- E. Schweizerbart'sche Verlagsbuchhandlung, D-70176 Stuttgart
Textures formed during crystallization of the eutectic composition in the system Orthoclase-Quartz-H2O at 500 MPa and 50, 100, and 200°C undercooling have been studied experimentally and simulated using a two-dimensional Ising model. The experiments performed at 50°C undercooling did not produce complex, interesting textures but only very rare, isolated K-feldspar and quartz crystals. At 100°C undercooling the most common texture is a fine-grained, submicrometre to micrometre-scale, spherulitic quartz-K-feldspar intergrowth; set within this inter-growth are larger individual crystals of quartz or K-feldspar. Experiments performed at 200°C undercooling are remarkable for the occurrence of micrometre-scale graphic textures and millimetre scale spherulitic textures, characterized by quartz-K-feldspar intergrowths in the core and dominated by K-feldspar at the rims. Simulations of crystal growth, performed to complement and to interpret the experimental products, investigated what combination of growth (G) and diffusion (D) conditions can give rise to the crystal shapes and textures found in the experiments. These conditions correspond to growth rates between ∼ 1 × 10−10 and 5 × 10−9 m s−1 and diffusion coefficients between 10−17 m2 s−1 in the melt phase and 10−8 m2 s−1 in the fluid phase. The simulations, despite their limitations, provide textures similar to the experimental ones. In particular, simulations produced a quartz-K-feldspar intergrowth when G = D and singular, large quartz and K-feldspar crystals when G < D. These changes in the G:D ratio, in the experiments and in natural rocks, are attributed to a change in the growth of the crystal from a silicate melt to an aqueous fluid. The most interesting results of this study are that highly undercooled melts of a simplified pegmatite composition produce textures remarkably similar to natural pegmatites and that simulations provide a powerful tool to understand what processes cause these textures in experimental run products and natural rocks.
This paper was presented at the EMPG VIII meeting in Bergamo, Italy (April 2000)
The textures of igneous rocks contain the potential to provide useful information on the conditions under which the rocks crystallized. The importance of textures has long been recognized and qualitatively applied by petrologists (chronicled in Lofgren, 1980). However, only within the last 30 years have quantitative studies on crystal growth and textural development in basaltic (see reviews by Dowty, 1980; Lofgren, 1980; Basaltic Volcanism Study Project, 1981; Kirkpatrick, 1981) and granitic rocks (Fenn, 1977, 1986; Swanson, 1977; Swanson & Fenn, 1986; MacLellan & Trembath, 1991; London, 1992, 1996) been performed. These studies provide relationships between undercooling and crystal shape and texture. All researchers agree that crystal shape and texture in undercooled silicate systems are significantly affected by the ratio of crystal growth rates to diffusion in the melt (op. cit.). Unfortunately, quantitative application of this result has not been achieved yet, partially because chemical diffusivities in silicate melts of geological interest have become known only in the last 10 years (see review by Watson, 1994). Additionally, the crystal growth rate/diffusion ratio is not an independent variable controllable by the experimentalist, but is typically determined (frequently unknown) by the intrinsic and extrinsic variables of the system under investigation.
Computer models of crystal growth are a complementary technique for the study of crystal shape and texture. Although models can not either replace experiments or exactly simulate nature they provide a mechanism for the identification and quantification of the most important variables. Models allow the independent control of all possible variables during crystallization. In particular the ratio of crystal growth to diffusion at any undercooling is directly under the control of the modeler and can be varied at will. Recent advances in Ising models (Jackson et al., 1995; Beatty & Jackson, 1997) applied to the study of pegmatite textures (Baker & Freda, 1999) produced textures similar to those found in experiments and in natural rocks. Although the successful application of these models to crystallization is encouraging, they need to be further tested and their limitations must be understood.
This paper reports a combined experimental and simulation study designed to test the application of Ising models to undercooled crystallization in a hydrous binary system bounding the haplogranitic system. The binary system chosen was SiO2-KAlSi3O8 because of its simple eutectic behaviour at water-saturated conditions. As will be demonstrated below, simulations provide a remarkable tool for the interpretation of the crystal morphologies and textures seen in the experiments.
Experimental and analytical techniques
The starting glass composition (Table 1) was synthesized by mixing glasses of orthoclase and quartz compositions together with 2.00 wt% Rb2CO3 to make a starting mixture similar in composition to that of the water-saturated eutectic melt at 500 MPa, 58 wt% orthoclase (Johannes & Holtz, 1996). The Rb was added to the system to increase phase contrast in backscattered images, to investigate the effects of crystallization at undercooled conditions on Rb partitioning between feldspars and melt, and to provide a mechanism to measure the relative times of crystallization of K-feldspars in the experiments. This mixture was melted 3 times, each with a duration of 1 hour, at 1400°C in air with intermediate grinding between melting. After the last fusion the glass was ground to an average grain size of 15 μm and stored at 110°C. Quartz crystals used as seeds were collected from the Jucumba Pegmatite District (Southern California). Crystals were ultrasonically cleaned in distilled water, crushed, and sieved to produce a grain size between 90 and 106 μm.
