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Surprising Charge-Radius Kink in the Sc Isotopes at N = 20

For this work, charge radii of neutron deficient 40 Sc and 41 Sc nuclei were determined using collinear laser spectroscopy. With the new data, the chain of Sc charge radii extends below the neutron magic number N=20 and shows a pronounced kink, generally taken as a signature of a shell closure, but one notably absent in the neighboring Ca, K, and Ar isotopic chains. Theoretical models that explain the trend at N=20 for the Ca isotopes cannot reproduce this puzzling behavior.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Slow ferromagnetic fluctuations in the kagome metal Sc 3 ⁢ Mn 3 ⁢Al 7 ⁢ Si 5 revealed by 27 Al NMR

Static and dynamical magnetic and electronic properties of the kagome metal Sc 3 ⁢Mn 3 ⁢ Al 7⁢ Si 5 have been investigated by 27 Al nuclear magnetic resonance (NMR) measurements. Two distinct 27 Al -NMR signals with two different values of quadrupolar frequencies of 𝜈 Q = 1.55(2) and 1.07(2) MHz are observed, which are assigned to Al(1) and Al(2), respectively. From the detailed NMR spectrum measurements under three different magnetic field directions and the density functional theory calculations, the principal axes of the electric field gradient for each Al site have been determined. The temperature dependence of Knight shift (𝐾) shows a similar temperature dependence of the DC magnetic susceptibility 𝜒 except for the low-temperature region below ∼50 K where 𝐾 is almost constant while 𝜒 keeps increasing, which suggests that the increase in 𝜒 at low temperatures is not intrinsic. 27 Al spin-lattice relaxation rate divided by temperature (1/𝑇 1 ⁢𝑇) is found to be constant, confirming the metallic state of Sc 3 ⁢Mn 3 ⁢ Al 7⁢ Si 5 from a microscopic point of view. Based on a Korringa ratio analysis using the 𝑇 1 and 𝐾 data, ferromagnetic fluctuations are found to dominate in Sc 3 ⁢Mn 3 ⁢ Al 7⁢ Si 5 . In conclusion, these fluctuations are suggested to be very slow with frequencies on the order of kilohertz or lower.

Ding, Qing-Ping [Ames Laboratory (AMES), Ames, IA ↗

Development and Integration of a Stochastic Clad Damage Propagation Model into PRONGHORN-SC Subchannel Analysis Code

The failure of fuel pins in nuclear reactors is intrinsically stochastic. Typically, a combination of variation in manufacturing that affects the material characteristics and the fuel assembly dimensions, variation in operating conditions, such as local power, coolant flow rate, and irradiation induced changes in material properties lead to a large uncertainty in failure margin of the fuel pins. Failure, therefore, may occur in exceptional pins with adverse combinations of these variations. Upon a metal fuel pin (U-Pu-Zr/HT9) failure, depressurization of the fuel pin takes place by release of fission gas, liquid sodium bond, and potentially solid fuel particles or molten/eutectic fuel droplets through the hole in cladding. The effect of a fission gas jet on neighbor fuel pins and possible propagation of a clad damage during normal operation was studied experimentally in 1970s and it was found that the post-failure fission gas jet insulates the jet impingement area of the target fuel pin surface and could increase the target pin’s surface temperature by as much as 100 – 200 K during the failed pin depressurization. It was concluded that the effect should not lead to fuel pin failure propagation during normal operation. In accident scenarios of sodium and lead fast reactors such as Unprotected Loss-Of-Flow (ULOF) or Unprotected Transient Over Power (UTOP), the fuel pins can be subjected to higher clad temperatures and fuel pin pressures or fuel clad mechanical/chemical interaction where thermal creep margin becomes significantly lower compared to the normal operation conditions. Therefore, possible stochastic failure and the post-failure fission gas/fuel jet impingement could be critical in order to predict fuel pin failure propagation. Pin depressurization due to fission gas release may degrade the heat transfer by formation of a gas blanket on a neighboring pin surface, which is a local phenomenon, and by causing coolant flow deceleration and starvation, which could affect a surrounding region as well. Furthermore, the potential presence of solid fuel particles or molten fuel at the time of clad failure could boost post-failure jet induced degradation even further. The present study models the U-Pu-Zr/HT9 metal fuel pin failure and stochastic clad damage propagation by biased sampling based on a Cumulative Damage Fraction (CDF) type clad failure criterion and the normal distribution of fuel failure probability density as a function of logarithm of Cumulative Damage Fraction. In addition, the effect of post-failure fission gas jet on heat transfer degradation is modeled for the target pins. This model is called stochastic Clad Damage Propagation (CDAP). The CDAP model is now fully integrated into developmental version of PRONGHORN-SC subchannel analysis code, allowing for modeling local failures and its propagation potential. Section 2 describes the components of the CDAP models. Section 3 describes the model implementation to PRONGHORN-SC and input specifications. Section 4 describes the CDAP model validation coupled to PRONGHORN-SC.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Efficient Reformulation and Optimization for SC-ACOPF with Line Switching

