Boundary Melting Research Articles

Effect of Nonlinear Thermal Radiation on MHD Boundary Layer Flow and Melting Heat Transfer of Micro-Polar Fluid over a Stretching Surface with Fluid Particles Suspension

A comprehensive numerical study is conducted to investigate effect of nonlinear thermal radiation on MHD boundary layer flow and melting heat transfer of micro polar fluid over a stretching surface with fluid particles suspension. Using suitable transformations, the governing equations of the problem are transformed in to a set of coupled nonlinear ordinary differential equations and then they are solved numerically using the Runge–Kutta–Fehlberg-45 method with the help of shooting technique. Authentication of the current method is proved by having compared with established results with limiting solution. The impact of the various stimulating parameters on the flow and heat transfer is analyzed and deliberated through plotted graphs in detail. We found that the velocity, angular velocity and temperature fields increase with an increase in the melting process of the stretching sheet. Also it is visualize that the shear stress factor is lower for micro polar fluids as compared to Newtonian fluids, which may be beneficial in flow and heat control of polymeric processing.

Invariant electrical resistivity of Co along the melting boundary

The Earth's core is comprised mainly of Fe and Ni with some light alloying element(s) and the electrical resistivity behavior of these elements is an important property for characterizing geodynamo action, determining energy sources, and for understanding core thermal evolution. Knowledge of the electrical resistivity of solid and liquid transition metals with electronic structures similar to Fe reinforces our understanding of core properties. The electrical resistivity of high purity Co has been measured at pressures up to 5 GPa in a large volume press and at temperatures up to 100 K above the melting temperature. The results demonstrate that resistivity of Co is invariant along the melting boundary. This is interpreted in terms of the antagonistic effects of P-induced reduction in the amplitude of lattice vibrations tending to decrease resistivity, and the P-induced shift of the Fermi level closer to the d-resonance which tends to increase resistivity. We calculated the electronic thermal conductivity of Co using the Wiedemann–Franz law and show that it increases with pressure both in the solid and liquid states and decreases with temperature in the solid and increases in the liquid state. The pressure dependences of electrical resistivity and electronic thermal conductivity calculated from equations involving bulk modulus and the Gruneisen parameter are in reasonable agreement with values measured in this study. The constant resistivity of Co along its melting boundary found in our study portends similar behavior for its electronic structural analog, Fe. This prediction suggests that the electronic thermal conductivity of Fe at Earth's inner core boundary could be similar to its 1 atm value at the melting point. Using this value of thermal conductivity for the inner core boundary would admit thermal convection as an energy source for the geodynamo prior to the birth of the inner core.

Diffusive fractionation of volatiles and their isotopes during bubble growth in magmas

Bubbles grow in decompressing magmas by simple expansion and by diffusive supply of volatiles to the bubble/melt interface. The latter phenomenon is of significant geochemical interest because diffusion can fractionate elements and isotopes (or isotopologues) of dissolved components. This raises the possibility that the character of volatile components in bubbles may not reflect that of volatiles dissolved in the host melt over the lifetime of a bubble—even in the absence of equilibrium vapor/melt isotopic fractionation. Recent experiments have confirmed the existence of an isotope mass effect on diffusion of the volatile element Cl in silicate melt [Fortin et al. (Isotopic fractionation of chlorine during chemical diffusion in a dacitic melt and its implications for isotope behavior during bubble growth (abstract), 2016 Fall AGU Meeting, 2016)], so there is a clear need to understand the efficacy of diffusive fractionation during bubble growth. In this study, numerical models of diffusion and mass redistribution during bubble growth were implemented for both “passive” volatiles—those whose concentrations are generally well below saturation levels—and “active” volatiles such as CO2 and H2O, whose elevated concentrations and limited solubilities are the cause of bubble nucleation and growth. Both diffusive and convective bubble-growth scenarios were explored. The magnitude of the isotope mass effect on passive volatiles partitioned into bubbles growing at a constant rate R in a static system depends upon R/DL, Kd and DH/DL (Kd = bubble/melt partition coefficient; DH/DL = diffusivity ratio of the heavy and light isotopes). During convective bubble growth, the presence of a discrete (physical) melt boundary layer against the growing bubble (of width xBL) simplifies outcomes because it leads to the quick onset of steady-state fractionation during growth, the magnitude of which depends mainly upon R∙xBL/DL and DH/DL (bubble/melt fractionation is maximized at R∙xBL/DL ≈0.1). Constant R is unrealistic for most real systems, so other scenarios were explored by including the solubility and EOS of an “active” volatile (e.g., CO2) in the numerical simulations. For plausible decompression paths, R increases exponentially with time—leading, potentially, to larger isotopic fractionation of species partitioned into the growing bubble. For volatile species whose isotope mass effects on diffusion have been measured (Cl, Li), predicted isotope fractionation in the exsolved vapor can be as large as −4‰ for Cl and −25‰ for Li.