Experiments were performed in a piston-cylinder apparatus at 500 MPa and 690, 640, and 540°C. These temperatures correspond to undercoolings below the water-saturated orthoclase-quartz eutectic of approximately 50, 100, and 200°C, respectively (Holtz et al., 1992; Johannes & Holtz, 1996). The addition of 0.008 mole of Rb per 100 g of melt to the system is expected to lower the melting temperature. The melting temperature depression due to Rb addition can be approximated by applying the van't Hoff relationship to the melting of endmember minerals, quartz and orthoclase. Combining the melting temperatures of pure quartz at 500 MPa, water-saturated conditions, 1070°C (Johannes & Holtz., 1996) with the enthalpy of melting, 9600 J/mol (Navrotsky, 1995), yields a melting depression of 3°C. The melting temperature of water-saturated potassium feldspar at 500 MPa is 876°C (Johannes & Holtz, 1996) and the enthalpy of melting is 56000 J/mol (Navrotsky, 1995); these values lead to a melting depression of 2°C. These calculations indicate that the small amount of Rb added to the system will have little effect on the eutectic temperature. Experiments used Au75Pd25 capsules. Capsules were loaded with distilled and deionized water (either 8 or 14 wt%), quartz seeds (approximately 0.8 mg), and the starting glass (about 18 mg), welded closed in a water bath to avoid volatile loss, and stored in an oven at 110°C for at least 2 hours. Capsules were placed into 1.91 cm NaCl-pyrex glass-crushable alumina assemblies (Hudon et al., 1994). To avoid water loss during the experiments capsules were surrounded by pyrophyllite powder (Freda et al., 2000). Run conditions were reached by simultaneously pressurizing and heating the assembly to ∼ 700 MPa and a superliquidus temperature of 1000°C. This step was performed to ensure chemical homogeneity of the melt. Temperature was held constant for one hour and pressure was allowed to fall to 620 MPa. After this first step experiments were cooled at 50°C/min while maintaining constant pressure until 200°C above the final set point, then pressure was allowed to fall to run conditions. Experiments were maintained between 560 and 510 MPa nominal pressure. Although our pressure calibration at 500 MPa, 920°C using the melting of NaCl (Bohlen, 1984) demonstrated no need for a pressure correction, we are not sanguine about the exact pressure of our experiments because of their low temperatures. On the other hand, the water-saturated orthoclase-quartz eutectic temperature is only weakly dependent upon pressure near 500 MPa (Bohlen et al., 1983; Holtz et al., 1992; Johannes & Holtz, 1996), so that an error of 200 MPa, which is 10 times the precision of our calibration, is unlikely to affect significantly (i.e., more than 35°C) the degree of undercooling. Factory calibrated Type C thermocouples were used, and temperature gradients along the capsules were less than 15°C (Hudon et al., 1994). Experiments were quenched isobarically to 250°C.
Quenched capsules were mounted longitudinally in epoxy, then ground and polished for electron microprobe analysis. The elements Si, Al, K, and Rb were analyzed in crystals and glass (quenched melt) using a 15 kV, 10 nA electron beam. Counting times on the peaks were 50 s for Rb and 20 s for all other elements. Counting times on backgrounds were one-half those used on peaks. A 1–2 μm diameter beam was used for the analysis of crystals and a 10 μm diameter for glasses. All data were reduced using the ZAF correction technique. The instrument was calibrated using quartz (Si), orthoclase (Al and K) and synthetic feldspar glass (Rb) standards. Experimental run products were mapped using backscattered electrons to document crystal shapes and textures.
Experimental conditions and results are reported in Table 2. Crystalline products, when present, are K-feldspar and quartz. The structure of the K-feldspar was not determined for any experimental run product. The temperatures of most experiments fell in the β-quartz stability field with the exception of experiments at 540°C, which were in the α-quartz field. We use shape to describe the morphology of individual crystals and texture to refer to spatial relationships between different crystals. Crystal shapes can be discemed only when crystals are greater than one micrometre. Because we did not make thin sections of our run products we cannot be certain of the optical orientations of the crystals (thin sections were not made in a deliberate attempt to maintain the spatial relationships between crystals, glass, and the capsule walls, and because our attempt to fabricate one thin section was a dismal failure resulting in almost total loss of the sample). We use the term dendrite to refer to crystals which have a morphology defined by a main body with smaller branches growing from it. We use the term spherulite to refer to a mass of crystals with a radial structure.
