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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Probing Molecular Packing of Amorphous Pharmaceutical Solids Using X-ray Atomic Pair Distribution Function and Solid-State NMR

The structural investigation of amorphous pharmaceuticals is of paramount importance in comprehending their physicochemical stability. However, it has remained a relatively underexplored realm primarily due to the limited availability of high-resolution analytical tools. Here in this study, we utilized the combined power of X-ray pair distribution functions (PDFs) and solid-state nuclear magnetic resonance (ssNMR) techniques to probe the molecular packing of amorphous posaconazole and its amorphous solid dispersion at the molecular level. Leveraging synchrotron X-ray PDF data and employing the empirical potential structure refinement (EPSR) methodology, we unraveled the existence of a rigid conformation and discerned short-range intermolecular C–F contacts within amorphous posaconazole. Encouragingly, our ssNMR 19 F– 13 C distance measurements offered corroborative evidence supporting these findings. Furthermore, employing principal component analysis on the X-ray PDF and ssNMR data sets enabled us to gain invaluable insights into the chemical nature of the intermolecular interactions governing the drug–polymer interplay. These outcomes not only furnish crucial structural insights facilitating the comprehension of the underlying mechanisms governing the physicochemical stability but also underscore the efficacy of synergistically harnessing X-ray PDF and ssNMR techniques, complemented by robust modeling strategies, to achieve a high-resolution exploration of amorphous structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Tomography of ultrarelativistic nuclei with polarized photon-gluon collisions

A linearly polarized photon can be quantized from the Lorentz-boosted electromagnetic field of a nucleus traveling at ultrarelativistic speed. When two relativistic heavy nuclei pass one another at a distance of a few nuclear radii, the photon from one nucleus may interact through a virtual quark-antiquark pair with gluons from the other nucleus, forming a short-lived vector meson (e.g., ρ 0 ). In this experiment, the polarization was used in diffractive photoproduction to observe a unique spin interference pattern in the angular distribution of ρ 0 → π + π – decays. The observed interference is a result of an overlap of two wave functions at a distance an order of magnitude larger than the ρ0 travel distance within its lifetime. The strong-interaction nuclear radii were extracted from these diffractive interactions and found to be 6.53 ± 0.06 fm ( 197 Au) and 7.29 ± 0.08 fm ( 238 U), larger than the nuclear charge radii. The observable is demonstrated to be sensitive to the nuclear geometry and quantum interference of nonidentical particles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Insights on the structure and properties of sodium iron phosphate glasses from molecular dynamics simulations

Iron phosphate glasses are promising nuclear waste forms while more detailed understanding of their structures and structure-property relations are still needed to better design waste glass compositions. In this work we report studies of three series of sodium iron phosphate (NFP) glasses: 60P 2 O 5 -(40-x)Fe 2 O 3 -xNa 2 O (x = 0→40), (100–2x)P 2 O 5 -xFe 2 O 3 -xNa 2 O (x = 5→17.5) and one with different iron redox ratio, to understand the composition as well as the iron redox effects on the structure and properties of these glasses using molecular dynamics simulations with effective two-body and three-body potentials. Structural analyses, including pair distribution function, bond angle distribution, Q n distribution, and polyhedral connectivity, were performed to obtain in-depth information on short-range and medium-range structural features. The P-O pair distributions showed a first peak splitting with phosphorus-bridging and non-bridging oxygen contributions. This and the average P-O and other cation-oxygen bond distances are in excellent agreement with experiments. The coordination number of P 5+ remained four while that of Fe 3+ increased from 4.30 to 4.72 with decreasing Fe/Na ratio. Polyhedral linkage analysis showed [PO 4 ] units linked with [PO 4 ] and [FeO x ] through corner-sharing while the [PO 4 ]-[FeO x ] linkages become dominant for compositions with Fe 2 O 3 larger than 15 mol%. The effect of iron redox ratio on the structure of NFP glasses was also studied and it was found that bond lengths and coordination numbers were not strongly affected, while the reduction of iron introduced higher network distortions, as evident by O-P-O bond angle and Q n distribution. The glass transition temperature (T g ) showed a monotonic increase with Fe 2 O 3 in the first series, in good agreement with experiments, while those of the second series showed a maximum at P 2 O 5 = 82 mol%. Here, calculated elastic moduli were found to increase with Fe 2 O 3 in the first glass series, which was be explained by the increase of network connectivity, while those of the second series decrease with Fe 2 O 3 due to decrease of P 2 O 5 .

