The significance of intergranular diffusion to the mechanisms and kinetics of porphyroblast crystallization

The spatial disposition, compositional zoning profiles, and size distributions of garnet crystals in 11 specimens of pelitic schist from the Picuris Range of New Mexico (USA) demonstrate that the kinetics of intergranular diffusion controlled the nucleation and growth mechanisms of porphyroblasts in these rocks. An ordered disposition of garnet centers and a significant correlation between crystal radius and near-neighbor distances manifest suppressed nucleation of new crystals in diffusionally depleted zones surrounding pre-existing crystals. Compositional zoning profiles require diffusionally controlled growth, the rate of which increases exponentially as temperature increases with time; an acceleration factor for growth rate can be estimated from a comparison of compositional profiles for crystals of different sizes in each specimen. Crystal size distributions are interpreted as the result of nucleation rates that accelerate exponentially with increasing temperature early in the crystallization process, but decline in the later stages because of suppression effects in the vicinity of earlier-formed nuclei. Simulations of porphyroblast crystallization, based upon thermally accelerated diffusionally influenced nucleation kinetics and diffusionally controlled growth kinetics, quantitatively replicate textural relations in the rocks. The simulations employ only two variable parameters, which are evaluated by fitting of crystal size distributions. Both have physical significance. The first is an acceleration factor for nucleation, with a magnitude reflecting the prograde increase during the nucleation interval of the chemical affinity for the reaction in undepleted regions of the rock. The second is a measure of the relative sizes of the porphyroblast and the diffusionally depleted zone surrounding it. Crystal size distributions for the Picuris Range garnets correspond very closely to those in the literature from a variety of other localities for garnet and other minerals. The same kinetic model accounts quantitatively for crystal size distributions of porphyroblastic garnet, phlogopite, sphene, and pyroxene in rocks from both regional and contact metamorphic occurrences. These commonalities indicate that intergranular diffusion may be the dominant kinetic factor in the crystallization of porphyroblasts in a wide variety of metamorphic environments.     

Crystallization kinetics during regional metamorphism of porphyroblastic rocks

Numerical simulations of diffusion‐controlled nucleation and growth of garnet porphyroblasts in regionally metamorphosed rocks constrain interfacial energy and rates of nucleation and Al intergranular diffusion. The 13 rocks analysed in this study were collected from seven localities exhibiting a diverse range of crystallization conditions. Kinetic parameters governing nucleation and intergranular diffusion were adjusted iteratively to achieve fits between simulated and natural porphyroblastic textures. Model fits were assessed primarily from textural characteristics precisely measured by high‐resolution X‐ray computed tomography. Interfacial energy for heterogeneous nucleation ranges from 0.007 to 0.255 J m^?2 for the sample suite, assuming shape factors in the range 0.01–1.0. Nucleation rates change through space and time due to growth and impingement of Al depletion zones surrounding porphyroblasts. In some models, the overall rock‐wide nucleation rate rises steeply, achieves a steady state, and then falls rapidly as reactants are consumed; in others, the steady state is not achieved, but instead the rate simply peaks before falling. Maximum rock‐wide nucleation rates range from 10^?14.7 to 10^?10.7 nuclei cm^?3 s^?1, and maximum local rates range from 10^?13.7 to 10^?9.7 nuclei?cm^?3 s^?1 depending on Al supersaturation. Diffusive fluxes of Al are well constrained by the simulated textures, but rates of intergranular diffusion are subject to uncertainties in Al solubility and interconnected porosity. Best estimates of Al diffusivities at 600 °C span 10^?12.3 to 10^?10.5 m² s^?1 for the sample suite, a narrow range considering natural variability and the uncertainties in solubility and porosity. Eliminating some models suspected of higher uncertainty for these quantities yields diffusivities at 600 °C near 10^?11.0 m² s^?1, with dispersion of less than half an order of magnitude. These simulations, which are among the first attempted for regionally metamorphosed rocks, emphasize that: (i) nucleation rates vary markedly in time and space during crystallization; (ii) nucleation extends well beyond equilibrium conditions; (iii) Al diffusivity likely varies over only a narrow range across common metamorphic circumstances; and (iv) better determinations of both Al solubility and interconnected porosity are needed to constrain rates of Al intergranular diffusion more precisely.     