K-feldspar crystals grew with tabular or dendritic shapes. Quartz crystals are either subhedral to euhedral or dendritic (Swanson & Fenn, 1986) and typically elongated with dendrites branching off the main crystal. Based upon previous studies (Swanson, 1977; Swanson & Fenn, 1986; MacLelland & Trembath, 1991) the axis of elongation in quartz is most probably the c-axis. Crystal growth rates were estimated by dividing the lengths of the largest crystals, or the diameter of spherulitic intergrowths, by two and then by the duration of the experiment at the final temperature. Because it is impossible to date exactly the start of crystal growth in any experiment, or determine if growth rates were constant, the growth rates reported can not be exact, but instead are time-averaged minimum values. The volumes of crystals in experiments are estimates based upon backscattered images of the entire capsule cross-section.
Partitioning of Rb between K-feldspar and melt
Before discussing the crystal shapes and textures in the individual experiments it is necessary to present the determination of the Rb partition coefficient between K-feldspar and melt, DRb (wt% Rb in crystal divided by wt% Rb in melt), because its constancy provides a tool for the interpretation of the relative timing of crystal growth. Measurement of Rb in both quenched melts and adjoining K-feldspar crystals was used to determine the partition coefficient. Partition coefficients between tabular K-feldspars and melt in experiments with 8 wt% H2O, XLGl2, XLG5, and XLG26, are 0.9, 1.0, and 0.8 respectively. Submicrometre intergrowths of quartz and K-feldspar (discussed below) found in some experiments were also used to determine Rb partitioning. These intergrowths were carefully examined using backscattered images at magnifications up to x3000 to ensure that only quartz and K-feldspar were present. The Rb concentration of the K-feldspar in the submicrometre quartz-K-feldspar intergrowth in XLG12 and XLG5 (discussed below) was estimated by correcting the measured concentration by the fraction of K-feldspar analyzed. The fraction of K-feldspar was determined from the Al2O3 concentration in the intergrowth analysis and in the tabular feldspars in the same experiment; in both XLG12 and XLG5 DRb between the K-feldspar in the intergrowth and melt is 0.9. Experiments with an initial H2O concentration of 14 wt% XLG29, XLG7, and XLG27, produced DRb’s of 1.0, 1.1, and 0.8 respectively. The differences in partition coefficients are small, much of the variation is due to microprobe counting statistics. These results indicate that Rb partitioning appears insensitive to both crystal growth rate and initial water concentration in the experiments of this study. The lack of sensitivity to growth conditions allows us to use natural K-feldspar crystals as record of Rb concentrations in the melts from which they grew. Comparison of the average value of DRb measured between 33 crystal-melt pairs in this study, 1.0 ± 0.1 (1 standard deviation about the mean), with that from Icenhower & London (1996) for peraluminous melts at equilibrium conditions, 1.03, demonstrates excellent interlaboratory agreement.
Crystal shapes and textures observed
Experiments performed without quartz seeds failed to grow any crystals with the exception of the 50-hour experiment at 100°C undercooling (XLG6) which contains only a trace of subhedral quartz of 15 to 20 μm in length. Such difficulties in nucleating crystals are not surprising based upon previous studies of crystal nucleation and growth in granitic systems (Fenn, 1977; Swanson, 1977; Swanson & Fenn, 1986; London et al., 1989; MacLelland & Trembath, 1991; London, 1992, 1996). Importantly, this one crystal-bearing experiment demonstrates that even without seeds, quartz was the first phase to crystallize. The relative rapidity of quartz nucleation may be due either to the kinetics of quartz and K-feldspar nucleation, or due to our melt composition.
Seeded experiments at 50°C undercooling, 690°C
In the 50°C undercooling experiment with 8 wt% H2O (XLG12) a few quartz crystals are visible; most of these crystals show a dendritic shape, a very few are euhedral; their growth rate is 1 × 10−10 m s−1. This run also contains a small K-feldspar crystal (∼ 28 μm long, 8 × 10−11 m s−1 growth rate) surrounded by a submicrometrescale quartz K-feldspar spherulitic intergrowth (4 × 10−10 m s−1 growth rate). Vesicles in this sample are less than 1 μm in size; a few bigger (25 μm) vesicles close to the crystals are also present. The experiment with 14 wt% H2O at 50°C undercooling (XLG14) was water-saturated and only contained quartz crystals that were dominantly dendritic; their growth rate was 1 × 10−10 m s−1. Vesicles in this sample reach sizes of 300 μm in diameter and provide the evidence of water saturation of the melt in this experiment and all other experiments with 14 wt% H2O. Both XLG12 and XLG14 contain less than 5 % crystals.
