crystallization mechanism to predict textural characteristics, such as grain size distributions. In turn, data on porphyroblast textures for natural samples are used to infer which mechanism dominated during their formation. Whereas previous models assume that the rate‐limiting step for a porphyroblast producing reaction is either transport or growth, the model advanced in this study considers the production of nutrients for porphyroblasts as a potentially rate‐limiting factor. This production reflects the breakdown of (metastable) reactants, which at a specific pressure (P) and temperature (T) depends on the bulk composition of the sample. The production of nutrients that potentially contribute to the formation of porphyroblasts is computed based on thermodynamic models. The conceptual model assumes that these nutrients feed into some intergranular medium, and products form by nutrient consumption from that medium, with rates depending on reaction affinity. For any sequence of P–T conditions along a P–T–t path, the numerical model first computes an effective supersaturation (σ_eff) of the product phase(s), then an effective nucleation rate (J), and finally the amount of (porphyroblast) growth. As a result, the model is useful in investigating how the textural characteristics of a sample (of given bulk composition) depend on the P–T–t path followed during porphyroblast crystallization. The numerical model is tested and validated by comparing simulation results with quantitative textural data for garnet porphyroblasts measured in samples from the Swiss Central Alps.     

Sigmoidal inclusion trails, punctuated fabric development, and interactions between metamorphism and deformation

Porphyroblast inclusion fabrics are consistent in style and geometry across three Proterozoic metamorphic field gradients, comprising two pluton-related gradients in central Arizona and one regional gradient in northern New Mexico. Garnet crystals contain curved ‘sigmoidal’ inclusion trails. In low-grade chlorite schists, these trails can be correlated directly with matrix crenulations of an older schistosity (S1). The garnet crystals preferentially grew in crenulation hinges, but some late crenulations nucleated on existing garnet porphyroblasts. At higher grade, biotite, staurolite and andalusite porphyroblasts occur in a homogeneous S2 foliation primarily defined by matrix biotite and ilmenite. Biotite porphyroblasts have straight to sigmoidal inclusion trails that also represent the weakly folded S1 schistosity. Staurolite and andalusite contain distinctive inclusion-rich and inclusion-poor domains that represent a relict S2 differentiated crenulation cleavage. Together, the inclusion relationships document the progressive development of the S2 fabric through six stages. Garnet and biotite porphyroblasts contain stage 2 or 3 crenulations; staurolite and andalusite generally contain stage 4 crenulations, and the matrix typically contains a homogeneous stage 6 cleavage. The similarity of inclusion relationships across spatially and temporally distinct metamorphic field gradients of widely differing scales suggests a fundamental link between metamorphism and deformation. Three end-member relationships may be involved: (1) tectonic linkages, where similar P-T-time histories and similar bulk compositions combine to produce similar metamorphic and structural signatures; (2) deformation-controlled linkages, where certain microstructures, particularly crenulation hinges, are favourable environments for the nucleation and/or growth of porphyroblasts; and (3) reaction-controlled linkages, where metamorphic reactions, particularly dehydration reactions, are associated with an increase in the rate of fabric development. A general model is proposed in which (1) garnet and biotite porphyroblasts preferentially grow in stage 2 or 3 crenulation hinges, and (2) chlorite-consuming metamorphic reactions lead to pulses in the rate of fabric evolution. The data suggest that fabric development and porphyroblast growth may have been quite rapid, of the order of several hundreds of thousands of years, in these rocks. These microstructures and processes may be characteristic of low-pressure, first-cycle metamorphic belts.