Crystal Size Distribution Measurements Research Articles

Modeling of zircon nucleation and growth rates using crystal size distributions in a cooling magmatic intrusion

With a rapid increase in the use of zircons for geochronology and in situ isotopic and chemical analyses it is important to quantify growth rates and nucleation rates of zircons in natural magmatic systems. Here we present a mathematical model of the nucleation and growth of a population of zircon crystals in a cooling magmatic intrusion and apply nucleation laws to derive zircon crystal size distributions (CSD) and particle number density (n per cm3 of melt) from first principles. The model is based on a numerical solution of the one-dimensional diffusion equation that accounts for the nucleation and growth of individual crystals and the dependence of the equilibrium concentration of Zr on temperature. As experimental studies of zircon nucleation at natural concentration levels of Zr are nearly impossible, we rely on measured CSDs of age-invariant (within error of the method <±5ky) zircon populations in rapidly quenched eruptive products of known crystallization duration to calibrate our model. The CSDs of zircon crystals are calculated at different rates of cooling of the magma chamber and are compared to measurements. The combination of the zircon growth software with measurements of zircon CSDs and particle number density permits direct estimation of the zircon nucleation rates and their evolution with time in cooling magmatic systems. We observe a delayed zircon nucleation of 500–2000 years after the melt becomes zircon saturated. Zr supersaturations that drive grown in simulations range from 1 to ∼30ppm and vary non-monotonically as crystallization proceeds. Initially, the nucleation rates increase exponentially from 10−3 to ∼1crystals/cm3/yr but then decrease by an order of magnitude as the distance between zircons decreases. Growth rates stay in 10−15cm/s range for the most duration of zircon growth. The ratio of growth to nucleation rates in our model also varies insignificantly and is used to estimate crystallization time based on the CSD slope, which decreases with the increased duration of cooling. Flatter slopes correspond to longer crystallization durations as is also noted for major phases. Due to non-monotonic variations in growth and nucleation rates with time, the observed deficiency of small zircons resulting in concave up CSD shapes can be reproduced from first principles assuming monotonic cooling of the magmatic system. Variations in the mode of cooling from linear to monotonic during conductive heat loss of a cooling intrusion, and minor coeval precipitation (<10vol%) of major phases has little impact on zircon CSD and its evolution. This study has implication to individual zircons IDTIMS dates and demonstrates that most zircons crystallize much later than magma becomes saturated with Zr, despite sometimes having nominally long tail crystallization rate in the inherited cores. For natural CSDs from eight different eruptions randomly selected zircons predate eruption age only by ∼300–1000years.

A Novel Shadowgraphic Inline Measurement Technique for Image-Based Crystal Size Distribution Analysis

A novel shadowgraphic inline probe to measure crystal size distributions (CSD), based on acquired greyscale images, is evaluated in terms of elevated temperatures and fragile crystals, and compared to well-established, alternative online and offline measurement techniques, i.e., sieving analysis and online microscopy. Additionally, the operation limits, with respect to temperature, supersaturation, suspension, and optical density, are investigated. Two different substance systems, potassium dihydrogen phosphate (prisms) and thiamine hydrochloride (needles), are crystallized for this purpose at 25 L scale. Crystal phases of the well-known KH2PO4/H2O system are measured continuously by the inline probe and in a bypass by the online microscope during cooling crystallizations. Both measurement techniques show similar results with respect to the crystal size distribution, except for higher temperatures, where the bypass variant tends to fail due to blockage. Thiamine hydrochloride, a substance forming long and fragile needles in aqueous solutions, is solidified with an anti-solvent crystallization with ethanol. The novel inline probe could identify a new field of application for image-based crystal size distribution measurements, with respect to difficult particle shapes (needles) and elevated temperatures, which cannot be evaluated with common techniques.

Constraining pre-eruptive magma conditions and unrest timescales during the Monte Nuovo eruption (1538 ad; Campi Flegrei, Southern Italy): integrating textural and CSD results from experimental and natural trachy-phonolites