This project aims to develop efficient and robust computational methods for solving the security-constrained alternating current optimal power flow problem (SC-ACOPF). The SC-ACOPF problem is a central problem in operating the electric power grids in the United States. It determines the most economically efficient way to operate the generation and transmission system to meet daily electricity demand. The solution found by solving an SC-ACOPF problem must satisfy the physics of the alternating current (AC) power flows, various generator and network operational constraints, and must maintain secure operation under various contingency scenarios, where a generator, a transmission branch, or a transformer may unexpectedly trip offline.

97 MATHEMATICS AND COMPUTING↗

$K^{*}(892)^0$ production and the time between freeze-outs in $^{40}$Ar+$^{45}$Sc collisions by NA61/SHINE at the CERN SPS

The analysis of the production of strange $K^{*}(892)^0$ resonances allows us to better understand the temporal evolution of high-energy nucleus--nucleus collisions. In particular, the ratio of $K^{*}(892)^0$ to charged kaon yields is used to determine the time interval between chemical and kinetic freeze-outs. In this paper, the first measurements of $K^{*}(892)^0$ production in central $^{40}$Ar+$^{45}$Sc collisions at the CERN Super Proton Synchrotron are reported. They were performed by NA61/SHINE at collision center-of-mass energies per nucleon pair $\sqrt{s_\mathrm{NN}}$ = 8.8, 11.9, 16.8 GeV. The obtained $\langle K^{*}(892)^0 \rangle/\langle K^{+} \rangle $ and $\langle K^{*}(892)^0 \rangle/\langle K^{-} \rangle$ mean multiplicity ratios are compared with corresponding results in $p$+$p$ collisions, allowing for an estimate of the time interval between chemical and thermal freeze-outs in the $^{40}$Ar+$^{45}$Sc system. These are the first such results reported for $^{40}$Ar+$^{45}$Sc collisions.

Adrich, P. [NCBJ, Warsaw] (ORCID:0000000270195451)↗

Materials Data on Sc(US2)3 by Materials Project

U3ScS6 crystallizes in the orthorhombic Pnnm space group. The structure is three-dimensional. there are three inequivalent U3+ sites. In the first U3+ site, U3+ is bonded in a 8-coordinate geometry to eight S2- atoms. There are a spread of U–S bond distances ranging from 2.77–2.95 Å. In the second U3+ site, U3+ is bonded to seven S2- atoms to form distorted US7 pentagonal bipyramids that share a cornercorner with one ScS6 octahedra, edges with two equivalent ScS6 octahedra, and edges with two equivalent US7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 32°. There are a spread of U–S bond distances ranging from 2.68–2.87 Å. In the third U3+ site, U3+ is bonded in a 8-coordinate geometry to eight S2- atoms. There are a spread of U–S bond distances ranging from 2.77–3.14 Å. There are two inequivalent Sc3+ sites. In the first Sc3+ site, Sc3+ is bonded to six S2- atoms to form ScS6 octahedra that share edges with two equivalent ScS6 octahedra and edges with four equivalent US7 pentagonal bipyramids. There are two shorter (2.56 Å) and four longer (2.58 Å) Sc–S bond lengths. In the second Sc3+ site, Sc3+ is bonded to six S2- atoms to form ScS6 octahedra that share corners with two equivalent US7 pentagonal bipyramids and edges with two equivalent ScS6 octahedra. There are two shorter (2.45 Å) and four longer (2.59 Å) Sc–S bond lengths. There are six inequivalent S2- sites. In the first S2- site, S2- is bonded to three U3+ and one Sc3+ atom to form distorted SScU3 trigonal pyramids that share corners with two equivalent SScU4 square pyramids, corners with five SSc2U3 trigonal bipyramids, corners with three equivalent SScU3 trigonal pyramids, and a faceface with one SU5 trigonal bipyramid. In the second S2- site, S2- is bonded in a 5-coordinate geometry to three U3+ and two equivalent Sc3+ atoms. In the third S2- site, S2- is bonded to three U3+ and two equivalent Sc3+ atoms to form distorted SSc2U3 trigonal bipyramids that share corners with five SSc2U3 trigonal bipyramids, corners with three equivalent SScU3 trigonal pyramids, edges with four equivalent SScU4 square pyramids, and edges with three SU5 trigonal bipyramids. In the fourth S2- site, S2- is bonded to four U3+ and one Sc3+ atom to form distorted SScU4 square pyramids that share a cornercorner with one SScU4 square pyramid, corners with four equivalent SU5 trigonal bipyramids, corners with two equivalent SScU3 trigonal pyramids, edges with two equivalent SScU4 square pyramids, and edges with five SSc2U3 trigonal bipyramids. In the fifth S2- site, S2- is bonded to five U3+ atoms to form distorted SU5 trigonal bipyramids that share corners with four equivalent SScU4 square pyramids, a cornercorner with one SSc2U3 trigonal bipyramid, corners with two equivalent SScU3 trigonal pyramids, an edgeedge with one SScU4 square pyramid, edges with four SSc2U3 trigonal bipyramids, and a faceface with one SScU3 trigonal pyramid. In the sixth S2- site, S2- is bonded in a 5-coordinate geometry to five U3+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Sc(SiNi)2 by Materials Project

