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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Quantifying Epistemic Uncertainty in Binary Classification via Accuracy Gain

ABSTRACT Recently, a surge of interest has been given to quantifying epistemic uncertainty (EU), the reducible portion of uncertainty due to lack of data. We propose a novel EU estimator in the binary classification setting, as the posterior expected value of the empirical gain in accuracy between the current prediction and the optimal prediction. In order to validate the performance of our EU estimator, we introduce an experimental procedure where we take an existing dataset, remove a set of points, and compare the estimated EU with the observed change in accuracy. Through real and simulated data experiments, we demonstrate the effectiveness of our proposed EU estimator.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Gamma-ray spectra analyses of molten salts in spent nuclear fuels pyroprocessing facilities for mass measurement

To evaluate radioactive tracer dilution and gamma spectroscopy as a safeguards technique for monitoring the mass of liquid salt in molten salt systems, the gamma spectroscopy data of salt samples from the pyroprocessing facilities in Idaho National Laboratory were acquired and analyzed. The primary focus is the uncertainty analysis of the gamma radioactivity of 154 Eu isotope in the molten salts. The facilities include an electrorefiner for pyroprocessing spent oxide fuels (SOF-ER) and Mark-IV ER for processing the metallic fuels from Experimental Breeder Reactor-II (EBR-II). The relative gamma radioactivity uncertainty was consistently at 3% for 137 Cs for both Mark-IV ER and SOF-ER salts. However, for 154 Eu, it was 8% for SOF-ER salt and 7% for Mark-IV ER salt. Here, the main reason for the higher uncertainty for 154 Eu is believed to be the lower counting statistics in gamma spectroscopy. To improve the gamma radioactivity uncertainty of isotope 154 Eu, a longer data acquisition time (12 h instead of 4 h) and a higher count rate gamma detector for gamma spectroscopy were tested and it was found that the uncertainty for 154 Eu was significantly improved from 7% or 8–3%.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Vertical Strain-Driven Antiferromagnetic to Ferromagnetic Phase Transition in EuTiO 3 Nanocomposite Thin Films

Three-dimensional (3D) strain induced in self-assembled vertically aligned nanocomposite (VAN) epitaxial films provides an unrivaled method to induce very large strains in thin films. Here, by growing VAN films of EuTiO 3 (ETO)–Eu 2 O 3 (EO) with different EO fractions, the vertical strain was systematically increased in ETO, up to 3.15%, and the Eu–Ti–Eu bond angle along $\langle$111$\rangle$ decreased by up to 1°, leading to a weakening of the antiferromagnetic interactions and switching from antiferromagnetic to ferromagnetic behavior. Our work has shown for the first time that Eu–Ti–Eu superexchange interactions play a key role in determining the magnetic ground state of ETO. Broadly, our work serves as an exemplar to show that multifunctionalities in strong spin–lattice coupling perovskite oxides can be uniquely tuned at the atomic scale using simple VAN structures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Dopant site-dependent luminescence from rare-earth doped dibarium octafluorohafnate Ba 2 HfF 8 nanocubes for radiation detection

Development of new host materials containing heavy elements for radiation detection is highly desirable. In this work, dibarium octafluorohafnate, Ba 2 HfF 8 , doped with rare-earth ions, was synthesized as cube-shaped nanocrystals via a facile hydrothermal method. The host lattice contains two Ba 2+ crystallographic sites, and dopants on these sites exhibit site-dependent photoluminescence (PL), cathodoluminescence (CL) and X-ray excited radioluminescence (RL) characteristics. Single doping contents were optimized as 25 mol% Tb 3+ and 5 mol% Eu 3+ . In Ba 2 HfF 8 :Tb 3+ –Eu 3+ codoped nanocrystals, preferrable occupation of Eu 3+ and Tb 3+ at two different Ba 2+ sites in the host lattice was observed. The nanocubes exhibited enhanced emissions over micron sized particles. In PL, the presence of Tb3+ ions significantly enhanced the emission intensity of Eu 3+ ions due to energy transfer from the Tb 3+ to Eu 3+ ions, while under high-energy irradiation in CL or RL, Tb 3+ emission was intensified. X-ray induced RL with afterglow in seconds was observed. Finally, it was found that the codoped sample showed higher sensitivity than the singly doped sample, indicating that codoping is an effective strategy to develop a scintillator with this host structure for high-energy radiation detection.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2023