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.     

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.     

Relationship between plagioclase crystallization and cooling rate in basaltic melts

Rock textures commonly preserve a record of the near-surface crystallization history of volcanic rocks. Under conditions of simple cooling without convection or mixing, textures will reflect sample cooling rate, the temperature at which crystallization was initiated, and the distribution of mineral phase precipitation across the crystallization interval. Compilation of plagioclase size and number density data on natural (dike, sill and lava lake) and experimental samples suggests that (1) growth and nucleation rates of plagioclase in natural basaltic samples are a predictable function of cooling rate, and (2) the observed crystallization rate dependence on cooling rate is similar to that observed in experiments initiated at subliquidus temperatures. Comparison of natural and experimental samples thus suggests that most basalts crystallize under conditions of heterogeneous nucleation, with the number density of preexisting nucleii partially controlling textural responses to cooling rate changes. Time scales of crystallization and cooling in magmatic systems are intimately linked through a balance between heat removal from the system and heat evolved through crystallization. Evaluation of textural data in the context of recent numerical models of crystallization in simple (one- and two-component systems) provides new insight into regularities in the crystallization behavior of basaltic magmas. For example, the rate of change in crystal size (and number density, as dictated by mass balance) has been used as a measure of the relative importance of time scales of crystallization and cooling in numerical models of crystallizing systems. In natural samples, plagioclase size scales with the length scale of cooling such that a logarithmic plot of grain size as a function of normalized distance across the dike has a slope that appears approximately independent of dike width (solidification time). Comparison with available textural data for other phenocryst phases suggests that the same may be true for pyroxene and magnetite crystallization, with each phase having a characteristic slope probably controlled by the thermodynamic properties of the crystallizing phase. Measured crystal size distributions are unimodal and show maximum frequencies in the smaller size classes; distributions broaden and the grain size at peak frequency increases with increasing crystallization times (decreasing cooling rates). In contrast, partially crystallized Makaopuhi lava lake samples have crystal size distributions that decrease exponentially with increasing crystal size. Measured size distributions in dikes can be explained by late stage modification of Makaopuhi-type distributions through loss of small crystals, possibly the consequence of growth without nucleation. Finally, this compilation of the textural response of basaltic magmas to changes in cooling rate suggests that empirical calibrations of crystallization rate dependence on cooling rate from natural samples provide a reasonable model for plagioclase crystallization in near-surface basaltic systems. Predicted growth rates will be slow and relatively constant (10^-10–10^-11 cm/s) for crystallization times expected in most shallow volcanic systems (<1000 years).     

Magnitudes of departures from equilibrium during regional metamorphism of porphyroblastic rocks

Numerical models of diffusion‐controlled nucleation and growth of garnet crystals, which successfully replicate diverse textures in 13 porphyroblastic rocks, yield quantitative estimates of the magnitudes of departures from equilibrium during crystallization. These estimates are derived from differences in chemical potential between subvolumes containing stable product assemblages and those containing persistent but metastable reactant assemblages. The magnitude of disequilibrium is evaluated in terms of the thermal overstepping, which is commonly referenced to the garnet‐in isograd; the reaction affinity in the intergranular fluid at the site and time of each nucleation event, and on average throughout the rock, and the ‘latent energy of reaction’ per unit volume, a measure of the average unreacted capacity of the bulk rock, which describes its overall metastability. Across all of the models, the first crystals nucleate after 5–67 °C of thermal overstepping (correspondingly, 0.7–5.8 kJ mol^?1 of 12‐oxygen garnet); the maximum reaction affinity averaged across the intergranular fluid is between 4.7 and 16.0 kJ mol^?1 of 12‐oxygen garnet; and the maximum latent energy of reaction ranges from 7.3 to 51.7 J cm^?3. These results demonstrate that impediments to crystallization significantly delay nucleation and retard reaction, with the consequence that nucleation of new crystals extends throughout nearly the entire crystallization interval. This potential for protracted reaction during prograde metamorphism, with reactions continuing to temperatures and pressures well beyond equilibrium conditions, suggests the likelihood of overstepping of multiple – possibly competing – reactions that can progress simultaneously. Isograds and ranges of stability for metamorphic assemblages along a metamorphic field gradient may therefore be significantly offset from the positions predicted from calculations based on equilibrium assumptions, which poses a substantial challenge to accurate interpretations of metamorphic conditions and processes.     

