Release the crackin': The in�uence of brittle behavior on gas retention in crystal-rich magma

13 Crystal-rich silicic lavas commonly erupt from hazardous lava dome-forming volcanoes, 14 characterized by both effusive and explosive eruptions. Magma explosivity is inherently dependent 15 on its ability to store pressurized gas, which can be released through permeable pathways like 16 fractures or connected bubbles, yet the role crystals play in regulating gas escape is poorly constrained 17 in crystal-rich systems. We explored the gas storage capacity and outgassing efficiency of crystal-18 rich magmas through experimental vesiculation of hydrous dacite samples containing crystal volume 19 fractions ( 𝜙 𝑥 ) between 0.5 and 0.8. The maximum unconnected gas volume (isolated porosity) 20 decreases exponentially with increasing crystallinity. We quantify the relative outgassing efficiency 21 as a function of 𝜙 𝑥 using changes in isolated melt porosity during open-system degassing 22 (outgassing). Mean isolated porosity, for 𝜙 𝑥 = 0.5, increases from ~0.33 at the start of outgassing to 23 ~0.67 by the end, doubling its trapped bubbles. For 𝜙 𝑥 = 0.7, isolated porosity increases from ~0.1 to 24 ~0.2, implying gas retention and outgassing efficiency are strongly dependent on crystallinity. 25 Outgassing occurs rapidly via fracturing at porosities < 0.1 when


Introduction
Magmas can erupt effusively as lava flows and domes or explosively to produce tephra, depending on many factors, of which perhaps the most important is their ability to release gas (outgassing) during ascent in volcanic conduits (e.g., Eichelberger et al. 1986;Jaupart and Allègre 1991;Woods and Koyaguchi 1994).The intensity of volcanic eruptions depends on the amount of overpressured gas retained in the magma as it approaches the surface (e.g., Massol and Jaupart 1999;Sparks 2003;Melnik et al. 2005).The gas phase forms by exsolution and bubble growth (degassing) through diffusion of volatile components such as H2O, CO2, and sulfur species (e.g., Sparks 1978;Gerlach 1986;Gardner et al. 1999;Lensky et al. 2001;Newman and Lowenstern 2002).Degassing, or vesiculation, of silicate melt occurs upon decompression, crystallization, and/or temperature increase (e.g., Sisson and Bacon 1999;Lensky et al. 2004;Gonnermann and Manga 2007;Lavallée et al. 2015), often at depths less than a few kilometers (Wilson and Head 1981).During vesiculation, outgassing occurs when at least one cluster of interconnected pore space forms a permeable pathway that allows gas to exit the magma (Blower 2001;Walsh and Saar 2008).This occurs when the gas volume fraction or porosity () exceeds a critical value or bubble percolation threshold (  ) (Sahimi 1994).Porosity can be open/connected (effective porosity for permeability) or closed/isolated (ineffective porosity for permeability).
Once magma reaches a critical permeability (kc), or permeability threshold, sufficiently rapid gas escape prevents continued gas-driven expansion of the magma (Cashman and Sparks 2013).
Consequently, the porosity at kc characterizes one end-member of permeability development.
Most published permeability-porosity data from natural samples, regardless of eruption style, fall within a similar range of k = 10 -15 -10 -10 m 2 yet exhibit a wide range of porosities (Fig. 1; supplementary table and references in Online Resources 1 and 2).Prior to fragmentation, connected porosity in magma is unlikely to increase much with total porosity because increased connectivity intuitively reduces explosive potential.Therefore, the increased explosive potential of magma at high porosity reflected in Fig. 1 must be heavily attributed to increased gas retention in the form of isolated bubbles.Herein, we refer to the explosive potential of magma as a function of overpressure and gas retention (and loss), where gas retention is defined as the amount of trapped bubbles (isolated porosity) in a magma and thus exclude cases of Strombolian behavior where bubbles migrate throughout low to moderate viscosity magmas (e.g., Blackburn et al. 1976; Jaupart and Vergniolle 1988;Parfitt 2004).Rapid vesiculation (and expansion) of bubbles that remain isolated and coupled to the melt can increase buoyancy-controlled ascent rate (Gardner 2009;Edmonds and Wallace 2017).
Such changes in ascent rate have been suggested to be the dominant control on explosive-effusive transitions (Nguyen et al. 2014;Cassidy et al. 2018) because decompression and ascent rate directly affect gas overpressure (Parfitt et al. 1995;Namiki and Manga 2006;Okumura et al. 2019).Yet the influence of crystallinity (  ) on magma viscosity may play a large role in controlling eruption style (Colombier et al. 2022), and likely the mechanisms controlling gas retention (and loss).
The role crystals play in regulating degassing and outgassing is largely unexplored experimentally at high volume fractions (  > 0.5).The percolation threshold has been estimated theoretically (Sahimi 1994) and numerically (Garboczi et al. 1995) as low as ~0.3.Percolation thresholds based on natural products (e.g., Eichelberger et al. 1986;Klug and Cashman 1996;Saar and Manga 1999;Mueller et al. 2005;Nguyen et al. 2014;Gonnermann et al. 2017;Moitra and Houghton 2021;Colombier et al. 2022), experimental samples (Takeuchi et al. 2009), and analog materials (Namiki and Manga 2008) can vary up to ~0.7, yet crystallinity can have a strong influence on the percolation threshold (Blower 2001;Melnik and Sparks 2002).The presence of crystals tends to lower   during vesiculation (Parmigiani et al. 2016;Lindoo et al. 2017;deGraffenried et al. 2019;Colombier et al. 2020;Graham et al. 2023), because crystals impede isolated spherical bubble growth and promote distortion and connection or occupy space unavailable to bubbles (Walsh and Saar 2008).Experimental studies of vesiculation in crystal-bearing samples (  ≤ 0.4) have shown that bubble chain networks produce measurable permeability at low   ~0.05-0.2(Parmigiani et al. 2016;Colombier et al. 2020).Numerical approaches suggest that outgassing in moderate to crystal-rich systems (  = 0.4-0.7)occurs via "channeling" (Parmigiani et al. 2017;Degruyter et al. 2019;Collombet et al. 2021) where crystals limit bubble expansion and gas is concentrated in pathways between rigid particles (Oppenheimer et al. 2015), and characteristics of the pore network, such as bubble size and shape distribution, become less relevant in influencing permeability at high crystal fraction (Röding et al. 2020).Improvements in our understanding of the controls on outgassing in crystal-rich magmas are crucial to refine numerical models of gas escape (Colombier et al. 2020).
Experimental magma degassing studies have mainly tested crystal fractions ≤ 0.5 (e.g., Bai et al. 2011;Okumura et al. 2012Okumura et al. , 2019;;Lindoo et al. 2017;deGraffenried et al. 2019;Colombier et al. 2020;Cáceres et al. 2022;Graham et al. 2023;Kobayashi et al. 2023).This contribution describes an experimental study of vesiculation and outgassing of a hydrous dacitic melt containing crystal fractions between 0.5 and 0.8 at temperatures between 700 and 850 °C.Our experimental results provide much needed data exploring degassing and outgassing as suspensions approach and exceed the maximum packing fraction.Our experiments preserve the respective permeability thresholds for each crystal fraction, allowing us to characterize the outgassing mechanisms that triggered rapid outgassing and release of overpressure.