The effect of rare earth (RE 3+ ) ionic radii on transparent lanthanide-tellurite glass-ceramics: correlation between ‘hole-formalism’ and crystallization

Rare earth (RE) doped transparent tellurite glass-ceramics (GCs) are widely explored for their application as advanced photonic materials. Specifically, the growth of RE based “anti-glass” crystalline phases in transparent GCs enhances their effective functionality. Enormous studies on the properties of GCs revealed that optimization of glass composition and heat-treatment schedule are the foremost factors that affect the transparency of the GCs. Nevertheless, the direct effect of RE 3+ ions on the crystallization mechanism of glass has hardly been reported. Therefore, a base glass of the composition La 2 O 3 –Gd 2 O 3 –TiO 2 –TeO 2 (LGTT) is doped with RE 3+ ions (Ce 3+ , Pr 3+ , Nd 3+ , Sm 3+ , Eu 3+ , Tb 3+ , and Dy 3+ ) with varied ionic radii. Rietveld refinement from XRD of GCs confirms that (La/Gd) 2 Te 6 O 15 phases are precipitated, where dopants Ce, Pr and Nd occupy La sites, while Sm, Eu, Tb, and Dy occupy Gd sites. The configurational heat-capacity (ΔC p ) from DSC is found to be lower for larger ionic radii REs (Ce, Pr, Nd) than smaller ionic radii REs (Sm, Eu, Tb, Dy) thereby exhibiting higher chemical ordering followed by faster crystal growth rate in the former. However, the transparency retention profile of different RE-doped GCs follows the trend Eu:Tb > Sm:Dy > Nd > Pr > Ce, confirming the ionic radii effect. In addition to the ionic radii effect, in this work, we propose a ‘Hole-Formalism’ concept to explain the observed trend. It is further corroborated with an identical neutron diffraction pattern and ΔC p values for these ion pairs Sm 3+ : Dy 3+ (4f 5 : 4f 9 ) and Eu 3+ : Tb 3+ (4f 6 : 4f 8 ) results in a similar crystallization mechanism, transmission profile and fine-scale microstructures of these RE-based tellurite GCs.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Strong enhancement of magnetic ordering temperature and structural/valence transitions in EuPd 3 S 4 under high pressure

We present a comprehensive study of the inhomogeneous mixed-valence compound, EuPd 3 S 4 , by electrical transport, X-ray diffraction, time-domain 151 Eu synchrotron Mössbauer spectroscopy, and X-ray absorption spectroscopy measurements under high pressure. Electrical transport measurements show that the antiferromagnetic ordering temperature, T N , increases rapidly from 2.8 K at ambient pressure to 23.5 K at ~19 GPa and plateaus between ~19 and ~29 GPa after which no anomaly associated with T N is detected. A pressure-induced first-order structural transition from cubic to tetragonal is observed, with a rather broad coexistence region (~20 GPa to ~30 GPa) that corresponds to the T N plateau. Mössbauer spectroscopy measurements show a clear valence transition from approximately 50:50 Eu 2+ :Eu 3+ to fully Eu 3+ at ~28 GPa, consistent with the vanishing of the magnetic order at the same pressure. X-ray absorption data show a transition to a fully trivalent state at a similar pressure. Our results show that pressure first greatly enhances T N , most likely via enhanced hybridization between the Eu 4 f states and the conduction band, and then, second, causes a structural phase transition that coincides with the conversion of the europium to a fully trivalent state.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A-type antiferromagnetic order in semiconducting EuMg 2 Sb 2 single crystals

