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We review the class of continuous latent space (statistical) models for network data, paying particular attention to the role of the geometry of the latent space. In these models, the presence/absence of network dyadic ties are assumed to be conditionally independent given the dyads' unobserved positions in a latent space. In this way, these models provide a probabilistic framework for embedding network nodes in a continuous space equipped with a geometry that facilitates the description of dependence between random dyadic ties. Specifically, these models naturally capture homophilous tendencies and triadic clustering, among other common properties of observed networks. In addition to reviewing the literature on continuous latent space models from a geometric perspective, we highlight the important role the geometry of the latent space plays on properties of networks arising from these models via intuition and simulation. Finally, we discuss results from spectral graph theory that allow us to explore the role of the geometry of the latent space, independent of network size. We conclude with conjectures about how these results might be used to infer the appropriate latent space geometry from observed networks.

Semiconductor compounds are widely used for photocatalytic hydrogen production applications, where photogenerated electron–hole pairs are exploited to induce catalysis. Recently, powders of a metallic oxide (Sr 1− x NbO 3 , 0.03< x <0.20) were reported to show competitive photocatalytic efficiencies under visible light, which was attributed to interband absorption. This discovery expanded the range of materials available for optimized performance as photocatalysts. Here we study epitaxial thin films of SrNbO 3+ δ and find that their bandgaps are ∼4.1 eV. Surprisingly, the carrier density of the conducting phase exceeds 10 22  cm −3 and the carrier mobility is only 2.47 cm 2  V −1  s −1 . Contrary to earlier reports, the visible light absorption at 1.8 eV (∼688 nm) is due to the plasmon resonance, arising from the large carrier density. We propose that the hot electron and hole carriers excited via Landau damping (during the plasmon decay) are responsible for the photocatalytic property of this material under visible light irradiation. Metallic oxide SrNbO 3 has been identified as an efficient hydrogen evolution photocatalyst. Here, Venkatesan and co-workers show that its visible light absorption stems from plasmon resonance, thanks to its large carrier density (despite a large 4.1 eV bandgap), as opposed to from an interband transition.

Among many Sn-based intermetallics, Cu6Sn5 (η and η′) is ubiquitous in modern solder interconnects. Using the published structural models of η and η′ and also related structures, the total energies and equilibrium cohesive properties are calculated from first-principles employing electronic density-functional theory, ultrasoft pseudopotentials, and both the local density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange-correlation energy. The accuracy of our calculations is assessed through comparisons between theoretical results and experimental measurements for lattice parameters, elastic properties, and formation and transformation energies. The ambient-temperature experimental lattice constants of η and η′ are found to lie between the LDA and GGA level calculated zero-temperature lattice constants. The Wyckoff positions in the structural models of η and η′ agree very well with the ab initio results. The calculated formation energy of η′ lies between −3.2 and −4.0 kJ/mol, which is more positive by about 3 to 4 kJ/mol compared to reported experimental data obtained by solution calorimetry. Our systematic differential scanning calorimetry (DSC) experiments show that the η′ → η transformation enthalpy is 438 ± 18 J/mol, which is about 66% higher than the literature value. In view of our DSC results on heating and cooling, the nature of η′ → η and η → η′ is discussed. Our experimental bulk modulus of η and η′, and the heat of η′ → η transformation agree very well with the ab initio total energy calculations at the GGA level. Based on these results, we conclude that other isotropic elastic moduli (Young’s modulus, shear, and Poissons ratio) of η and η′ phases measured by pulse-echo technique are representative of their actual properties. The scatter in experimental elastic constants in the literature may be attributed to various factors, such as the measurement technique (pulse-echo versus nanoindentation), type of specimen (bulk, Cu6Sn5-layer in diffusion couple, thin-film), and anisotropy effects (particularly in Cu6Sn5-layer in diffusion couples).

The size distribution of particles, which is essential for many properties of nanomaterials, is equally important for the mechanical behaviour of the class of alloys whose strength derives from a dispersion of nanoscale precipitates. However, particle size distributions formed by solid-state precipitation are generally not well controlled. Here we demonstrate, through the example of core–shell precipitates in Al–Sc–Li alloys, an approach to forming highly monodisperse particle size distributions by simple solid-state reactions. The approach involves the use of a two-step heat treatment, whereby the core formed at high temperature provides a template for growth of the shell at lower temperature. If the core is allowed to grow to a sufficient size, the shell develops in a ‘size focusing’ regime, where smaller particles grow faster than larger ones. These results suggest strategies for manipulating precipitate size distributions in similar systems through simple variations in thermal treatments. A crucial aspect for many applications of nanoparticles is the ability to control their size and, in particular, the size homogeneity within a nanoparticle ensemble. An approach to form highly monodisperse particles through simple solid-state reactions is now demonstrated. The results could lead to efficient ways to control size distributions through simple thermal treatments.

