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Gravitational Wave Scattering via the Born Series: Scalar Tidal Matching to 𝒪⁡(𝐺 7 ) and Beyond

We introduce a novel method to compute gravitational wave amplitudes within the framework of effective field theory. By reinterpreting the Feynman diagram expansion as a Born series, our method offers several key advantages. It directly yields partial wave amplitudes, streamlining the matching with black hole perturbation theory. Long-distance gravitational interactions are unambiguously factorized from short-distance tidal effects, including dissipation, which are systematically incorporated via an in-in worldline effective action. Crucially, at every order in perturbation theory, integrals are expressed in terms of harmonic polylogarithms, enabling an end-to-end computation scalable to arbitrary orders. We illustrate the method with new predictions for scalar black hole Love numbers and their renormalization group equations to 𝒪⁡(𝐺 7 ).

effective field theory↗

Ferromagnetism in Pr-rich binary Pr 7 Ru 3 intermetallic compound

We present the synthesis and experimental characterization of the binary intermetallic compound Pr 7 Ru 3 . The polycrystalline sample was prepared by arc melting pure Pr and Ru, followed by homogenization at 500 °C and 600 °C for 48 and 89 h, respectively. Powder x-ray diffraction confirms that Pr 7 Ru 3 crystallizes in an orthorhombic crystal structure (Pnma, space group no. 62) with the lattice parameters: a = 7.3606(7) Å, b = 23.120(1) Å and c = 6.5959(5) Å. Magnetization, resistivity, and heat capacity measurements reveal a ferromagnetic transition in Pr 7 Ru 3 with the Curie temperature T C ~ 24.5 K. The bulk transition is confirmed by a large λ-shape anomaly observed in the specific heat measurement. The magnetic susceptibility above the transition obeys the modified Curie-Weiss law with a positive Curie-Weiss temperature $\ominus$ CW = 30(1) K and an effective magnetic moment of 3.39(1) μ B /Pr. Resistivity data for Pr 7 Ru 3 reveals metallic-like behavior with a clear anomaly at the transition temperature which is smeared by an applied magnetic field. We also synthesized high-quality nonmagnetic analog La 7 Ru 3 for which superconducting transition is observed with T c = 1.95 K, in agreement with the literature.

36 MATERIALS SCIENCE↗

Materials Data on Re3(TeI)7 by Materials Project

Re3(TeI)7 crystallizes in the triclinic P-1 space group. The structure is two-dimensional and consists of one Re3(TeI)7 sheet oriented in the (0, 0, 1) direction. there are three inequivalent Re7+ sites. In the first Re7+ site, Re7+ is bonded to five Te2- atoms to form edge-sharing ReTe5 square pyramids. There are a spread of Re–Te bond distances ranging from 2.71–2.73 Å. In the second Re7+ site, Re7+ is bonded to five Te2- atoms to form edge-sharing ReTe5 square pyramids. There are a spread of Re–Te bond distances ranging from 2.69–2.74 Å. In the third Re7+ site, Re7+ is bonded to five Te2- atoms to form edge-sharing ReTe5 square pyramids. There are a spread of Re–Te bond distances ranging from 2.71–2.73 Å. There are seven inequivalent Te2- sites. In the first Te2- site, Te2- is bonded in a 4-coordinate geometry to one Re7+ and three I1- atoms. There are a spread of Te–I bond distances ranging from 2.80–3.36 Å. In the second Te2- site, Te2- is bonded in a 3-coordinate geometry to one Re7+ and three I1- atoms. There are a spread of Te–I bond distances ranging from 2.80–3.85 Å. In the third Te2- site, Te2- is bonded in a 3-coordinate geometry to one Re7+ and three I1- atoms. There are a spread of Te–I bond distances ranging from 2.79–3.72 Å. In the fourth Te2- site, Te2- is bonded in a 7-coordinate geometry to three Re7+ and two equivalent I1- atoms. There are one shorter (4.06 Å) and one longer (4.27 Å) Te–I bond lengths. In the fifth Te2- site, Te2- is bonded in a 6-coordinate geometry to three Re7+ and one I1- atom. The Te–I bond length is 4.12 Å. In the sixth Te2- site, Te2- is bonded in a 11-coordinate geometry to three Re7+ atoms. In the seventh Te2- site, Te2- is bonded in a 6-coordinate geometry to three Re7+ and two equivalent I1- atoms. There are one shorter (4.36 Å) and one longer (4.60 Å) Te–I bond lengths. There are seven inequivalent I1- sites. In the first I1- site, I1- is bonded in a distorted single-bond geometry to one Te2- atom. In the second I1- site, I1- is bonded in a single-bond geometry to one Te2- atom. In the third I1- site, I1- is bonded in a distorted single-bond geometry to one Te2- atom. In the fourth I1- site, I1- is bonded in a 1-coordinate geometry to eight Te2- atoms. In the fifth I1- site, I1- is bonded in a single-bond geometry to one Te2- atom. In the sixth I1- site, I1- is bonded in a distorted single-bond geometry to one Te2- atom. In the seventh I1- site, I1- is bonded in a distorted single-bond geometry to one Te2- atom.

36 MATERIALS SCIENCE↗

Materials Data on Re3(TeBr)7 by Materials Project

Re3(TeBr)7 crystallizes in the trigonal R-3 space group. The structure is two-dimensional and consists of three Re3(TeBr)7 sheets oriented in the (0, 0, 1) direction. Re7+ is bonded to five Te2- atoms to form edge-sharing ReTe5 square pyramids. There are a spread of Re–Te bond distances ranging from 2.70–2.72 Å. There are three inequivalent Te2- sites. In the first Te2- site, Te2- is bonded in a 7-coordinate geometry to three equivalent Re7+ and four Br1- atoms. There are a spread of Te–Br bond distances ranging from 3.79–4.15 Å. In the second Te2- site, Te2- is bonded in a 2-coordinate geometry to one Re7+ and three Br1- atoms. There are a spread of Te–Br bond distances ranging from 2.56–3.34 Å. In the third Te2- site, Te2- is bonded in a 9-coordinate geometry to three equivalent Re7+ atoms. There are three inequivalent Br1- sites. In the first Br1- site, Br1- is bonded in a single-bond geometry to two Te2- atoms. In the second Br1- site, Br1- is bonded in a distorted single-bond geometry to two Te2- atoms. In the third Br1- site, Br1- is bonded in a 3-coordinate geometry to nine Te2- atoms.

36 MATERIALS SCIENCE↗

Integrative path modeling and QTL mapping identify maturity, stem strength, and cell wall composition driving lettuce resistance to Sclerotinia minor

Lettuce ( Lactuca sativa ) is highly vulnerable to Sclerotinia minor , the pathogen causing lettuce drop. Breeding for resistance is the most effective control strategy; however, full resistance has not been achieved, and current partial resistance sources are often linked with undesirable traits, such as early bolting. This study aimed to unravel the genetic basis of partial resistance to S. minor and its relationship with plant maturity (bolting), stem mechanical strength (SMS), and cell wall composition (CWC) using a recombinant inbred line (RIL) population derived from a cross between the susceptible iceberg cv. ‘Salinas’ and the resistant oil-seed accession PI 251246. Field evaluations indicated that resistance was linked to earlier bolting, stronger stems, and higher pentose content. Path analysis demonstrated that earlier-maturing plants exhibited increased resistance through enhanced SMS and modified CWC, particularly with higher xylose and lower arabinose levels. Further analysis indicated a significant relationship between syringyl lignin content and resistance, especially in plants with varying bolting responses. Three key quantitative trait loci (QTLs) on linkage groups (LG) 2, 6, and 7 were consistently associated with resistance, bolting, and SMS. Importantly, residual QTL analysis revealed that the resistance locus on LG7 acted independently of maturity, suggesting a distinct resistance mechanism. Callose synthase emerged as a key candidate gene within the LG7 resistance QTL, located near - but distinct from - genes associated with plant maturity and flowering. These findings provide valuable insights into decoupling resistance from early bolting, suggesting a pathway for breeding lettuce cultivars with improved disease resistance and delayed bolting.