Experimental vesiculation
We simulated decompression-driven vesiculation of hydrous glass samples above their glass transition temperature (Tg = 483 ±3 °C) following the approach of Pistone et al. (2017).The starting glass structure reflects the high-pressure configuration imposed during rapid cooling (60 °C/min) from 1200 °C to Tg at 68 MPa.Dacite glasses containing 4.2 wt.% dissolved H2O and different aliquots of quartz particles (  = 0, 0.5, 0.6, 0.7 and 0.8, named F0, F50, F60, F70 and F80 respectively) were synthesized in a hot isostatic press (described in Pistone et al. 2016).Quartz particles display an average size of 68 m with an average aspect ratio of 1:3 allowing   to exceed the maximum random packing fraction of ~0.6 for equant particles (Marsh 1981) Cylindrical cores of ~5 mm diameter and ~10 mm length (Fig. 2) were heated in a Theta Industries Rheotronic III 1000C parallel-plate viscometer at room pressure (σ2 = σ3 ~0.1 MPa) with a load of 1500 g, equivalent to a uniaxial stress of ~0.6 MPa (σ1).The experimental setup is similar to those of other vesiculation and magma rheology studies (e.g., Heap et al. 2015a;Pistone et al. 2017;Cáceres et al. 2022).During vesiculation, connected pore networks are allowed to intersect the sample edge (outgassing pathways), not unlike torsion experiments (e.g., Caricchi et al. 2011;Shields et al. 2014;Kushnir et al. 2017).To evaluate the interaction between vesiculating melt pockets and the crystal framework required that samples be unconfined.Interference from a casing, for example, would likely cause compaction along the sample periphery or introduce squeeze-ups (Burgisser and Gardner 2004), altering porosity and gas escape.The imposed constraints on two sides approaches the geometry of a dike or sill, rather than the more commonly implemented cylindrical pipe.Dikes and pipes represent end-members with actual conduit geometries varying between the two (Mitchell 2005;Costa et al. 2007).
Samples were heated at 20 °C/min to a target temperature between 650 and 850 °C, recorded by a K-type thermocouple, followed by an isothermal dwell (excluding F0).Changes in sample length were measured using a linear variable differential transducer (±0.1 μm).Length data were recorded every 30 s at T < 400 °C and every 3 s at T > 400 °C.Above Tg, decreases in sample height allowed for the measurement of bulk viscosity (η).As the melt relaxed from its 68 MPa quench pressure to ambient pressure, H2O exsolved as bubbles.Bubble-driven expansion was monitored via the sample height increase during vesiculation.Once sample inflation ceased, samples were cooled to room temperature at 20 °C/min.Thermal contraction of the melt and porosity change during cooling are expected to be negligible.Melt dehydration increases Tg (Dingwell et al. 1996) and, assuming residual dissolved H2O is ~0.1 wt.%, Tg, following degassing, is estimated to approach temperatures of the experiments (Giordano et al. 2008), implying quenching should have occurred soon after cooling began.