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.     

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.     

Strain rates at high temporal resolution from curved inclusion trails in garnet,Passo del Sole,Central Swiss Alps

Quantitative strain rates at outcrop scale are very difficult to obtain, but they may be estimated from crystals with curved inclusion trails by calculating rotation rates from growth rates and corresponding deflections of the internal foliation. Garnet in a quartzose pelite at Passo del Sole in the central Swiss Alps is extraordinarily valuable for calculation of strain rates during Alpine orogenesis, because the unusual zoning patterns clearly define the kinetics of its nucleation and growth. Complex concentric zoning patterns can be correlated from one crystal to another in a hand sample, based on compositional and microstructural similarities; the ubiquity of these features demonstrates that all garnet crystals nucleated at nearly the same time. Compositional bands whose radial widths are proportional to crystal size provide evidence for growth governed by the kinetics of intergranular diffusion of locally sourced nutrients. Together, these constraints increase the reliability of estimates of rates of garnet growth, and the strain‐rate calculations that depend on them. To obtain growth rates, P–T conditions during garnet crystallization were modelled in a series of pseudosections, and compositional evolution was connected to rates of garnet growth by means of an independently determined heating rate. These growth rates, combined with measured amounts of curvature of inclusion trails, indicate that the time‐averaged strain rate at Passo del Sole during Alpine metamorphism was on the order of 10^?14 s^?1. Strain rates calculated using rotational v. non‐rotational models are similar in magnitude. The constraints on crystallization kinetics also allow direct calculation of strain rates during individual stages of garnet growth, revealing short‐term increases to values on the order of 10^?13 s^?1. These higher strain rates are correlated with the growth of concentric high‐Ca or high‐Mn zones in garnet, which implies that strain softening associated with the transient passage of fluids is responsible for acceleration of deformation during these intervals.     

Interplay between equilibrium and kinetics in prograde metamorphism of pelites: an example from the Nelson aureole, British Columbia

The distribution of metapelitic mineral assemblages in the Nelson aureole, British Columbia, generally conforms to what is predicted from phase equilibria. However, in detail, the sequence and spacing of isograds, mineral textures and mineral compositions and mineral chemical zoning do not. Two of the main disequilibrium features in the aureole are: (i) delay in the onset and progress of several reactions, i.e. overstepping in temperature; and (ii) unreactivity of staurolite and especially garnet porphyroblasts when they are reactants in prograde reactions. The thermal overstepping is ascribed to difficulty of nucleation of the product porphyroblasts and sluggishness of dissolution of porphyroblasts when they are reactants. The extent to which these kinetic barriers delay the onset of reaction is related to the reaction affinity of each reaction, defined herein as the Gibbs free‐energy difference between the thermodynamically stable, but not‐yet‐crystallized, products and the metastable reactants. For oversteps in temperature (ΔT), reaction affinity is, in turn, related to the difference in entropy (ΔS) between these two states through the relation A = ΔT * ΔS. Mineral reactions which release large quantities of H₂O, such as chlorite‐consuming reactions, have a higher entropy change per unit of temperature overstep, and therefore a higher reaction affinity, than those which release little or no H₂O, such as the chlorite‐free staurolite‐consuming reaction. Thermal overstepping is consequently expected to be less for the former than for the latter, as was estimated in the aureole where 0 to 30 °C overstepping was required for garnet, staurolite and andalusite growth from a muscovite + chlorite‐bearing precursor rock and ～70 °C overstepping was required for the growth of Al₂SiO₅ from a staurolite‐bearing, chlorite‐free precursor. In all cases, reaction progress was strongly influenced by the presence or absence of fluid, with presence of fluid lowering kinetic barriers to nucleation and growth and therefore the degree of thermal overstepping. Textural features of rocks from the nearly coincident garnet, staurolite and andalusite isograds are suggestive of a fluid‐catalysed ‘cascade effect’ in which reaction took place in a narrow temperature interval; several competing muscovite + chlorite‐consuming reactions, some metastable, appear to have occurred in parallel. Metamorphic reaction, fluid release and possibly fluid presence in general in the aureole were episodic rather than continuous, and in several cases well removed from equilibrium conditions. The extent to which these findings apply to regional metamorphism depends on several factors, a major one being enhanced deformation, which is expected to lower kinetic barriers to nucleation and growth.     