Lactuca↗

Sarecycline interferes with tRNA accommodation and tethers mRNA to the 70S ribosome

Sarecycline is a new narrow-spectrum tetracycline-class antibiotic approved for the treatment of acne vulgaris. Tetracyclines share a common four-ring naphthacene core and inhibit protein synthesis by interacting with the 70S bacterial ribosome. Sarecycline is distinguished chemically from other tetracyclines because it has a 7-[[methoxy(methyl)amino]methyl] group attached at the C7 position of ring D. To investigate the functional role of this C7 moiety, we determined the X-ray crystal structure of sarecycline bound to the Thermus thermophilus 70S ribosome. Our 2.8-Å resolution structure revealed that sarecycline binds at the canonical tetracycline binding site located in the decoding center of the small ribosomal subunit. Importantly, unlike other tetracyclines, the unique C7 extension of sarecycline extends into the messenger RNA (mRNA) channel to form a direct interaction with the A-site codon to possibly interfere with mRNA movement through the channel and/or disrupt A-site codon–anticodon interaction. Based on our biochemical studies, sarecycline appears to be a more potent initiation inhibitor compared to other tetracyclines, possibly due to drug interactions with the mRNA, thereby blocking accommodation of the first aminoacyl transfer RNA (tRNA) into the A site. Overall, our structural and biochemical findings rationalize the role of the unique C7 moiety of sarecycline in antibiotic action.

59 BASIC BIOLOGICAL SCIENCES↗

Effect of different organic acid additives on the fermentation quality and bacterial community of paper mulberry (Broussonetia papyrifera) silage

To investigate the effects of different organic acid additives and their concentrations on the fermentation quality and bacterial community of paper mulberry silage, paper mulberry was left untreated (control) or was treated with ethylenediaminetetraacetic acid (EDTA), propionic acid (PA) or citric acid (CA), the amount of each additive was 2 g.kg −1 FM, 5 g.kg −1 FM and g.kg −1 FM. All groups were ensiled for 3, 7, 15, 30 and 60 days. Compared to the control, adding EDTA reduced protein breakdown, preserved more water-soluble carbohydrates of the silages (WSCs, 24.74 g.kg −1 DM), and high concentrations of EDTA inhibited the activity of undesirable microorganisms. Adding PA increased the abundance of Lactiplantibacillus and decreased the abundance of Enterococcus , and it caused a rapid decrease in the pH of the silage at an early stage (from 6.50 to 5.31) while altering the microbiota, and low concentrations of PA resulted in high LA (66.22 g.kg −1 DM) concentration and low PA (9.92 g.kg −1 DM) concentration at 60 days of ensiling. Different concentrations of additives altered the microbial community of paper mulberry to different degrees. High concentrations of PA and CA can increase the abundance of Lactiplantibacillus . High concentrations of CA resulted in a rapid decrease in silage pH at an early stage and higher WSC concentration. These results suggest that EDTA, PA and CA can be used as additives to improve the quality of paper mulberry silage.

Li, Mengxin↗

Intramedullary Unicortical Button and All-Suture Anchors Provide Similar Maximum Strength for Onlay Distal Biceps Tendon Repair

To evaluate the biomechanical profile of onlay distal biceps repair with an intramedullary unicortical button versus all-suture anchors under cyclic loading and maximal load to failure. Twenty paired fresh-frozen human cadaveric elbows were randomized to onlay distal biceps repair with either a single intramedullary button or with two 1.35-mm all-suture anchors. A 1.3-mm high tensile strength tape was used in a Krackow stitch to suture the tendons in both groups. Specimens and repair constructs were loaded for 3,000 cycles and then loaded to failure. Maximum load to failure, mode of failure, and construct elongation were recorded. Mean (± standard deviation) maximum load to failure for the unicortical intramedullary button and all-suture anchor repairs were 503.23 ± 141.77 N and 537.33 ± 262.13 N (P = .696), respectively. Mean maximum displacement after 3,000 cycles (± standard deviation) was 4.17 ± 2.05 mm in the button group and 2.06 ± 1.05 mm in the suture anchor group (P = .014). Mode of failure in the button group was suture tape rupture in 7 specimens, failure at the tendon–suture interface in 2 specimens, and button pullout in 1 specimen. Anchor pullout was the mode of failure in all suture anchor specimens. There were no tendon ruptures or radial tuberosity fractures in either group. In conclusion, this study demonstrates that onlay distal biceps repair with 2 all-suture anchors has similar maximum strength to repair with an intramedullary button and that both are viable options for fixation.