Sample Characterization
Tomographic X-ray microscopy and image segmentation Samples with a target experimental temperature of 750 °C were analyzed pre-and post-experiment using tomographic X-ray microscopy (µCT), conducted on a Zeiss Xradia 510 Versa X-ray microscope at the University of Missouri X-ray Microanalysis Laboratory.Depending on their X-ray transmittance, samples were scanned at a beam voltage and power of either 40 or 50 kV, and 3 or 4 W respectively, with LE1 or LE2 beam filters applied, and for 3-5 seconds of exposure time.A total of 1601 projections were taken at 180 degrees of rotation + fan using a 0.4X objective.With these conditions, analyses yielded a spatial resolution of 14.04-18.27µm per voxel.Some samples were also imaged via scanning electron microscopy (SEM) on a Zeiss Sigma 500 VP using a highdefinition, 5-segment backscattered electron detector (HDBSE), in variable pressure mode, with an accelerating voltage of 20 keV, a 60 µm aperture, and a working distance ranging from ~10 to 13 mm.
Grayscale µCT images were segmented using AVIZO 2019.1 to examine microstructures, estimate permeability, and quantify total sample volume of non-cylindrical post-experiment samples (Fig. 3).Total volumes were measured for bulk samples rather than using subvolumes to maintain original crystal volume fractions and remove bias given the internal heterogeneity of post-experiment samples.Post-experiment samples are very small with fragile and irregular external surfaces, and achieving a seal to measure volume or permeability directly would have been extremely difficult.
Permeabilities of porous silicic glasses at similar mm-scale were measured by Takeuchi et al. (2009) but were under the detection limit and unable to be quantified despite the samples having higher porosity (≥ 0.45) and larger bubbles (~60 μm in diameter) than our samples.Alternatively, µCT is a powerful non-destructive tool for characterizing delicate samples with resolvable pore space on the order of 10 µm while providing high resolution data of textural features and spatial relationships (e.g., Polacci et al. 2006;Giachetti et al. 2011;Pistone et al. 2015b).Accuracy of the image segmentation was tested using the straightforward cylindrical geometry of pre-experiment F0.Total segmented volume from AVIZO agreed to within 1% of the geometrically measured volume.

Density and porosity measurements
Sample porosities were determined from density measurements before and after experiments and CT data (Table 1).Density was measured using the Archimedean method following the approach of Avard and Whittington (2012) where samples were immersed in a solution of anhydrous ethanol.(2) Subsequently, isolated porosity was calculated as the difference between connected and total porosities: Archimedean porosity (  ) was calculated based on the change in Archimedean volumes for all samples following experiments at temperatures between 650 and 850 °C: Because   excludes connected pore volumes, this allows us to compare isolated porosities across all samples, not just those for which CT data was collected.

Experimental degassing
The glass, which was originally quenched at 68 MPa with 4.2 wt.% dissolved H2O, maintains a highpressure configuration below the glass transition temperature.Above Tg, the melt is able to relax to ambient conditions (~0.1 MPa).Water is no longer able to remain dissolved and exsolves as bubbles.
The maximum decompression rates for our crystal-bearing experiments, associated with decompression from 68 to 0.1 MPa, are 0.13-0.23MPa/s.Maximum decompression rate was estimated based on the timescale between the sample reaching Tg and rapid bubble growth.The minimum decompression rates are 0.005-0.04MPa/s, based on the timescales between the samples reaching Tg and the end of sample expansion when overpressure is no longer driving sample inflation.
Here we assume complete sample relaxation from 68 MPa to ~0.1 MPa and loss of volatiles to ~0.1 wt.% dissolved H2O.These decompression rates equate approximately to ascent velocities associated with explosive behavior of 0.1-10 m/s (e.g., Carey and Sigurdsson 1985;Dobran 1992;Rutherford and Hill 1993;Jaupart 1996;Cassidy et al. 2018).We recorded changes in sample height as a proxy for volume change due to bubble growth (Fig. 4; supplementary table in Online Resource 3).Sample volume change due to relaxation and thermal expansion of the melt (when T > Tg) is expected to be negligible compared to bubble-driven expansion.
During heating, upon crossing Tg at ~28 minutes, the crystal-free sample (F0) underwent slight sample growth due to melt relaxation, then shortening due to viscous deformation.Rapid bubble growth commenced at ~34 minutes, at 614 °C and a viscosity of ~10 8.5 Pa•s, resulting in height increases between 41 and 55%, and ended abruptly at ~37 minutes.Decompression rates for F0 range between 0.08 and 0.22 MPa/s.Archimedean (isolated) porosity varies between 0.66 and 0.81 ±0.01, depending on temperature-time histories.Expansion of F0 was used as a benchmark for vesiculation unimpeded by crystals.

Textural observations
SEM and µCT data (Fig. 3 and supplementary movies in Online Resources 4-8) were used to examine textural features and identify outgassing mechanisms.Post-experiment F0 shows two distinct bubble families: (1) large bubbles up to ~1.2 mm diameter, which likely originated from pre-existing bubbles and in some cases have spawned radial fractures (Fig. 3a, b), and (2) numerous small spherical bubbles < 50 µm.
Textures in crystal-bearing samples mimic those documented by Pistone et al. (2017).F60 and F70 show thin ribbons of glass surrounded by bubbles.Glass pockets between crystals typically comprise multiple impinging bubbles separated by thin films of glass.Melt pockets in the sample interiors expanded due to bubble growth, leading to heterogeneous repositioning of the crystal framework by viscous deformation, producing non-circular sample cross-sections (Fig. 3b).Internal melt pockets in F70 and F80 grew very little, leaving the samples mostly cylindrical.
Fracturing was observed at all crystal fractions.Figure 3b, c shows mode I tensile fractures propagating outwards from bubbly glass pockets, especially in F80, implying that fracturing was driven by bubble expansion and not thermal contraction on cooling.Fractures penetrate both crystals and glass, with most connectivity existing as cracks within crystals (Fig. 3d).Some fractures in the glass are partially healed (Fig. 3g), preferentially preserving cracks within crystals, implying that brittle and ductile deformation occurred penecontemporaneously above Tg.