We present crystallization experiments representing a broad range of growth conditions of alkali feldspar and sodalite in a trachy-phonolite magma composition during later stages of evolution. Our results include (i) textural data and mineral assemblages of synthetic samples; (ii) feldspar nucleation kinetics and growth rate estimates; and (iii) textural data, mineral abundances, and crystal size distribution measurements on samples representative of the Monte Nuovo eruption (1538 ad), the last eruption of Campi Flegrei, Southern Italy. Experiments reproduced the texture and feldspar content of natural products indicating that kinetic data can provide insights into processes within the volcanic system shortly before and during this small-magnitude eruption and, particularly, about magma ascent timescale. We suggest that the groundmass crystallization of Monte Nuovo magma started between 4 and 7 km depth (∼100–200 MPa) at a temperature between 825 and 840 °C (close to the liquidus of alkali feldspar). The crystallization kinetics of alkali feldspar and the absence of sodalite in most of the natural samples indicate that magma ascent rate increased in the shallow part of the conduit from about 3 km depth to the quenching level (possibly fragmentation point; ∼30 MPa), during the first phases of the eruption. The crystallization time of the magma requires that it ascended from pre-eruptive storage to the quenching level in several hours to a few days. We also observe that a small decrease in pressure can induce a dramatic increase in crystallinity, with associated rheological changes, leading to changes in the eruption style, and such changes could occur on timescales of hours to several days. The products from the later phases of the Monte Nuovo eruption are more crystalline and contain sodalite in response to the decrease in magma ascent rate, which in turn allowed for more degassing during ascent, resulting in more time spent at very shallow depths.

Primary and secondary fragmentation of crystal-bearing intermediate magma

Crystal-rich intermediate magmas are subjected to both primary and secondary fragmentation processes, each of which may produce texturally distinct tephra. Of particular interest for volcanic hazards is the extent to which each process contributes ash to volcanic plumes. One way to address this question is by fragmenting pyroclasts under controlled conditions. We fragmented pumice samples from Soufriere Hills Volcano (SHV), Montserrat, by three methods: rapid decompression in a shock tube-like apparatus, impact by a falling piston, and milling in a ball mill. Grain size distributions of the products reveal that all three mechanisms produce fractal breakage patterns, and that the fractal dimension increases from a minimum of ~2.1 for decompression fragmentation (primary fragmentation) to a maximum of ~2.7 by repeated impact (secondary fragmentation). To assess the details of the fragmentation process, we quantified the shape, texture and components of constituent ash particles. Ash shape analysis shows that the axial ratio increases during milling and that particle convexity increases with repeated impacts. We also quantify the extent to which the matrix is separated from the crystals, which shows that secondary processes efficiently remove adhering matrix from crystals, particularly during milling (abrasion). Furthermore, measurements of crystal size distributions before (using x-ray computed tomography) and after (by componentry of individual grain size classes) decompression-driven fragmentation show not only that crystals influence particular size fractions across the total grain size distribution, but also that free crystals are smaller in the fragmented material than in the original pumice clast. Taken together, our results confirm previous work showing both the control of initial texture on the primary fragmentation process and the contributions of secondary processes to ash formation. Critically, however, our extension of previous analyses to characterisation of shape, texture and componentry provides new analytical tools that can be used to assess contributions of secondary processes to ash deposits of uncertain or mixed origin. We illustrate this application with examples from SHV deposits.

Spectral optical layer properties of cirrus from collocated airborne measurements and simulations

Abstract. Spectral upward and downward solar irradiances from vertically collocated measurements above and below a cirrus layer are used to derive cirrus optical layer properties such as spectral transmissivity, absorptivity, reflectivity, and cloud top albedo. The radiation measurements are complemented by in situ cirrus crystal size distribution measurements and radiative transfer simulations based on the microphysical data. The close collocation of the radiative and microphysical measurements, above, beneath, and inside the cirrus, is accomplished by using a research aircraft (Learjet 35A) in tandem with the towed sensor platform AIRTOSS (AIRcraft TOwed Sensor Shuttle). AIRTOSS can be released from and retracted back to the research aircraft by means of a cable up to a distance of 4 km. Data were collected from two field campaigns over the North Sea and the Baltic Sea in spring and late summer 2013. One measurement flight over the North Sea proved to be exemplary, and as such the results are used to illustrate the benefits of collocated sampling. The radiative transfer simulations were applied to quantify the impact of cloud particle properties such as crystal shape, effective radius reff, and optical thickness τ on cirrus spectral optical layer properties. Furthermore, the radiative effects of low-level, liquid water (warm) clouds as frequently observed beneath the cirrus are evaluated. They may cause changes in the radiative forcing of the cirrus by a factor of 2. When low-level clouds below the cirrus are not taken into account, the radiative cooling effect (caused by reflection of solar radiation) due to the cirrus in the solar (shortwave) spectral range is significantly overestimated.