60 APPLIED LIFE SCIENCES↗

Materials Data on KBa6Zn4(GaO3)7 by Materials Project

KBa6Zn4(GaO3)7 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are two inequivalent K1+ sites. In the first K1+ site, K1+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of K–O bond distances ranging from 2.87–2.97 Å. In the second K1+ site, K1+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of K–O bond distances ranging from 2.89–2.97 Å. There are twelve inequivalent Ba2+ sites. In the first Ba2+ site, Ba2+ is bonded to six O2- atoms to form distorted BaO6 octahedra that share corners with two BaO6 octahedra, corners with two ZnO4 tetrahedra, corners with seven GaO4 tetrahedra, and an edgeedge with one ZnO4 tetrahedra. The corner-sharing octahedral tilt angles are 73°. There are a spread of Ba–O bond distances ranging from 2.64–2.83 Å. In the second Ba2+ site, Ba2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ba–O bond distances ranging from 2.57–2.87 Å. In the third Ba2+ site, Ba2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ba–O bond distances ranging from 2.58–2.87 Å. In the fourth Ba2+ site, Ba2+ is bonded to six O2- atoms to form distorted BaO6 octahedra that share corners with two BaO6 octahedra, corners with two ZnO4 tetrahedra, corners with seven GaO4 tetrahedra, and an edgeedge with one ZnO4 tetrahedra. The corner-sharing octahedral tilt angles are 73°. There are a spread of Ba–O bond distances ranging from 2.65–2.82 Å. In the fifth Ba2+ site, Ba2+ is bonded to six O2- atoms to form BaO6 octahedra that share corners with two BaO6 octahedra, corners with three ZnO4 tetrahedra, corners with six GaO4 tetrahedra, and an edgeedge with one ZnO4 tetrahedra. The corner-sharing octahedra tilt angles range from 74–76°. There are a spread of Ba–O bond distances ranging from 2.64–2.82 Å. In the sixth Ba2+ site, Ba2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ba–O bond distances ranging from 2.56–2.86 Å. In the seventh Ba2+ site, Ba2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ba–O bond distances ranging from 2.61–2.85 Å. In the eighth Ba2+ site, Ba2+ is bonded to six O2- atoms to form BaO6 octahedra that share corners with two BaO6 octahedra, a cornercorner with one ZnO4 tetrahedra, corners with eight GaO4 tetrahedra, and an edgeedge with one ZnO4 tetrahedra. The corner-sharing octahedral tilt angles are 73°. There are a spread of Ba–O bond distances ranging from 2.65–2.79 Å. In the ninth Ba2+ site, Ba2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ba–O bond distances ranging from 2.59–2.83 Å. In the tenth Ba2+ site, Ba2+ is bonded to six O2- atoms to form distorted BaO6 octahedra that share corners with two BaO6 octahedra, corners with two ZnO4 tetrahedra, corners with seven GaO4 tetrahedra, and an edgeedge with one ZnO4 tetrahedra. The corner-sharing octahedra tilt angles range from 73–76°. There are a spread of Ba–O bond distances ranging from 2.62–2.83 Å. In the eleventh Ba2+ site, Ba2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ba–O bond distances ranging from 2.57–2.83 Å. In the twelfth Ba2+ site, Ba2+ is bonded to six O2- atoms to form distorted BaO6 octahedra that share corners with two BaO6 octahedra, corners with three ZnO4 tetrahedra, corners with six GaO4 tetrahedra, and an edgeedge with one GaO4 tetrahedra. The corner-sharing octahedra tilt angles range from 73–74°. There are a spread of Ba–O bond distances ranging from 2.69–2.79 Å. There are eight inequivalent Zn2+ sites. In the first Zn2+ site, Zn2+ is bonded to four O2- atoms to form ZnO4 tetrahedra that share corners with three BaO6 octahedra, a cornercorner with one ZnO4 tetrahedra, and corners with four GaO4 tetrahedra. The corner-sharing octahedra tilt angles range from 70–84°. There are a spread of Zn–O bond distances ranging from 1.96–2.09 Å. In the second Zn2+ site, Zn2+ is bonded to four O2- atoms to form ZnO4 tetrahedra that share a cornercorner with one BaO6 octahedra, a cornercorner with one ZnO4 tetrahedra, corners with four GaO4 tetrahedra, and an edgeedge with one BaO6 octahedra. The corner-sharing octahedral tilt angles are 74°. There are a spread of Zn–O bond distances ranging from 1.97–2.10 Å. In the third Zn2+ site, Zn2+ is bonded to four O2- atoms to form ZnO4 tetrahedra that share a cornercorner with one BaO6 octahedra, corners with five GaO4 tetrahedra, and an edgeedge with one BaO6 octahedra. The corner-sharing octahedral tilt angles are 73°. There are a spread of Zn–O bond distances ranging from 1.96–2.08 Å. In the fourth Zn2+ site, Zn2+ is bonded to four O2- atoms to form ZnO4 tetrahedra that share corners with three BaO6 octahedra, a cornercorner with one ZnO4 tetrahedra, and corners with four GaO4 tetrahedra. The corner-sharing octahedra tilt angles range from 70–81°. There are a spread of Zn–O bond distances ranging from 1.98–2.02 Å. In the fifth Zn2+ site, Zn2+ is bonded to four O2- atoms to form ZnO4 tetrahedra that share a cornercorner with one BaO6 octahedra, corners with five GaO4 tetrahedra, and an edgeedge with one BaO6 octahedra. The corner-sharing octahedral tilt angles are 74°. There are a spread of Zn–O bond distances ranging from 1.96–2.06 Å. In the sixth Zn2+ site, Zn2+ is bonded to four O2- atoms to form ZnO4 tetrahedra that share a cornercorner with one BaO6 octahedra, a cornercorner with one ZnO4 tetrahedra, corners with four GaO4 tetrahedra, and an edgeedge with one BaO6 octahedra. The corner-sharing octahedral tilt angles are 75°. There are a spread of Zn–O bond distances ranging from 1.97–2.09 Å. In the seventh Zn2+ site, Zn2+ is bonded to four O2- atoms to form ZnO4 tetrahedra that share a cornercorner with one BaO6 octahedra, a cornercorner with one ZnO4 tetrahedra, corners with four GaO4 tetrahedra, and an edgeedge with one BaO6 octahedra. The corner-sharing octahedral tilt angles are 73°. There are a spread of Zn–O bond distances ranging from 1.98–2.06 Å. In the eighth Zn2+ site, Zn2+ is bonded to four O2- atoms to form ZnO4 tetrahedra that share corners with two BaO6 octahedra, a cornercorner with one ZnO4 tetrahedra, and corners with five GaO4 tetrahedra. The corner-sharing octahedra tilt angles range from 70–71°. There are a spread of Zn–O bond distances ranging from 1.97–2.02 Å. There are fourteen inequivalent Ga3+ sites. In the first Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with two BaO6 octahedra, corners with three ZnO4 tetrahedra, and corners with three GaO4 tetrahedra. The corner-sharing octahedra tilt angles range from 64–66°. There are a spread of Ga–O bond distances ranging from 1.85–1.94 Å. In the second Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with two BaO6 octahedra, corners with three ZnO4 tetrahedra, and corners with three GaO4 tetrahedra. The corner-sharing octahedra tilt angles range from 65–67°. There are a spread of Ga–O bond distances ranging from 1.85–1.94 Å. In the third Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with three BaO6 octahedra and corners with three ZnO4 tetrahedra. The corner-sharing octahedra tilt angles range from 43–44°. There is three shorter (1.86 Å) and one longer (1.95 Å) Ga–O bond length. In the fourth Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with six BaO6 octahedra, a cornercorner with one GaO4 tetrahedra, and corners with two ZnO4 tetrahedra. The corner-sharing octahedra tilt angles range from 60–70°. There are a spread of Ga–O bond distances ranging from 1.86–1.93 Å. In the fifth Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with two BaO6 octahedra, corners with three ZnO4 tetrahedra, and corners with three GaO4 tetrahedra. The corner-sharing octahedra tilt angles range from 66–69°. There are a spread of Ga–O bond distances ranging from 1.85–1.94 Å. In the sixth Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with three BaO6 octahedra, corners with two ZnO4 tetrahedra, and corners with three GaO4 tetrahedra. The corner-sharing octahedra tilt angles range from 69–81°. There are a spread of Ga–O bond distances ranging from 1.86–1.91 Å. In the seventh Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with three BaO6 octahedra, corners with two ZnO4 tetrahedra, and corners with three GaO4 tetrahedra. The corner-sharing octahedra tilt angles range from 69–81°. There are a spread of Ga–O bond distances ranging from 1.86–1.91 Å. In the eighth Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with two BaO6 octahedra, corners with three ZnO4 tetrahedra, and corners with three GaO4 tetrahedra. The corner-sharing octahedra tilt angles range from 68–69°. There are a spread of Ga–O bond distances ranging from 1.85–1.92 Å. In the ninth Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with two BaO6 octahedra, corners with three ZnO4 tetrahedra, and corners with three GaO4 tetrahedra. The corner-sharing octahedra tilt angles range from 67–69°. There are a spread of Ga–O bond distances ranging from 1.85–1.92 Å. In the tenth Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with three BaO6 octahedra, a cornercorner with one GaO4 tetrahedra, and corners with two ZnO4 tetrahedra. The corner-sharing octahedra tilt angles range from 42–46°. There are a spread of Ga–O bond distances ranging from 1.84–1.94 Å. In the eleventh Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with three BaO6 octahedra, corners with two GaO4 tetrahedra, and corners with three ZnO4 tetrahedra. The corner-sharing octahedra tilt angles range from 70–82°. There are a spread of Ga–O bond distances ranging from 1.87–1.90 Å. In the twelfth Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with three BaO6 octahedra, corners with two GaO4 tetrahedra, and corners with three ZnO4 tetrahedra. The corner-sharing octahedra tilt angles range from 66–79°. There are a spread of Ga–O bond distances ranging from 1.85–1.92 Å. In the thirteenth Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share a cornercorner with one BaO6 octahedra, corners with two GaO4 tetrahedra, corners with three ZnO4 tetrahedra, and an edgeedge with one BaO6 octahedra. The corner-sharing octahedral tilt angles are 70°. There are a spread of Ga–O bond distances ranging from 1.86–1.91 Å. In the fourteenth Ga3+ site, Ga3+ is bonded to four O2- atoms to form GaO4 tetrahedra that share corners with six BaO6 octahedra and corners with three GaO4 tetrahedra. The corner-sharing octahedra tilt angles range from 62–67°. There are a spread of Ga–O bond distances ranging from 1.85–1.90 Å. There are forty-two inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to two Ba2+ and two Ga3+ atoms. In the second O2- site, O2- is bonded to two Ba2+, one Zn2+, and one Ga3+ atom to form distorted OBa2ZnGa tetrahedra that share corners with five OBa3Ga tetrahedra and a cornercorner with one OKBa3Ga trigonal bipyramid. In the third O2- site, O2- is bonded in a 3-coordinate geometry to one K1+, one Zn2+, and two Ga3+ atoms. In the fourth O2- site, O2- is bonded in a 5-coordinate geometry to one K1+, two Ba2+, and two Zn2+ atoms. In the fifth O2- site, O2- is bonded to two Ba2+, one Zn2+, and one Ga3+ atom to form distorted OBa2ZnGa tetrahedra that share corners with six OBa3Ga tetrahedra and a cornercorner with one OKBa3Ga trigonal bipyramid. In the sixth O2- site, O2- is bonded in a 4-coordinate geometry to two Ba2+, one Zn2+, and one Ga3+ atom. In the seventh O2- sit