Model of nucleation and growth of crystals in cooling magmas

The nucleation and growth of liquidus phases in cooling magmas at constant rates are modeled taking into account homogeneous nucleation, diffusion-limited growth, and depletion of crystallizing component from melt, and the temperature-dependent diffusivity. The formulation of governing equations shows that four dimensionless parameters, whose physical meanings are the nucleation difficulty, the fusion enthalpy, the ratio of the growth rate to the cooling rate, and the activation energy of diffusion, control the crystallization phenomena. The nucleation behavior with time (or temperature) is determined primarily by the competition between increasing nucleation rate with cooling and the reduced supersaturation with depletion by progressive growth of crystals previously nucleated. The maximum nucleation rate and the number density of crystals increase with decreasing interfacial tension and diffusivity, and with increasing fusion enthalpy and cooling rate. Quantitative expressions of the time or temperature interval for which the nucleation remains appreciable, the peak nucleation rate, the number density of crystals and the mean crystal radius are derived as functions of controlling parameters, and can be used to estimate the cooling rate or other unknown parameters from the number density of crystals of a rock.     

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.     

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.     

The clustered nucleation and growth processes of garnet in regional metamorphic rocks from north-west Connecticut,USA

Serial sectioning and imaging with a flatbed scanner yielded the three-dimensional size and spatial distribution of garnet porphyroblasts in two garnet schists and one staurolite-bearing schist from the Everett Formation, north-west Connecticut. The dominant garnet-producing reaction in all samples was chlorite+quartz=garnet+H₂O. The appearance of staurolite, and additional garnet growth in the staurolite-bearing sample, was due to the reaction chloritoid=garnet+staurolite+chlorite. Statistical measures of garnet spatial distributions, using the pair correlation function (PCF), indicate that garnet crystals are weakly to strongly clustered at length scales between 2 and 10 mm. Such clustered nucleation may reflect minor bulk compositional variations. Covariance measures between garnet size and nearest-neighbour distance, using the mark covariance function (MCF), suggest a very weak correlation between crystal size and nearest-neighbour distance for length scales of 2 mm or less. These statistical data suggest that if diffusional gradients were present around growing garnet crystals, they did not influence nucleation and growth patterns at length scales greater than c. 2 mm. Compositional maps, through the garnet centres, show that the smaller crystals have lower Mn core compositions relative to larger crystals, consistent with progressive nucleation during pro-grade metamorphism. Radius-rate plots calculated from compositional X-ray maps show similar growth rates for garnet crystals of different size, consistent with an interface-controlled growth model for garnet. The presence of minor diffusional gradients around growing garnet cannot be entirely dismissed, but the lack of observable reaction rims, the clustered spatial distribution and the radius-rate data are most consistent with an interface-controlled garnet growth model.     