An image analysis method to detect CSD on rocks with adjusted color images

Purpose – The purpose of this paper is to provide crystal size distribution (CSD) using photogrammetric and image analysis techniques. A new algorithm is proposed to detect CSDs and a comparison is carried out with conventional watershed segmentation algorithm. Design/methodology/approach – Polished granite plates were prepared to designate the metrics of CSD measurements. There are many important metrics for measurements on CSD. Some of them are orientation, size, position, area, aspect ratio, convexity, circularity, perimeter, convex hull, bounding box, eccentricity, shape, max-min length of CSD's fitted and corrected ellipse, and population density in a per unit area. Prior to image processing stage, camera calibration was performed to remove the image distortion errors. Image processing techniques were applied to corrected images for detecting the CSD parameters. Findings – The proposed algorithm showed the improved preservation of size and shape characteristics of the crystal material when compared to the watershed segmentation. According to the experimental results, proposed algorithm revealed promising results in identifying CSDs more easily and efficiently. Originality/value – This paper describes CSD of granitic rocks by using automated grain boundary detection methods in polished plate images. Some metrics of CSDs were detected by employing a new procedure. A computer-based image analysis technique was developed to measure the CSDs on the granitic rock plates. A validation is done by superimposing digitally detected CSD metrics to original samples.

Measurement of Two-Dimensional Crystal Shape Using Digital Holography

A digital holography based method for online measurement of crystal size distribution is presented. The main advantage of holography over conventional imaging techniques lies in its capability to measure the three-dimensional volume information, thereby overcoming limitations associated with the depth of focus. In the proposed method, 3D volume information (holography) is stored and tailored image analysis routines are used to extract the size and shape information from the stored holograms. The method is applied to experimental batch cooling crystallization of two systems, namely, oxalic acid and potash alum. The measured crystal size and shape distribution are found to be in good agreement with offline microscopy measurements.

The formation of columnar joints produced by cooling in basalt at Staffa, Scotland

Columnar jointing in basaltic lava flows on the island of Staffa, NW Scotland, was studied using a combination of field mapping and measurement of column dimensions, sample petrology and measurements of plagioclase crystal size distributions (CSDs) interpreted using theoretical models of cooling. Four different lava flow units were measured, and column ordering was assessed using the hexagonality index and relative standard deviations of column side length, top area and internal angle. Upper and lower colonnades consist of dominantly 5-, 6- and 7-sided columns, with a hexagonality index value very similar to that of Giant’s Causeway and other basaltic columnar jointed localities. CSDs from samples at different heights within one colonnade were used to infer the propagation of the solidus isotherm, which was consistent with a convective cooling mechanism within the colonnade interior. Sample petrology and CSD measurements suggest that entablature can form both by the interaction of propagating joint sets and flooding of the flow surface by water, and the most widely exposed unit on Staffa shows evidence of both mechanisms operating on the same flow. Crystal size distribution measurements can provide a useful tool for field interpretation of lava flow cooling mechanisms.

Rapid online calibration for ATR-FTIR spectroscopy during batch crystallization of ammonium sulphate in a semi-industrial scale crystallizer

The knowledge of solute concentration throughout a batch crystallization process is essential from process control perspective. Despite the progress in process analytical technology (PAT), there still exist several challenges for online measurement of solute concentration at industrial scale. In this study, concentration monitoring was realized using attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy at lab as well as semi-industrial scale. Applications of the calibration model developed at lab scale for the measurements at the semi-industrial scale however resulted into strongly biased concentration predictions, caused by the differences in the curvature of fiber optics and the uneven thermal expansion of the probe. Therefore an alternative rapid online calibration method was developed during the start-up phase of the process. With this method, the time required for developing a working calibration model for concentration monitoring during crystallization of ammonium sulphate in a semi-industrial scale draft tube crystallizer has been reduced approximately by 90%. With the help of simultaneous concentration and crystal size distribution measurements at semi-industrial scale, the descriptive capability of the model was improved due to better kinetic parameters.

