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<jats:title>Abstract</jats:title> <jats:p>Since their introduction in 1929, Pauling’s five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al. (2020), who performed a statistical analysis of the performance of Pauling’s five rules for about 5000 oxide crystal structures. They concluded that only 13% of the oxides satisfy the last four rules simultaneously and that the second rule has the most exceptions. They also found that Pauling’s first rule is satisfied for only 66% of the coordination environments tested and concluded that no simple rule linking ionic radius to coordination environment will be predictive due to the variable quality of univalent radii.</jats:p> <jats:p>We address these concerns and discuss quantum mechanical calculations that complement Pauling’s rules, particularly his first (radius sum and radius ratio rule) and second (electrostatic valence rule) rules. We also present a more realistic view of the bonded radii of atoms, derived by determining the local minimum in the electron density distribution measured along trajectories between bonded atoms known as bond paths, i.e., the bond critical point (rc). Electron density at the bond critical point is a quantum mechanical observable that correlates well with Pauling bond strength. Moreover, a metal atom in a polyhedron has as many bonded radii as it has bonded interactions, resulting in metal and O atoms that may not be spherical. O atoms, for example, are not spherical in many oxide-based crystal structures. Instead, the electron density of a bonded oxygen is often highly distorted or polarized, with its bonded radius decreasing systematically from ~1.38 Å when bonded to highly electropositive atoms like sodium to 0.64 Å when bonded to highly electronegative atoms like nitrogen. Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al. (2020) is not surprising. We offer a modified, more fundamental version of Pauling’s first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction.</jats:p> <jats:p>Pauling’s second rule implicitly assumes that bond strength is invariant with bond length for a given pair of bonded atoms. Many studies have since shown that this is not the case, and Brown and Shannon (1973) developed an equation and a set of parameters to describe the relation between bond length and bond strength, now redefined as bond valence to avoid confusion with Pauling bond-strength. Brown (1980) used the valence-sum rule, together with the path rule and the valence-matching principle, as the three axioms of bond-valence theory (BVT), a powerful method for understanding many otherwise elusive aspects of crystals and also their participation in dynamic processes. We show how a priori bond-valence calculations can predict unstrained bond-lengths and how bond-valence mapping can locate low-Z atoms in a crystal structure (e.g., Li) or examine possible diffusion pathways for atoms through crystal structures.</jats:p> <jats:p>In addition, we briefly discuss Pauling’s third, fourth, and fifth rules, the first two of which concern the sharing of polyhedron elements (edges and faces) and the common instability associated with structures in which a polyhedron shares an edge or face with another polyhedron and contains high-valence cations. The olivine [α-(MgxFe1–x)2SiO4] crystal structure is used to illustrate the distortions from hexagonal close-packing of O atoms caused by metal-metal repulsion across shared polyhedron edges.</jats:p> <jats:p>We conclude by discussing several applications of BVT to Earth materials, including the use of BVT to: (1) locate H+ ions in crystal structures, including the location of protons in the crystal structures of nominally anhydrous minerals in Earth’s mantle; (2) determine how strongly bonded (usually anionic) structural units interact with weakly bonded (usually cationic) interstitial complexes in complex uranyl-oxide and uranyl-oxysalt minerals using the valence-matching principle; (3) calculate Lewis acid strengths of cations and Lewis base strengths of anions; (4) determine how (H2O) groups can function as bond-valence transformers by dividing one bond into two bonds of half the bond valence; (5) help characterize products of sorption reactions of aqueous cations (e.g., Co2+ and Pb2+) and oxyanions [e.g., selenate (Se6+O4)2− and selenite (Se4+O3)2−] at mineral-aqueous solution interfaces and the important role of protons in these reactions; and (6) help characterize the local coordination environments of highly charged cations (e.g., Zr4+, Ti4+, U4+, U5+, and U6+) in silicate glasses and melts.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We examined pressure-induced phase transitions in Fe2S based on high-pressure and high-temperature X-ray diffraction measurements in a laser-heated diamond-anvil cell. Fe2S is not stable at ambient pressure but is known to form above 21 GPa with the Fe2P-type (C22) structure. Our experiments demonstrate a novel phase transition in Fe2S from the C22 to C23 phase with the Co2P-type cotunnite structure above ~30 GPa. The experiments also reveal a transformation from the C23 to C37 (Co2Si-type) phase above ~130 GPa. While the C23 and C37 structures exhibit the same crystal-lographic symmetry (orthorhombic Pnma), the coordination number of sulfur increases from nine in C23 to ten in C37. Such a sequence of pressure-induced phase transitions in Fe2S, C22 → C23 → C37, are similar to those of Fe2P, while they are not known in oxides and halogens that often adopt the C23 cotunnite-type structure. The newly found cotunnite-type Fe2S phase could be present in solid iron cores of planets, including Mars.