Crystal Size Distribution of Plagioclase and Amphibole from Soufriere Hills Volcano, Montserrat: Evidence for Dynamic Crystallization-Textural Coarsening Cycles

The crystal size distributions (CSDs) of plagioclase and amphibolewere determined from andesites of the Soufrière Hillsvolcano, Montserrat. Plagioclase occurs as separate crystalsand as chadocrysts in large amphibole oikocrysts. The chadocrystsrepresent an earlier stage of textural development, preservedby growth of the oikocryst. Seventeen rock and eight chadocrystplagioclase CSDs are considered together as a series of samplesof textural development. All are curved, concave up, and coincident,differing only in their maximum crystal size. Three amphiboleCSDs have a similar shape and behaviour, but at a differentposition from the plagioclase CSDs. A dynamic model is proposedfor the origin of textures in these rocks. Crystallization ofplagioclase started following emplacement of andesite magmaat a depth of at least 5 km. A steep, straight CSD developedby nucleation and growth. This process was interrupted by theinjection of mafic magma into the chamber, or convective overturnof hotter magma. The magma temperature rose until it was buffered,initially by plagioclase solution and later by crystallization.During this period textural coarsening (Ostwald ripening) ofplagioclase and amphibole occurred: small crystals dissolvedsimultaneously with the growth of large crystals. The CSD becameless steep and extended to larger crystal sizes. Early stagesof this process are preserved in coarsened amphibole oikocrysts.Repetitions of this cycle generated the observed family of CSDs.Textural coarsening followed the ‘Communicating Neighbours’model. Hence, each crystal has its own, unique growth–solutionhistory, without appealing to mixing of magmas that crystallizedin different environments. KEY WORDS: Ostwald ripening; textural coarsening; oikocryst; CSD; texture     

Formation of K-feldspar megacrysts in granodioritic plutons by thermal cycling and late-stage textural coarsening

K-feldspar megacrysts in granite and granodiorite plutons are generally inferred to be early crystallizing phases (grown to large sizes when the magma was mostly liquid) owing to their large size, euhedral form, and features that suggest deposition by magmatic sedimentation. However, phase equilibrium experiments and natural examples of crystallization and partial melting demonstrate that K-feldspar is one of the last phases to nucleate and that most crystal growth must occur after the magma has exceeded 50% crystallization and is thus largely incapable of flow and sedimentation. Megacryst size distributions, compositions, and textural relationships from the Cretaceous Tuolumne Intrusive Suite, California, reveal that the gradational transition from equigranular to megacrystic granodiorite likely occurred via textural coarsening caused by thermal cycling. Experimental and theoretical studies demonstrate that rising temperature induces relatively more melting in small crystals than in large ones, whereas linear growth rates during cooling are similar. Thus, during thermal cycling material is transferred from small crystals to larger ones. Megacryst growth via thermal cycling during incremental emplacement is consistent with the required late growth of K-feldspar, explains the presence of megacrysts in the inner parts of theTuolumne Intrusive Suite and elsewhere, and may be a common process in formation of megacrystic granitic rocks.     

Unraveling the Schneeberg garnet puzzle: a numerical model of multiple nucleation and coalescence

A quantitative kinetic model for the growth of the different garnet porphyroblast microstructures (type 1 and type 2) of the Western Schneeberg Complex (WSC) is presented. These porphyroblasts formed by a multiple nucleation and coalescence mechanism. Our numerical simulation shows that at constant diffusion rates: (1) low interface reaction rates result in a fully amalgamated porphyroblast (type 2); (2) intermediate reaction rates result in a porphyroblast, where coalescence of grains closer to the margin prevented amalgamation of those in the centre (similar to type 1 porphyroblasts); and (3) high interface reaction rates result in a porphyroblast microstructure with an atoll form. All three microstructures are characterised by distinctive cluster size distributions. A 2-D cluster size distribution analysis of type 1 porphyroblasts of WSC shows that these did not form because of intermediate interface reaction rates, but because the diffusion rate of nutrients was too low to keep pace with the interface reaction rate.Editorial responsibility: T.L. Grove     

Petrogenesis of the Eppawala carbonatites, Sri Lanka: A cathodoluminescence and electron microprobe study