36 MATERIALS SCIENCE↗

Materials Data on Sm4AlSi5(NO)7 by Materials Project

Sm4AlSi5(NO)7 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are twelve inequivalent Sm3+ sites. In the first Sm3+ site, Sm3+ is bonded in a 7-coordinate geometry to four N3- and four O2- atoms. There are a spread of Sm–N bond distances ranging from 2.32–2.97 Å. There are a spread of Sm–O bond distances ranging from 2.30–3.06 Å. In the second Sm3+ site, Sm3+ is bonded in a 7-coordinate geometry to four N3- and three O2- atoms. There are a spread of Sm–N bond distances ranging from 2.31–2.67 Å. There are a spread of Sm–O bond distances ranging from 2.43–2.73 Å. In the third Sm3+ site, Sm3+ is bonded in a 6-coordinate geometry to four N3- and one O2- atom. There are a spread of Sm–N bond distances ranging from 2.20–2.55 Å. The Sm–O bond length is 2.70 Å. In the fourth Sm3+ site, Sm3+ is bonded in a 6-coordinate geometry to three N3- and three O2- atoms. There are a spread of Sm–N bond distances ranging from 2.28–2.63 Å. There are a spread of Sm–O bond distances ranging from 2.34–2.54 Å. In the fifth Sm3+ site, Sm3+ is bonded in a 7-coordinate geometry to three N3- and four O2- atoms. There are a spread of Sm–N bond distances ranging from 2.39–2.67 Å. There are a spread of Sm–O bond distances ranging from 2.25–2.77 Å. In the sixth Sm3+ site, Sm3+ is bonded in a 9-coordinate geometry to six N3- and three O2- atoms. There are a spread of Sm–N bond distances ranging from 2.46–2.86 Å. There are a spread of Sm–O bond distances ranging from 2.38–2.78 Å. In the seventh Sm3+ site, Sm3+ is bonded in a 6-coordinate geometry to three N3- and three O2- atoms. There are a spread of Sm–N bond distances ranging from 2.23–2.58 Å. There are a spread of Sm–O bond distances ranging from 2.31–2.53 Å. In the eighth Sm3+ site, Sm3+ is bonded in a 8-coordinate geometry to six N3- and two O2- atoms. There are a spread of Sm–N bond distances ranging from 2.49–2.85 Å. There are one shorter (2.32 Å) and one longer (2.38 Å) Sm–O bond lengths. In the ninth Sm3+ site, Sm3+ is bonded in a 4-coordinate geometry to six N3- and two O2- atoms. There are a spread of Sm–N bond distances ranging from 2.35–2.97 Å. There are one shorter (2.44 Å) and one longer (2.60 Å) Sm–O bond lengths. In the tenth Sm3+ site, Sm3+ is bonded in a 4-coordinate geometry to four N3- and one O2- atom. There are a spread of Sm–N bond distances ranging from 2.32–2.69 Å. The Sm–O bond length is 2.42 Å. In the eleventh Sm3+ site, Sm3+ is bonded in a 8-coordinate geometry to five N3- and two O2- atoms. There are a spread of Sm–N bond distances ranging from 2.38–2.69 Å. There are one shorter (2.27 Å) and one longer (2.80 Å) Sm–O bond lengths. In the twelfth Sm3+ site, Sm3+ is bonded in a 8-coordinate geometry to five N3- and three O2- atoms. There are a spread of Sm–N bond distances ranging from 2.44–2.58 Å. There are a spread of Sm–O bond distances ranging from 2.45–2.81 Å. There are three inequivalent Al3+ sites. In the first Al3+ site, Al3+ is bonded in a 5-coordinate geometry to one N3- and four O2- atoms. The Al–N bond length is 1.97 Å. There are a spread of Al–O bond distances ranging from 1.85–1.98 Å. In the second Al3+ site, Al3+ is bonded to three N3- and one O2- atom to form distorted AlN3O tetrahedra that share a cornercorner with one SiN2O2 tetrahedra. There are a spread of Al–N bond distances ranging from 1.87–2.01 Å. The Al–O bond length is 1.77 Å. In the third Al3+ site, Al3+ is bonded in a distorted trigonal non-coplanar geometry to three O2- atoms. There are a spread of Al–O bond distances ranging from 1.82–1.87 Å. There are fifteen inequivalent Si4+ sites. In the first Si4+ site, Si4+ is bonded in a trigonal non-coplanar geometry to one N3- and two O2- atoms. The Si–N bond length is 1.77 Å. There is one shorter (1.69 Å) and one longer (1.70 Å) Si–O bond length. In the second Si4+ site, Si4+ is bonded in a tetrahedral geometry to two N3- and two O2- atoms. There is one shorter (1.67 Å) and one longer (1.75 Å) Si–N bond length. There is one shorter (1.67 Å) and one longer (1.69 Å) Si–O bond length. In the third Si4+ site, Si4+ is bonded in a T-shaped geometry to one N3- and two O2- atoms. The Si–N bond length is 2.01 Å. There is one shorter (1.73 Å) and one longer (1.82 Å) Si–O bond length. In the fourth Si4+ site, Si4+ is bonded in a 5-coordinate geometry to two N3- and three O2- atoms. There is one shorter (1.80 Å) and one longer (1.82 Å) Si–N bond length. There are a spread of Si–O bond distances ranging from 1.69–2.20 Å. In the fifth Si4+ site, Si4+ is bonded in a bent 120 degrees geometry to one N3- and one O2- atom. The Si–N bond length is 1.83 Å. The Si–O bond length is 1.65 Å. In the sixth Si4+ site, Si4+ is bonded in a trigonal non-coplanar geometry to two N3- and one O2- atom. There is one shorter (1.76 Å) and one longer (1.80 Å) Si–N bond length. The Si–O bond length is 1.64 Å. In the seventh Si4+ site, Si4+ is bonded in a distorted trigonal non-coplanar geometry to two N3- and one O2- atom. There is one shorter (1.75 Å) and one longer (1.85 Å) Si–N bond length. The Si–O bond length is 1.68 Å. In the eighth Si4+ site, Si4+ is bonded in a T-shaped geometry to two N3- and one O2- atom. There is one shorter (1.79 Å) and one longer (1.82 Å) Si–N bond length. The Si–O bond length is 1.72 Å. In the ninth Si4+ site, Si4+ is bonded in a distorted trigonal non-coplanar geometry to three O2- atoms. There are a spread of Si–O bond distances ranging from 1.67–1.73 Å. In the tenth Si4+ site, Si4+ is bonded in a trigonal non-coplanar geometry to three O2- atoms. There are a spread of Si–O bond distances ranging from 1.64–1.68 Å. In the eleventh Si4+ site, Si4+ is bonded in a see-saw-like geometry to two N3- and two O2- atoms. There is one shorter (1.74 Å) and one longer (1.85 Å) Si–N bond length. There is one shorter (1.72 Å) and one longer (1.77 Å) Si–O bond length. In the twelfth Si4+ site, Si4+ is bonded in a trigonal non-coplanar geometry to one N3- and two O2- atoms. The Si–N bond length is 1.71 Å. There is one shorter (1.66 Å) and one longer (1.70 Å) Si–O bond length. In the thirteenth Si4+ site, Si4+ is bonded to two N3- and two O2- atoms to form corner-sharing SiN2O2 trigonal pyramids. There is one shorter (1.74 Å) and one longer (1.78 Å) Si–N bond length. There is one shorter (1.80 Å) and one longer (1.94 Å) Si–O bond length. In the fourteenth Si4+ site, Si4+ is bonded in a tetrahedral geometry to two N3- and two O2- atoms. There is one shorter (1.71 Å) and one longer (1.78 Å) Si–N bond length. There is one shorter (1.65 Å) and one longer (1.72 Å) Si–O bond length. In the fifteenth Si4+ site, Si4+ is bonded to two N3- and two O2- atoms to form SiN2O2 tetrahedra that share a cornercorner with one AlN3O tetrahedra and a cornercorner with one SiN2O2 trigonal pyramid. There is one shorter (1.70 Å) and one longer (1.77 Å) Si–N bond length. There is one shorter (1.67 Å) and one longer (1.69 Å) Si–O bond length. There are twenty-one inequivalent N3- sites. In the first N3- site, N3- is bonded in a 1-coordinate geometry to four Sm3+ and one Si4+ atom. In the second N3- site, N3- is bonded in a 1-coordinate geometry to four Sm3+ and one Al3+ atom. In the third N3- site, N3- is bonded in a distorted bent 120 degrees geometry to two Sm3+ and two Si4+ atoms. In the fourth N3- site, N3- is bonded in a 1-coordinate geometry to two Sm3+, one Si4+, and one N3- atom. The N–N bond length is 1.49 Å. In the fifth N3- site, N3- is bonded in a 2-coordinate geometry to two Sm3+ and two Si4+ atoms. In the sixth N3- site, N3- is bonded in a 1-coordinate geometry to three Sm3+, one Si4+, and one N3- atom. In the seventh N3- site, N3- is bonded in a 1-coordinate geometry to two Sm3+, one Si4+, and one N3- atom. The N–N bond length is 1.48 Å. In the eighth N3- site, N3- is bonded in a 2-coordinate geometry to one Sm3+, two Si4+, and one N3- atom. The N–N bond length is 1.48 Å. In the ninth N3- site, N3- is bonded in a 5-coordinate geometry to three Sm3+, one Al3+, and one N3- atom. In the tenth N3- site, N3- is bonded in a distorted single-bond geometry to three Sm3+, one Si4+, and one N3- atom. The N–N bond length is 1.54 Å. In the eleventh N3- site, N3- is bonded in a 4-coordinate geometry to three Sm3+ and one N3- atom. The N–N bond length is 1.45 Å. In the twelfth N3- site, N3- is bonded in a 2-coordinate geometry to one Sm3+, two Si4+, and one N3- atom. In the thirteenth N3- site, N3- is bonded in a 1-coordinate geometry to three Sm3+, one Si4+, and one N3- atom. In the fourteenth N3- site, N3- is bonded in a 2-coordinate geometry to two Sm3+, one Al3+, one Si4+, and one N3- atom. The N–N bond length is 1.49 Å. In the fifteenth N3- site, N3- is bonded in a 1-coordinate geometry to three Sm3+, one Si4+, and one N3- atom. The N–N bond length is 1.50 Å. In the sixteenth N3- site, N3- is bonded in a 4-coordinate geometry to two Sm3+, one Al3+, and one N3- atom. In the seventeenth N3- site, N3- is bonded in a 1-coordinate geometry to two Sm3+, one Si4+, and one N3- atom. In the eighteenth N3- site, N3- is bonded in a 1-coordinate geometry to three Sm3+, one Si4+, and one N3- atom. In the nineteenth N3- site, N3- is bonded in a distorted trigonal pyramidal geometry to three Sm3+ and one Si4+ atom. In the twentieth N3- site, N3- is bonded in a 4-coordinate geometry to three Sm3+ and one Si4+ atom. In the twenty-first N3- site, N3- is bonded in a 2-coordinate geometry to two Sm3+ and two Si4+ atoms. There are twenty-one inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to three Sm3+ and one Al3+ atom. In the second O2- site, O2- is bonded in a 3-coordinate geometry to two Sm3+ and one Si4+ atom. In the third O2- site, O2- is bonded in a 1-coordinate geometry to three Sm3+ and one Si4+ atom. In the fourth O2- site, O2- is bonded in a 2-coordinate geometry to two Sm3+ and two Si4+ atoms. In the fifth O2- site, O2- is bonded in a 1-coordinate geometry to three Sm3+ and one Si4+ atom. In the sixth O2- site, O2- is bonded in a distorted T-shaped geometry to one Sm3+ and two Si4+ atoms. In the seventh O2- site, O2- is bonded in a 2-coordinate geometry to one Sm3+ and two Si4+ atoms. In the eighth O2- site, O2- is bonded in a 1-coordinate geometry to three Sm3+ and one Si4+ atom. In the ninth O2- site, O2- is bonded in a 1-coordinate geometry to two Sm3+ and one Si4+ atom. In the tenth O2- site, O2- is bonded in a 3-coordinate geometry to one Sm3+ and two Si4+ atoms. In the eleventh O2- site, O2- is bonded in a distorted T-shaped geometry to one Sm3+, one Al3+, and one Si4+ atom. In the twelfth O2- site, O2- is bonded in a distorted water-like geometry to one Sm3+ and two Si4+ atoms. In the thirteenth O2- site, O2- is bonded in a 3-coordinate geometry to one Sm3+, one Al3+, and one Si4+ atom. In the fourteenth O2- site, O2- is bonded in a 3-coordinate geometry to one Sm3+, one Al3+, and one Si4+ atom. In the fifteenth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Sm3+ and two Si4+ atoms. In the sixteenth O2- site, O2- is bonded in a bent 150 degrees geometry to two Si4+ atoms. In the seventeenth O2- site, O2- is bonded in a 2-coordinate geometry to one Sm3+, one Al3+, and one Si4+ atom. In the eighteenth O2- site, O2- is bonded in a 2-coordinate geometry to one Sm3+ and two Si4+ atoms. In the nineteenth O2- site, O2- is bonded in a 3-coordinate geometry to one Sm3+, one Al3+, and one Si4+ atom. In the twentieth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Sm3+, one Al3+, and one Si4+ atom. In the twenty-first O2- site, O2- is bonded in a 2-coordinate geometry to one Sm3+, one Al3+, and two Si4+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Ca9Mn(PO4)7 by Materials Project