Constant electrical resistivity of Ni along the melting boundary up to 9 GPa

AbstractCharacterization of transport properties of liquid Ni at high pressures has important geophysical implications for terrestrial planetary interiors, because Ni is a close electronic analogue of Fe and it is also integral to Earth's core. We report measurements of the electrical resistivity of solid and liquid Ni at pressures 3–9 GPa using a 3000 t multianvil large volume press. A four‐wire method, in conjunction with a rapid acquisition meter and polarity switch, was used to overcome experimental challenges such as melt containment and maintaining sample geometry and to mitigate the extreme reactivity/solubility of liquid Ni with most thermocouple and electrode materials. Thermal conductivity is calculated using the Wiedemann‐Franz law. Electrical resistivity of solid Ni exhibits the expected P dependence and is consistent with earlier experimental values. Within experimental uncertainties, our results indicate that resistivity of liquid Ni remains invariant along the P‐dependent melting boundary, which is in disagreement with earlier prediction for liquid transition metals. The potential reasons for such behavior are examined qualitatively through the impact of P‐independent local short‐range ordering on electron mean free path and the possibility of constant Fermi surface at the onset of Ni melting. Correlation among metals obeying the Kadowaki‐Woods ratio and the group of late transition metals with unfilled d‐electron band displaying anomalously shallow melting curves suggests that on the melting boundary, Fe may exhibit the same resistivity behavior as Ni. This could have important implications for the heat flow in the Earth's core.

Electrical resistivity of solid and liquid Cu up to 5 GPa: Decrease along the melting boundary

The electrical resistivity of high purity Cu has been investigated by both experiments and first principle calculations at pressures up to 5 GPa and at temperatures in the liquid phase up to 1730 K. The resistivity decreases with P and increases with T and our data are in very good agreement in relation to 1 atm data. Our melting temperature data agree with other experimental studies. We show that resistivity of Cu decreases along the P,T-dependent melting boundary in disagreement with prediction of resistivity invariance along the melting boundary. These findings are interpreted in terms of the competing effects of P and T on the electronic structure of liquid Cu. The electronic thermal conductivity is calculated from resistivity data using the Wiedemann-Franz law and is shown to increase with P in both the solid and liquid states but upon T increase, it decreases in the solid and increases in the liquid state.

Constant electrical resistivity of Zn along the melting boundary up to 5 GPa

ABSTRACTWe measured the electrical resistivity of high purity Zn along the melting boundary, up to 5 GPa in a large volume press. The electrical resistivity remained constant on the melting boundary, as predicted in a thermodynamics-based model for simple metals. The effects of pressure and temperature on the electrical resistivity of the solid and liquid states are interpreted in terms of their antagonistic effects on the electronic structure of Zn. Within the error of measurements, our melting temperature data agree well with those of the previous studies. The electronic thermal conductivity was calculated from resistivity data using the Wiedemann–Franz law and shows a decrease with temperature in the solid state and an increase in the liquid state, with a large decrease on melting. Comparison of calculated electronic and measured total thermal conductivities indicates that the electronic component dominates over the phonon component in Zn.

Heat & mass transfer and interface temperature during simulated melt-concrete interaction with composition variation in ARTEMIS 2D experiment