36 MATERIALS SCIENCE↗
DOE OSTI2024

Different structural behavior of MgSiO 3 and CaSiO 3 glasses at high pressures

Knowledge of the structural behavior of silicate melts and/or glasses at high pressures provides fundamental information for discussing the nature and properties of silicate magmas in the Earth’s interior. The behavior of Si-O structures under high-pressure conditions has been widely studied, while the effect of cation atoms on the high-pressure structural behavior of silicate melts or glasses has not been well investigated. Here, in this study, we investigated the structures of MgSiO 3 and CaSiO 3 glasses up to 5.4 GPa by in situ X-ray pair distribution function measurements to understand the effect of different cations (Mg 2+ and Ca 2+ ) on high-pressure structural behavior of silicate glasses. We found that the structural behavior of MgSiO 3 and CaSiO 3 glasses are different at high pressures. The structure of MgSiO 3 glass changes by shrinking of Si-O-Si angle with increasing pressures, which is consistent with previous studies for SiO 2 and MgSiO 3 glasses. On the other hand, CaSiO 3 glass shows almost no change in Si-Si distance at high pressures, while the intensities of two peaks at ~3.0 and ~3.5 Å change with increasing pressure. The structural change in CaSiO 3 glass at high pressure is interpreted as the change in the fraction of the edge-shared and corner-shared CaO 6 -SiO 4 structures. The different high-pressure structural behavior observed in MgSiO 3 and CaSiO 3 glasses may be the origin of differences in properties, such as viscosity between MgSiO 3 and CaSiO 3 melts at high pressures. This signifies the importance of different structural behaviors due to different cations in investigations of the nature and properties of silicate magmas in Earth’s interior.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Bimetallic Copper/Ruthenium/Osmium Complexes: Observation of Conformational Differences Between the Solution Phase and Solid State by Atomic Pair Distribution Function Analysis

Abstract High‐energy X‐ray scattering and pair distribution function analysis (HEXS/PDF) is a powerful method to reveal the structure of materials lacking long‐range order, but is underutilized for molecular complexes in solution. We demonstrate the application of HEXS/PDF with 0.26 Å resolution to uncover the solution structure of five bimetallic Cu I /Ru II /Os II complexes. HEXS/PDF of each complex in acetonitrile solution confirms the pairwise distances in the local coordination sphere of each metal center as well as the metal⋅⋅⋅metal distances separated by over 12 Å. The metal⋅⋅⋅metal distance detected in solution is compared with that from the crystal structure and molecular models to confirm that distortions to the metal bridging ligand are unique to the solid state. This work presents the first example of observing sub‐Ångström conformational differences by direct comparison of solution phase and solid‐state structures and shows the potential for HEXS/PDF in the determination of solution structure of single molecules.

Xie, Zhu‐Lin↗
DOE OSTI2021

Amorphous dispersions of flubendazole in hydroxypropyl methylcellulose: Formulation stability assisted by pair distribution function analysis

Here, we use X-ray pair distribution function (PDF) analysis applied to high-energy synchrotron X-ray powder diffraction data to evaluate the amorphous solid dispersions interactions and their aging stability. The obtained systems are based on hydroxypropyl methylcellulose (hypromellose) derivatives and flubendazole (FBZ) drug dispersions prepared using a spray-dryer technique. We carry out stability studies under aging parameters (40 °C/75% relative humidity) to tune the systems’ recrystallization. The results reveal that ion-base interactions between the drug-polymer matrix are responsible for reducing clustering processes yielding slower recrystallization and different ordering in the hypromellose phthalate (HPMCP/FBZ) and hypromellose acetate succinate (HPMC-AS/FBZ) systems and complete drug clustering in hypromellose (HPMC-E3/FBZ). The structural ordering was accessed using differential X-ray PDFs that revealed the region between 3.5 Å and 5.0 Å could be related to FBZ intermolecular interactions and is more ordered for the least stable system (HPMC-E3/FBZ) and less ordered for the most stable system (HPMCP/FBZ). These results show that the ion-base interactions between drug and matrix occur at these intermolecular distances.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Probing lead acetate in solution using X-ray diffraction