Seeded experiments at 100°C undercooling, 640°C, with 8 wt% H2O
Five seeded experiments were performed with 8 wt% H2O at 100°C undercooling and different durations (0, 25, 50, and 100 hours). A zero time run (XLG18) was performed by heating a capsule to 1000°C followed by cooling to 640°C, then immediate quenching to room temperature. The purpose of this zero time run was to check the development of crystals during cooling from superliquidus to subsolidus temperatures and during quenching. This run produced a glass and, at its top, the fragmented quartz seed crystals. Vesicles in this experiment are small, 1 micrometre, and are interpreted to be formed upon quench. Thus, experiments with 8 wt% H2O were not initially water-saturated, consistent with previous measurements reviewed in Johannes & Holtz (1996). The glass far from the seeds is homogeneous (Table 1), but between the seeds it is variably enriched in silica (to a maximum of 85 wt% SiO2) due to their dissolution at 1000°C. The region of silica-enriched melt extends no more than 30 μm away from the crystals. This experiment demonstrated that the crystals observed in all other experiments are neither quench crystals nor crystals grown during the high-temperature homogenization step.
During the 25-hour experiments (XLG8, XLG24) only quartz crystals grew (less than 5 % of the capsule volume). The shape of the quartz is dominantly dendritic, but a few euhedral and a few skeletal crystals are also present. Growing crystals, 1 to 40 μm, formed a vermicular overgrowth, 30 μm wide, around some seeds (Fig. 1a), in the area enriched in SiO2 due to quartz dissolution during the high-temperature step of the experiment. Growth rates can be estimated by assuming growth began immediately upon reaching the final experimental temperature; the estimated growth rate of the longest crystals is 2 × 10−10 m s−1. This growth rate is within the range of growth rates measured by Swanson (1977), 3 × 10−10 to 1 × 10−12 m s−1. Vesicles in these experiments are from 25 to 100 μm in diameter and are interpreted as evidence of water saturation of the melt, which is between 8 and 9 wt% H2O. Thus, during the growth of the crystals in these experiments the melt became water-saturated.
In the 50-hour experiment (XLG5) both quartz and K-feldspar crystals grew and filled approximately 40 % of the capsule. This experiment is characterized by the presence of a large spherulitic region on one end of the capsule surrounded by large (100 μm diameter) vesicles (Fig. 1b). This region consists of quartz seeds, newly nucleated quartz (mostly subhedral), and tabular K-feldspar crystals (10 to ∼ 150 μm in maximum dimension) set in a submicrometre spherulitic intergrowth of the same two minerals (Fig. 1c). The abundance of the larger K-feldspar crystals increases near the rim of the intergrowth. The estimated growth rate for the largest individual crystals of either quartz or K-feldspar is 5 × 10−10 m s−1, similar to that determined in the 25-hour experiments. The growth rate of the entire submicrometre spherulitic intergrowth is 4 × 10−9 m s−1. These growth rates are significantly slower than those measured by Fenn (1977) in his most orthoclase-rich alkali feldspar bulk composition, 1 to 6 × 10−8 m s−1 from a bulk composition of 50 wt% albite and 50 wt% orthoclase. Growth of quartz and K-feldspar also occurred along the capsule wall in a corner (Fig. 1b). The texture in most of this region is the same as in the large crystallized region. Portions of this region contain a micrometre-scale quartz-K-feldspar intergrowth. This intergrowth appears to be an extension of the vermicular quartz seen in the 25 h experiment (Fig. 1a), but by 50 h melt between quartz crystals has been replaced by K-feldspar. Unlike the 25-hour experiment, no skeletal quartz was observed.
The 100-hour experiment (XLG26) is dominated by the same textures as seen in the 50-hour experiment. Approximately 70 % of the melt crystallized. The largest K-feldspar crystal is approximately 375 μm, slightly more than twice the longest crystal in the 50-hour experiment, giving a growth rate of 5 × 10−10 m s−1. The combined results of the 50- and 100-hour experiments suggest that crystal growth rate was constant. The bigger crystals in this experiment appear to comprise a larger proportion of the spherulitic intergrowth than in the 50-hour experiment (Fig. 1d). These bigger crystals of quartz and K-feldspar increase in abundance from core to rim. At the edges of the spherulitic intergrowth the crystals are fibrous in shape. The spherulite growth rate was 4 × 10−9 m s−1. One part of this experiment contains an intergrowth of euhedral quartz crystals set in a K-feldspar matrix; this texture may be a spherulitic (or possibly graphic, Fig. 1d, on the lower left-hand corner) one seen edge on.
The Rb2O concentrations in large K-feldspars in the spherulitic intergrowth increase from 1.11 to 2.07 wt% (over a distance of 1050 μm) as the crystals approach the edge of the intergrowth. Increases in Rb are seen in individual crystals and between separate crystals. Because of the lack of any observed variation in the Rb partition coefficient measured in coexisting feldspars and melt, the increasing Rb concentrations in K-feldspars are the result of melt fractionation due to crystal growth.