The alteration of chromian spinel is a key process during serpentinization and metamorphism of ultramafic rocks controlled by oxygen fugacity (fO2) and Fe2+ ↔ Fe3+ exchange during fluid–rock interaction. Chromian spinel alteration is better recorded in less permeable chromitite than in peridotites where extensive fluid–rock interaction frequently overprints the record of earlier stages of alteration. To shed light on that process we have studied the distribution of Fe2+ and Fe3+ in variably altered chromian spinel grains from a set of chromitite samples from the same mining district using synchrotron-based microscopic chemical imaging and spatially resolved X-ray absorption near edge structure spectroscopy. Our results show that early stages of alteration do not involve changes in Cr3+ and Fe2+ contents or in Fe speciation but only depletion in Al3+ and Mg2+ resulting in the formation of porous chromite. With ongoing alteration Fe3+ migrates into porous chromite mainly along fracture walls and fracture zones as well as along grain boundaries. Sheared-type chromitites record the maximum rates of fluid–rock interaction because in these chromitite-types the accommodation of deformation on porous chromite allowed higher rates of diffusion of Fe3+ and Fe2+ (a magnetite component with Fe3+/Fetotal = 0.66) into the newly formed neoblasts. In porous chromite-type texture (all the original chromite grains fully transformed to porous chromite) the deformation and accompanying diffusion processes result in the formation of homogenous ferrian chromite grains. In contrast, in partly altered-type texture (chromite grains with original cores surrounded by porous chromite), such processes are only restricted to the porous rims, giving rise to zoned chromian spinel-ferrian chromite grains.

Liquid lead–bismuth eutectic (LBE) can serve as a heat transfer fluid for advanced nuclear applications as well as concentrated solar power but poses corrosion challenges for the structural materials at elevated temperatures. Oxide passivation of the surfaces of these materials during exposure to liquid LBE can inhibit such material degradation. In this study, transmission electron microscopy of oxides formed on Fe-Cr-Al alloy during exposure to low-oxygenated LBE at 800°C has been performed. A complex structure of the oxide film has been revealed, consisting of a homogeneous inner layer of mostly Al 2 O 3 and a heterogeneous outer layer.

The Caldes de Boí geothermal waters show important differences in pH (6.5–9.6) and temperature (15.9ºC–52ºC) despite they have a common origin and a very simple circuit at depth (4km below the recharge area level). Thes differences are the result of secondary processes such as conductive cooling, mixing with colder shallower waters, and input of external CO2, which affect each spring to a different extent in the terminal part of the thermal circuit. In this paper, the secondary processes that control the geochemical evolution of this system have been addressed using a geochemical dataset spanning over 20 years and combining different approaches: classical geochemical calculations and geochemical modelling. Mixing between a cold and a thermal end-member, cooling and CO2 exchange are the processes affecting the spring waters with different intensity over time. These differences in the intensity of the secondary processes could be controlled by the effect of climate and indirectly by the geomorphological and hydrogeological setting of the different springs. Infiltration recharging the shallow aquifer is dominant during the rainy seasons and the extent of the mixing process is greater, at least in some springs.Moreover, significant rainfall can produce a decrease in the ground temperature favouring the conductive cooling. Finally, the geomorphological settings of the springs determine the thickness and the hydraulic properties of the saturated layer below them and, therefore, they affect the extent of the mixing process between the deep thermal waters and the shallower cold waters. The understanding of the compositional changes in the thermal waters and the main factors that could affect them is a key issue to plan the future management of the geothermal resources of the Caldes de Boí system. Here, we propose to use a simple methodology to assess the effect of those factors, which could affect the quality of the thermal waters for balneotherapy at long-term scale. Furthermore, the methodology used in this study can be applied to other geothermal systems.