Sc(NiSi)2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Sc3+ is bonded in a distorted body-centered cubic geometry to eight equivalent Si4- atoms. All Sc–Si bond lengths are 2.93 Å. Ni+2.50+ is bonded to four equivalent Si4- atoms to form a mixture of edge and corner-sharing NiSi4 tetrahedra. All Ni–Si bond lengths are 2.27 Å. Si4- is bonded in a 9-coordinate geometry to four equivalent Sc3+, four equivalent Ni+2.50+, and one Si4- atom. The Si–Si bond length is 2.32 Å.

36 MATERIALS SCIENCE↗

Materials Data on Sc(TiN)9 by Materials Project

Sc(TiN)9 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. Sc3+ is bonded to six N3- atoms to form ScN6 octahedra that share corners with six TiN5 square pyramids, edges with six TiN6 octahedra, and edges with six TiN5 square pyramids. There are two shorter (2.18 Å) and four longer (2.19 Å) Sc–N bond lengths. There are five inequivalent Ti+2.67+ sites. In the first Ti+2.67+ site, Ti+2.67+ is bonded to five N3- atoms to form TiN5 square pyramids that share corners with two equivalent ScN6 octahedra, corners with seven TiN5 square pyramids, an edgeedge with one ScN6 octahedra, edges with five TiN6 octahedra, and edges with two TiN5 square pyramids. The corner-sharing octahedra tilt angles range from 2–3°. There are a spread of Ti–N bond distances ranging from 2.06–2.13 Å. In the second Ti+2.67+ site, Ti+2.67+ is bonded to six N3- atoms to form TiN6 octahedra that share corners with three TiN6 octahedra, corners with three equivalent TiN5 square pyramids, edges with two equivalent ScN6 octahedra, edges with two TiN6 octahedra, and edges with eight TiN5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ti–N bond distances ranging from 2.11–2.19 Å. In the third Ti+2.67+ site, Ti+2.67+ is bonded to five N3- atoms to form TiN5 square pyramids that share corners with four TiN6 octahedra, corners with five TiN5 square pyramids, an edgeedge with one ScN6 octahedra, edges with three TiN6 octahedra, and edges with four TiN5 square pyramids. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Ti–N bond distances ranging from 2.06–2.16 Å. In the fourth Ti+2.67+ site, Ti+2.67+ is bonded to five N3- atoms to form TiN5 square pyramids that share a cornercorner with one ScN6 octahedra, corners with eight TiN5 square pyramids, an edgeedge with one ScN6 octahedra, edges with four TiN6 octahedra, and edges with three TiN5 square pyramids. The corner-sharing octahedral tilt angles are 2°. There are a spread of Ti–N bond distances ranging from 2.07–2.14 Å. In the fifth Ti+2.67+ site, Ti+2.67+ is bonded to six N3- atoms to form TiN6 octahedra that share corners with four equivalent TiN6 octahedra, corners with two equivalent TiN5 square pyramids, edges with two equivalent ScN6 octahedra, edges with two equivalent TiN6 octahedra, and edges with eight TiN5 square pyramids. The corner-sharing octahedra tilt angles range from 2–3°. There are four shorter (2.13 Å) and two longer (2.14 Å) Ti–N bond lengths. There are five inequivalent N3- sites. In the first N3- site, N3- is bonded to one Sc3+ and five Ti+2.67+ atoms to form a mixture of corner and edge-sharing NScTi5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the second N3- site, N3- is bonded to one Sc3+ and five Ti+2.67+ atoms to form NScTi5 octahedra that share corners with six NTi6 octahedra and edges with eleven NScTi5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the third N3- site, N3- is bonded to six Ti+2.67+ atoms to form a mixture of corner and edge-sharing NTi6 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. In the fourth N3- site, N3- is bonded to one Sc3+ and five Ti+2.67+ atoms to form a mixture of corner and edge-sharing NScTi5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the fifth N3- site, N3- is bonded to six Ti+2.67+ atoms to form NTi6 octahedra that share corners with six NTi6 octahedra and edges with ten NScTi5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°.