Eu-based Zintl-phase materials EuA 2 Pn 2 (A = Mg, In, Cd, Zn; Pn = Bi, Sb, As, P) have generated significant recent interest owing to the complex interplay of magnetism and band topology. Here, we investigated the crystallographic, magnetic, and electronic properties of the layered Zintlphase single crystals of EuMg 2 Sb 2 with the trigonal CaAl 2 Si 2 crystal structure (space group $P\bar{3}m1$). Electrical resistivity measurements complemented with angle-resolved photoemission spectroscopy (ARPES) studies and density functional theory (DFT) calculations find an activated behavior with intrinsic conductivity at high temperatures indicating a semiconducting electronic ground state with a narrow energy gap of 370 meV. Magnetic susceptibility and zero-field heat capacity measurements indicate that the compound undergoes antiferromagnetic (AFM) ordering at the Néel temperature T N = 8.0(2) K. Here, zero-field neutron-diffraction measurements reveal that the AFM ordering is A-type where the Eu spins (Eu 2+ , S = 7/2) arranged in ab-plane layers are aligned ferromagnetically in the ab plane and the Eu spins in adjacent layers are aligned antiferromagnetically. Eu-moment reorientation within the ab planes in the trigonal AFM domains associated with a very weak inplane magnetic anisotropy is also evident below T N at low fields < 0.05 T. Although isostructural semimetallic EuMg 2 Bi 2 is reported to host Dirac surface states, the observation of narrow-gap semiconducting behavior in EuMg 2 Sb 2 implies a strong role of spin-orbit coupling (SOC) in tuning the electronic states of these materials. Our DFT studies also suggest, besides the SOC, the more electronegative and smaller Sb than Bi shifts the low-lying conduction bands along the Γ-A direction to higher energy, resulting in an indirect bulk band gap between the Γ and M points for EuMg 2 Sb 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Technical report with results for 156Eu

The evaluated γ-ray branching ratio values after the decay of 156 Eu are based on measurements done in the 1960s and 1970s which improve upon measurements done back in the 1950s. These experiments, while improving on each other, were not able to produce nearly pure samples and impurities produced along with the sample ( 152 Eu, 154 Eu, and 155 Eu) interfered with the study of the beta spectrum for 156Eu. The values for the branching ratios of 156 Eu from National Nuclear Data Center (NNDC) [4] have uncertainties of ranging from 7-14% for the 10 most intense γ rays and up to 30% for the weaker ones. This work aims to improve the precision on the majority of these γ-ray branches.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Materials Data on EuCu5 by Materials Project

EuCu5 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Eu is bonded in a 6-coordinate geometry to eighteen Cu atoms. There are six shorter (2.98 Å) and twelve longer (3.28 Å) Eu–Cu bond lengths. There are two inequivalent Cu sites. In the first Cu site, Cu is bonded to four equivalent Eu and eight Cu atoms to form a mixture of face, edge, and corner-sharing CuEu4Cu8 cuboctahedra. There are four shorter (2.51 Å) and four longer (2.58 Å) Cu–Cu bond lengths. In the second Cu site, Cu is bonded in a 12-coordinate geometry to three equivalent Eu and six equivalent Cu atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on EuGa4 by Materials Project

EuGa4 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Eu is bonded in a 8-coordinate geometry to sixteen Ga atoms. There are eight shorter (3.39 Å) and eight longer (3.48 Å) Eu–Ga bond lengths. There are two inequivalent Ga sites. In the first Ga site, Ga is bonded in a 9-coordinate geometry to four equivalent Eu and five Ga atoms. There are one shorter (2.51 Å) and four longer (2.64 Å) Ga–Ga bond lengths. In the second Ga site, Ga is bonded in a 12-coordinate geometry to four equivalent Eu and four equivalent Ga atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on EuNi5 by Materials Project

