In situ observation of nanolite growth in volcanic melt: A driving force for explosive eruptions

This study shows how a few nanometer-sized crystals markedly increase the viscosity of a magma leading to explosive eruptions.

of Mt. Etna 122 BCE, we sampled different sizes (from ~1 to ~10 cm) of clasts of the Plinian phase. Furthermore, we also studied scoria erupted at Mt. Etna during a weak explosive eruption in 2011. The samples from the 2011 eruption were also subjected to SEM, TEM measurements and Raman spectroscopy analysis. Nanolites were not found.
The nanolite identification strategy was initially based on the use of Raman spectroscopy to map the presence of nanolites thanks to the relatively large spatial resolution of the analytical technique. We subsequently carried out TEM analyses on the sample areas identified by the Raman spectroscopy analysis. We observed neither a spatial nor a size distribution of nanolites from the edge (fast quench) towards the centre (slow quench) of samples. We thus exclude that post-fragmentation quench of clasts as a mechanism responsible for nanolite formation. The Mt. Etna experimental samples of Fig. 2 and Fig. 3 were subjected to Raman spectroscopy measurements after XRD-SAXS-WAXS measurement at the synchrotron to determine the spatial distribution of the nanolite. We did not find any variation in the Raman spectrum along the sample.

In situ XRD measurements
In fig. S1 the XRD scattering intensity for the pure Mt. Etna basalt melt at 1300°C (above the liquidus), and the glass when quenched to 25°C from 1300°C at the maximum possible quench rate (turning the furnace off), both in air, are shown in fig. S1a. The coherent reciprocal-space scattered intensity for the liquid and glass represented by the total structure factors S(q) are shown in fig. S1b. The corresponding real-space pair distribution G(r) functions shown in fig. S1c provides a measure of probability of finding two atoms a distance r apart. The liquid S(q) exhibits diffuse first and second peaks at 2.05 and 4.8 Å -1 . On quenching to a glass, these peaks become slightly more pronounced, indicating an increase in atomic-scale ordering. In real-space, the first peak in G(r) at ~1.6 Å in both the liquid and glass arises from the nearest-neighbour T-O bond in tetrahedral units (where T is Si 4+ , Al 3+ , Fe 3+ ). A second peak at 3.06 Å corresponds to the Si-Si bond length, while the peak at 4.08 Å is attributed to the second nearest-neighbour Si-O bond. A small feature appearing in the glass G(r) at ~ 2.5 Å is consistent with O-O correlations becoming more pronounced on vitrification. Due to the complexity of the sample composition, no other cation-O or cation-cation correlations are resolved. Figure S1. Results of in situ XRD measurements. (a) Diffraction patterns obtained for the liquid basalt at 1300°C and rapidly quenched glass at 25°C, (b) the liquid and glass structure factors, S(q), and (c) the corresponding pair distribution G(r) functions, as obtained by Fourier transforming the corresponding structure factors in (b). The arrows indicate the position of the small angle nanolite peak. For clarity, the glass data have been displaced vertically.
The rapidly-quenched glass also exhibits a sharp diffraction peak at 0.3° (0.2 Å -1 ), indicated by the black arrows in fig. S1a and fig. S1b. The peak is truncated at low scattering angles by the shadow of the tungsten beam-stop. The characteristically glassy structure factor combined with the sharp very-small-angle scattering peak is consistent with coexistence between a glass matrix and 'particles' on the order of nanometers in size (45). Unfortunately, the peak is truncated at low scattering angles below 0.3° (0.2 Å -1 ) by the shadow of the tungsten beam-stop (see fig. S1 and Fig. 2). This precludes full exploitation of this small angle peak that is potentially a rich source of information.

In situ SAXS-WAXS measurements
The evolution with time of the SAXS pattern reported in Fig. 3c suggests an increase in both the particle size and interaction. A 'hard sphere model' was used to describe the SAXS patterns. This model calculates the interparticle structure factor for monodisperse spherical particles interacting through hard sphere (excluded volume) interactions. Parameters involved in the model are the effective hard sphere radius and the volume percent occupied by the spheres. After 65 seconds into the 950°C isothermal crystallization event the volume percent occupied by the first population of spheres only is estimated to be about 25 volume %. The second local maxima due to a second population of nanolites was fitted independently as a unimodal distribution of hard spheres.
For the initial XRD collection the resolution was optimised for a liquid diffraction pattern so the q step size is too large to resolve small peaks that might arise from the nanolites in Fig. 2b. Therefore, it is difficult to know if these features are crystalline, immiscible melts, or heterogeneities in the melt structure. However, the WAXS data shown in Fig. 3b, with higher q-space resolution, clearly demonstrates these are crystalline features. The Bragg peak intensity increases slowly between 15  This again demonstrates the fast development of these features at these near-liquidus temperatures. The nanolite peak height at 890°C is the same as the quenched sample suggesting all the growth occurs above this temperature with little more happening down to the glass transition temperature at 700°C. Applied to a natural eruption, this clearly demonstrates that nanolites can grow much more quickly than microlites and are a feature of rapid undercooling. The natural nanolites shown in Fig. 1 are, therefore, the result of rapid growth and are more likely to result from a dynamic pre-eruptive environment than the rapid quenching produced post-fragmentation as magma is ejected.