Seeded experiments at 100°C undercooling, 640°C, with 14 wt% H2O
Experiments were performed with 14 wt% H2O to ensure water saturation during the entire experiment. In the 25-hour experiment (XLG25) quartz grew in subhedral, skeletal, and dendritic shapes that form a radiating vermicular overgrowth, 40 μm wide, around some seeds (less than 5 % of the capsule volume). The growth rate of this overgrowth was 5 × 10−10 m s−1. Individual crystals grew at 1 × 10−10 m s−1. Vesicles of tens to hundreds of micrometres outline the edge of the region where quartz grew.
Quartz and K-feldspar were produced in the 50-hour long experiment (XLG7). The shapes and textures of these crystals are comparable with the 50-hour seeded experiment with 8 wt% H2O (XLG5). However, skeletal quartz was observed in XLG7. An additional difference between XLG5, which was not initially water-saturated, and XLG7 is that the quartz-K-feldspar intergrowth present in XLG7 is of a micrometre, not submicrometre scale. The amount of crystals in the run is approximately 10 %; the longest K-feldspar crystals reached 100 μm in length, but the quartz crystals are about two-thirds this length. The quartz and K-feldspar growth rate in this experiment is 3 × 10−10 and 4 × 10−10 m s−1, respectively.
In the 100-hour experiment (XLG27) the textures and shapes of the crystals are similar to those in XLG26 (not initially water saturated): large (hundreds of micrometres long) crystals set in a submicrometre-to-micrometre scale quartz-K-feldspar spherulitic intergrowth. The crystals in this experiment fill about 30 % of the capsule. As observed in the submicrometre intergrowths in experiments with 8 wt% H2O, the abundance of the large K-feldspar crystals is greater at the spherulite rim than near the core. The maximum length of any crystal in this experiment is that of a 625-μm long K-feldspar crystal which appears to have grown into a vapor bubble, yielding a growth rate of 9 × 10−10 m s−1. The spherulitic intergrowth grew at a rate of 1 × 10−9 m s−1.
Seeded experiments at 200°C undercooling, 540°C, with 8 wt% H2O
During the experiment performed for 25 hours at these conditions (XLG28) only subhedral and dendritic quartz crystallized (no more than 5 % of the volume of the capsule). In some cases the crystals form radiating vermicular overgrowths, ∼ 38 μm wide, around some seeds; their growth rate was 4 × 10−10 m s−1. Individual crystals grew at a rate of 1 × 10−10 m s−1.
The two experiments performed for 50 hours at the same conditions (XLG20 and XLG21) are dominated by millimetre-scale spherulitic intergrowths; no residual melt was observed. K-feldspars often enclose subhedral to euhedral quartz crystals which apparently were growing into vapour bubbles during the experiment (Fig. 2a). Between these regions of large crystals, micrometre-scale graphic intergrowths (Fig. 2b) were formed. Some of these graphic integrowths separate the millimetre-scale spherulitic intergrowths from the capsule walls and therefore appear to predate the formation of the spherulites. The longest K-feldspars in these experiments had growth rates of 2.4 × 10−9 m s−1 (XLG20) and 3 × 10−9 m s−1 (XLG21). Quartz growth rates in these experiments were 1.8 × 10−9 m s−1 (XLG20) and 1.2 × 10−9 m s−1 (XLG21). Analyses of Rb2O concentrations in K-feldspars suggest that the largest crystals, which are associated with quartz crystals and voids (Fig. 2a), grew earlier (from less evolved melts) than K-feldspars surrounding smaller voids and in many graphic intergrowths. A traverse of K-feldspars in a graphic intergrowth was made in XLG20. The Rb2O concentration in these K-feldspars varied from a high of 3.85 near the capsule wall to a low of 3.37 wt% where the graphic intergrowth merges with a K-feldspar surrounding a former vapour bubble at a distance of 460 μm from the capsule.
Seeded experiments at 200°C undercooling, 540°C, with 14 wt% H2O
The 25-hour experiment at these conditions (XLG29) contains only 10 % crystals of both quartz and K-feldspar. The intergrowths of these minerals are on a micrometre scale, and some of the K-feldspars reach 950 μm in length. The growth rate of the longest feldspar is 5 × 10−9 m s−1 and of the longest quartz is 1 × 10−9 m s−1.
The shapes and textures of the crystals grown in the 50-hour experiment at the same conditions (XLG22) are very similar to that observed in the 8 wt% H2O experiments (XLG20 and XLG21). No quenched melt was observed in this experiment. The growth rate of the largest K-feldspar crystals is 2 × 10−9 m s−1.
Ising model simulations of crystal growth
Simulations of crystal growth were performed to complement and interpret the experimental run products. The simulations used the Jackson, Gilmer, and Temkin (JGT) formulation of a 2-dimensional Ising model (Jackson et al., 1995; Beatty & Jackson, 1997). The simulations used our previously described version of this model with minor modifications (Baker & Freda, 1999), so only a brief summary will be presented here.