EuNi5 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Eu is bonded in a 6-coordinate geometry to eighteen Ni atoms. There are six shorter (2.89 Å) and twelve longer (3.17 Å) Eu–Ni bond lengths. There are two inequivalent Ni sites. In the first Ni site, Ni is bonded in a 12-coordinate geometry to three equivalent Eu and six equivalent Ni atoms. All Ni–Ni bond lengths are 2.42 Å. In the second Ni site, Ni is bonded to four equivalent Eu and eight Ni atoms to form a mixture of corner, edge, and face-sharing NiEu4Ni8 cuboctahedra. All Ni–Ni bond lengths are 2.50 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on EuZn5 by Materials Project

EuZn5 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Eu is bonded in a 6-coordinate geometry to eighteen Zn atoms. There are six shorter (3.15 Å) and twelve longer (3.46 Å) Eu–Zn bond lengths. There are two inequivalent Zn sites. In the first Zn site, Zn is bonded to four equivalent Eu and eight Zn atoms to form a mixture of edge, corner, and face-sharing ZnEu4Zn8 cuboctahedra. There are four shorter (2.65 Å) and four longer (2.73 Å) Zn–Zn bond lengths. In the second Zn site, Zn is bonded in a 9-coordinate geometry to three equivalent Eu and six equivalent Zn atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Eu4Cl6O by Materials Project

Eu4OCl6 crystallizes in the hexagonal P6_3mc space group. The structure is three-dimensional. there are two inequivalent Eu2+ sites. In the first Eu2+ site, Eu2+ is bonded in a 1-coordinate geometry to one O2- and seven Cl1- atoms. The Eu–O bond length is 2.37 Å. There are a spread of Eu–Cl bond distances ranging from 2.95–3.30 Å. In the second Eu2+ site, Eu2+ is bonded in a 1-coordinate geometry to one O2- and six Cl1- atoms. The Eu–O bond length is 2.35 Å. There are three shorter (2.97 Å) and three longer (3.16 Å) Eu–Cl bond lengths. O2- is bonded in a tetrahedral geometry to four Eu2+ atoms. There are two inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a 5-coordinate geometry to five Eu2+ atoms. In the second Cl1- site, Cl1- is bonded in a 4-coordinate geometry to four Eu2+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on EuAg5 by Materials Project

EuAg5 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Eu is bonded in a distorted hexagonal planar geometry to eighteen Ag atoms. There are six shorter (3.31 Å) and twelve longer (3.70 Å) Eu–Ag bond lengths. There are two inequivalent Ag sites. In the first Ag site, Ag is bonded in a 12-coordinate geometry to three equivalent Eu and nine Ag atoms. There are six shorter (2.87 Å) and three longer (3.31 Å) Ag–Ag bond lengths. In the second Ag site, Ag is bonded to four equivalent Eu and eight Ag atoms to form a mixture of corner, edge, and face-sharing AgEu4Ag8 cuboctahedra. All Ag–Ag bond lengths are 2.86 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Eu2B5ClO9 by Materials Project