Evidence for ice particles in the tropical stratosphere from in-situ measurements

Abstract. In-situ ice crystal size distribution measurements are presented within the tropical troposphere and lower stratosphere. The measurements were performed using a combination of a Forward Scattering Spectrometer Probe (FSSP-100) and a Cloud Imaging Probe (CIP), which were installed on the Russian high altitude research aircraft M55 "Geophysica" during the SCOUT-O3 campaign in Darwin, Australia. One of the objectives of the campaign was to characterise the Hector convective system, which appears on an almost daily basis during the pre-monsoon season over the Tiwi Islands, north of Darwin. In total 90 encounters with ice clouds, between 10 and 19 km altitude were selected from the dataset and were analysed. Six of these encounters were observed in the lower stratosphere, up to 1.4 km above the local tropopause. Concurrent lidar measurements on board "Geophysica" indicate that these ice clouds were a result of overshooting convection. Large ice crystals, with a maximum dimension up to 400 μm, were observed in the stratosphere. The stratospheric ice clouds included an ice water content ranging from 7.7×10−5 to 8.5×10−4 g m−3 and were observed at ambient relative humidities (with respect to ice) between 75 and 157%. Three modal lognormal size distributions were fitted to the average size distributions for different potential temperature intervals, showing that the shape of the size distribution of the stratospheric ice clouds are similar to those observed in the upper troposphere. In the tropical troposphere the effective radius of the ice cloud particles decreases from 100 μm at about 10 km altitude, to 3 μm at the tropopause, while the ice water content decreases from 0.04 to 10−5 g m−3. No clear trend in the number concentration was observed with altitude, due to the thin and inhomogeneous characteristics of the observed cirrus clouds. The ice water content calculated from the observed ice crystal size distribution is compared to the ice water content derived from two hygrometer instruments. This independent measurement of the ice water content agrees within the combined uncertainty of the instruments for ice water contents exceeding 3×10−4g m−3. Stratospheric residence times, calculated based on gravitational settling, and evaporation rates show that the ice crystals observed in the stratosphere over the Hector storm system had a high potential of humidifying the stratosphere locally. Utilizing total aerosol number concentration measurements from a four channel condensation particle counter during two separate campaigns, it can be shown that the fraction of ice particles to the number of aerosol particles remaining ranges from 1:300 to 1:30 000 for tropical upper tropospheric ice clouds with ambient temperatures below −75°C.

Decryption of Igneous Rock Textures: Crystal Size Distribution Tools

Research Article| January 01, 2008 Decryption of Igneous Rock Textures: Crystal Size Distribution Tools Pietro Armienti Pietro Armienti Dipartimento di Scienze della Terra, via S. Maria 53, Pisa, Italy, armienti@dst.unipi.it Search for other works by this author on: GSW Google Scholar Author and Article Information Pietro Armienti Dipartimento di Scienze della Terra, via S. Maria 53, Pisa, Italy, armienti@dst.unipi.it Publisher: Mineralogical Society of America First Online: 13 Jul 2017 © The Mineralogical Society Of America Reviews in Mineralogy and Geochemistry (2008) 69 (1): 623–649. https://doi.org/10.2138/rmg.2008.69.16 Article history First Online: 13 Jul 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Pietro Armienti; Decryption of Igneous Rock Textures: Crystal Size Distribution Tools. Reviews in Mineralogy and Geochemistry 2008;; 69 (1): 623–649. doi: https://doi.org/10.2138/rmg.2008.69.16 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyReviews in Mineralogy and Geochemistry Search Advanced Search Abstract In this overview it is planned to show how quantitative determination of mineral modes data, by means of Crystal Size Distribution (CSD), may help in deciphering the kinetics of magmatic crystallization both in natural and experimental conditions. Some stereological considerations will be discussed to provide criteria for the choice of numbers and lengths of size intervals for CSD computations. Equations for the balance of number and size of crystals, in steady state crystallization and in dynamic regime, will be used to define the time frame of magmatic processes, in the context of the case studies of Stromboli and Etna volcanoes.The functional dependence of crystal size (L) and crystal number from time is explicitly derived by interpreting experiments of olivine crystallization that report CSD data, thus obtaining evaluation of thermodynamic parameters from CSD measurements. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Crystallization of Monohydrate Citric Acid. 1. In Situ Monitoring through the Joint Use of Raman Spectroscopy and Image Analysis

Seeded batch crystallizations of monohydrate citric acid were performed under isothermal conditions (15 °C). Continuous monitoring of the overall solid concentration during the crystallization process was developed using in situ Raman spectroscopy. Quantitative estimation of the crystal size distribution (CSD) was made possible thanks to in situ image acquisition: off-line CSD measurements were further computed from the recorded pictures. The growth rate of monohydrate citric acid was estimated from solid concentration. Through in situ particle size visualization and quantitative analysis of the pictures, activated surface secondary nucleation was also shown to significantly impact the final CSD. It is underlined that, in addition to continuous Raman in situ spectroscopic concentration measurements, image acquisition yields highly valuable data on the dispersed phase. Advantages and drawbacks of the technique for the monitoring of solution crystallization are discussed.