In a severe accident involving a water-cooled nuclear reactor, the core containing a mixture of oxides (U02 and ZrO2) heats up under the influence of decay heat. Within several hours from the start of the accident, core melting occurs and liquid materials (named corium) flow into the lower head and, ultimately, may relocate in the reactor pit. Thus, interaction between Molten Corium and Concrete (MCCI) occurs. Since containment integrity is a key objective in severe accident management, knowledge of the concrete ablation rate is required. Ablation rate and shape of concrete cavity depends on heat flux distribution. During MCCI concrete is melting between 1200°C and 1800°C and refractory solid species from the corium (UO2, ZrO2) may precipitate at the concrete interface due to the elevated liquidus temperature of the corium (Liquidus temperature is typically between 2200°C and 2500°C). Several complex phenomena (solidification, gas release, concrete entrainment) at the melt-concrete interface influence the interface temperature, and consequently the evolution of the heat flux distribution at the melt boundaries. In this framework, ARTEMIS 2D simulation tests were performed at CEA Grenoble (France) to investigate the non-eutectic material on the 2D transient melt-concrete interaction phenomena, focusing on the determination of the heat flux distribution along the corium cavity wall for non-eutectic mixtures. The present work contributes to a determination of the controlling phenomenology at the interface for both hydraulic and chemical aspects, during transient as well as in steady state. A model has been developed allowing predictions of corium-concrete interface temperature and heat & mass transfer evolutions during the ablation process in ARTEMIS 2D. This model proposes a single and consistent approach for various reactor situations involving In-Vessel-Retention, Ceramic Ablation and Corium-Concrete Interaction.

Phase Field Crystal Modeling of Coherent Interfaces in Lithium Batteries

The aim is to study the role of material crystallography in the formation of coherent interfaces in lithium ferrous phosphate (LFP) electrodes. In a typical LFP electrode, lithiated crystals with different orientations nucleate heterogeneously and little is known about how they interact to form coherent interfaces. The current work provides insights on how lithiated crystals interact, and the effects of coherency stresses at interface and grain boundaries. A key limitation of the battery performance is the structural instability of the electrodes with continuous usage, resulting in its failure [1]. In a battery cycle the electrode microstructures typically operate in a two-phase window that comprises of a moving coherent interface. Theoretical studies [2-4] indicate that a moving coherent interface causes anisotropic expansion of electrode [2], and affects Li-ion kinetics [4]. These factors affect battery performance, and it is therefore important to explore how interfaces form. In recent years, phase field models have been developed to describe microstructures in electrodes, and use Li-ion concentration as the order parameter [3-6]. While these models reveal insights on nucleation barrier [4] and stress generation at the coherent interface [6], the anisotropic properties arising from material crystallography is not captured. This limits understanding on the role of coherent interfaces on in-situ battery operation. In the present study, we apply a phase field crystal (PFC) model to investigate the formation of coherent interfaces in LFP electrodes [7,8]. PFC models offer the advantage of describing crystal growth on atomic scales, while solving diffusive time equations [7]. This modeling method has been applied to describe grain boundary melting [9], graphene defect structures [8], and has been well established to solve for a range of crystal symmetries. Here, we define a two-dimensional spatial density field, ψ, of a group of atoms to represent the orthorhombic (rectangular in 2D) symmetry of LFP crystals. A challenge here is to model ψ (order parameter) as a function of Li-ion concentration to differentiate the lithiated and unlithiated phases of the electrode. The free energy of the system is then described as a function of ψ, and is equal to the sum of bulk and excess energy terms [8]. The excess energy terms incorporate the two-point and the three-point interactions, which set the lattice spacings (a = 6.008Å, c = 10.334Å), and the lattice symmetry [10]. Finally, we control the evolution of the density field by a generalized equation of motion for conserved fields [8]. The coherency stresses and diffusion barriers at interfaces are captured by the PFC simulation. The results provide insights and strategies for doping electrode materials so as to reduce coherency stresses in electrodes.

Grain growth during selective laser melting of a Co–Cr–Mo alloy

Modes of solidification during selective laser melting (SLM) of metallic alloys, including Co–Cr–Mo alloy, are still not fully understood. This understanding is important in SLM to achieve acceptable properties and part reliability. Using a typical SLM condition and Co–Cr–Mo alloys, microstructures of tracks were characterized in this study. As is commonly observed, solidification starts from epitaxial growth in the boundary of melt track. Cells were found to grow immediately from the melt boundary, without forming a planar zone. This is explained by the growth velocity being sufficiently high that planar growth condition is not favorable. Epitaxial growth has been found to have two possible crystallographic orientations of : either a continuation of the same orientation as in previous track or a change of 90° to another orientation. The selection is in response to scan direction-dependent heat flux direction. The crystal growth direction in relation to heat flux direction also explains that a grain (a group of cells) after epitaxial growth could either stop or continue to the track surface. No equiaxed grains were observed, and this can be explained by the continuation of cellular growth in the whole track.