Here, for the purpose of water purification involving toxic metal sensing and removal, high energy X-ray diffraction experiments have been performed on lead acetate Pb(Ac) 2 solutions, liquid and amorphous glutathione disulfide (GSSG), and their mixtures. The data have been interpreted using Empirical Potential Structure Refinement and pair distribution function analysis. At the highest concentration of 1 M Pb(Ac) 2 in water, the lead molecules are found to cluster and the second shell in the water structure becomes slightly more ordered as the water molecules become compressed. Liquid and amorphous GSSG are found to hydrogen bond primarily via OH-O interactions, while NH-O bonds are much more distorted. Aqueous solutions of Pb(Ac) 2 + GSSG show the closest Pb-O (carboxyl) and Pb-N (amine) bonds both at a distance of 2.5 ± 0.1 Å at a concentration of 1 M Pb(Ac) 2 in water. At 0.75 M Pb(Ac) 2 in water, strong Pb-S bonds are found at a distance of 2.8 ± 0.1 Å. The implications for lead removal using capacitive deionization are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A confocal laser-induced fluorescence diagnostic with an annular laser beam

Here, in this work, we report an annular beam confocal laser-induced fluorescence (LIF) configuration, which allows for high spatial resolution measurements of plasma properties in plasma setups and sources with limited optical access. The proposed LIF configuration utilizes the annular laser beam generated by a pair of diffractive axicons. The LIF signal is collected along the main optical axis within the ring region. It is shown experimentally that at a focal distance of 300 mm, a spatial resolution of ~5.3 mm can be achieved. Using geometric optics estimations, we showed that ~1 mm resolution at the same focal distance could potentially be achieved by modifying laser beam parameters. This approaches the localization accuracy of conventional LIF collection methods (with crossing laser beam injection and fluorescence collection optical paths). Measurements of the ion velocity distribution function in an argon plasma using both the confocal LIF with an annular laser beam and conventional LIF demonstrate a satisfactory agreement. The proposed LIF setup has potential applications for diagnostics in various plasma processing equipment and plasma sources, such as hollow cathodes, microplasmas, electric propulsion, etc.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Weak scaling of the contact distance between two fluctuating interfaces with system size

A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers-of-mass remain separated by a nonzero distance ℓ. An example of such a situation is the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Here we present a general approach to calculate the probability distribution of the contact distance ℓ and determine how its most likely value ℓ* depends on the surfaces' lateral size L. Using the Edward-Wilkinson equation as a model for interfaces, we demonstrate that ℓ* scales weakly with system size, i.e., the dependence of ℓ* on L for both (1+1)- and (2+1)-dimensional interfaces is such that lim L→∞ (ℓ*/L) = 0. In particular, for (2+1)-dimensional interfaces ℓ* is an algebraic function of logL, a result that is confirmed by computer simulations of slab-shaped domains formed under periodic boundary conditions. Overall, this weak scaling implies that such domains remain topologically intact until ℓ becomes very small compared to the lateral size of the interface, contradicting expectations from equilibrium thermodynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-informed Deep Generative Models

