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Three‐dimensional crystal and bubble sizes and distributions in experimentally produced vesicular crystal‐bearing Stromboli basalts and natural scoria were studied with X‐ray microtomography (μCT) at high (1.85 μm) and low (5.46–9.0 μm) resolution. The permeabilities from lattice Boltzmann (LB) simulations and experimental measurements are about 1–2 orders of magnitude higher than in aphyric Stromboli basalts at porosity 31.6–55.3%. We propose that the higher permeability in crystal‐bearing samples results in highly efficient degassing in shallow, highly porphyritc (HP) magma as opposed to the deeper, aphyric (LP) magma. In paroxysmal explosions, the LP magma flows up in a cylindrical conduit due to the density and viscosity difference between the two magmas. This type of convection can cause the LP magma with exsolved gas to be efficiently transferred through the overlying HP magma, potentially resulting in the more‐violent paroxysmal explosions. Key Points Crystals significantly affect bubble growth, bubble sizes and distributions Crystals produce significanly high permeabilites in Stromboli basaltic magma Stromboli volcanic eruption styles are influenced by crystals

A population balance-based model was developed to describe the crystallization kinetics of the SAPO-34 zeotype through the hydrothermal method at three distinct temperatures of 180, 200, and 220 °C. The synthesized SAPO-34 catalysts were characterized by XRD, FESEM, BET, and DLS analysis. The model was constructed based on XRD patterns and incorporated established kinetic expressions for homogeneous nucleation and diffusion-controlled crystal growth. The developed model was also employed in a well-mixed batch system to predict the crystal size distribution. To solve the model equations, the Grey Wolf Optimization technique, as a powerful tool for optimizing complex systems, was applied. Then, the experimental data and the model’s predictions from zeolite synthesis were compared. Specifically, the nucleation rate, growth rate, crystallization profiles, and mean size of the resulting product crystals of SAPO-34 were evaluated for the first time. Remarkably, a notable agreement between the model and the experimental outcomes, particularly concerning the mean crystal size, was demonstrated. This connection between theory and experiment underlined the effectiveness of the population balance-based model in describing the complex crystallization process of the SAPO-34 zeotype across the range of temperatures. Indeed, this investigation demonstrated valuable insights into the hydrothermal synthesis of SAPO-34, showing the value of population balance modeling in predicting and optimizing crystallization processes. In addition, such findings indicated a great deal of promise for enhancing the precision and control of zeolite crystallization, a key element in several industrial applications, such as catalysis, ion exchange, and adsorption.

Supersaturation Nucleation and Growth of Plagioclase (SNGPlag) is a numerical model that predicts the nucleation and growth of plagioclase crystals in a decompressing magma as a function of time. The model is written in Matlab, but is available as a standalone compiled program. SNGPlag uses the MELTS webservice to determine equilibrium plagioclase mode, for a user-defined magma composition, as a function of pressure and temperature. User inputs include decompression path, the presence and size distributions of antecrysts and phenocrysts, and crystal shape. At each time step, the model evaluates the difference between the calculated crystallinity and equilibrium crystallinity for a given pressure and temperature to determine the degree of supersaturation, which then sets plagioclase nucleation and growth rates. Growth rates are used to grow the existing crystals whereas nucleation adds new crystals. SNGPlag produces results that can be compared to quantitative textures in natural volcanic rocks, including total crystallinity, microlite number density, microlite crystal size distribution, the characteristic size of microlite crystals, as well as a time series of crystallinity. Model results are consistent with the established crystallization theory. As expected, microlite crystallinity increases as decompression rate slows. Decompression path greatly affects microlite textures. For the same average decompression rate, single-step paths have higher crystallinities and microlite number densities than multi-step decompressions, which are in turn more crystalline than continuous paths. Pre-existing crystals damp microlite crystallization, as these crystals provide a substrate to accommodate crystal growth and thus reduce supersaturation. The size distribution and volume fraction of these pre-existing crystals determines the magnitude of the damping. SNGPlag predicts that melt composition and temperature also exert important controls. Higher temperatures and higher silica contents both reduce microlite crystallization. In comparison with the previous studies of decompression rate based on microlite crystallization experiments, SNGPlag generally predicts minimum decompression rates that are up to three-to-four times slower. The difference is likely because those studies applied single- or multi-step decompression experiments to simulate natural magma ascent, which may be better represented by continuous decompression pathways or series of continuous decompression intervals punctuated with pauses. Previous studies also fail to account for the effects of phenocrysts or antecrysts on microlite nucleation and growth.