Eu2B5O9Cl crystallizes in the orthorhombic Pnn2 space group. The structure is three-dimensional. there are two inequivalent Eu2+ sites. In the first Eu2+ site, Eu2+ is bonded in a 9-coordinate geometry to seven O2- and two Cl1- atoms. There are a spread of Eu–O bond distances ranging from 2.56–2.95 Å. There are one shorter (2.99 Å) and one longer (3.04 Å) Eu–Cl bond lengths. In the second Eu2+ site, Eu2+ is bonded in a 9-coordinate geometry to seven O2- and two Cl1- atoms. There are a spread of Eu–O bond distances ranging from 2.53–3.06 Å. There are one shorter (2.98 Å) and one longer (3.10 Å) Eu–Cl bond lengths. There are five inequivalent B3+ sites. In the first B3+ site, B3+ is bonded to four O2- atoms to form corner-sharing BO4 tetrahedra. There are a spread of B–O bond distances ranging from 1.47–1.49 Å. In the second B3+ site, B3+ is bonded to four O2- atoms to form corner-sharing BO4 tetrahedra. There are a spread of B–O bond distances ranging from 1.47–1.50 Å. In the third B3+ site, B3+ is bonded in a trigonal planar geometry to three O2- atoms. There is one shorter (1.37 Å) and two longer (1.38 Å) B–O bond length. In the fourth B3+ site, B3+ is bonded in a trigonal planar geometry to three O2- atoms. There are a spread of B–O bond distances ranging from 1.36–1.39 Å. In the fifth B3+ site, B3+ is bonded to four O2- atoms to form corner-sharing BO4 tetrahedra. There are a spread of B–O bond distances ranging from 1.46–1.52 Å. There are nine inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Eu2+ and two B3+ atoms. In the second O2- site, O2- is bonded in a 2-coordinate geometry to one Eu2+ and two B3+ atoms. In the third O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Eu2+ and two B3+ atoms. In the fourth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Eu2+ and two B3+ atoms. In the fifth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two Eu2+ and two B3+ atoms. In the sixth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two Eu2+ and two B3+ atoms. In the seventh O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two Eu2+ and two B3+ atoms. In the eighth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two Eu2+ and two B3+ atoms. In the ninth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two Eu2+ and two B3+ atoms. There are two inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a rectangular see-saw-like geometry to four Eu2+ atoms. In the second Cl1- site, Cl1- is bonded in a 4-coordinate geometry to four Eu2+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Eu2B5BrO9 by Materials Project

Eu2B5O9Br crystallizes in the orthorhombic Pnn2 space group. The structure is three-dimensional. there are two inequivalent Eu2+ sites. In the first Eu2+ site, Eu2+ is bonded in a 9-coordinate geometry to seven O2- and two Br1- atoms. There are a spread of Eu–O bond distances ranging from 2.57–3.07 Å. There are one shorter (3.04 Å) and one longer (3.10 Å) Eu–Br bond lengths. In the second Eu2+ site, Eu2+ is bonded in a 9-coordinate geometry to seven O2- and two Br1- atoms. There are a spread of Eu–O bond distances ranging from 2.55–3.12 Å. There are one shorter (3.03 Å) and one longer (3.13 Å) Eu–Br bond lengths. There are five inequivalent B3+ sites. In the first B3+ site, B3+ is bonded in a trigonal planar geometry to three O2- atoms. There is two shorter (1.37 Å) and one longer (1.40 Å) B–O bond length. In the second B3+ site, B3+ is bonded in a trigonal planar geometry to three O2- atoms. There is one shorter (1.37 Å) and two longer (1.38 Å) B–O bond length. In the third B3+ site, B3+ is bonded to four O2- atoms to form corner-sharing BO4 tetrahedra. There is three shorter (1.48 Å) and one longer (1.50 Å) B–O bond length. In the fourth B3+ site, B3+ is bonded to four O2- atoms to form corner-sharing BO4 tetrahedra. There are a spread of B–O bond distances ranging from 1.46–1.50 Å. In the fifth B3+ site, B3+ is bonded to four O2- atoms to form corner-sharing BO4 tetrahedra. There are a spread of B–O bond distances ranging from 1.45–1.53 Å. There are nine inequivalent O2- sites. In the first O2- site, O2- is bonded in a 2-coordinate geometry to one Eu2+ and two B3+ atoms. In the second O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Eu2+ and two B3+ atoms. In the third O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two Eu2+ and two B3+ atoms. In the fourth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two Eu2+ and two B3+ atoms. In the fifth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Eu2+ and two B3+ atoms. In the sixth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two Eu2+ and two B3+ atoms. In the seventh O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two Eu2+ and two B3+ atoms. In the eighth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Eu2+ and two B3+ atoms. In the ninth O2- site, O2- is bonded in a bent 120 degrees geometry to two Eu2+ and two B3+ atoms. There are two inequivalent Br1- sites. In the first Br1- site, Br1- is bonded in a 4-coordinate geometry to four Eu2+ atoms. In the second Br1- site, Br1- is bonded in a distorted rectangular see-saw-like geometry to four Eu2+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Eu4Br6O by Materials Project