Here, we propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple “snapshots.” Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots. By training a physics-informed generative model that generates “fake” sample paths, we aim to fit the observed particle ensemble distributions with a curve in the probability measure space, which is induced from the inferred particle dynamics. We employ different metrics to quantify the differences between distributions, e.g., the sliced Wasserstein distances and the adversarial losses in generative adversarial networks. We refer to this method as generative “ensemble-regression” (GER), in analogy to the classic “point-regression,” where we infer the dynamics by performing regression in the Euclidean space. We illustrate the GER by learning the drift and diffusion terms of particle ensembles governed by SODEs with Brownian motions and Lévy processes up to 100 dimensions. We also discuss how to treat cases with noisy or truncated observations. Apart from systems consisting of independent particles, we also tackle nonlocal interacting particle systems with unknown interaction potential parameters by constructing a physics-informed loss function. Finally, we investigate scenarios of paired observations and discuss how to reduce the dimensionality in such cases by proving a convergence theorem that provides theoretical support.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

In Situ Visualization of Local Distortions in the High- T c Molecule-Intercalated Li x (C 5 H 5 N) y Fe 2– z Se 2 Superconductor

A time-resolved synchrotron X-ray total scattering study sheds light on the evolution of the different structural length scales involved during the intercalation of the layered iron–selenide host by organic molecular donors, aiming at the formation of the expanded-lattice Li x (C 5 H 5 N) y Fe 2– z Se 2 hybrid superconductor. The intercalates are found to crystallize in the tetragonal ThCr 2 Si 2 -type structure at the average level, however, with an enhanced interlayer iron–selenide spacing ( d = 16.2 Å) that accommodates the heterocyclic molecular spacers. Quantitative atomic pair distribution function (PDF) analysis at variable times suggests distorted FeSe 4 tetrahedral local environments that appear swollen with respect to those in the parent β-FeSe. Simultaneously acquired in situ synchrotron X-ray powder diffraction data disclose that secondary phases (α-Fe and Li 2 Se) grow significantly when a higher lithium concentration is used in the solvothermal reaction or when the solution is aged. These observations are in line with the strongly reducing character of the intercalation medium’s solvated electrons that mediate the defect chemistry of the expanded-lattice superconductor. In the latter, intralayer correlated local distortions indicate electron-donating aspects that reflect in somewhat enlarged Fe–Se bonds. Additionally, they also reveal a degree of relief of chemical pressure associated with a large distance between Fe and Se sheets (“taller” anion height) and a stretched Fe–Fe square planar topology. The elongation of the latter, derived from the in situ PDF study, speaks for a plausible increase in the Fe-site vacancy concentration. The evolution of the local structural parameters suggests an optimum reaction window where kinetically stabilized phases resemble the distortions of the edge-sharing Fe–Se tetrahedra, required for a high- T c in expanded-lattice iron-chalcogenides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Two-Nucleon Short-Range Correlations in Light Nuclei

Understanding the nucleon-nucleon interaction is a fundamental task in nuclear physics, as NN interaction models are a crucial input to modern nuclear structure calculations. While great progress has been made toward understanding this interaction, the available state-of-the-art models predict significantly different behaviors at short distances and high momenta (scale-and-scheme dependence), where two-nucleon Short-Range Correlations (SRCs) dominate the nuclear wave function. Thus, SRCs are a unique tool to constrain the NN interaction and vice versa. SRCs are naturallyoccurring high-local-density NN pairs that, as a result of their short-distance (approx. 0.1 fm) repulsive interaction, fly apart with high momenta, hence populating momentum states above the Fermi level. The study of SRCs also has significant implications for other fields, such as the astrophysics of neutron stars and the behavior of cold atomic gasses. This thesis describes experimental and phenomenological studies of the short-distance / high-momentum structure of the NN interaction through the study of SRCs and vice versa. Experimentally, I report the first measurement of the 3He and 3H(e,e'p) reactions in Hall A of the Thomas Jefferson National Accelerator Facility in kinematics in which the measured cross sections should be sensitive to the underlying nucleon momentum distributions in the range 40 to 500 MeV/c. The resulting cross-section ratios and absolute cross sections were compared to momentum-distribution ratios and precise cross-section calculations respectively. Phenomenologically, I report the generalization of the Contact Formalism (GCF) to nuclear systems, which exploits scale separation and universality to describe nucleons at short distances and high momenta.