This study demonstrates a processing sequence used to generate coherent, two-phase L[2.sub.1]-[Ni.sub.2]TiAl/B2-NiAl precipitates in a ferritic matrix, and documents their microstructural evolution. Dark-field and energy-filtered transmission electron microscopy in combination with energy-dispersive X-ray analysis are used to determine the structure and composition of the different phases in the course of the processing and aging treatment. Through rapid solidification, coherent L[2.sub.1]-[Ni.sub.2]TiAl type precipitates with an internal network of curved, isotropic 1/2(100) antiphase boundaries form within the bcc-Fe matrix. The average width of the precipitates in the as-quenched state is 15 nm. During the subsequent aging heat treatment thin, anisotropic B2-NiAl zones are established, resulting in a three-tiered hierarchical microstructure. The L[2.sub.1]-[Ni.sub.2]TiAl precipitates are coherent with the bcc-Fe matrix, while the fine B2-NiAl zones are coherently embedded in the [Ni.sub.2]TiAl precipitates and aligned along the (100) directions. The L[2.sub.1]-[Ni.sub.2]TiAl parent precipitates have a width of 40 nm in the heat-treated stage and the B2-NiAl zones are 3-7 nm wide. Hence, the addition of Ti to Fe-rich Fe-NiAl alloys leads to the formation of coherent L[2.sub.1]-[Ni.sub.2]TiAl precipitates in the bcc-Fe matrix with an internal network of fine, anisotropic B2-NiAl zones arranged in a hierarchical manner. These microstructures are of potential interest for designing and optimizing the mechanical properties of precipitation-strengthened ferritic alloys.

The main processes controlling the hydrochemistry of an alluvium-covered evaporite karst area with high sinkhole risk (Ebro Valley, NE Spain) are examined by means of multivariate analyses (Principal Component Analysis and Hierarchical Cluster Analysis), ion correlations and geochemical speciation-solubility calculations. The hydrogeochemistry of the studied system seems to be governed by the interaction between the groundwater from the salt-bearing evaporitic karst aquifer and from the overlying Ebro River alluvial aquifer. The observed hydrochemical features in the alluvial-karst aquifer system are mainly determined by the relative contribution of gypsum/anhydrite and halite dissolution, showing a wide spectrum from relatively fresh recharge waters (mainly irrigation waters) to highly evolved groundwater from the evaporitic aquifer. The variability of these contributions is especially evident at sinkhole ponds which, in some cases, seem to be associated with discharge areas of the karst aquifer in the valley bottom alluvium. Calculated saturation indexes suggest that, in contrast to gypsum, the amounts of halite in the sampled portions of evaporitic aquifer are not large enough to attain equilibrium, which is consistent with the predominance of gypsum/anhydrite reported for these materials. Furthermore, the observed Na:Cl and Ca:SO4 correlations and stoichiometries suggest that other possible processes, such as glauberite dissolution or Na/Ca-exchange, generally play a minor role (compared to halite and gypsum dissolution) in this system. Another important process in the system is the dissolution of carbonate minerals (dolomite and, possibly, calcite) fostered by the input of CO2(g), which is probably produced by pedogenic processes. Dolomite dissolution seems to be particularly relevant in the evaporitic materials probably due to dedolomitisation triggered by gypsum/anhydrite dissolution.

In order to study the nature of the precipitates formed on arsenopyrite and marcasite after reacting with neutral to alkaline solutions, a combination of techniques including Scanning Electron Microscope-Energy Dispersive Spectroscopy (SEM-EDS), X-ray Photoelectron Spectroscopy (XPS) and synchrotron-based techniques such as micro-X-Ray diffraction (μXRD) and Micro-X-ray Absorption Near Edge Structure (μXANES) have been used. The results showed that the oxidation of marcasite and arsenopyrite under neutral to alkaline conditions leads to the formation of an Fe rich coating which seems to prevent the oxidation of these sulphides. SEM observations confirmed the presence newly-formed phases after the sulphides reaction under the studied conditions. XPS analysis showed that iron, sulphur and arsenic in the case of the arsenopyrite are in oxidized states in the sulphide surfaces. The microscale analysis of the S and Fe speciation performed by μXANES suggested that due to the sulphide oxidation an increase in the oxidation state of those elements took place together with an increase of the sulphate content in the surface layer (grain boundary). Micro-X-ray diffraction results indicated that goethite (α-FeOOH) is the only crystalline newly-formed phase when the reaction occurs at pH 12 whereas at lower pH the products formed on the sulphide surfaces seem to be poorly crystalline and they do not contribute to the diffraction effects in the XRD diagrams.