Modelling of nano-particle agglomeration
The idea here is that agglomerates of particles entrap and immobilise liquid, effectively increasing the volume percent of solids. In other words, the volume of an agglomerate is larger than the sum of the particle volumes. Agglomerates can rapidly grow in volume as the particle concentration increases (77)(78) and/or shearing (36) promoting the observed early onset of non-Newtonian behaviour at extremely low volume fraction ϕ and the dramatic increase in the bulk viscosity observed in Fig. 4. We here consider the volume of agglomerates and whether we can thereby account for the observed rheology. The approach is entirely geometrical. The calculations below allow us to gauge the scale of liquid entrapment and hence whether it might feasibly explain the rheology.
For simplicity, we consider agglomerates of spherical particles with uniform radius . This is entirely appropriate for our experimental suspensions, as the particles used were spherical. We assume furthermore that agglomerates are formed in a fcc close-packed arrangement ( fig. S2). In general, a stack of layers will contain particles: The smallest such agglomerate involves 2 layers with 4 identical spherical particles in a tetrahedral arrangement such that the centre of each particle sits on one vertex of a tetrahedron ( fig. S3a). Each particle is surrounded by a film of immobile liquid of thickness = where ≥ 0 gives the film thickness as a fraction of the particle radius . The radius of particle plus the liquid film is then: Moreover we assume that liquid trapped between the particles is immobile. For the smallest agglomerate of just 4 particles, each face will look as shown in fig. S3b. The 4 th particle will sit on top of these 3 particles. The green colour shows the immobile liquid. In order to work out the volume of particles plus entrapped liquid, we must first work out the volume of the smallest tetrahedron that encloses the particles. Fig. S4 shows the base of a 2layer stack of 4 particles. The 3 particles in the base layer are in contact with the tetrahedron's basal face a perpendicular distance below their centre points A, B and C. The 4 th particle is placed above these 3 particles (see figs S2 and S3b).
Consider the tetrahedron that contains only the centres of all the spheres in the layers. In the 2-layer system shown in fig. S3b the base of this tetrahedron is given by the triangle ABC. In the general case with layers, the edge length ���� of this tetrahedron containing only the centres of the spheres is: (i.e. just 2 in fig. S4 as = 2) and its height is (see Appendix Equation A7): We now need to move all sides outwards by so that the spheres will be fully contained. The perpendicular distance from the centre of the volume to the face is ′ = ℎ′ 4 ⁄ (see Appendix Equation A12). This becomes = ℎ′ 4 ⁄ + after shifting and hence the tetrahedron fully enclosing the spheres has a height of: and an edge length of: Furthermore, we can see that: and that the length ���� , which is the perpendicular distance from the centre of one of the spheres to an edge, is given by: The base extends beyond particles in all directions because the faces are not perpendicular to the base. The faces touch the spheres tangentially some distance above the base. The volume of the tetrahedron is: However this volume is larger than the volume shown in fig. S3b because of the excess volume beyond the spheres along the edges and in the vertices. Consider first the excess volume in the vertices. We can work out this volume by calculating the volume of a tetrahedron that encloses a single particle (i.e. we have a single layer so = 1). Subtracting the volume of the sphere gives us the excess volume in at vertices. For = 1, from Equation (S6) we get: The volume of the tetrahedron is then using Equation (S9): The excess volume at the vertices is then: Note that is independent of the number of layers as there are always 4 vertices and they always have the same volume. Consequently, this excess volume is appreciable only for small agglomerates. For our limiting case of a single particle, the excess volume is more than twice the volume of the sphere itself.
Now consider the excess volume along the edges. This volume consists of the grey area shown in fig. S4 extending along the edge perpendicular to the page (refer to fig. S5 and Equation  A14 in the Appendix). This extends along the edge for the distance between the centres of the spheres 2 ( − 1). So the excess volume along an edge is: The total volume of the agglomerate plus liquid is then, using equations (S9), (S12) and (S14): For our smallest agglomerate with 2 layers ( = 2) and 4 spheres ( = 4) Equation (S16) reduces to: which is ~50% increase in volume.