Features of bicrystal growth during the directional crystallization of metal melts

The factors responsible for the formation of different configurations of boundaries between adjacent crystallites during their growth from melt by Bridgman and Czochralski methods have been considered by an of example Fe–20 wt % Ga alloy and Ni bicrystals. It is found that the configuration of intercrystallite boundary is related to the features of crystallite growth, caused by the strained state of intercrystallite and interphase (crystal–melt) boundaries, the difference in the linear thermal expansion coefficients of the crystallite boundaries and bulk, and the shape (geometry) of the bicrystal cross section. It is suggested that the strained state of boundaries and the formation of substructure in crystallites during directional crystallization from metal melt are significantly affected by their deformation under the melt weight.

Thermal conductivity and Seebeck coefficient of Fe and Fe-Si alloys: Implications for variable Lorenz number

The Wiedemann-Franz Law is often used to calculate the thermal conductivity of Fe from experimental measurements of the electrical conductivity. It is shown by measurements of the Seebeck coefficient (S) of solid and liquid Fe at pressures up to 6GPa and temperatures up to 2100K that the Sommerfeld value (L0=2.445×10−8WΩK−2) of the Lorenz number (L) represents more than 99% of the electronic component of the thermal conductivity of Fe. Using experimental values of electrical resistivity and thermal conductivity of Fe, L/L0 is shown to vary by as much as 1.22 in the solid state and 1.32 in the liquid state, signifying a non-negligible phonon component. An expression for the pressure dependence of L at the melting boundary up to 5GPa is derived for electron-phonon scattering. For Fe-Si alloys, L/L0 varies more than for pure Fe and generally increases with increasing Si and state of disorder. New values for the conductive heat flow in a pure Fe core of Mercury are presented.

Effect of PWHT on the Hardness and fractured microstructure of IS-103Cr1 welded joint

During the welding process change of chemical and physical properties takes place due to uneven heating and cooling for improving regaining their properties heat treatment processes is one of the best methods. In the similar or dissimilar welded joints, at the welded portion it can be exist in more than one crystalline form and the carbon atom is only 1/30th size of the iron atom.In this weldment phase changes occurs in solid state due to heating or cooling (allotropic transformation).At welded portion liquid metals cools and solidification temperature approaches initial crystals are formed. These are grown in to large solid grains and each grain acts as different crystallization with the atom. A random grain growth again takes place within the melt boundary, results in a low strength. Within HAZ the grain become coarse only possible to PWHT processes.The weldments are underlying their properties so to achieve the better results that are possible through heat treatment processes.

Investigation of α-phase and liquid uranium by the method of quantum molecular dynamics

The thermodynamic properties of α-phase and liquid uranium have been investigated by the method of quantum molecular dynamics. The isotherms and equilibrium properties (pressure, temperature, and internal energy) along isochores and isotherms have been calculated for densities of 16.5–41.1 g/cm3 and temperatures up to 60000 K. The dependence of the thermal pressure on temperature and internal energy is analyzed. The melting boundary of α-phase uranium is estimated. The shock adiabat is calculated for pressures up to 1.5 TPa based on the equation of state derived here. The results obtained are in good agreement with the published experimental data and the results of calculations according to different theoretical models.

Sliding of temperate basal ice on a rough, hard bed: creep mechanisms, pressure melting, and implications for ice streaming

Abstract. Basal ice motion is crucial to ice dynamics of ice sheets. The classic Weertman model for basal sliding over bedrock obstacles proposes that sliding velocity is controlled by pressure melting and/or ductile flow, whichever is the fastest; it further assumes that pressure melting is limited by heat flow through the obstacle and ductile flow is controlled by standard power-law creep. These last two assumptions, however, are not applicable if a substantial basal layer of temperate (T ∼ Tmelt) ice is present. In that case, frictional melting can produce excess basal meltwater and efficient water flow, leading to near-thermal equilibrium. High-temperature ice creep experiments have shown a sharp weakening of a factor 5–10 close to Tmelt, suggesting standard power-law creep does not operate due to a switch to melt-assisted creep with a possible component of grain boundary melting. Pressure melting is controlled by meltwater production, heat advection by flowing meltwater to the next obstacle and heat conduction through ice/rock over half the obstacle height. No heat flow through the obstacle is required. Ice streaming over a rough, hard bed, as possibly in the Northeast Greenland Ice Stream, may be explained by enhanced basal motion in a thick temperate ice layer.