Ca9Mn(PO4)7 crystallizes in the trigonal R3c space group. The structure is three-dimensional. there are three inequivalent Ca2+ sites. In the first Ca2+ site, Ca2+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Ca–O bond distances ranging from 2.40–2.65 Å. In the second Ca2+ site, Ca2+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Ca–O bond distances ranging from 2.34–2.79 Å. In the third Ca2+ site, Ca2+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Ca–O bond distances ranging from 2.36–2.68 Å. Mn3+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six PO4 tetrahedra. There are three shorter (2.12 Å) and three longer (2.14 Å) Mn–O bond lengths. There are three inequivalent P5+ sites. In the first P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one MnO6 octahedra. The corner-sharing octahedral tilt angles are 46°. There are a spread of P–O bond distances ranging from 1.54–1.58 Å. In the second P5+ site, P5+ is bonded in a tetrahedral geometry to four O2- atoms. There is one shorter (1.53 Å) and three longer (1.57 Å) P–O bond length. In the third P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one MnO6 octahedra. The corner-sharing octahedral tilt angles are 50°. There are a spread of P–O bond distances ranging from 1.53–1.59 Å. There are ten inequivalent O2- sites. In the first O2- site, O2- is bonded in a 1-coordinate geometry to three Ca2+ and one P5+ atom. In the second O2- site, O2- is bonded in a 1-coordinate geometry to two Ca2+ and one P5+ atom. In the third O2- site, O2- is bonded in a 1-coordinate geometry to three Ca2+ and one P5+ atom. In the fourth O2- site, O2- is bonded in a 1-coordinate geometry to three Ca2+ and one P5+ atom. In the fifth O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Ca2+, one Mn3+, and one P5+ atom. In the sixth O2- site, O2- is bonded in a 1-coordinate geometry to three Ca2+ and one P5+ atom. In the seventh O2- site, O2- is bonded in a single-bond geometry to one P5+ atom. In the eighth O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Ca2+, one Mn3+, and one P5+ atom. In the ninth O2- site, O2- is bonded in a 1-coordinate geometry to three Ca2+ and one P5+ atom. In the tenth O2- site, O2- is bonded in a 1-coordinate geometry to two Ca2+ and one P5+ atom.