Cruz Torres, Reynier↗
DOE OSTI2023

Evolution of the age-included nearest pair distribution in disperse multiphase flows

The age of the nearest particle pair is introduced as the difference between the current time and the most recent time when the nearest particle pair was formed. The evolution equation for the age-included nearest pair distribution function is derived. With the assumption of random destruction of the nearest particle pairs, the evolution equation predicts the exponential probability distribution of the ages of the nearest particle pairs. Particle-resolved numerical simulations with moving particles are performed to verify this prediction. The equation is then used to derive the evolution equation for the particle–fluid–particle (PFP) stress, which is known to be related to hyperbolicity of the two-fluid equations. It is found that the relaxation time of the age probability distribution is also the relaxation time for the PFP stress. Guided by the closure terms in the PFP stress evolution equation, we study kinematics of the nearest particle pairs in the particle-resolved simulations for flows caused by sedimentation of the particles with initially isotropic and homogeneous particle distributions. At the steady states, the particle Reynolds numbers are around 20. Anisotropy and inhomogeneity of particle distributions are seen to develop in these flows. The mean distances to the nearest particles and evolution of the distribution of the Voronoi cell volumes are studied. We also found the PFP stress is closely related to the changes in these inter-particle scale quantities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Node Distortion as a Tunable Mechanism for Negative Thermal Expansion in Metal–Organic Frameworks

Chemically functionalized series of metal–organic frameworks (MOFs), with subtle differences in local structure but divergent properties, provide a valuable opportunity to explore how local chemistry can be coupled to long-range structure and functionality. Using in situ synchrotron X-ray total scattering, with powder diffraction and pair distribution function (PDF) analysis, we investigate the temperature dependence of the local- and long-range structure of MOFs based on NU-1000, in which Zr 6 O 8 nodes are coordinated by different capping ligands (H 2 O/OH, Cl – ions, formate, acetylacetonate, and hexafluoroacetylacetonate). We show that the local distortion of the Zr 6 nodes depends on the lability of the ligand and contributes to a negative thermal expansion (NTE) of the extended framework. Using multivariate data analyses, involving non-negative matrix factorization (NMF), we demonstrate a new mechanism for NTE: progressive increase in the population of a smaller, distorted node state with increasing temperature leads to global contraction of the framework. The transformation between discrete node states is noncooperative and not ordered within the lattice, i.e., a solid solution of regular and distorted nodes. Density functional theory calculations show that removal of ligands from the node can lead to distortions consistent with the Zr···Zr distances observed in the experiment PDF data. Control of the node distortion imparted by the nonlinker ligand in turn controls the NTE behavior. Furthermore, these results reveal a mechanism to control the dynamic structure of MOFs based on local chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Atomic-Scale Imaging of Condensed Counterions

Here, the functioning of a wide variety of charged macromolecules, from DNA to fuel cell membranes, is dependent on how the counterions surrounding them are arranged. In order to decrease Coulombic repulsion, some of the fixed charges on these molecules are neutralized by a fraction of the counterions-this phenomenon is called counterion condensation. The nature of counterion condensation can be only be inferred indirectly from traditional experiments such as X-ray scattering and modern experiments such as single molecule electrometry. The prevalent conclusion in the literature, based on both theory and experiment, is that the distribution of counterions is peaked right next to the macromolecule, i.e., condensation results in the formation of contact ion pairs. In this study, cryogenic electron microscopy (cryo-EM) was used to study the arrangement of condensed halide counterions near a positively charged polypeptoid nanofiber. The locations of both condensed and fixed charges were determined directly from atomic-scale images. Our experimentally determined counterion distributions were peaked at distances of about 5 Å away from the fixed positive charge, indicating the presence of a layer of water molecules between condensed ion pairs. We posit that this distribution is driven by the entropy of the condensed ions.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Local structure of zinc–indium–tin oxide films via grazing-incidence x-ray pair-distribution functions and theoretical methods