Electro-thermal-based finite element simulation and experimental validation of material removal in static gap single-spark die-sinking electro-discharge machining process

Existing single spark models are subjected to too simplistic assumptions such as uniform or point heat source, constant plasma radius, invariable materials properties and constant surface temperature during discharge making them far from reality. In this study, more realistic assumptions including Gaussian type distribution of spark heat flux, temperature dependent materials properties, latent heat of melting and expanding plasma channel with pulse current and time have been made to establish a comprehensive modeling platform. The ABAQUS FEM software has been used to simulate the mechanism of crater formation due to a single discharge. The non-uniform thermal flux was programmed through the DFLUX subroutine. The simulation results show that the temperature of work piece decreases as the discharge time increases while the volume of melted and evaporated material increases. A specially designed single spark experimental set-up was developed in laboratory to carry out a few single spark tests for verification purposes. The obtained craters morphologies were examined by optical microscopy and scanning profilometer. It has been shown that the present approach outperforms other previously developed thermal models with respect to cavity outline and size possessing the maximum confirmation errors of 18.1% and 14.1% in predicting crater radius and depth, respectively. Parametric analysis reveals that the melting boundary moves onward by increasing discharge current, whereas it moves back prolonging discharge time. Finally, a closer proximity to experimental material removal rates than those predicted by analytical approach has been recognized which confirms its more precise generalization capabilities towards the real state EDM process.

The role of subgrain boundaries in partial melting

Evidence for partial melting along subgrain boundaries in quartz and plagioclase is documented for rocks from the Lost Creek Gneiss of the Llano Uplift, central Texas, the Wet Mountains of central Colorado, and the Albany-Fraser Orogen, southwestern Australia. Domains of quartz or plagioclase crystals along subgrain boundaries are preferentially involved in partial melting over unstrained domains of these minerals. Material along subgrain boundaries in quartz and plagioclase has the same morphology as melt pseudomorphs present along grain boundaries and is commonly laterally continuous with this former grain boundary melt, indicating the material along subgrain boundaries can also be categorized as a melt pseudomorph. Subgrain boundaries consist of arrays of dislocations within a crystal lattice, and unlike fractures would not act as conduits for melt migration. Instead, the presence of former melt along subgrain boundaries requires that partial melting occurred in these locations because it is kinetically more favorable for melting reactions to occur there. Preferential melting in high strain locations may be attributed to strain energy, which provides a minor energetic contribution to the reaction and leads to preferential melting in locations with weakened bonds, and/or the presence of small quantities of water associated with dislocations, which may enhance diffusion rates or locally lower the temperature needed for partial melting.

Microstructure and mechanical properties of Al-Fe-V-Si aluminum alloy produced by electron beam melting

Atomized, pre-alloyed Al-8.5Fe-1.3V-1.7Si (wt%) powder was used to fabricate solid components by electron beam melting (EBM). The residual porosity, chemical composition, microstructure and mechanical properties have been investigated. Results show that the relative density of as-built alloy under the optimized processing parameters was 98.2%. Compare to the initial alloy powder, the EBM parts demonstrated a restricted aluminum loss (~1wt%) and a quite low oxygen pickup. The microstructure of the deposits was non-uniform. The fusion zone and heat affected zone exhibited a large number of fine spherical Al12(Fe,V)3Si particles (30–110nm) distributed uniformly in the α-Al matrix. Some coarser Fe- and V-riched rectangle-like AlmFe phase (m=4.0–4.4) with 100–400nm in size was precipitated in the melting boundary zone. The microhardness of the EBM samples was 153 HV in average. The average ultimate tensile strength (UTS) reached 438MPa with the elongation of 12%. A ductile fracture mode of the tensile specimens was also revealed.