The bond energies in the simulations were chosen so that the liquidus temperatures of orthoclase and quartz corresponded to those measured at 500 MPa and water-saturated conditions. The bond energy between orthoclase adatoms (the fundamental units of crystal growth in the simulations) in the crystal was set to 1430 J/k (where k is Boltzmann's constant) and the bond energy between quartz adatoms in the crystal was set to 1750 J/k. The latter value was adjusted from the value used for quartz in Baker & Freda (1999), 1800 J/k, to better fit the melting temperature of quartz. The interaction parameter between adatoms of crystalline quartz and orthoclase was set at 1000 J/k. Interaction parameters between adatoms in the melt phase were set to zero.
Diffusion in the melt was calculated from granitic melt viscosities (Baker, 1998) using the Eyring equation. These calculated diffusion coefficients correspond to Si-Al chemical diffusion in silicate melts (Baker, 1992). The diffusion coefficient calculated from viscosity is 2.0 × 10−16, 6.6 × 10−17, and 5.2 × 10−18 m2 s−1 at 690, 640, and 540°C, respectively. Diffusion in the crystals was assumed to be zero.
Simulations were performed on a 500 × 500 lattice with reflecting boundaries on the sides using a Monte Carlo technique. The top row of the lattice was constrained to always remain liquid. Seeds were placed either at the bottom 10 rows of the simulation or in the centre 10 × 10 rows and columns of the simulation. In almost all simulations the crystal used as the seed was quartz; experiments using K-feldspar seeds produced the same results as those with quartz seeds. The duration of a typical simulation was between 200,000 and 1,000,000 time steps. Temperatures of the simulations were the same as those used in experiments, 690, 640, and 540°C. The simulations of this study do not contain any crystallographic constraints, nor do they explicitly investigate the effects of water and added Rb2O. The size of the adatoms (pixels in the images) in the simulations is of the order of 1 nm; the final 500 × 500 lattice therefore represents a crystallized region on the order of 0.5 × 0.5 μm. Additionally, these simulations are 2-dimensional, rather than 3-dimensional. Because of these limitations the models cannot be expected to produce exact replicas of the experiments. However, as will soon be demonstrated, the simulations, despite their limitations, provide textures similar to those found in many of the experiments.
Experiments performed at 50°C undercooling for 50 hours did not show any complex textures; they either do not contain K-feldspar (XLG14), or only have one K-feldspar crystal surrounded by an embryonic spherulite with a submicrometre intergrowth (XLG12). At 100°C undercooling the textural development during crystallization commences with the formation of subhedral, skeletal, and dendritic quartz which occurred in the first 25 hours. Most of this initial crystallization is associated with seeds or with the capsule wall, although it is apparent that in some cases internal nucleation of quartz occurs (XLG6). Tabular K-feldspar has nucleated and grown between the quartz in the 50-hour experiments. In the longer duration experiments these minerals continue to crystallize with only minor changes in shape and texture. The most common texture seen in the experiments is spherulitic with quartz-K-feldspar intergrowths varying from submicrometre to micrometres in size; set within this intergrowth are either individual crystals of quartz and K-feldspar or intergrowths of these two minerals with dimensions of tens or even hundreds of micrometres. In general the abundance of K-feldspar increases from core to rim of the spherulitic growth. The only significant difference seen between experiments that were initially water saturated and those with 8 wt% H2O is the absence of a spherulitic texture and the submicron intergrowth in one water-saturated experiment (XLG7). The experiments performed at 200°C undercooling are remarkable for the occurrence of graphic textures on the micrometre scale and spherulitic textures reaching the millimetre scale (XLG20, XLG21, XLG22).
Simulations vs. experiments
As we already pointed out many authors agree that crystal shape and texture in undercooled silicate systems are significantly affected by the ratio of the probability of crystal growth to diffusion in the melt (G:D ratio). This variable is not controllable during crystallization experiments but can be easily controlled and varied at will during crystallization simulations. We therefore chose to use models as an aid to understanding three dominant textures seen in the experiments. The first is the formation of intergrowths at different scales (submicrometres to tens of micrometres), including the graphic texture formed only in experiments at 200°C undercooling. The second is the formation of spherulitic textures in almost all experiments; these textures are characterized by an increase of crystal size and K-feldspar abundance from the core to the rim of spherulites. The third is the growth of large crystals (100 μm) in a fine-grained matrix (micrometres or less) typical of experiments at 100°C undercooling.