The above calculations for 2 and 3 layers assume no additional thin film around the particles, i.e. α = 0 and so = in Equation (S2) above. To work out the film thickness (i.e. α as defined in equation S2) we need to explain the rheology, we need first to determine what volume fraction of (micro) particles would produce the observed behaviour. We can use the following graph ( fig. S6) from Mader et al. (26). Figure S6. Graph of normalized consistency (equivalent to relative viscosity) as a function of particle volume fraction for particles with different aspect ratio (26). At = 0.04 of nano-particles, the viscosity is increased by a factor of 100. This would be at = 0.6 for micro-particles (see the yellow line for spheres in fig. S5). This is an increase of a factor of 15 in volume fraction. In other words, we need to find the value of α such that the agglomerate volume given by Equation (S16) is 15 × × We write the volume of the agglomerate as: The condition on we seek is then: (1 + ) 3 The graph in fig. S7 shows that grows rapidly with agglomerate size, given by the number of layers . Note that the point at = 1 is for a single particle, so not really an agglomerate. reaches a stable value of just over ~1 for agglomerates with ≥ 2 layers (i.e. 4 particles or more). In other words, we would need a thickness of immobile liquid around each particle of around ~ (a particle radius -see Equation S2 for the definition of ). Figure S7. Graph of the film thickness (film thickness as fraction of particle radius) as a function of (numbers of layers). Figures S8a, b show optical microscope images of the nanolite-bearing basaltic pumice in Fig. 5b (STA Experiment 1). Note the high number of micrometric bubbles. Figure S8c shows Raman spectra of the nanolite-bearing basaltic pumice (STA Experiment 1, Fig. 5a) and black and dense glass recovered after the STA Experiment 2 that was stopped at 620°C. The signature at ~670 cm -1 , similar to that in Fig. 1, arises from FeO-bearing nanolites dispersed in the glass matrix (30), whilst the contribution at ~930 cm -1 arises from the Fe 3+ in the glass structure (79). The peak at ~670 cm -1 is more developed in the Raman spectrum of the basalticpumice (STA Experiment 1). On the other hand, the contribution at ~930 cm -1 is much more developed in the Raman spectra collected from visually-unaffected sample from the STA Experiment 2, suggesting that most of the iron is still-structurally bonded to the glass structure. Interpretations of Raman spectra agree with observations (i.e. size and relative number density of nanolites, see main text for a discussion) derived from HAADF-STEM and STEM-EDS analyses of the two samples (Figs. 5c, d, e, f, g). Figure S8. (a, b) Optical microscope images of the nanolite-bearing pumice (Fig. 5b) obtained with the STA Experiment 1 (Fig. 5a) 5a); the nanolite-bearing basaltic pumice (figs. 5b, c, d, e and figs. S8a, b), and STA Experiment 2 that was stopped at 620°C, where the sample recovered at the end of the STA Experiment 2 was visually unaffected with respect to its initial state (i.e., a dense black glass). See HAADF-STEM and STEM-EDS images in figs. 5f, g. Figure S9a shows the relationship between the maximum packing fraction (ϕ m ) and the particle size obtained combining our results from rheological measurements of nanosuspensions and those from Del Gaudio et al. (64) who used micro-suspensions. The maximum packing fraction decreases significantly with decreasing particle size, reflecting the sizedependence of the particle agglomeration process, namely the interplay between the particle size, their interaction, and the size of the immobile layer α (see "Modelling of nano-particle agglomeration" section above). , the relative viscosity is plotted as function of particle size (c) and of time (d), assuming the relationship between particle size and the maximum packing fraction (a) and the timescale of particle growth (b). Figure S9b shows the evolution of the nanolite radius with time (first population of nanolites appearing) by fitting our data in Fig. 3c with an exponential law. The combination of dependence of ϕ m as a function of particle size ( fig. S9a) with the evolution of the nanolite size with time ( fig. S9b) allows us to describe and extrapolate ϕ m through time. Figures S9c, d show, for different volume % of particles, the relationship between the relative viscosity of the suspension as a function of particle size and time, respectively. In particular, fig. S9c shows the dramatic increase in relative viscosity for just 4 volume % of particles with reducing particle size (i.e. from micro to nano) which reflects the equally dramatic reduction in maximum packing with reducing particle size shown in fig. S9a. Figure  S9d shows the rapid reduction in viscosity with time as the particles grow. Initially, when the particles are in the nano-size range, the viscosity is very large because the maximum packing fraction is very low. As the particles grow into the micro-size range this effect vanishes and we reach the conventional regime where the viscosity increase is controlled primarily by volume percent rather than particle size.

Appendix: Relationships used in agglomeration modelling
This section summarises some of the geometrical relationships of equilateral triangles and regular tetrahedra used in the previous section 'Modelling of nano-particle agglomeration'. We can also work out several important angles.
The angle between faces can be worked out from the cosine rule: Using Equation A8, we get =