Flowage differentiation in an andesitic dyke of the Motru Dyke Swarm (Southern Carpathians, Romania) inferred from AMS, CSD and geochemistry

Two dykes of different thickness (5.5 m for TJ31 and 23 m for TJ34) from the late Pan-African calc-alkaline Motru Dyke Swarm (S. Carpathians, Romania) have been studied by electron microprobe (mineral chemistry), crystal size distribution (CSD), anisotropy of magnetic susceptibility (AMS) and whole-rock geochemistry. All the physical and chemical variations observed across the dyke's width point to concordant results and show that the variations of both modal abundance and size of the amphibole and biotite microphenocrysts inside the dykes (deduced from the classical CSD measurements) are the result of a mechanical segregation of suspended crystals during magmatic transport. Despite a pene-contemporaneous regional tectonic, the flow-induced differentiation in the thicker dyke is characterized by the concentration of pre-existing Ti-rich pargasite-tschermakite, clinopyroxene and plagioclase crystals in the core of the dyke and of the extracted differentiated liquid near the walls. This mechanical differentiation induces a chemical differentiation with a basaltic andesite composition for the core of the dyke whereas the margins are andesitic. Thus the chilled margins appear as a slightly more evolved liquid with a Newtonian behaviour when compared to the average composition of the dyke. The localization of the liquid on both sides of the dyke has certainly facilitated the ascent of the central part of the dyke that behaved as a Binghamian mush.

On‐line monitoring of a crystallization process

AbstractThe application of ultrasonic spectroscopy for particle‐size measurements was investigated during the batch crystallization of (L)‐glutamic acid α‐polymorph from an aqueous solution. The technique, based on measurements of the attenuation of ultrasonic waves through the suspension, was applied using a prototype ultrasonic spectrometer with a flow‐through cell. High‐precision measurements of ultrasonic attenuation in the frequency range 7–110 MHz were performed, the deconvolution of which enabled in‐process measurement of crystal size distribution and solid concentration throughout the crystallization process. In addition to evincing secondary nucleation, growth and crystal breakage on‐line in real time, the experimental results were used to obtain kinetic parameters essential for process design, including secondary nucleation rate and growth rate.

Effects of Undersaturation on Crystal Size Distribution in Cooling Type Batch Crystallization.

In the cooling type batch crystallization, the influence of undersaturation operation on crystal size distribution was investigated, and the effectiveness of this operation was discussed. In batch crystallization with seeding, it was clear that undersaturation operations in the early stages of the cooling operation was effective in dissolving the micro-crystals which were generated by the initial bleeding, whereas undersaturation operations halfway through cooling was effective in dissolving the micro-crystals which were generated by attrition.From the results of applying this cooling temperature program to non-seeded batch crystallization, the design strategy of the temperature program for non-seeded operation was able to be determined. And it became clear that the crystal size distribution was improved by using undersaturation operations also in the case of non-seeded operation. This strategy of undersaturation operations was confirmed from measurement of crystal size distribution using an in-line sensor.

Airborne retrieval of cirrus cloud optical and microphysical properties using Airborne Remote Earth Sensing System 5.1–5.3 and 3.7‐μm channel data

We present an airborne retrieval algorithm to infer cirrus cloud temperature, optical depth, and mean effective sizes using the Airborne Remote Earth Sensing System (ARES) hyperspectral spectrometer data for the 5.1–5.3 and 3.7 μm channels. The algorithm, development and the selection of the channels are based on the principle and parameterization of radiative transfer involving cirrus clouds and the associated atmospheric and surface properties. It has been applied to a selected case of the ARES data collected over the western Boston area on September 16, 1995. Validation of the retrieved parameters was carried out using the collocated and coincident ground‐based 8.6‐mm radar data and ice crystal size distribution measurements obtained from the 2D‐P probe on board the high‐altitude reconnaissance platform (HARP). We show that the retrieved cirrus cloud temperature, mean effective ice crystal size, and optical depth match closely with those derived from the observations.