Bubble growth regimes
Sample inflation data allow us to identify stages within permeability development.Magma expansion slows significantly once it becomes permeable, despite continued volatile exsolution (Rust and Cashman 2011).Inflection points were observed up to 16 minutes after the onset of inflation, where sample growth began to decelerate (Fig. 7).These inflection points are inferred to signal the effective transition from closed to open-system degassing at time tc, when overpressurized gas can escape the sample.It is unlikely that sample growth decelerated due to dehydration of the melt, because the diffusivity of water in dacitic melt is slow at temperatures ≤ 850˚C (Ni et al. 2009).Diffusive water loss through the surface of the sample can produce dehydrated rinds that may limit vesiculation (von Aulock et al. 2017), but likely negligibly affects viscosity on the timescale of our experiments (Whittington et al. 2004).Calculated maximum rind thicknesses are ≤ 150 μm for the short timescales of our experiments, based on H2O diffusivity in dacitic melts (Ni et al. 2009).Using the power-law relationship in Fig. 5 between porosity and sample inflation, the amount of inflation at time tc was applied to calculate the critical porosity,   , at the inferred start of outgassing when t = tc, for samples whose total porosities were measured (Table 2).The percolation threshold   ±0.04 is inversely related to crystallinity such that   = 0.05-0.16.The percolation threshold for F0,   = 0.58, is consistent with previous degassing studies of crystal-free melts.
The experimental length-time curves in Fig. 8 have a sigmoidal shape that closely resemble published in situ vesiculation data (e.g., Bagdassarov et al. 1996;Stevenson et al. 1997;Cáceres et al. 2022).Length data were fitted using the Avrami equation (Avrami 1939(Avrami , 1940)): at t varying between t0 (onset of bubble-driven inflation) and tc (end of closed-system degassing when  =   ).The exponent, n, is generally between 2.5 and 4, but because vesiculation occurred at high temperatures >> Tg, n can be less than 2.5 (Bagdassarov et al. 1996) and can decrease to ~1.5 during degassing (Navon and Lyakhovsky 1998).The Avrami coefficient,   , represents the characteristic timescale for bubble-driven expansion (Bagdassarov et al. 1996).When extrapolated to times t > tc, the fitted curves predict the expansion that would occur if bubble-driven sample growth continued as a closed system (dashed curves in Fig. 8).However, open-system degassing starting at tc leads to slower inflation.Increasing temperature and decreasing crystallinity strongly increases the total amount of expansion (Fig. 4), while increasing temperature lowers the characteristic timescales of expansion (Figs. 8 and 9).To determine the temperature dependence of   , data were fitted again from the point in which a constant temperature was established (±5 °C) to the end of inflation.The temperature dependence of   can be expressed as an Arrhenian function of temperature (Fig. 9), and has an activation energy, Ea, of 103.1 ±4.2 kJ/mol when n = 1.5, which falls between the activation energies of bulk water diffusion for 4.2 wt.% (84.3 kJ/mol) and 0.1 wt.% (136.4 kJ/mol) based on Ni et al. (2009).
Prior to bubble-driven sample inflation, viscosities for F0 and F50 exhibited a parabolic trend during heating, where viscosity minima at ~615 °C indicate rapid bubble nucleation.This was followed by a brief increase in viscosity due to water loss from the melt, where viscosity increased ~0.8 log units for both F0 and F50 by ~635 °C, followed by sample inflation during which measurement of viscosity was no longer possible.Calculated estimates for viscosity at 614 °C with 4.2 wt.% dissolved H2O vary between 10 6.9±0.3Pa•s (synthetic dacite viscosity model of Whittington et al. 2009) and 10 7.3±0.35Pa•s (general silicate melt viscosity model of Giordano et al. 2008).Water loss from the melt prior to rapid bubble growth may account for the ~1.5 log unit gap between model estimates and the measured melt viscosity (10 8.5 Pa•s).To reconcile the discrepancy, viscosity models would agree with measurements if the melt actually contained between ~2.1 and 2.6 wt.% H2O, suggesting the melt had already exsolved ~40-50% of its water prior to rapid bubble growth and sample inflation.These water contents are consistent with estimates from Pistone et al. ( 2017) at similar temperatures.Therefore, ~2 wt.% H2O must exist in small overpressurized bubbles at the onset of rapid inflation.
We can better understand the kinetics of volume expansion by relating timescales for viscous deformation and diffusion using the dimensionless Péclet number (Lyakhovsky et al. 1996): where R is bubble radius and  H 2 O t is bulk water diffusivity.Applying a melt viscosity of 10 8.5 Pa•s, diffusivities from Ni et al. (2009), and assuming Δ ≈ 68 MPa at time t0 (since only nucleation has occurred up to this point with minimal bubble growth), we calculate that Pe > 1 for R >1 μm.This implies that vesiculation at the start of bubble-driven inflation was controlled by diffusion.In Fig. 9, if we exclude   = 0.8 at 850 °C to gain a better fit and representative Ea across all crystal fractions at 700-800 °C, the temperature dependence of the Avrami growth rate then displays an activation energy of 115.6 ±3.8 kJ/mol (with n ≈ 1.5).An equivalent Ea of diffusion corresponds to ~2 wt.% dissolved H2O (Fig. 10), consistent with estimations from viscosity models (Giordano et al. 2008;Whittington et al. 2009).