36 MATERIALS SCIENCE↗

Materials Data on Sm4AlSi5(NO)7 by Materials Project

Sm4AlSi5(NO)7 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are twelve inequivalent Sm3+ sites. In the first Sm3+ site, Sm3+ is bonded in a 7-coordinate geometry to three N3- and three O2- atoms. There are a spread of Sm–N bond distances ranging from 2.31–2.72 Å. There are a spread of Sm–O bond distances ranging from 2.31–2.42 Å. In the second Sm3+ site, Sm3+ is bonded in a 4-coordinate geometry to three N3- and two O2- atoms. There are a spread of Sm–N bond distances ranging from 2.31–2.85 Å. There are one shorter (2.42 Å) and one longer (2.48 Å) Sm–O bond lengths. In the third Sm3+ site, Sm3+ is bonded in a 5-coordinate geometry to four N3- and one O2- atom. There are a spread of Sm–N bond distances ranging from 2.19–2.54 Å. The Sm–O bond length is 2.66 Å. In the fourth Sm3+ site, Sm3+ is bonded in a 6-coordinate geometry to three N3- and three O2- atoms. There are a spread of Sm–N bond distances ranging from 2.27–2.54 Å. There are a spread of Sm–O bond distances ranging from 2.39–2.49 Å. In the fifth Sm3+ site, Sm3+ is bonded in a 6-coordinate geometry to two N3- and four O2- atoms. There are one shorter (2.39 Å) and one longer (2.59 Å) Sm–N bond lengths. There are a spread of Sm–O bond distances ranging from 2.29–2.42 Å. In the sixth Sm3+ site, Sm3+ is bonded in a 9-coordinate geometry to six N3- and three O2- atoms. There are a spread of Sm–N bond distances ranging from 2.48–2.93 Å. There are a spread of Sm–O bond distances ranging from 2.35–2.66 Å. In the seventh Sm3+ site, Sm3+ is bonded in a 6-coordinate geometry to three N3- and three O2- atoms. There are a spread of Sm–N bond distances ranging from 2.21–2.45 Å. There are a spread of Sm–O bond distances ranging from 2.31–2.63 Å. In the eighth Sm3+ site, Sm3+ is bonded in a 7-coordinate geometry to five N3- and two O2- atoms. There are a spread of Sm–N bond distances ranging from 2.43–2.81 Å. There are one shorter (2.30 Å) and one longer (2.42 Å) Sm–O bond lengths. In the ninth Sm3+ site, Sm3+ is bonded in a 7-coordinate geometry to five N3- and two O2- atoms. There are a spread of Sm–N bond distances ranging from 2.23–2.94 Å. There are one shorter (2.38 Å) and one longer (2.61 Å) Sm–O bond lengths. In the tenth Sm3+ site, Sm3+ is bonded in a 7-coordinate geometry to five N3- and two O2- atoms. There are a spread of Sm–N bond distances ranging from 2.30–3.03 Å. There are one shorter (2.36 Å) and one longer (2.98 Å) Sm–O bond lengths. In the eleventh Sm3+ site, Sm3+ is bonded in a 7-coordinate geometry to five N3- and two O2- atoms. There are a spread of Sm–N bond distances ranging from 2.40–2.62 Å. There are one shorter (2.28 Å) and one longer (2.63 Å) Sm–O bond lengths. In the twelfth Sm3+ site, Sm3+ is bonded in a 8-coordinate geometry to five N3- and three O2- atoms. There are a spread of Sm–N bond distances ranging from 2.40–2.68 Å. There are a spread of Sm–O bond distances ranging from 2.51–2.79 Å. There are three inequivalent Al3+ sites. In the first Al3+ site, Al3+ is bonded in a distorted trigonal bipyramidal geometry to one N3- and four O2- atoms. The Al–N bond length is 1.90 Å. There are a spread of Al–O bond distances ranging from 1.82–2.17 Å. In the second Al3+ site, Al3+ is bonded to three N3- and one O2- atom to form AlN3O tetrahedra that share a cornercorner with one SiN2O2 tetrahedra and a cornercorner with one SiN3O trigonal pyramid. There is two shorter (1.89 Å) and one longer (2.02 Å) Al–N bond length. The Al–O bond length is 1.80 Å. In the third Al3+ site, Al3+ is bonded in a trigonal non-coplanar geometry to three O2- atoms. There are a spread of Al–O bond distances ranging from 1.80–1.87 Å. There are fifteen inequivalent Si4+ sites. In the first Si4+ site, Si4+ is bonded in a trigonal non-coplanar geometry to one N3- and two O2- atoms. The Si–N bond length is 1.75 Å. There is one shorter (1.66 Å) and one longer (1.69 Å) Si–O bond length. In the second Si4+ site, Si4+ is bonded in a tetrahedral geometry to two N3- and two O2- atoms. There is one shorter (1.67 Å) and one longer (1.73 Å) Si–N bond length. There is one shorter (1.66 Å) and one longer (1.70 Å) Si–O bond length. In the third Si4+ site, Si4+ is bonded in a water-like geometry to two O2- atoms. There is one shorter (1.68 Å) and one longer (1.70 Å) Si–O bond length. In the fourth Si4+ site, Si4+ is bonded to two N3- and two O2- atoms to form corner-sharing SiN2O2 tetrahedra. There is one shorter (1.78 Å) and one longer (1.79 Å) Si–N bond length. There is one shorter (1.64 Å) and one longer (1.71 Å) Si–O bond length. In the fifth Si4+ site, Si4+ is bonded in a water-like geometry to one N3- and one O2- atom. The Si–N bond length is 1.82 Å. The Si–O bond length is 1.66 Å. In the sixth Si4+ site, Si4+ is bonded in a trigonal non-coplanar geometry to two N3- and one O2- atom. There is one shorter (1.76 Å) and one longer (1.81 Å) Si–N bond length. The Si–O bond length is 1.66 Å. In the seventh Si4+ site, Si4+ is bonded in a distorted trigonal non-coplanar geometry to two N3- and one O2- atom. There is one shorter (1.72 Å) and one longer (1.89 Å) Si–N bond length. The Si–O bond length is 1.68 Å. In the eighth Si4+ site, Si4+ is bonded to three N3- and one O2- atom to form distorted SiN3O trigonal pyramids that share a cornercorner with one AlN3O tetrahedra and a cornercorner with one SiN2O2 tetrahedra. There are a spread of Si–N bond distances ranging from 1.79–2.07 Å. The Si–O bond length is 1.81 Å. In the ninth Si4+ site, Si4+ is bonded in a trigonal non-coplanar geometry to three O2- atoms. There are a spread of Si–O bond distances ranging from 1.69–1.73 Å. In the tenth Si4+ site, Si4+ is bonded in a trigonal non-coplanar geometry to three O2- atoms. There are a spread of Si–O bond distances ranging from 1.62–1.68 Å. In the eleventh Si4+ site, Si4+ is bonded in a see-saw-like geometry to two N3- and two O2- atoms. There is one shorter (1.77 Å) and one longer (1.90 Å) Si–N bond length. There is one shorter (1.71 Å) and one longer (1.82 Å) Si–O bond length. In the twelfth Si4+ site, Si4+ is bonded in a trigonal non-coplanar geometry to one N3- and two O2- atoms. The Si–N bond length is 1.71 Å. There is one shorter (1.68 Å) and one longer (1.72 Å) Si–O bond length. In the thirteenth Si4+ site, Si4+ is bonded in a trigonal non-coplanar geometry to two N3- and one O2- atom. There is one shorter (1.71 Å) and one longer (1.72 Å) Si–N bond length. The Si–O bond length is 1.68 Å. In the fourteenth Si4+ site, Si4+ is bonded in a tetrahedral geometry to two N3- and two O2- atoms. There is one shorter (1.70 Å) and one longer (1.77 Å) Si–N bond length. There is one shorter (1.65 Å) and one longer (1.69 Å) Si–O bond length. In the fifteenth Si4+ site, Si4+ is bonded to two N3- and two O2- atoms to form SiN2O2 tetrahedra that share a cornercorner with one AlN3O tetrahedra. There is one shorter (1.69 Å) and one longer (1.79 Å) Si–N bond length. Both Si–O bond lengths are 1.68 Å. There are twenty-one inequivalent N3- sites. In the first N3- site, N3- is bonded in a 1-coordinate geometry to three Sm3+ and one Si4+ atom. In the second N3- site, N3- is bonded in a 2-coordinate geometry to three Sm3+, one Al3+, and one Si4+ atom. In the third N3- site, N3- is bonded in a 2-coordinate geometry to two Sm3+ and two Si4+ atoms. In the fourth N3- site, N3- is bonded in a 1-coordinate geometry to two Sm3+ and one Si4+ atom. In the fifth N3- site, N3- is bonded in a distorted trigonal non-coplanar geometry to one Sm3+ and two Si4+ atoms. In the sixth N3- site, N3- is bonded in a 1-coordinate geometry to three Sm3+ and one Si4+ atom. In the seventh N3- site, N3- is bonded in a 4-coordinate geometry to two Sm3+, one Si4+, and one N3- atom. The N–N bond length is 1.48 Å. In the eighth N3- site, N3- is bonded in a 2-coordinate geometry to two Si4+ and one N3- atom. The N–N bond length is 1.51 Å. In the ninth N3- site, N3- is bonded in a 1-coordinate geometry to three Sm3+, one Al3+, and one N3- atom. In the tenth N3- site, N3- is bonded in a 1-coordinate geometry to two Sm3+ and one Si4+ atom. In the eleventh N3- site, N3- is bonded in a 4-coordinate geometry to three Sm3+ and one N3- atom. The N–N bond length is 1.45 Å. In the twelfth N3- site, N3- is bonded in a 2-coordinate geometry to one Sm3+, two Si4+, and one N3- atom. In the thirteenth N3- site, N3- is bonded in a 1-coordinate geometry to three Sm3+ and one Si4+ atom. In the fourteenth N3- site, N3- is bonded in a 1-coordinate geometry to three Sm3+, one Al3+, and one N3- atom. The N–N bond length is 1.53 Å. In the fifteenth N3- site, N3- is bonded in a 1-coordinate geometry to two Sm3+, one Si4+, and one N3- atom. The N–N bond length is 1.55 Å. In the sixteenth N3- site, N3- is bonded in a 2-coordinate geometry to three Sm3+, one Al3+, and one N3- atom. In the seventeenth N3- site, N3- is bonded in a 1-coordinate geometry to two Sm3+, one Si4+, and one N3- atom. In the eighteenth N3- site, N3- is bonded in a 4-coordinate geometry to three Sm3+, one Si4+, and one N3- atom. In the nineteenth N3- site, N3- is bonded in a distorted trigonal pyramidal geometry to three Sm3+ and one Si4+ atom. In the twentieth N3- site, N3- is bonded in a distorted tetrahedral geometry to three Sm3+ and one Si4+ atom. In the twenty-first N3- site, N3- is bonded in a 2-coordinate geometry to two Sm3+ and two Si4+ atoms. There are twenty-one inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to three Sm3+ and one Al3+ atom. In the second O2- site, O2- is bonded in a 3-coordinate geometry to two Sm3+ and one Si4+ atom. In the third O2- site, O2- is bonded in a 1-coordinate geometry to three Sm3+ and one Si4+ atom. In the fourth O2- site, O2- is bonded in a 2-coordinate geometry to one Sm3+ and two Si4+ atoms. In the fifth O2- site, O2- is bonded in a 1-coordinate geometry to three Sm3+ and one Si4+ atom. In the sixth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to two Sm3+ and one Si4+ atom. In the seventh O2- site, O2- is bonded in a bent 120 degrees geometry to two Si4+ atoms. In the eighth O2- site, O2- is bonded in a 4-coordinate geometry to three Sm3+ and one Si4+ atom. In the ninth O2- site, O2- is bonded in a 1-coordinate geometry to two Sm3+ and one Si4+ atom. In the tenth O2- site, O2- is bonded in a bent 120 degrees geometry to one Sm3+ and two Si4+ atoms. In the eleventh O2- site, O2- is bonded in a 3-coordinate geometry to one Sm3+, one Al3+, and one Si4+ atom. In the twelfth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Sm3+ and two Si4+ atoms. In the thirteenth O2- site, O2- is bonded in a 3-coordinate geometry to one Sm3+, one Al3+, and one Si4+ atom. In the fourteenth O2- site, O2- is bonded in a 3-coordinate geometry to one Sm3+, one Al3+, and one Si4+ atom. In the fifteenth O2- site, O2- is bonded in a 2-coordinate geometry to one Sm3+ and two Si4+ atoms. In the sixteenth O2- site, O2- is bonded in a bent 150 degrees geometry to two Si4+ atoms. In the seventeenth O2- site, O2- is bonded in a 2-coordinate geometry to one Sm3+, one Al3+, and one Si4+ atom. In the eighteenth O2- site, O2- is bonded in a 2-coordinate geometry to one Sm3+ and two Si4+ atoms. In the nineteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Sm3+, one Al3+, and one Si4+ atom. In the twentieth O2- site, O2- is bonded in a 3-coordinate geometry to one Sm3+, one Al3+, and one Si4+ atom. In the twenty-first O2- site, O2- is bonded in a 3-coordinate geometry to one Sm3+, one Al3+, and one Si4+ atom.