Field and petrographic investigations, cathodoluminescence (CL) studies as well as microprobe analyses of major rock-forming minerals were conducted to establish the crystallization processes in the Eppawala carbonatites, Sri Lanka. The well preserved magmatic textures and crystal morphologies combined with the chemistry of apatite, calcite and dolomite indicate two major stages of crystal growth, which were accompanied by dynamic crystallization conditions. Initially, nucleation of apatite, ilmenite and possibly olivine was associated with rapid crystal growth during slow cooling of the carbonatite melt at depth. The heat loss through the roof and crystallization processes induced the development of turbulent convective currents, which in turn prevented further nucleation and growth of crystals and led to the dispersion of these earlier formed crystals within the magma chamber. Then, rapid upward movement of magma along structural weaknesses led to (i) the transport of mineral clusters, (ii) deformation of ilmenite, (iii) fracturing of apatite and (iv) the emplacement of the carbonatite melt as dykes. Here, the conditions were favourable for the simultaneous crystallization of magnetite, calcite and dolomite in a non-turbulent environment. Subsequent subsolidus alteration caused the hydrothermal overprint of the documented mineral assemblages, particularly along grain boundaries. The study demonstrates that detailed textural examinations of carbonatites combined with mineral chemical analyses and CL investigations can reveal the crystallization processes within carbonatite melts.     

Plagioclase replacement textures in partially eclogitised gabbros from the Sanddal mafic-ultramafic complex, Greenland Caledonides

The Sanddal mafic‐ultramafic complex (SMUK) is a cluster of variably eclogitised mafic and ultramafic bodies that comprise the westernmost known eclogite facies locality in the North‐East Greenland eclogite province (NEGEP). Although there are no true eclogites in the SMUK, we interpret three distinct textural types of plagioclase replacement to record sequential stages in adjustment of SMUK olivine gabbro‐norites to eclogite facies conditions. The earliest stage, in which plagioclase was replaced by omphacite/spinel symplectite before nucleation of garnet (Type 1A & 1B) has not previously been described. Documentation of this texture provides clear evidence that, at least in some cases, garnet nucleation is delayed relative to nucleation of omphacite and is a rate‐limiting step for eclogitisation. Type 1C domains were produced by scattered nucleation of garnet in the same sample. In Type 2 domains, plagioclase was replaced by a layered corona with an outer layer of garnet, an inner layer of omphacite and an interior of inclusion‐rich plagioclase. In Type 3 domains, the omphacite layer was overgrown by the garnet rim, and omphacite is preserved only as inclusions in garnet. In more coarse grained leucogabbros, recrystallization was more complete, plagioclase replacement textures were less localised, and could not be divided into distinct stages. Plagioclase replacement in SMUK samples was not isochemical, and required diffusion of at least Mg and Fe from replacement of mafic phases in the surroundings. Strong compositional gradients in garnet reflect disequilibrium and were controlled by the different diffusion rates of Mg/Fe and Ca, different local chemical environments, and progress of the plagioclase breakdown reaction. The presence of small amounts of hydrous minerals (amphibole, phlogopite and clinozoisite) in local equilibrium in plagioclase domains of most SMUK samples indicates that a small amount of H₂O was present during high pressure metamorphism.     

Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization

Crystal-size in crystalline rocks is a fundamental measure of growth rate and age. And if nucleation spawns crystals over a span of time, a broad range of crystal sizes is possible during crystallization. A population balance based on the number density of crystals of each size generally predicts a log-linear distribution with increasing size. The negative slope of such a distribution is a measure of the product of overall population growth rate and mean age and the zero size intercept is nucleation density. Crystal size distributions (CSDs) observed for many lavas are smooth and regular, if not actually linear, when so plotted and can be interpreted using the theory of CSDs developed in chemical engineering by Randolph and Larson (1971). Nucleation density, nucleation and growth rates, and orders of kinetic reactions can be estimated from such data, and physical processes affecting the CSD (e.g. crystal fractionation and accumulation, mixing of populations, annealing in metamorphic and plutonic rocks, and nuclei destruction) can be gauged through analytical modeling. CSD theory provides a formalism for the macroscopic study of kinetic and physical processes affecting crystallization, within which the explicit affect of chemical and physical processes on the CSD can be analytically tested. It is a means by which petrographic information can be quantitatively linked to the kinetics of crystallization, and on these grounds CSDs furnish essential information supplemental to laboratory kinetic studies. In this three part series of papers, Part I provides the general CSD theory in a geological context, while applications to igneous and metamorphic rocks are given, respectively, in Parts II and III.