36 MATERIALS SCIENCE↗

Materials Data on Sc(CoSi)2 by Materials Project

Sc(CoSi)2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Sc3+ is bonded in a distorted body-centered cubic geometry to eight equivalent Si4- atoms. All Sc–Si bond lengths are 2.92 Å. Co+2.50+ is bonded to four equivalent Si4- atoms to form a mixture of edge and corner-sharing CoSi4 tetrahedra. All Co–Si bond lengths are 2.24 Å. Si4- is bonded in a 9-coordinate geometry to four equivalent Sc3+, four equivalent Co+2.50+, and one Si4- atom. The Si–Si bond length is 2.38 Å.

36 MATERIALS SCIENCE↗

Materials Data on Sc(FeSi)2 by Materials Project

Sc(FeSi)2 crystallizes in the orthorhombic Pbcm space group. The structure is three-dimensional. Sc3+ is bonded in a 6-coordinate geometry to eight Si4- atoms. There are a spread of Sc–Si bond distances ranging from 2.69–3.11 Å. There are two inequivalent Fe+2.50+ sites. In the first Fe+2.50+ site, Fe+2.50+ is bonded in a 5-coordinate geometry to five Si4- atoms. There are a spread of Fe–Si bond distances ranging from 2.26–2.43 Å. In the second Fe+2.50+ site, Fe+2.50+ is bonded to five Si4- atoms to form a mixture of distorted corner and edge-sharing FeSi5 trigonal bipyramids. There are a spread of Fe–Si bond distances ranging from 2.40–2.48 Å. There are two inequivalent Si4- sites. In the first Si4- site, Si4- is bonded in a 9-coordinate geometry to four equivalent Sc3+ and five Fe+2.50+ atoms. In the second Si4- site, Si4- is bonded in a 11-coordinate geometry to four equivalent Sc3+, five Fe+2.50+, and two equivalent Si4- atoms. Both Si–Si bond lengths are 2.49 Å.

36 MATERIALS SCIENCE↗

Materials Data on Sc(PO3)3 by Materials Project

Sc(PO3)3 crystallizes in the cubic I-43d space group. The structure is three-dimensional. Sc3+ is bonded to six O2- atoms to form ScO6 octahedra that share corners with six equivalent PO4 tetrahedra. There are three shorter (2.09 Å) and three longer (2.10 Å) Sc–O bond lengths. P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two equivalent ScO6 octahedra and corners with two equivalent PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 14–32°. There are a spread of P–O bond distances ranging from 1.49–1.62 Å. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded in a linear geometry to one Sc3+ and one P5+ atom. In the second O2- site, O2- is bonded in a bent 150 degrees geometry to two equivalent P5+ atoms. In the third O2- site, O2- is bonded in a bent 150 degrees geometry to one Sc3+ and one P5+ atom.