Crystallization is one of the important unit operations for the separation and purification of solid products in the chemical, pharmaceutical, and pesticide industries, especially for realizing high-end, high-value solid products. The precise control of the solution crystallization process determines the polymorph, crystal shape, size, and size distribution of the crystal product, which is of great significance to improve product quality and production efficiency. In order to develop the crystallization process in a scientific method that is based on process parameters and data, process analysis technology (PAT) has become an important enabling platform. In this paper, we review the development of PAT in the field of crystallization in recent years. Based on the current research status of drug crystallization process control, the monitoring methods and control strategies of feedback control in the crystallization process were systematically summarized. The focus is on the application of model-free feedback control strategies based on the solution and solid information collected by various online monitoring equipment in product engineering, including improving particle size distribution, achieving polymorphic control, and improving purity. In this paper, the challenges of feedback control strategy in the crystallization process are also discussed, and the development trend of the feedback control strategy has been prospected.

Crystalline products with a narrow and uniform distribution of crystals by size (CSD), characterized by a desired average size, are necessary in many practices. Therefore, extensive, but mostly experimental, research is devoted to the problem of obtaining such CSDs. Alternatively, this manuscript presents a theoretical approach for calculating CSD resulting from crystallization in unstirred solutions. First, classical equations for the rates of diffusion-controlled and kinetically controlled growth of crystals are used to discuss the size-dependent growth of the nucleated crystals and the initial CSD (which arises from the non-simultaneous nucleation of crystals). Then, applying the law of conservation of matter, it is proved that the CSD continues to expand during the growth stage. Furthermore, it is substantiated that, due to their uneven spatial distribution, crystals of the same size can grow at different rates. This depends on whether the crystals are outside the diffusion fields of other crystals or are clustered together in “nests”. Moreover, by calculating the growth rates of crystals in “nests”, an explanation is given for the observation that closely spaced crystals are smaller in size than the separately growing crystals. Finally, the CSD established during the Ostwald ripening is discussed quantitatively, step-by-step.

Four types of crystal-rich lava flow were observed as the primary products of Satonda volcano (Nusa Tenggara Barat, Indonesia), with clinopyroxene and olivine crystals occurring as the key points for distinguishing each type. The gray-weakly porphyritic lava (GwP) shows a linear-steep crystal size distribution (CSD) pattern of small clinopyroxene phenocrysts and is typically olivine poor (< 1 vol%). The gray-porphyritic lava (GP) and gray-strongly porphyritic lava (GsP) display a kinked CSD pattern consisting of small and large clinopyroxene crystals; also, both types are similarly dominated by clinopyroxene and have rare olivine (< 2 vol%), but the maxima clinopyroxene size of GP lava is smaller than type GsP lava (3.5 and 6 mm, respectively). The black porphyritic lava (BP) also displays the kinked clinopyroxene CSD with a maximum size of 3 mm; however, it is typically rich in olivine (~ 20 vol%). Whole-rock XRF analysis reveals that GwP, GP, and GsP lavas are similarly classified as trachybasalts (49–51 wt.% SiO 2 ; 8–15 ppm Cr), whereas BP lava is classified as basalts (~ 48 wt.% SiO 2 ) with abundant Cr content (51–66 ppm). This means that the extrusion of trachybasalt and basalt form GwP-GP-GsP and BP lavas, respectively. Large clinopyroxenes yield higher P–T crystallization conditions than small clinopyroxenes, indicating that large clinopyroxene crystals represent the earlier crystallization stage and are primarily stored at the marginal part of the magma reservoir ash mush zone. Multiple recharge event plays an important role in disrupting the mush, where the higher recharge intensity allows a larger input of the large clinopyroxene populations (GP, GsP, and BP lavas) and vice versa (BP lava). The high Ba/Nb, Th/Yb, and Rb/Ta values, coupled with the low Nb and La/Yb values, suggest that all Satonda magma received significant input from slab components with a relatively low contribution of mantle melting. Finally, K/Ar dating on various lava types reveals the eruption age of 115–74 ka.