Shooting at a moving target: phase equilibria modelling of high‐temperature metamorphism

AbstractThermodynamic modelling and calculation of P–T pseudosections are commonly employed for quantifying the P–T evolution of metamorphic rocks. A key assumption involved in interpreting a P–T pseudosection is that the bulk‐rock composition used is representative of the effective bulk composition (EBC) from which apparently equilibrated mineral assemblages grew. Choosing an EBC can be difficult in cases where the rock has evolved significantly throughout the P–T history and has become domainal for whatever reason (e.g. loss of fluid and/or melt), particularly at suprasolidus conditions. During partial melting, melt migration may not only change the bulk composition by melt loss but also may generate local variations due to the variable consumption/loss of melt from domain to domain to create volumes of rock that were once internally equilibrated in the presence of a grain boundary melt, but which departed from equilibrium as inter‐granular mobility was slowed by local reductions in melt volume. As well as careful consideration of an EBC, the results of thermodynamic modelling are highly dependent on the specific thermodynamic data set and solution models used, as updates to these data sets may lead to substantially different calculated phase equilibria. This contribution addresses: (1) how consideration of evolving EBCs at multiple scales of observation can be used to resolve the history of complex high‐grade rocks, and (2) how use of different thermodynamic data sets and a–x models (i.e. thermocalc ds5.5 v. ds6) can result in different interpretations of metamorphic evolution. This study investigates the evolution of a mineralogically heterogeneous and texturally complex hand sample of granulite from the Gruf Complex (Central Alps). At the hand‐specimen scale, an EBC can be identified and used to constrain the P–T conditions at which the ‘whole rock’ was last in mutual equilibrium, in the presence of intergranular melt that has subsequently been lost or consumed. Smaller macrodomains (~cm scale) and microdomains (~mm scale) can be identified that represent subsequent evolution during and after melt channelization and loss, and P–T pseudosections can be calculated for the compositions of these domains. Using this approach reveals that the sample experienced a clockwise P–T path marked by near‐isothermal decompression following attainment of peak UHT conditions (~960 °C, 8.5 kbar). The approach enables construction of a P–T history of a rock for which P–T pseudosections are otherwise difficult to interpret. Thermodynamic modelling using ds6 yields similar results to those stated above, but suggests: (1) near‐isothermal decompression occurred over a wider pressure range (~0.5 kbar v. 1.5 kbar), and (2) that not all microdomains record this part of the P–T evolution.

Torsional vibration measurement of the viscosity of a metallic melt

The liquid Co91B9 alloy is used as an example to study the influence of boundary conditions at the upper melt boundary on the results of viscosity measurements using torsional vibrations. Specific features related to film effects and wetting phenomena are shown to appear in the temperature dependence of logarithmic decrement. To exclude the influence of these effects and phenomena, viscosity measurements should be performed under the experimental conditions where the melt to be studied is in closed volume and the internal crucible walls are fully wetted. The temperature dependence of the kinematic viscosity of the Co91B9 melt that is obtained under such experimental conditions has a monotonic character.

On progress and rate of the peritectic reaction Fo + SiO2 → En in natural andesitic arc magmas

Using a high resolution ion microprobe with SCAPS imaging, the peritectic reaction of forsterite+silica to enstatite was studied down to submicron level in a natural andesitic tephra from the Central Plateau of North Island, New Zealand. The fayalitic component of natural olivines is stable in high-silica melts, and therefore the reaction is in fact a two-step progress: 1. Dissolution of Mg-rich olivine, rate-limited by Fe–Mg interdiffusion at the crystal rim, results in enrichment of Fe in the crystal rim and of Mg in the c. 1μm wide melt boundary layer around the crystal. 2. Magnesian pyroxenes preferentially but not exclusively nucleate in the melt boundary layer and grow; as soon as these microlites touch the rim of the dissolving olivine, they shield the crystals from the silica-rich melt, thereby preventing further olivine dissolution. At this point, Fe–Mg interdiffusion begins to destroy the Fe-enrichment of the olivine rim. The reaction is completed when the dissolving olivine crystal is completely mantled by magnesian pyroxene microlites. Thick pyroxene mantles are likely the result of pyroxene overgrowth rather than due to peritectic transformation. The morphology of the olivine rim preserves information about the reaction history of the grain. Modeling of Fe–Mg interdiffusion in the olivine rim following its shielding from the melt by pyroxene overgrowth may yield the rates of olivine dissolution and the rates of pyroxene growth if temperature is known. For the tephra we have studied, microlite thermometry yields a temperature of 1137 (±41)°C, indicating an olivine dissolution rate of 3–6×10−11ms−1 and an initially volumetric pyroxene growth rate of 2.2–5.6×10−21m3s−1. This points to timescales between olivine crystal uptake into the SiO2-rich melt and explosive eruption at the surface of a few hours to at most a day.