36 MATERIALS SCIENCE↗

Materials Data on Sc(VN)9 by Materials Project

Sc(VN)9 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. Sc3+ is bonded to six N3- atoms to form ScN6 octahedra that share corners with six VN5 square pyramids, edges with six VN6 octahedra, and edges with six VN5 square pyramids. There are four shorter (2.14 Å) and two longer (2.15 Å) Sc–N bond lengths. There are five inequivalent V+2.67+ sites. In the first V+2.67+ site, V+2.67+ is bonded to five N3- atoms to form VN5 square pyramids that share corners with two equivalent ScN6 octahedra, corners with seven VN5 square pyramids, an edgeedge with one ScN6 octahedra, edges with five VN6 octahedra, and edges with two VN5 square pyramids. The corner-sharing octahedra tilt angles range from 5–6°. There are a spread of V–N bond distances ranging from 2.00–2.13 Å. In the second V+2.67+ site, V+2.67+ is bonded to six N3- atoms to form VN6 octahedra that share corners with three VN6 octahedra, corners with three equivalent VN5 square pyramids, edges with two equivalent ScN6 octahedra, edges with two VN6 octahedra, and edges with eight VN5 square pyramids. The corner-sharing octahedra tilt angles range from 0–7°. There are a spread of V–N bond distances ranging from 2.01–2.17 Å. In the third V+2.67+ site, V+2.67+ is bonded to five N3- atoms to form VN5 square pyramids that share a cornercorner with one ScN6 octahedra, corners with eight VN5 square pyramids, an edgeedge with one ScN6 octahedra, edges with four VN6 octahedra, and edges with three VN5 square pyramids. The corner-sharing octahedral tilt angles are 5°. There are a spread of V–N bond distances ranging from 1.96–2.16 Å. In the fourth V+2.67+ site, V+2.67+ is bonded to five N3- atoms to form VN5 square pyramids that share corners with four VN6 octahedra, corners with five VN5 square pyramids, an edgeedge with one ScN6 octahedra, edges with three VN6 octahedra, and edges with four VN5 square pyramids. The corner-sharing octahedra tilt angles range from 1–7°. There are a spread of V–N bond distances ranging from 2.02–2.19 Å. In the fifth V+2.67+ site, V+2.67+ is bonded to six N3- atoms to form VN6 octahedra that share corners with four equivalent VN6 octahedra, corners with two equivalent VN5 square pyramids, edges with two equivalent ScN6 octahedra, edges with two equivalent VN6 octahedra, and edges with eight VN5 square pyramids. The corner-sharing octahedra tilt angles range from 4–7°. There are a spread of V–N bond distances ranging from 2.04–2.12 Å. There are five inequivalent N3- sites. In the first N3- site, N3- is bonded to one Sc3+ and five V+2.67+ atoms to form a mixture of corner and edge-sharing NScV5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the second N3- site, N3- is bonded to one Sc3+ and five V+2.67+ atoms to form a mixture of corner and edge-sharing NScV5 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the third N3- site, N3- is bonded to six V+2.67+ atoms to form a mixture of corner and edge-sharing NV6 octahedra. The corner-sharing octahedra tilt angles range from 4–8°. In the fourth N3- site, N3- is bonded to one Sc3+ and five V+2.67+ atoms to form a mixture of corner and edge-sharing NScV5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the fifth N3- site, N3- is bonded to six V+2.67+ atoms to form a mixture of corner and edge-sharing NV6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°.

36 MATERIALS SCIENCE↗

Materials Data on Sc(CuSi)2 by Materials Project

Sc(CuSi)2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Sc3+ is bonded in a distorted body-centered cubic geometry to eight equivalent Si4- atoms. All Sc–Si bond lengths are 2.93 Å. Cu+2.50+ is bonded to four equivalent Si4- atoms to form a mixture of corner and edge-sharing CuSi4 tetrahedra. All Cu–Si bond lengths are 2.36 Å. Si4- is bonded in a 9-coordinate geometry to four equivalent Sc3+, four equivalent Cu+2.50+, and one Si4- atom. The Si–Si bond length is 2.28 Å.

36 MATERIALS SCIENCE↗

Materials Data on Sc(CuO2)2 by Materials Project

Sc(CuO2)2 crystallizes in the tetragonal I4_1/amd space group. The structure is three-dimensional. Sc3+ is bonded in a tetrahedral geometry to four equivalent O2- atoms. All Sc–O bond lengths are 2.02 Å. Cu+2.50+ is bonded in a square co-planar geometry to four equivalent O2- atoms. All Cu–O bond lengths are 1.90 Å. O2- is bonded in a distorted trigonal planar geometry to one Sc3+ and two equivalent Cu+2.50+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Sc(CuO2)2 by Materials Project