The rhyodacitic magma discharged during the 30–80 km3 DRE (dense rock equivalent) Late Bronze Age (LBA; also called ‘Minoan’) eruption of Santorini caldera is known from previous studies to have had a complex history of polybaric ascent and storage prior to eruption. We refine the timescales of these processes by modelling Mg–Fe diffusion profiles in orthopyroxene and clinopyroxene crystals. The data are integrated with previously published information on the LBA eruption (phase equilibria studies, melt inclusion volatile barometry, Mg-in-plagioclase diffusion chronometry), as well as new plagioclase crystal size distributions and the established pre-LBA history of the volcano, to reconstruct the events that led up to the assembly and discharge of the LBA magma chamber. Orthopyroxene, clinopyroxene and plagioclase crystals in the rhyodacite have compositionally distinct rims, overgrowing relict, probably source-derived, more magnesian (or calcic) cores, and record one or more crystallization (plag ≫ opx > cpx) events during the few centuries to years prior to eruption. The crystallization event(s) can be explained by the rapid transfer of rhyodacitic melt from a dioritic/gabbroic region of the subcaldera pluton (mostly in the 8–12 km depth range), followed by injection, cooling and mixing in a large melt lens at 4–6 km depth (the pre-eruptive magma chamber). Since crystals from all eruptive phases yield similar timescales, the melt transfer event(s), the last of which took place less than 2 years before the eruption, must have involved most of the magma that subsequently erupted. The data are consistent with a model in which prolonged generation, storage and segregation of silicic melts were followed by gravitational instability in the subcaldera pluton, causing the rapid interconnection and amalgamation of melt-rich domains. The melts then drained to the top of the pluton, at fluxes of up to 0.1–1 km3 year− 1, where steep vertical gradients of density and rheology probably caused them to inject laterally, forming a short-lived holding chamber prior to eruption. This interpretation is consistent with growing evidence that some large silicic magma chambers are transient features on geological timescales. A similar process preceded at least one earlier caldera-forming eruption on Santorini, suggesting that it may be a general feature of this rift-hosted magmatic system.

Crystallization of groundmass minerals may record the physicochemical conditions of magmatic processes upon eruption and is thus a topic of interdisciplinary research in the disciplines of mineralogy, petrology, and volcanology. Recent studies have reported that the groundmass crystals of some volcanic rocks exhibit a break in their crystal size distribution (CSD) slopes that range from a few micrometers to hundreds of nanometers. The crystals consisting of the finer parts of the break were defined as nanolites. In this study, we report the presence of nanometer-scale crystals down to 1 nm in the pyroclasts of the 2011 eruption of Shinmoedake, the Kirishima volcano group, based on field emission-scanning electron microscopy (FE-SEM) and transmission electron microscopy (TEM). We discovered a gap (hiatus) from ∼100 to ∼30 nm in the size distribution of pyroxene in a dense juvenile fragment of a vulcanian explosion. The pyroxene crystals ∼20-30 nm on a diameter were ferroaugite (C2/c), while those a few hundred nanometers in width had a composite structure consisting of the domains of orthopyroxene (Pbca), augite (C2/c), and sub-calcic augite (C2/c). In high-angle annular dark-field scanning TEM images of the same sample, bright spots ∼1-2 nm in diameter were recognized with a gap in size from ∼10-20 nm titanomagnetite (Fd,3m). They are presumed to have Fe-rich compositions, although their phases were too small to be determined. In addition, we found that crystals smaller than a few tens of nanometers for pyroxene and 100 nm for plagioclase did not exist or their number densities were too low for accurate determination. This indicates that there are practical minimum sizes of the crystals. These observations show that nucleation of the nanoscale crystals almost paused (froze) in the late stage of groundmass crystallization, possibly due to a decrease in undercooling, increase in interfacial free energy, and decrease in diffusivity in a dehydrated melt, whereas crystal growth was mostly continuous. In this paper, we introduce the novel term \"ultrananolite,\" to refer to crystals smaller than 30 nm in diameter, and redefine \"nanolite\" simply as those 30 nm to 1 µm in width, complementing the size interval of crystals in volcanic groundmass smaller than microlites (1-30 µm). In the transient nucleation process, the presence of subcritical size clusters is required. The observed ultrananolite-sized particles might partly include subcritical clusters. The difference in the slope of CSDs, presence of gaps in size distribution, and minimum crystal size among the eruption styles of the 2011 Shinmoedake eruption may be interpreted by considering the difference in magma residence time and fragmentation pressure in the shallow conduit, and possibly the rewelding process in the crater.