Magma deformation in response to gas expansion
The textural arrangement of bubbles, crystals, and melt controls the bulk rheology of magma, which exerts a first-order control on deformation mechanisms (e.g., Pistone et al. 2012Pistone et al. , 2013;;Mader et al. 2013;Truby et al. 2015;Birnbaum et al. 2021).Deformation, in turn, controls the formation of permeable pathways through which gas escapes via outgassing mechanisms like bubble coalescence (viscous-controlled outgassing) and fracturing (brittle-controlled outgassing) (e.g., Namiki and Manga 2008;Castro et al. 2012;Lavallée et al. 2013;Gaunt et al. 2014).The rheological regime for   = 0.5-0.8 is likely determined by the crystal phase more than the interstitial melt viscosity (Lavallée et al. 2007).Textural observations (Fig. 3) indicate brittle failure was the dominant mechanism that led to outgassing at low porosities (  = 0.05-0.16).The length change of < 1% upon cooling indicates that post-experiment textures preserve characteristics of the pore network (k and ) formed during gas exsolution and escape, allowing us to accurately classify the mechanisms that facilitated outgassing.
Adjustment of the crystal framework by viscous deformation occurred despite the high apparent viscosities measured for F50 ( ≥ 10 10 Pa•s).Timescales for viscous dissipation (λ), where λ =  Δ ⁄ (Sparks et al. 1994), are sufficient to accommodate sample strain during the start of inflation, but not by the end when melt viscosity has increased and overpressure (Δ) has decreased from ~68 MPa towards ~0.1 MPa.Adjustment of the crystal framework in response to expansion of bubbly melt pockets likely led to localized jamming of crystals, increasing local bulk viscosity.This provides strong resistance to gas expansion, which we infer led to fracturing becoming the dominant outgassing mechanism.Bubbles that remain trapped in highly viscous melt can increase magma pressurization (Sparks 1997;Girona et al. 2014) and reduce its strength (Heap et al. 2015a).
Subsequent pore pressure-induced embrittlement, which has been proposed for edifice-forming rocks (Farquharson et al. 2016), could either introduce local zones of weakness, where rapid decompression of overpressurized pores could lead to violent fragmentation, or increase local permeability and facilitate outgassing, forestalling explosive behavior.
Recent numerical modeling by Crozier et al. (2022) has established the importance of magma fracturing to sustaining non-violent effusive behavior and influencing explosive-effusive transitions.
Our samples exhibit fractures that emanated from bubbly melt pockets and penetrated the surrounding magma.Compressibility of magma surrounding expanding bubbles decreases with increasing crystallinity, leading to an increase in pressurization at higher   (Degruyter et al. 2017), consistent with the higher degree of fracturing observed in our samples with   > 0.6.The observed decrease in maximum inflation rate with crystallinity (Fig. 7) reflects the decreased compressibility.Assuming each sample began inflation with similar overpressures, the reduction in max inflation rate indicates that samples maintain high overpressures more effectively with increasing crystallinity.
Consequently, the increased rate of overpressure buildup, brought on by increased viscous retardation, likely facilitated higher degrees of pore pressure-induced cracking with crystallinity and outgassing at increasingly lower porosities (Table 2; Fig. 11a).Despite connected porosities being low, our samples were able to reach a critical permeability due to very efficient outgassing through fractures.We infer that a shift in the predominant deformation mechanism may occur at   ~0.67 where connected porosity exceeds isolated porosity (Fig. 11b).This is consistent with the apparent inflection point among percolation thresholds (Fig. 11a) between   of 0.6 and 0.7.This transition within the narrow crystallinity interval of 0.6-0.7 may coincide with rapid changes in bulk magma rheology that occur near the maximum packing fraction,   ~0.64 (Kohlstedt and Zimmerman 1996;Petford 2003;Lavallée et al. 2007).