The presence of intergrowths at different scales is a common feature of these experiments, especially those at 100°C undercooling, and was reproduced, at different scales, in simulations of crystal growth. Simulations were initially performed at growth probabilities equal to 0.1, 1, 10, and 100 times the diffusion probability. All these simulations produced a quartz-K-feldspar intergrowth whose grain size was controlled by the growth to diffusion probability, G:D ratio (Fig. 3a, b, c). The coarseness of intergrowths scales inversely with the G:D ratio. Average widths of quartz and K-feldspar crystals are similar to each other in all simulations, but as the G:D ratio increases from 0.1 to 10 the crystal width decreases by a factor of 3. Increasing the G:D ratio to 100 only decreases the width by an additional factor of 0.6. A significant difference between simulations in which G:D is greater than or equal to 1, as opposed to less than 1, is that the former simulations exhibit a random distribution of quartz and K-feldspar throughout the growth (Fig. 3b, c), whereas the latter are zoned from quartz-rich at the beginning to K-feldspar-rich at the termination of the simulation (Fig. 3a). Simulations with a K-feldspar seed also displayed the same zoning pattern. As simulations indicate, the quartz-K-feldspar intergrowths of equant dimensions and similar modal abundances seen in many experiments are produced when the G:D ratio is equal to or higher than 1. Therefore the positive correlation between increasing experimental intergrowth coarseness with undercooling indicates a falling G:D ratio. The formation of graphic textures at 200°C undercooling is due to conditions at which the G:D ratio is low, but still high enough to prevent the formation of mineralogical zoning in the experiments; the simulations indicate this value is near 1.
The simulations producing spherulites which show a mineralogical zonation similar to that observed in many experiments were those with a G:D ratio changing from near 1 to a lower value. A time series of results from one such simulation are shown in Fig. 4. The spherulite that grows from the quartz seed is initially quartz rich (Fig. 4a); then with time it develops K-feldspar rich regions near its perimeter (Fig. 4b and c). The intergrowth near the core is extremely finegrained, but the intergrowth size increases with increasing distance from the core. Although poorly developed, alternating concentric zones rich in either quartz or K-feldspar can be seen in the simulated spherulite. Even though the simulations have no preferred crystallographic orientations the K-feldspars grow in a radiating pattern away from the core. The quartz and K-feldspar of the spherulite grow approximately simultaneously, not sequentially. All of these characteristics of the simulated spherulite are similar to those of spherules grown in many experiments (Fig. 1b, and 2a). These textures were never seen in simulations with growth probabilities equal to or higher than the diffusion probability, but are present when growth probabilities are even less than 0.1 times the diffusion probability.
The presence of large (tens to hundreds of μm in length) quartz and K-feldspar crystals set in a fine-grained matrix of the same two minerals can be simulated by lowering the G:D ratio below 1 in a small portion of the simulation (Fig. 5). This simulation has a growth probability equal to the diffusion probability except in the small region where the G:D ratio was reduced to 0.5. This region with a lower growth probability contains much coarser crystals of quartz and K-feldspar than those found in neighbouring regions with the higher growth probability.
Causes for changes in the G:D ratio
The simulations indicate that changes in the G:D ratio exert a significant effect on the textures formed during crystallization in the quartz-orthoclase-water system at high undercooling. Obviously, changes in the ratio can be due to changes in diffusion, growth, or both.
Changes in the crystal growth rate during experiments may have occurred but are expected to be minor. Fenn (1977) demonstrated that increasing H2O concentration decreases alkali feldspar growth rates, but by less than a factor of two. Changes in the growth rate as the system evolves from a far-from-equilibrium to a nearequilibrium state are expected, but our measurements of crystal growth rates (Table 2) do not demonstrate any obvious decreases in growth rates with increasing experimental duration. Instead, the experiments suggest that crystals are growing at constant, or nearly constant, rates. Any changes in the G:D ratio on the order of a factor of 10appear due to changes in the diffusion coefficient, not in the growth rate.
Changes in the diffusion coefficient of cations in the melt are unlikely during the isothermal growth of the crystals at undercooled conditions. The diffusion coefficient in a silicate melt is controlled by the melt's anhydrous composition, volatile content, and temperature and pressure. During each experiment the temperature and pressure remain constant and microprobe analyses of residual glasses in the experiments demonstrate that major element compositions remain close to the original eutectic composition (within 5 relative percent for SiO2 and A12O3, 10 relative percent for K2O). The only variable that changes during the experiments with 8 wt% H2O is the increase in water concentration until saturation is reached at about 9 wt%. Melts with 14 wt% H2O do not change water concentration because they begin water saturated. However, at water concentrations above 4 wt% the effect of additional water on cation diffusion is small (Watson, 1994), approximately less than a factor of 2. Thus, none of the variables affecting cation diffusion in the melt seem able to affect a significant change in the G:D ratio. However, during these experiments with 8 wt% H2O added a separate fluid phase forms and often can be found at the growing faces of crystals (Fig. 1b).
Once a separate fluid phase forms the diffusion of cations in the fluid phase will far exceed their diffusion in the silicate melt. The measurements of silica diffusion in an aqueous fluid at high temperatures and pressures by Watson & Wark (1997) yield diffusion coefficients between 1 and 4 × 10−8 m2 s−1 at the experimental conditions of this study. These values are many orders of magnitude above those for cation diffusion in silicate melts, which are estimated to be between 10−17 to 10−15 m2s−1 in these experiments (discussed above). Thus at a fixed growth rate the G:D ratio will be lower for a crystal growing from a fluid phase than from a silicate melt.