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The density of liquid iron-nickel-sulfur (Fe46.5Ni28.5S25) alloy was determined at pressures up to 74 GPa and an average temperature of 3400 K via pair distribution function (PDF) analysis of synchrotron X-ray diffraction (XRD) data obtained using laser-heated diamond-anvil cells. The determined density of liquid Fe46.5Ni28.5S25 at 74 GPa and 3400 K is 8.03(35) g/cm3, 15% lower than that of pure liquid Fe. The obtained density data were fitted to a third-order Vinet equation of state (EoS), and the determined isothermal bulk modulus and its pressure derivative at 24.6 GPa are KTPr = 110.5(250) GPa and KTPr′ = 7.2(25), respectively, with a fixed density of rPr = 6.43 g/cm3 at 24.6 GPa. The change in the atomic volume of Fe46.5Ni28.5S25 upon melting was found to be ~10% at the melting temperature, a significantly larger value than that of pure Fe (~3%). Combined with the above EoS parameters and the thermal dependence reported in the literature, our data were extrapolated to the outer core conditions of the Earth. Assuming that S is the only light element and considering the range of suggested Ni content, we estimated a 5.3–6.6 wt% S content in the Earth’s outer core.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>A systematic survey of 57 different paragenetic modes distributed among 5659 mineral species reveals patterns in the diversity and distribution of minerals related to their evolving formational environments. The earliest minerals in stellar, nebular, asteroid, and primitive Earth contexts were dominated by relatively abundant chemical elements, notably H, C, O, Mg, Al, Si, S, Ca, Ti, Cr, and Fe. Significant mineral diversification subsequently occurred via two main processes, first through gradual selection and concentration of rarer elements by fluid-rock interactions (for example, in hydro-thermal metal deposits, complex granite pegmatites, and agpaitic rocks), and then through near-surface biologically mediated oxidation and weathering.</jats:p> <jats:p>We find that 3349 mineral species (59.2%) are known from only one paragenetic context, whereas another 1372 species (24.2%) are associated with two paragenetic modes. Among the most genetically varied minerals are pyrite, albite, hornblende, corundum, magnetite, calcite, hematite, rutile, and baryte, each with 15 or more known modes of formation.</jats:p> <jats:p>Among the most common paragenetic modes of minerals are near-surface weathering/oxidation (1998 species), subsurface hydrothermal deposition (859 species), and condensation at volcanic fumaroles (459 species). In addition, many species are associated with compositionally extreme environments of highly differentiated igneous lithologies, including agpaitic rocks (726 species), complex granite pegmatites (564 species), and carbonatites and related carbonate-bearing magmas (291 species). Biological processes lead to at least 2707 mineral species, primarily as a consequence of oxidative weathering but also through coal-related and other taphonomic minerals (597 species), as well as anthropogenic minerals, for example as byproducts of mining (603 minerals). However, contrary to previous estimates, we find that only ~34% of mineral species form exclusively as a consequence of biological processes. By far the most significant factor in enhancing Earth’s mineral diversity has been its dynamic hydrological cycle. At least 4583 minerals—81% of all species—arise through water-rock interactions.</jats:p> <jats:p>A timeline for mineral-forming events suggests that much of Earth’s mineral diversity was established within the first 250 million years. If life is rare in the universe, then this view of a mineralogically diverse early Earth provides many more plausible reactive pathways over a longer timespan than previous models. If, however, life is a cosmic imperative that emerges on any mineral- and water-rich world, then these findings support the hypothesis that life on Earth developed rapidly in the early stages of planetary evolution.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>How does one best subdivide nature into kinds? All classification systems require rules for lumping similar objects into the same category, while splitting differing objects into separate categories. Mineralogical classification systems are no exception. Our work in placing mineral species within their evolutionary contexts necessitates this lumping and splitting because we classify “mineral natural kinds” based on unique combinations of formational environments and continuous temperature-pressure-composition phase space. Consequently, we lump two minerals into a single natural kind only if they: (1) are part of a continuous solid solution; (2) are isostructural or members of a homologous series; and (3) form by the same process. A systematic survey based on these criteria suggests that 2310 (~41%) of 5659 IMA-approved mineral species can be lumped with one or more other mineral species, corresponding to 667 “root mineral kinds,” of which 353 lump pairs of mineral species, while 129 lump three species. Eight mineral groups, including cancrinite, eudialyte, hornblende, jahnsite, labuntsovite, satorite, tetradymite, and tourmaline, are represented by 20 or more lumped IMA-approved mineral species. A list of 5659 IMA-approved mineral species corresponds to 4016 root mineral kinds according to these lumping criteria.