Plagioclase microlites in a magma nucleate and grow in response to melt supersaturation (Δ ϕ plag ). The resultant frozen plagioclase crystal size distribution (CSD) preserves the history of decompression pathways ( dP/dt ). SNGPlag is a numerical model that calculates the equilibrium composition of a decompressing magma and nucleates and grows plagioclase in response to an imposed Δ ϕ plag . Here, we test a new version of SNGPlag calibrated for use with basaltic andesite magmas and model dP/dt for the ca. 12.6 ka Curacautín eruption of Llaima volcano, Chile. Instantaneous nucleation ( N plag ) and growth ( G plag ) rates of plagioclase were computed using the experimental results of Shea and Hammer (J Volcanol Geotherm Res 260:127–145, 10.1016/j.jvolgeores.2013.04.018, 2013) and used for SNGPlag modeling of basaltic andesite composition. Maximum N plag of 6.1 × 10 5  cm h −1 is achieved at a Δ ϕ plag of 44% and the maximum G plag of 27.4 μm h −1 is achieved at a Δ ϕ plag of 29%. Our modeled log dP/dt avg range from 2.69 ± 0.09 to 6.89 ± 0.96 MPa h −1 (1σ) with an average duration of decompression from 0.87 ± 0.25 to 16.13 ± 0.29 h assuming a starting pressure P i of 110–150 MPa. These rates are similar to those derived from mafic decompression experiments for other explosive eruptions. Using assumptions for lithostatic pressure gradients ( dP/dz ), we calculate ascent rates of < 1–6 m s −1 . We conducted a second set of Monte Carlo simulations using P i of 15–30 MPa to investigate the influence of shallower decompression, resulting in log dP/dt avg from 2.86 ± 0.49 to 6.00 ± 0.86 MPa h −1 . The dP/dt modeled here is two orders of magnitude lower than those calculated by Valdivia et al. (Bull Volcanol, 10.1007/s00445-021-01514-8, 2022) for the same eruption using a bubble number density meter, and suggests homogeneous nucleation raises dP/dt by orders of magnitude in the shallow conduit. Our modeling further supports the rapid-ascent hypothesis for driving highly explosive mafic eruptions.

Orthopyroxenite cumulates throughout the Critical Zone of the Bushveld Complex commonly contain prominent euhedral crystals of bottle-green augite, typically around 1 cm in size and surrounded by “haloes” of nearly pure plagioclase. On close examination, the augite grains can be seen to be oikocrysts, containing extensively resorbed chadacrysts of orthopyroxene, indicating an effective peritectic reaction relationship between the two pyroxenes. A detailed textural study of one such layer from the UG3 Unit in the Eastern Bushveld reveals some distinctive grain-scale features, including the presence of extensively 3D-interconnected chains of thousands of cumulus chromite grains that surround the orthopyroxene grains and extend through the augite oikocrysts. The high degree of interconnectivity is remarkable in view of the relatively low (5 vol.%) modal proportion of chromite in the sample. Other noteworthy features include zoning of the oikocrysts towards higher incompatible element contents in the rims and the presence of the plagioclase haloes around the augite oikocrysts. These haloes are essentially narrow zones devoid of orthopyroxene inclusions developed within large plagioclase oikocrysts that overgrow all the other phases. We propose a mechanism whereby the plagioclase oikocrysts grow early in communication with the main magma body within an initial crystal mush of orthopyroxene and chain-textured chromite. The clinopyroxene oikocrysts grew in the remaining pore space in such a way that dissolution of orthopyroxene occurred within a narrow few-mm wide chemical boundary layer ahead of the advancing oikocryst margin. The relative rates of crystallisation and dissolution were controlled by limited chemical diffusion through the boundary layer such that orthopyroxene grains more than a few grain diameters away showed no reaction at all. The plagioclase haloes developed as a result of continuing growth of the plagioclase oikocrysts to overtake the growing pyroxene oikocrysts, locking in the orthopyroxene-depleted boundary layer, and preserving euhedral cumulus morphologies away from the pyroxene oikocrysts. This texture represents a circumstance whereby oikocrysts in the same rock develop at different overlapping stages: plagioclase oikocrysts forming early in diffusive connection with the magma column, and clinopyroxene forming peritectic poikilitic textures within residual liquid pockets chemically isolated from the overlying magma body.