The Relation between Adsorption of Additives and Crystal Growth Rate of L-Alanine

The growth kinetics of L-alanine from solution in the presence and absence of L-phenylalanine and L-leucine has been studied. L-Alanine crystal growth, from crystal size distribution measurements, is independent of the agitation rate suggesting that the growth mechanism is surface controlled. The dependence of growth rate on supersaturation at constant additive concentration suggests that there is no change in the growth mechanism of L-alanine due to the presence of additive. The growth rate of L-alanine is reduced by 50% with a mol fraction of 5 × 10-5 of L-phenylalanine and 2 × 10-4 of L-leucine. The solubility of L-alanine is not significantly affected by the presence of these additives in solution. The effect of these additives on the growth kinetics is due to their adsorption onto the growing L-alanine crystals. The extent of this effect is satisfactorily explained assuming both that (i) the inhibition of the growth rate is proportional to the degree of surface coverage and that (ii) the crystal surface is homogeneous with respect to the energy of adsorption sites.

Crystallization of Mount St. Helens 1980?1986 dacite: A quantitative textural approach

Quantitative measurements of crystal size distributions (CSDs) have been used to obtain kinetic information on crystallization of industrial compounds (Randolph and Larson 1971) and more recently on Hawaiian basalts (Cashman and Marsh 1988). The technique is based on a population balance resulting in a differential equation relating the population densityn of crystals to crystal sizeL, i.e., at steady staten =no exp(−L/itGτ), whereno is nucleation density,G is the average crystal growth rate,τ is the average growth time, and the nucleation rateJ =noG. CSD (Inn vsL) plots of plagioclase phenocrysts in 12 samples of Mount St. Helens “blast” dacite and 14 samples of dacite from the 1980–1986 Mount St. Helens dome are similar and averageGτ = 9.6 (± 1.1) × 10−3 cm andno = 1−2 × 106 cm−4. Reproducibility of the measurements was tested by measuring CSDs of 12 sections cut from a single sample in three mutually perpendicular directions; precision of the size distributions is good in terms of relative, but not necessarily absolute values (± 10%). Growth and nucleation rates for plagioclase have been calculated from these measurements using time brackets ofτ = 30–150 years; growth ratesG are 3−10 × 10−12cm/s, and nucleation ratesJ are 5−21 × 10−6/cm3 s.G andJ for Fe-Ti oxides calculated from CSD data areG = 2−13 ± 10−13 cm/sec andJ = 7−33 × 10−5/cm3 s, respectively. The higher nucleation rate and lower growth rate of oxides resulted in a smaller average crystal size than for plagioclase. Sizes of plagioclase microlites (<0.01 mm) in the blast dacite groundmass have been measured from backscatter SEM photographs. Nucleation of these microlites was probably triggered by intrusion of material into the cone of Mount St. Helens in spring 1980. This residence time of 52 days gives minimum crystallization estimates ofG = 1−3 × 10−11 cm/s andJ = 9−16 × 1O3/cm3 s. The skeletal form of the microlites provides evidence for nucleation and growth at high values of undercooling (ΔT) relative to the phenocrysts. A comparison of nucleation and growth rates for the two crystal populations (phenocrysts vs microlites) suggests that while growth rate seems to be only slightly affected by changes inΔT, nucleation rate is a very strong function of undercooling. A comparison of plagioclase nucleation and growth rates measured in the Mount St. Helens dacite and in basalt from Makaopuhi lava lake in Hawaii suggests that plagioclase nucleation rates are not as dependent on composition. Groundmass textures suggest that plagioclase microphenocrysts crystallized at depth rather than in the conduit, in the dome, or after extrusion onto the surface. Most of this crystallization appears to be in the form of crystal growth (coarsening) of groundmass microphenocrysts at small degrees of undercooling rather than extensive nucleation of new crystals. This continuous crystallization in a shallow magmatic reservoir may provide the “overpressurization” needed to drive the continuing periodic domebuilding extrusions, which have been the pattern of activity at Mount St. Helens since December 1980.

Analysis of ice crystallization in continuous crystallizers based on a particle size-dependent growth rate model

To predict the ice crystal size distribution in MSMPR type crystallizers easily, the population balance equation with respect to the crystal size was solved under steady state conditions with a size-dependent growth rate model, that is G = g −1/ r + g 0. The kinetic parameters g −1 and g 0 obtained from the measurement of crystal size distribution in a dextran solution were consistent with those estimated by assuming that the growth process of ice crystals is governed by heat transfer process. We confirmed that the kinetic parameter β, determined from experiments in a batch crystallizer, can be adopted as the parameter for the nucleation rate per crystal in an MSMPR type crystallizer.