Crystallinity and gas retention
Theoretically, at each temperature regardless of the crystallinity, the melt of each sample with the same starting water concentration must generate the same level of total porosity (translated in gas expansion).Despite this, we observed variation in expansion with crystallinity (Fig. 4).During our experiments, if samples inflated more than predicted based on their glass fraction (e.g., F50), then the amount of trapped gas must have increased relative to F0.This would imply that neither bubble coalescence nor magma fracturing were efficient outgassing mechanisms to release overpressure.
High magma viscosities of these concentrated suspensions impede bubble coalescence.The addition of bubbles to crystal-bearing magma lowers the critical failure stress when   < 0.44, but increases it when   = 0.44-0.65 (Pistone et al. 2015a).Increased failure stress allows a greater degree of degassing to occur before fracturing enables outgassing and overpressure to release.This positive feedback between the critical failure stress and gas retention increases the probability of overpressured gas storage in crystal-rich magmas.In our experiments, Archimedean (isolated) porosity increases dramatically between F70 (  = 0.02-0.14)and F50 (  = 0.38-0.70),demonstrating that relatively small changes in crystallinity can have a large impact on gas retention.
However, the influence of crystallinity on gas retention is better constrained when porosities are normalized to the glass fraction in this case because most of the isolated porosity exists in the glass phase.When normalized, Archimedean porosities, i.e. isolated melt porosities ( ̂), are 0.55-0.82for F50 and 0.05-0.34for F70 (Table 2; Fig. 6), more than a three-fold difference in trapped gas.
Depending on their volume fraction, crystals can therefore aid or hinder gas escape, and potentially play a crucial role in controlling the explosivity of magma.Pistone et al. (2015a) observed transitional deformation mechanisms, that either enhance or impede gas escape, when   = 0.4-0.5 and  ≤ 0.2.We observed similar behavior at higher crystal fractions (  = 0.5-0.6)and porosities ( = 0.31-0.43).The measured Archimedean porosities of our samples are an exponential function of crystallinity that asymptotically approaches 1 at   ~0.47 (Fig. 11c), which falls within the estimated range for transitional viscous to brittle behavior from Pistone et al. (2015a).A crystal fraction ~0.45-0.5 potentially marks the maximum in gas retention for a regime in which outgassing is controlled by brittle behavior.

Variation of outgassing efficiency with crystallinity
The relative outgassing efficiency among our samples can be quantified by comparing changes in isolated melt porosity during outgassing.We use the difference between  ̂ at the start and end of outgassing as a proxy for outgassing efficiency-less efficient outgassing leads to more trapped gas.
Archimedean porosity is proportional to bubble-driven sample inflation (Fig. 6).Using this relationship, we calculated  ̂ at the start of outgassing when t = tc (Table 2) by applying the same method in which   was calculated from total porosity (see section on bubble growth regimes).For   = 0.5, Table 2 shows that the mean  ̂ increased from ~0.33 at the start of outgassing to ~0.67 by the end, doubling its trapped bubbles.For   = 0.7,  ̂ also doubled during outgassing, but only increased from ~0.1 to ~0.2.The amounts in which   increased vary depending on temperature.The example data set shown in Fig. 11d demonstrates that subtle differences in crystallinity can amplify gas retention in magma significantly.Changes in isolated melt porosity during outgassing vary between F50 and F70 by a factor of at least 2.4.This variation in trapped gas implies outgassing efficiency in magmas is strongly dependent on crystallinity.

Critical porosity and permeability
High crystallinity can influence permeability development in a complex way (Lindoo et al. 2017).
Space limitations imposed by crystals can enhance bubble coalescence, lowering   .This implies the reduction in   should scale with increasing crystallinity (deGraffenried et al. 2019).Our findings corroborate those of previous studies at   ≤ 0.5 that increasing crystallinity decreases   during vesiculation (Fig. 11a; Table 2).Our results show that   decreases linearly with increasing crystallinity between   of 0.5 and 0.7.For   ≥ 0.7, the percolation threshold did not vary significantly.We infer from the lower-than-expected sample expansion at   ≥ 0.6 (Fig. 4) that outgassing through fractures led to very low critical porosities ~0.05-0.10 and limited expansion effectively, confirming that permeability can be achieved efficiently via pore-pressure induced cracking.
We infer that the termination of bubble-driven expansion signals efficient permeable outgassing and the release of overpressure was achieved.Although open-system degassing might have continued, the termination of growth indicates that most of the overpressure driving sample inflation has been released.Because each sample was quenched quickly once growth terminated, each experiment records the effective critical permeability, kc (permeability threshold), at which samples preserve their porosities and pathway geometries that facilitated permeable outgassing.The permeability threshold, illustrated in Fig. 12b, appears strongly dependent on porosity, for which kc can be fitted using a power-law relationship.The porosity at kc decreases substantially from 0.43 to 0.08 as   increases 0.5 to 0.8, while kc varies little more than an order of magnitude, as permeability at high crystallinity is crack-dominated rather than bubble-dominated.Despite outgassing beginning at   ≤ 0.16, total porosity increased to as high as 0.43 before reaching critical permeability, implying that vesiculation is more dependent on   , while the influence of the percolation threshold is lessened at high crystallinity.We interpreted these results to reflect two forms of permeability development when  >   (Fig. 12b) in which permeability abruptly increases (F80) owing to sufficient fracturing or traverses higher porosities by following a shallower slope before reaching critical permeability (F50).
The porosity at kc characterizes one end-member of permeability development.When permeability develops through vesiculation, it tends to follow a hysteresis loop, with bubbles forming and then collapsing, leaving larger bubbles preferentially intact (Kennedy et al. 2016), which enables high permeability to be preserved even at low porosity (Rust and Cashman 2004;Cashman and Sparks 2013).Our experiments show that the permeability threshold can be achieved at low porosities by fracturing, without needing to achieve higher porosity followed by bubble deformation.This confirms another mechanism that can lead to permeable outgassing: dilatant microcracks that form around vesiculating melt pockets, which may in turn coalesce into macroscopic fractures.
Coalescence of microcracks into macroscopic fractures could lead to a system-spanning connected network that would enhance outgassing (Heap et al. 2014a(Heap et al. , 2015a)).Bubble networks and permeable wall rocks are probably not permeable enough to cause effusive eruptions of low porosity silicic lavas, emphasizing the importance that outgassing through magma fracturing may have (Crozier et al. 2022).Moreover, because fracturing can facilitate outgassing in crystal-rich systems, which our experiments imply can occur at  ≤ 0.1, the concept of a bubble percolation threshold appears to be of limited utility in crystal-rich magmas.Fracture-dominated magmas could rapidly achieve critical permeability even at low porosity, while bubble-dominated magmas may only achieve significant permeability at high porosity, increasing explosive potential.The explosive potential of crystal-rich magmas with   ≥ 0.5 will depend on the onset and efficacy of crack-dominated outgassing.