The measured growth rates from these experiments and the coefficients of diffusion in either the melt or the fluid phase can be used to estimate the experimental G:D ratio for quantitative comparison with the simulations. The estimated G:D ratio for growth from a melt varies between 0.01 and 1, whereas for growth from a fluid the G:D ratio lies between 10−11 and 10−10. Direct quantitative comparison between simulations and experiments at G:D ratios characteristic of growth from a fluid phase are impossible using our computational resources. However, the average widths of crystals in the simulations follow a power-law relationship over approximately 4 orders of magnitude and this relationship can be used to extrapolate the simulation results to lower G:D ratios (Fig. 6).
The G:D ratios for both simulations and crystals that appear to have grown from the melt phase are consistent to within an order of magnitude or better (Fig. 6). Extrapolating from the simulated region near G:D = 1 where individual crystals are on the order of 1 to 10 μm in size down to conditions that produce crystals 100 to 1000 times larger requires G:D ratios between 10−9 and 10−12. These ratios encompass the range estimated directly from experiments in which we hypothesize that crystals grew in contact with the fluid phase. The simulations indicate that a change in the G:D ratio from near 1 to near 10−11 can explain the change in crystal sizes seen in many experiments. The crystal growth rates combined with silica diffusion in the fluid indicate that G:D ratios near 10−11 are consistent with the growth of large crystals from the fluid phase.
We attribute the differences in crystal texture to the presence or absence of a fluid phase at the surface of a growing crystal. Thus, the finegrained and graphic intergrowths seen in many experiments are hypothesized to grow at locations in the melt far from any fluid phase whereas the large crystals set in a fine-grained groundmass grew in contact with a fluid phase. An interesting observation in support of this hypothesis is that large crystals are seen growing into vesicles and that the size of the coarser crystals in the finegrained spherulites are always similar to the size of the vesicles found in experiments. Growth of these larger crystals could be terminated when the vapour bubble detaches itself from the growing crystal surface and is replaced by silicate melt with a much lower diffusion coefficient. Interestingly, no fluid inclusions were observed in the crystals.
Petrogenetic implications and conclusions
This study demonstrated that highly undercooled melts of a simplified pegmatite composition produce complex textures that can be modelled to be due to changes in the G:D ratio. These experimentally produced and simulated textures are remarkably similar to natural pegmatites and provide a powerful tool to understand what processes cause pegmatite textures.
Comparing natural pegmatitic textures with experimental textures one can note that:
The fine-grained submicrometre intergrowths at the cores of the experimental spherulites and the graphic intergrowth that grew at the beginning of crystallization (based upon Rb concentrations), resemble the wall zone (Černý, 1991) typical of heterogeneous zoned pegmatites. The simulations suggest that these textures crystallized at high degrees of undercooling from a melt with a G:D ratio near unity.
The K-feldspar crystals growing at the rim of the spherulites can be compared to the blocky K-feldspars of the intermediate zone (Černý, 1991) of pegmatites. Simulations demonstrated that the formation of large isolated crystals is related to the G:D ratio decrease; during the experiments (and in natural processes) this can be due to crystallization of anhydrous minerals which drives water concentrations to higher levels and undercoolings to lower values and eventually results in fluid saturation.
The quartz crystals and the terminations of the spherulites into melt and vapour-filled cavities are analogous to the central quartz core and pocket zone (Černý, 1991) of pegmatites. The quartz core possibly grew at the contact between fluid and melt, and the fluids remaining after quartz crystallization produced gem pockets at the pegmatite's centre.
The similarity of our experiments to natural pegmatites suggests to us that similar changes in the G:D ratio during crystallization at hundreds of degrees of undercooling are responsible for the textures found in pegmatites. Our results provide additional support for hypotheses espoused by London (1992, 1996) who stressed that pegmatite textures could be formed by crystallization from an undercooled and water-undersaturated melt. However, our combined experimental and simulation study indicates that the presence of a fluid phase plays an important role in the formation of the variety of pegmatite textures formed during crystallization of an undercooled granitic melt. The significance of changes in the G:D ratio in affecting the crystallization textures of severely undercooled melts appears great and indicates that only small changes in extrinsic or intrinsic thermodynamic variables may result in textures whose characteristic dimensions vary by many orders of magnitude.
Thoughtful reviews by D. Dingwell and an anonymous reviewer were appreciated. Funding for this research was provided by NSERC Research Grant OGP89662 with a partial contribution from the CNR Short-Term Mobility Programme to C.F.
- Received 26 May 2000.
- Modified version received 20 December 2000.
- Accepted 23 January 2001.