36 MATERIALS SCIENCE↗

Materials Data on Na4GeH28(Se2O7)2 by Materials Project

(Na2(H2O)7)2GeSe4 crystallizes in the monoclinic C2 space group. The structure is two-dimensional and consists of two GeSe4 clusters and one Na2(H2O)7 sheet oriented in the (0, 0, 1) direction. In each GeSe4 cluster, Ge4+ is bonded in a tetrahedral geometry to four Se2- atoms. There are two shorter (2.38 Å) and two longer (2.40 Å) Ge–Se bond lengths. There are two inequivalent Se2- sites. In the first Se2- site, Se2- is bonded in a distorted single-bond geometry to one Ge4+ atom. In the second Se2- site, Se2- is bonded in a single-bond geometry to one Ge4+ atom. In the Na2(H2O)7 sheet, there are two inequivalent Na1+ sites. In the first Na1+ site, Na1+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing NaO6 octahedra. The corner-sharing octahedral tilt angles are 63°. There are a spread of Na–O bond distances ranging from 2.38–2.45 Å. In the second Na1+ site, Na1+ is bonded to six O2- atoms to form a mixture of corner and face-sharing NaO6 octahedra. The corner-sharing octahedral tilt angles are 63°. There are a spread of Na–O bond distances ranging from 2.41–2.48 Å. There are fourteen inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the second H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the third H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the fourth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the fifth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the sixth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the seventh H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the eighth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 1.00 Å. In the ninth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.97 Å. In the tenth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 1.00 Å. In the eleventh H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 1.00 Å. In the twelfth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the thirteenth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the fourteenth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. There are seven inequivalent O2- sites. In the first O2- site, O2- is bonded in a water-like geometry to one Na1+ and two H1+ atoms. In the second O2- site, O2- is bonded in a water-like geometry to one Na1+ and two H1+ atoms. In the third O2- site, O2- is bonded in a distorted water-like geometry to two Na1+ and two H1+ atoms. In the fourth O2- site, O2- is bonded in a distorted water-like geometry to two Na1+ and two H1+ atoms. In the fifth O2- site, O2- is bonded in a distorted water-like geometry to two equivalent Na1+ and two H1+ atoms. In the sixth O2- site, O2- is bonded in a distorted water-like geometry to two Na1+ and two H1+ atoms. In the seventh O2- site, O2- is bonded in a distorted water-like geometry to two Na1+ and two H1+ atoms.