</jats:p> <jats:p>The evolutionary system of mineral classification assigns an IMA-approved mineral species to two or more mineral natural kinds under either of two splitting criteria: (1) if it forms in two or more distinct paragenetic environments, or (2) if cluster analysis of the attributes of numerous specimens reveals more than one discrete combination of chemical and physical attributes. A total of 2310 IMA-approved species are known to form by two or more paragenetic processes and thus correspond to multiple mineral natural kinds; however, adequate data resources are not yet in hand to perform cluster analysis on more than a handful of mineral species.</jats:p> <jats:p>We find that 1623 IMA-approved species (~29%) correspond exactly to mineral natural kinds; i.e., they are known from only one paragenetic environment and are not lumped with another species in our evolutionary classification. Greater complexity is associated with 587 IMA-approved species that are both lumped with one or more other species and occur in two or more paragenetic environments. In these instances, identification of mineral natural kinds may involve both lumping and splitting of the corresponding IMA-approved species on the basis of multiple criteria.</jats:p> <jats:p>Based on the numbers of root mineral kinds, their known varied modes of formation, and predictions of minerals that occur on Earth but are as yet undiscovered and described, we estimate that Earth holds more than 10 000 mineral natural kinds.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We have investigated the thermal expansion of 15 naturally occurring chemically diverse amphiboles utilizing high-temperature X-ray powder diffraction. As done in the first paper of this series on pyroxenes, volume-temperature data were analyzed using the physical Kroll and empirical Fei thermal expansion models. As in pyroxenes, orthorhombic amphibole end-members expand more than monoclinic ones, which is related to the greater kinking of the chains of tetrahedra permitted by the Pnma symmetry. In the case of chemically similar phases, increased Al in octahedral cation sites decreases expansion. Although the ranges of thermal expansion coefficients for amphiboles and pyroxenes are similar, expansion patterns are not the same. Amphiboles exhibit higher expansion along a*, but lower along b, just the reverse of that observed in pyroxenes. An exception to this is the data for pargasite, which shows higher expansion along the b axis due to the presence of Al in tetrahedral sites. Current data will be useful in modeling reactions involving amphiboles in both metamorphic and igneous environments.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Pressure-induced structural modifications in silicate melts play a crucial role in controlling dynamic processes in the deep interiors of the Earth and other planets. The correlation between structural and macroscopic properties of silicate liquids (densification, viscosity, chemical differentiation, etc.), however, remains poorly understood. Here we report the evolution of structural modifications and elastic properties of MgSiO3 glass to pressures up to ~70 GPa using a combination of experimental techniques, including micro-confocal Raman spectroscopy, angle-dispersive X-ray scattering, and Brillouin spectroscopy in the diamond-anvil cell. Our combined data set provides consistent and complementary evidence of a series of pressure-induced structural modifications in MgSiO3 glass at ~2, ~8, ~20, and ~40 GPa. Based on these results, a structural evolution model for MgSiO3 glass is proposed. We also discuss the role of Mg-O component in MgSiO3 and Mg2SiO4 glasses in controlling pressure-induced structural modifications and mechanical responses in these supercooled liquids.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Identifying and determining the origin of β-cristobalite, a high-temperature silica polymorph, in natural samples is challenging as it is rarely, if ever, preserved due to polymorphic transformation to α-cristobalite at low temperature. Formation mechanisms for β-cristobalite in high-silica rocks are difficult to discern, as superheating, supercooling, bulk composition, and trace element abundance all influence whether cristobalite crystallizes from melt or by devitrification. Here we report a study of α-cristobalite in Libyan Desert Glass (LDG), a nearly pure silica natural glass of impact origin found in western Egypt, using electron microprobe analysis (EMPA), laser ablation inductively coupled mass spectrometry (LA-ICP-MS), time-of-flight secondary ion mass spectrometry (ToF-SIMS), scanning electron microscopy (SEM), and electron backscatter