Eu4OBr6 crystallizes in the hexagonal P6_3mc space group. The structure is three-dimensional. there are two inequivalent Eu2+ sites. In the first Eu2+ site, Eu2+ is bonded in a 1-coordinate geometry to one O2- and seven Br1- atoms. The Eu–O bond length is 2.39 Å. There are a spread of Eu–Br bond distances ranging from 3.09–3.40 Å. In the second Eu2+ site, Eu2+ is bonded in a distorted single-bond geometry to one O2- and six Br1- atoms. The Eu–O bond length is 2.36 Å. There are three shorter (3.16 Å) and three longer (3.34 Å) Eu–Br bond lengths. O2- is bonded in a tetrahedral geometry to four Eu2+ atoms. There are two inequivalent Br1- sites. In the first Br1- site, Br1- is bonded in a 5-coordinate geometry to five Eu2+ atoms. In the second Br1- site, Br1- is bonded in a 4-coordinate geometry to four Eu2+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KEu2Si4O10F by Materials Project

KEu2Si4O10F crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. K1+ is bonded in a 9-coordinate geometry to eight O2- and one F1- atom. There are a spread of K–O bond distances ranging from 2.74–3.44 Å. The K–F bond length is 3.21 Å. There are two inequivalent Eu2+ sites. In the first Eu2+ site, Eu2+ is bonded in a 8-coordinate geometry to six O2- and two equivalent F1- atoms. There are a spread of Eu–O bond distances ranging from 2.54–3.00 Å. There are one shorter (2.43 Å) and one longer (2.70 Å) Eu–F bond lengths. In the second Eu2+ site, Eu2+ is bonded to five O2- and one F1- atom to form distorted EuO5F octahedra that share corners with five SiO4 tetrahedra and an edgeedge with one EuO5F octahedra. There are a spread of Eu–O bond distances ranging from 2.52–2.63 Å. The Eu–F bond length is 2.44 Å. There are four inequivalent Si4+ sites. In the first Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two equivalent EuO5F octahedra and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 57–64°. There are a spread of Si–O bond distances ranging from 1.61–1.66 Å. In the second Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share a cornercorner with one EuO5F octahedra and corners with three SiO4 tetrahedra. The corner-sharing octahedral tilt angles are 54°. There are a spread of Si–O bond distances ranging from 1.60–1.66 Å. In the third Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share a cornercorner with one EuO5F octahedra and corners with three SiO4 tetrahedra. The corner-sharing octahedral tilt angles are 45°. There are a spread of Si–O bond distances ranging from 1.60–1.67 Å. In the fourth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share a cornercorner with one EuO5F octahedra and corners with three SiO4 tetrahedra. The corner-sharing octahedral tilt angles are 64°. There are a spread of Si–O bond distances ranging from 1.60–1.66 Å. There are ten inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one K1+ and two Si4+ atoms. In the second O2- site, O2- is bonded in a bent 150 degrees geometry to one Eu2+ and two Si4+ atoms. In the third O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one K1+ and two Si4+ atoms. In the fourth O2- site, O2- is bonded in a distorted single-bond geometry to three Eu2+ and one Si4+ atom. In the fifth O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent K1+ and two Si4+ atoms. In the sixth O2- site, O2- is bonded in a 2-coordinate geometry to one K1+ and two Si4+ atoms. In the seventh O2- site, O2- is bonded in a bent 120 degrees geometry to one K1+ and two Si4+ atoms. In the eighth O2- site, O2- is bonded in a 1-coordinate geometry to three Eu2+ and one Si4+ atom. In the ninth O2- site, O2- is bonded in a distorted tetrahedral geometry to one K1+, two Eu2+, and one Si4+ atom. In the tenth O2- site, O2- is bonded in a distorted single-bond geometry to one K1+, two Eu2+, and one Si4+ atom. F1- is bonded in a 3-coordinate geometry to one K1+ and three Eu2+ atoms.

36 MATERIALS SCIENCE↗