36 MATERIALS SCIENCE↗

Benzoimidazolium-derived dimeric and hydride n-dopants for organic electron-transport materials: impact of substitution on structures, electrochemistry, and reactivity

1,3-Dimethyl-2,3-dihydrobenzo[ d ]imidazoles, 1H , and 1,1',3,3'-tetramethyl-2,2',3,3'-tetrahydro-2,2'-bibenzo[ d ]imidazoles, 1 2 , are of interest as n-dopants for organic electron-transport materials. Salts of 2-(4-(dimethylamino)phenyl)-4,7-dimethoxy-, 2-cyclohexyl-4,7-dimethoxy-, and 2-(5-(dimethylamino)thiophen-2-yl)benzo[ d ]imidazolium ( 1g–i + , respectively) have been synthesized and reduced with NaBH 4 to 1gH , 1hH , and 1iH , and with Na:Hg to 1g 2 and 1h 2 . Their electrochemistry and reactivity were compared to those derived from 2-(4-(dimethylamino)phenyl)- ( 1b + ) and 2-cyclohexylbenzo[ d ]imidazolium ( 1e + ) salts. E ( 1 + / 1 • ) values for 2-aryl species are less reducing than for 2-alkyl analogues, i.e., the radicals are stabilized more by aryl groups than the cations, while 4,7-dimethoxy substitution leads to more reducing E ( 1 + / 1 • ) values, as well as cathodic shifts in E ( 1 2 •+ / 1 2 ) and E ( 1H •+ / 1H ) values. Both the use of 3,4-dimethoxy and 2-aryl substituents accelerates the reaction of the 1H species with PC 61 BM. Because 2-aryl groups stabilize radicals, 1b 2 and 1g 2 exhibit weaker bonds than 1e 2 and 1h 2 and thus react with 6,13-bis(triisopropylsilylethynyl)pentacene ( VII ) via a “cleavage-first” pathway, while 1e 2 and 1h 2 react only via “electron-transfer-first”. 1h 2 exhibits the most cathodic E ( 1 2 •+ / 1 2 ) value of the dimers considered here and, therefore, reacts more rapidly than any of the other dimers with VII via “electron-transfer-first”. Crystal structures show rather long central C–C bonds for 1b 2 (1.5899(11) and 1.6194(8) Å) and 1h 2 (1.6299(13) Å).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Magnetic properties of the quasi-XY Shastry-Sutherland magnet ER 2 Be 2 SiO 7

Polycrystalline and single-crystal samples of the insulating Shastry-Sutherland compound Er 2 ⁢Be 2 ⁢SiO 7 were synthesized via a solid-state reaction and the floating zone method, respectively. The crystal structure, Er single-ion anisotropy, zero-field magnetic ground state, and magnetic phase diagrams along high-symmetry crystallographic directions were investigated with bulk measurement techniques, x-ray and neutron diffraction, and neutron spectroscopy. Here, we establish that Er 2 ⁢Be 2 ⁢SiO 7 crystallizes in a tetragonal space group with planes of orthogonal Er dimers and a strong preference for the Er moments to lie in the local plane perpendicular to each dimer bond. We also find that this system has a noncollinear ordered ground state in zero field with a transition temperature of 0.841 K consisting of antiferromagnetic dimers and in-plane moments. Finally, we mapped out the H-T phase diagrams for Er 2 ⁢Be 2 ⁢SiO 7 along the directions H ∥ [001], [100], and [110]. While an increasing in-plane field simply induces a phase transition to a field-polarized phase, we identify three metamagnetic transitions in the H ∥ [001] case. Single-crystal neutron diffraction results reveal that the H ∥ [001] phase diagram can be explained predominantly by the expected field-induced behavior of classical, anisotropic moments, although the microscopic origin of one phase requires further investigation.

36 MATERIALS SCIENCE↗

Hydrolysis of Small Oxo/Hydroxo Molecules Containing High Oxidation State Actinides (Th, Pa, U, Np, Pu): A Computational Study

The energetics of hydrolysis reactions for high oxidation states of oxo/hydroxo monomeric actinide species (Th IV O 2 , Pa IV O 2 , U IV O 2 , Pa V O 2 (OH), U V O 2 (OH), U VI O 3 , Np VI O 3 , Np VII O 3 (OH), and Pu VII O 3 (OH)) were calculated at the CCSD(T) level. The first step is the formation of a Lewis acid/base adduct with H 2 O (hydration), followed by a proton transfer to form a dihydroxide molecule (hydrolysis); this process is repeated until all oxo groups are hydrolyzed. The physisorption (hydration) for each H 2 O addition was predicted to be exothermic, ca. -20 kcal/mol. The hydrolysis products are preferred energetically over the hydration products for the +IV and +V oxidation states. The compounds with An VI are a turning point in terms of favoring hydration over hydrolysis. For An VII O 3 (OH), hydration products are preferred, and only two waters can bind; the complete hydrolysis process is now endothermic, and the oxidation state for the An in An(OH) 7 is +VI with two OH groups each having one-half an electron. The natural bond order charges and the reaction energies provide insights into the nature of the hydrolysis/hydration processes. The actinide charges and bond ionicity generally decrease across the period. Here, the ionic character decreases as the oxidation state and coordination number increase so that covalency increases moving to the right in the actinide period.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The eROSITA Final Equatorial-Depth Survey (eFEDS)

In 2019, the eROSITA telescope on board the Russian-German satellite Spectrum-Roentgen-Gamma (SRG) began to perform a deep all-sky X-ray survey with the aim of identifying ~100 000 clusters and groups over the course of four years. As part of its performance verification phase, a ~140 deg 2 survey, called eROSITA Final Equatorial-Depth Survey (eFEDS), was performed. With a depth typical of the all-sky survey after four years, it allows tests of tools and methods as well as improved predictions for the all-sky survey. As part of this effort, a catalog of 542 X-ray selected galaxy group and cluster candidates was compiled. Here, in this paper, we present the optical follow-up, with the aim of providing redshifts and cluster confirmation for the full sample. Furthermore, we aim to provide additional information on the dynamical state, richness, and optical center of the clusters. Finally, we aim to evaluate the impact of optical cluster confirmation on the purity and completeness of the X-ray selected sample. We used optical imaging data from the Hyper Suprime-Cam Subaru Strategic Program and from the Legacy Survey to identify optical counterparts to the X-ray detected cluster candidates. We make use of the multi-component matched filter cluster confirmation tool (MCMF), as well as of the optical cluster finder CAMIRA to derive cluster redshifts and richnesses. MCMF provided the probabilities with which an optical structure would be a chance superposition with the X-ray candidate. These probabilities were used to identify the best optical counterpart as well as to confirm an X-ray candidate as a cluster. The impact of this confirmation process on catalog purity and completeness was estimated using optical to X-ray scaling relations as well as simulations. The resulting catalog was furthermore matched with public group and cluster catalogs. Optical estimators of the cluster dynamical state were constructed based on density maps of the red-sequence galaxies at the cluster redshift. By providing redshift estimates for all 542 candidates, we construct an optically confirmed sample of 477 clusters and groups with a residual contamination of 6%. Of these, 470 (98.5%) are confirmed using MCMF, and 7 systems are added through cross-matching with spectroscopic group catalogs. Using observable-to-observable scaling and the applied confirmation threshold, we predict that 8 ± 2 real systems have been excluded with the MCMF cut required to build this low-contamination sample. This number agrees well with the 7 systems found through cross-matching that were not confirmed with MCMF. The predicted redshift and mass distribution of this catalog agree well with simulations. Thus, we expect that these 477 systems include >99% of all true clusters in the candidate list. Using an MCMF-independent method, we confirm that the catalog contamination of the confirmed subsample is 6 ± 3%. Application of the same method to the full candidate list yields 17 ± 3%, consistent with estimates coming from the fraction of confirmed systems of ~17% and with expectations from simulations of ~20%. We also present a sample of merging cluster candidates based on the derived estimators of the cluster dynamical state.

79 ASTRONOMY AND ASTROPHYSICS↗