diffraction (EBSD). The studied grains are mostly 250 μm in diameter and consist of ~150 μm wide cores surrounded by ~50 μm wide dendritic rims. Compositional layering in LDG continues across cristobalite grains and mostly corresponds to variations in Al content. However, layering is disrupted in cores of cristobalite grains, where Al distribution records oscillatory growth zoning, whereas in rims the high Al occurs along grain boundaries. Cristobalite cores thus nucleated within layered LDG at conditions that allowed mobility of Al into crystallographically controlled growth zones, whereas rims grew when Al was less mobile. Analysis of 37 elements indicates little evidence of preferential partitioning; both LDG and cristobalite are variably depleted relative to the upper continental crust, and abundance variations correlate to layering in LDG. Orientation analysis of {112} twin systematics in cristobalite by EBSD confirms that cores were formerly single β-cristobalite crystals. Combined with published experimental data, these results provide evidence for high-temperature (&amp;gt;1350 °C) magmatic crystallization of oscillatory zoned β-cristobalite in LDG. Dendritic rims suggest growth across the glass transition by devitrification, driven by undercooling, with transformation to α-cristobalite at low temperature. This result represents the highest formation temperature estimate for naturally occurring cristobalite, which is attributed to the near pure silica composition of LDG and anomalously high temperatures generated during melting by meteorite impact processes.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Using continuous and time-resolved spectroscopy, we investigate Raman and luminescence signals from synthetic hydroxylapatites doped with trivalent REE including Dy3+, Eu3+, Nd3+, and Sm3+, as well as REE in natural apatites, with laser excitations at 532 and 785 nm. We demonstrate that time-resolved spectroscopy is an efficient method to reduce luminescence from Raman spectra or, alternatively, to investigate the luminescence signals without interference from the Raman contribution. Time-resolved luminescence spectroscopy is a powerful technique for generating specific high-quality luminescence spectra for the REE emission activators in apatites by using appropriate combinations of delay and gate width for time synchronization of the laser pulse and ICCD detector. This allows the unambiguous detection and identification of the activators by avoiding overlapping of various emission signals in the luminescence spectra. This is particularly useful in the case of natural samples, which often have several activators for luminescence. In the case of synthetic REE-doped apatites, a quenching process for luminescence due to activator concentration is seen for Eu3+ and Sm3+, i.e., the higher the concentration, the shorter the luminescence decay time. The interpretation of luminescence decay time in natural apatites is promising but more complex because of energy transfers between the various luminescence activators present in the crystal lattice. Luminescence is a powerful technique for detecting the presence of REE in apatites down to parts per million levels, though quantifying the concentration is still a challenge.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The structure of opal-A was not fully understood due to its poorly crystalline nature. To better understand its structural characteristics, we have analyzed opal-AN (amorphous-network) and opal-AG (amorphous-gel) using synchrotron X-ray diffraction (XRD), pair-distribution function (PDF) analysis, and transmission electron microscopy (TEM). Opal-AN mainly exists as an aggregation of different sizes of nanospheres (&amp;lt;5 nm) generating banded features, whereas opal-AG displays close-packed silica nanospheres with a diameter of ~400 nm. TEM energy-dispersive X-ray spectroscopy (EDS) indicates that Na, Al, K, and Ca are present as trace elements in opal-AN and opal-AG. XRD patterns of both samples show one prominent peak at ~4.0 Å, together with broad peaks at ~2.0, ~1.45, and ~1.2 Å. Previous studies only identified the ~4.0 Å diffraction peak for the definition of opal-A. Hence, opal-A needs to be redefined by taking into account the newly observed three broad peaks. PDF patterns of opal-AN and opal-AG reveal short-range atomic pairs (&amp;lt;15 Å) with almost identical profiles. Both phases exhibit Si-O correlation at 1.61 Å and O-O correlation at 2.64 Å in their [SiO4] tetrahedra. The currently accepted opal structure is disordered intergrowths of cristobalite- and tridymite-like domains consisting of six-membered rings of [SiO4] tetrahedra. Our PDF analyses have identified additional, coesite-like nanodomains comprising four-membered [SiO4] rings. Moreover, we have identified eight-membered rings that can be generated by twinning and stacking faults from six-membered rings. The coesite nanodomains in opal-A may be a precursor for coesite micro-crystals formed by the impact of supersonic micro-projectiles at low pressures. More broadly, our study has also demonstrated that the combined approach of synchrotron XRD/PDF with TEM is a powerful approach to determine the structures of poorly crystallized minerals.</jats:p>