Implications for eruptive behavior
Permeability-porosity data from natural volcanic rocks can be used to delimit porosities associated with explosive behavior.Permeability-porosity relationships are commonly described by a modified Kozeny-Carman power-law equation (Kozeny 1927;Carman 1937) based on percolation theory (Sahimi 1994): where   <  ≤ 1 and n is a fitting parameter (e.g., Martys et al. 1994;Klug and Cashman 1996;Saar and Manga 1999;Blower 2001;Klug et al. 2002;Mueller et al. 2005;Nguyen et al. 2014;Gonnermann et al. 2017;Wadsworth et al. 2021).The field in Fig. 1 spanning  ~0.3-0.7, which contains data from products of both eruption styles, can be bounded by Eq. ( 7) where fitting parameters are kept constant and only   is allowed to vary (Fig. 12a).These curves are qualitatively similar to boundaries proposed in previous studies (Saar and Manga 1999;Mueller et al. 2005;deGraffenried et al. 2019) but are constrained using a much larger dataset.The boundary between effusive and explosive samples is even more clear in Fig. 12a when applied to crystal-rich rocks (  ≥ 0.4).The data in Fig. 12a reflect the end results of many processes capable of altering the pore network, including those after exiting the conduit (e.g., densification, fragmentation, and late-stage degassing).Consequently, Eq. ( 7) can be used to approximate a minimum threshold at   ~0.22 for explosive behavior, assuming permeability hysteresis, where magma above or to the left of this line apparently does not pose explosive hazards.
At  > 0.22, magma permeability can evolve to cross the boundary in Fig. 12a, either by a decrease in porosity due to collapse of permeable pathways (Saar and Manga 1999), or a rapid increase in permeability due to fracturing.Competing viscous and brittle mechanisms for   = 0.5 (see section on crystallinity and gas retention) likely reduced outgassing efficiency and sustained degassing, increasing inflation due to trapped gas.This caused our experimental samples to traverse higher porosities (Fig. 12b), which coincide with increased explosive potential in natural systems.At higher crystal fractions, fracturing becomes an efficient outgassing mechanism at the same time as the fraction of melt needing to outgas decreases.As discussed above, fracturing potentially controls outgassing for crystal fractions ~0.47 or greater (Fig. 11a-c), with gas percolation starting at porosities less than 0.2 (Fig. 12b), but is most effective when crystallinity is greater than ~0.65 and limits vesiculation (and porosity) during open-system degassing.
Characterization of the physical states of magma reservoirs will be crucial for volcanic monitoring and identifying volcanoes whose silicic magmas are characterized by solid fractions with a high gas storage capacity.Seismic observations in combination with laboratory data and numerical simulations can be used to infer the physical state of magma, including crystal and/or bubble fractions of magmas at depth (e.g., Paulatto et al. 2012;Tripoli et al. 2016;Pistone et al. 2021), and to detect rheological transitions in ascending magma (Collier et al. 2006).Ascending magmas are dynamic systems that can undergo changes in crystal content by processes such as degassing-induced crystallization, including the formation of both microlites (Cashman and Blundy 2000) and nanolites (Pistone et al. 2022).Magmas that stall at depth also allow for crystallization of microlites (O'Donnell and Gardner 2022).Crystallization of the groundmass may have a dominant influence on episodic eruptive behavior at lava dome-forming volcanoes like Mt.St. Helens (Fink et al. 1990;Swanson and Holcomb 1990).Our results suggest that continued crystallization of already crystal-rich systems may facilitate cracking and release of overpressure if   is greater than ~0.65.After magma reaches the permeability threshold, overpressure that was once driving inflation and gas escape begins to dissipate allowing for bubble collapse or densification.This could lead to a less permeable plug capping gascharged magma of relatively lower crystallinity ~0.5 that is unable to outgas efficiently.
Crystallization of magmas initially containing   < 0.4 may result in transitions from coalescencedominated outgassing, in which crystals aid gas connection and escape, into the more hazardous intermediate crystallinity window (  ~0.5-0.6),where neither viscous nor brittle deformation are efficient ways of relieving gas pressure.The inefficiency of these competing mechanisms increases gas storage in ascending magma, potentially increasing buoyancy-controlled ascent rates.The dramatic influence on bubble entrapment arising from small changes in crystallinity provides a mechanism for episodic eruptive behavior without need of external triggers.