A detailed experimental and theoretical study on the local (r ≤ 4.5 Å) atomic structure of amorphous and crystalline zinc–indium–tin oxide (ZITO) thin films using grazing-incidence x-ray Pair-Distribution Functions (PDFs), ab initio Molecular Dynamics (MD), and Empirical Potential Structure Refinement (EPSR) Monte Carlo simulations is presented. High-energy synchrotron x rays, a two-dimensional detector, and different incident angles were used to probe the depth uniformity of five (ZnO) 0.15 (In 2 O 3 ) 0.70 (SnO 2 ) 0.15 films that were deposited via pulsed-laser deposition at growth temperatures (T G ) ranging from 25 to 300 °C. Films deposited at T G ≤ 150 °C were amorphous. The partially crystalline (T G = 200 °C) and fully crystalline (T G = 300 °C) films were highly textured. Both crystalline and amorphous structures were investigated using ab initio MD and EPSR Monte Carlo simulations. The density of the amorphous films determined from the experimental data agreed with MD calculations. Coordination numbers, bond lengths, and distortion for metal–oxygen and for both the edge- and corner-shared In–metal shells up to 4.5 Å obtained from PDF analysis closely agreed with MD and EPSR simulations. There is a pronounced decrease in the edge- and corner-shared In–Zn distances arising from the shorter Zn–O bond length, Zn–O tetrahedral coordination, and In–O–Zn angle in amorphous ZITO compared to its crystalline counterpart. A maximum in electrical mobility was observed for the amorphous film just before crystallization occurred. While the peak is broad, consistent with nearly unchanged overall cation–oxygen coordination in the amorphous films, ESPR results indicate that the tetrahedral coordination follows the conductivity trend.

Grazing Incidence X-ray↗
DOE OSTI2022

Exclusive production of a pair of high transverse momentum photons in pion-nucleon collisions for extracting generalized parton distributions

We show that exclusive production of a pair of high transverse momentum photons in pion-nucleon collisions can be systematically studied in QCD factorization approach if the photon’s transverse momentum q T with respect to the colliding pion is much greater than Λ QCD . We demonstrate that the leading power non-perturbative contributions to the scattering amplitudes of this exclusive process are process-independent and can be systematically factorized into universal pion’s distribution amplitudes (DAs) and nucleon’s generalized parton distributions (GPDs), which are convoluted with corresponding infrared safe and perturbatively calculable short-distance hard parts. The correction to this factorized expression is suppressed by powers of 1/q T . We demonstrate quantitatively that this new type of exclusive processes is not only complementary to existing processes for extracting GPDs, but also capable of providing an enhanced sensitivity to the dependence of both DAs and GPDs on the active parton’s momentum fraction x. We also introduce additional, but the same type of exclusive observables to enhance our capability to explore GPDs, in particular, their x-dependence.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

The structure of CaO–MgO–Al 2 O 3 –SiO 2 melts and glasses doped with FeO X –NiO

Neutron and x-ray diffraction measurements have been performed on CaO–MgO–Al 2 O 3 –SiO 2 (CMAS) glasses doped with NiO–Fe X O at room temperature, along with x-ray measurements on aerodynamically levitated liquids at ≥2000 K. The disordered structures have been modeled using empirical potential structure refinement to investigate the relation between the aluminosilicate network and the modifying cations. The SiO 4 and AlO 4 tetrahedra are found to have wider Si–O and Al–O bond distance distributions in the glass, and the first Ca–O n coordination shell is highly distorted, redistributing different populations of long and short bonds between the liquid and the glass. The addition of Fe and Ni at low aluminosilicate content increases the number of free oxygens not bonded to AlO 4 or SiO 4 . Mg–O and Fe–O are both found to be predominantly fourfold and fivefold in the liquid and glassy states. Despite these low coordination numbers, their bond angle distributions indicate that they are predominantly in nontetrahedral-type geometries, with ferrous and ferric iron possessing similar coordination environments. The Ca–O and Mg–O average coordination numbers and enthalpies of solution are consistent with their higher reactivity within relatively acidic aluminosilicate melts.

36 MATERIALS SCIENCE↗