Conclusions
Our experimental results provide important clues to the gas storage capacity and outgassing efficiency of crystal-rich magmas undergoing degassing.The relationship between crystallinity and gas retention is closely tied to the influence of crystals on bulk rheology.Samples containing   = 0.5-0.6 exhibited viscous deformation by which the crystal framework underwent adjustment in response to bubble expansion.Bubble coalescence was kinetically limited, which augmented the gas storage in our samples, until rheological lock-up triggered brittle fracturing and rapid outgassing.These competing viscous and brittle mechanisms promote the trapping of overpressurized bubbles in the magma where neither bubble coalescence (viscous-controlled outgassing) nor magma fracturing (brittle-controlled outgassing) are efficient outgassing mechanisms to release overpressure.
Outgassing efficiency is inversely related to isolated porosity.Under equivalent conditions, there was about a three-fold difference in isolated porosity between   of 0.5 and 0.7.For   = 0.5, mean isolated melt porosity, increased from ~0.33 at the start of outgassing to ~0.67 by the end, doubling its trapped bubbles.For   = 0.7, however, the isolated gas fraction only increased from ~0.1 to ~0.2, implying both gas retention and outgassing efficiency are strongly dependent on   when ≥ 0.5.
Archimedean (isolated) porosities are an exponential function of crystallinity and approach a maximum between   of 0.45 and 0.5.This range likely marks a maximum in gas retention for a regime in which outgassing is controlled by brittle behavior.A range of   ~0.47-0.67 thus characterizes magmas with the greatest potential to alternate between effusive and explosive behavior where eruptive behavior may be controlled by the onset and efficacy of crack-dominated outgassing.
This work contributes to the growing collection of experimental studies on gas percolation in magma by exploring the influence of crystallinity and magma fractures on the percolation threshold.
Our findings indicate that the percolation threshold decreases linearly from 0.16 to 0.05 with increasing crystallinity between   of 0.5 and 0.7.For   ≥ 0.7, the percolation threshold did not vary significantly.The observed inflection point among percolation thresholds between   of 0.6 and 0.7 may be explained by rapid changes in bulk magma rheology that occur near the maximum packing fraction.We infer from the lower-than-expected sample inflation at   ≥ 0.6 (Fig. 4) that cracking facilitated rapid outgassing, confirming that critical permeability can be achieved via pore-pressure induced cracking.Percolation theory is of limited utility due to magma rheology favoring brittle deformation as suspensions approach or exceed the maximum packing fraction.Continued investigation into a possible regime in which outgassing is controlled by magma fracturing at crystal fractions closer to the maximum packing fraction and above will contribute to a broader understanding of the eruptibility of crystal-rich dome lavas.

Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 Fig. 12
Fig. 3 µCT and SEM images of experimental samples.Representative orthoslices of (a) pre-and (b) post-vesiculation showing pore space (black), degassed dacite glass (light gray), and quartz crystals (medium gray); (c) post-experiment 3D subvolumes showing pore space (blue), including vesicles and fractures, and dense rock (gray) with noted total volumetric inflation (ΔVtot); post-experiment samples in (b) and (c) were heated to 750 °C, except for F0 (706 °C); (d) HDBSE image of postexperiment F80 after heating to 850 °C showing glass extrusion that has breached the sample periphery (scale bar is 200 µm); (e) fractures penetrating glass and (f) crystal framework; (g) HDBSE image of F60 after heating to 750 °C (scale bar is 100 µm).Surface of glass extrusion shows evidence of healing (red circle) of potential outgassing pathways due to viscous relaxation Fig. 4 Change in sample height during vesiculation experiments.F-number and color correspond to sample crystallinity (vol%).Colored bars on right axis represent the expected range of vertical inflation based on results for F0, normalized to the glass fraction Fig. 5 Porosity-inflation relationship of post-experiment samples.Data are from samples shown in Fig. 3a-c.Change in sample height refers to bubble-driven inflation.Error bars are ±2σ Fig. 6 Isolated melt porosity versus sample inflation.The example best fit (solid curve) is for all data (95% c.i. ±0.12) Fig. 7 Vertical inflation rates of crystal-bearing samples shown in Fig. 3a-c.Dashed lines mark maximum inflation rates (at t = tc) and the inferred boundary between closed and open-system degassing

Figures Figure 1
Figures

Figure 3 µCT
Figure 3 . All pre-experiment samples contained < 2 vol% spherical bubbles up to ~200 µm diameter.All reported crystal fractions are based on a pore-free basis, such that   =   (  +   ) ⁄ where   is the volume of crystals and   is the volume of groundmass (or melt, when T > Tg).Porosity, unless otherwise noted, refers to the bubble volume fraction of the bulk sample, such that  =   (  +   +   ) ⁄ where   is the volume of pore space.

Table caption listingTable 1
Summary of laboratory measurements before and after experiments.Sample characterization includes volume (V), sample length (l), mass (m), and density (ρ).Subscript A denotes Archimedean measurements.Total volume,   , before experiments was estimated geometrically.Total volume after experiments was measured using μCT data.Reported uncertainties in parentheses are ±2σ.n.d.

Table 2
Estimations of porosities throughout bubble-driven sample inflation.Data recorded at the minimum sample length marking the start of bubble-driven sample inflation are denoted by subscript t0.Data recorded or calculated at maximum inflation rates are denoted by subscript tc.Isolated melt porosities,  ̂, are Archimedean porosities normalized by the glass fraction.Reported uncertainties are ±2σ.n.d. is not determined This is a list of supplementary les associated with this preprint.Click to download.