Sc(CuO2)2 crystallizes in the monoclinic C2/c space group. The structure is three-dimensional. Sc3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Sc–O bond distances ranging from 2.23–2.31 Å. There are two inequivalent Cu+2.50+ sites. In the first Cu+2.50+ site, Cu+2.50+ is bonded in a square co-planar geometry to four O2- atoms. There is two shorter (1.89 Å) and two longer (1.92 Å) Cu–O bond length. In the second Cu+2.50+ site, Cu+2.50+ is bonded in a square co-planar geometry to four O2- atoms. There is two shorter (1.89 Å) and two longer (1.91 Å) Cu–O bond length. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded to two equivalent Sc3+ and two Cu+2.50+ atoms to form a mixture of distorted edge and corner-sharing OSc2Cu2 tetrahedra. In the second O2- site, O2- is bonded to two equivalent Sc3+ and two Cu+2.50+ atoms to form a mixture of distorted edge and corner-sharing OSc2Cu2 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on Sc(VSi)5 by Materials Project

Sc(VSi)5 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. Sc2+ is bonded to seven Si+2.40- atoms to form ScSi7 pentagonal bipyramids that share corners with two equivalent ScSi7 pentagonal bipyramids, corners with eight VSi7 pentagonal bipyramids, edges with three equivalent ScSi7 pentagonal bipyramids, and faces with six VSi7 pentagonal bipyramids. There are a spread of Sc–Si bond distances ranging from 2.64–2.79 Å. There are four inequivalent V2+ sites. In the first V2+ site, V2+ is bonded in a 8-coordinate geometry to two equivalent V2+ and six Si+2.40- atoms. There are one shorter (2.45 Å) and one longer (2.48 Å) V–V bond lengths. There are a spread of V–Si bond distances ranging from 2.45–2.62 Å. In the second V2+ site, V2+ is bonded to seven Si+2.40- atoms to form distorted VSi7 pentagonal bipyramids that share corners with three equivalent ScSi7 pentagonal bipyramids, corners with five VSi7 pentagonal bipyramids, edges with four VSi7 pentagonal bipyramids, faces with two equivalent ScSi7 pentagonal bipyramids, and faces with four VSi7 pentagonal bipyramids. There are a spread of V–Si bond distances ranging from 2.38–2.75 Å. In the third V2+ site, V2+ is bonded to seven Si+2.40- atoms to form distorted VSi7 pentagonal bipyramids that share a cornercorner with one ScSi7 pentagonal bipyramid, corners with seven VSi7 pentagonal bipyramids, edges with four VSi7 pentagonal bipyramids, faces with two equivalent ScSi7 pentagonal bipyramids, and faces with four VSi7 pentagonal bipyramids. There are a spread of V–Si bond distances ranging from 2.41–2.74 Å. In the fourth V2+ site, V2+ is bonded to seven Si+2.40- atoms to form VSi7 pentagonal bipyramids that share corners with four equivalent ScSi7 pentagonal bipyramids, corners with six VSi7 pentagonal bipyramids, edges with three equivalent VSi7 pentagonal bipyramids, faces with two equivalent ScSi7 pentagonal bipyramids, and faces with four VSi7 pentagonal bipyramids. There are a spread of V–Si bond distances ranging from 2.57–2.82 Å. There are five inequivalent Si+2.40- sites. In the first Si+2.40- site, Si+2.40- is bonded in a 10-coordinate geometry to seven V2+ and three Si+2.40- atoms. There are one shorter (2.49 Å) and two longer (2.79 Å) Si–Si bond lengths. In the second Si+2.40- site, Si+2.40- is bonded in a 9-coordinate geometry to three equivalent Sc2+ and six V2+ atoms. In the third Si+2.40- site, Si+2.40- is bonded in a 11-coordinate geometry to one Sc2+ and eight V2+ atoms. In the fourth Si+2.40- site, Si+2.40- is bonded in a 10-coordinate geometry to two equivalent Sc2+, six V2+, and two equivalent Si+2.40- atoms. There are one shorter (2.43 Å) and one longer (2.50 Å) Si–Si bond lengths. In the fifth Si+2.40- site, Si+2.40- is bonded in a 10-coordinate geometry to one Sc2+, six V2+, and three Si+2.40- atoms. The Si–Si bond length is 2.40 Å.

36 MATERIALS SCIENCE↗

Materials Data on Sc(CuN)3 by Materials Project

Sc(CuN)3 crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. Sc3+ is bonded to six equivalent N3- atoms to form corner-sharing ScN6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Sc–N bond lengths are 2.13 Å. Cu2+ is bonded in a square co-planar geometry to four equivalent N3- atoms. All Cu–N bond lengths are 2.13 Å. N3- is bonded to two equivalent Sc3+ and four equivalent Cu2+ atoms to form a mixture of corner and edge-sharing NSc2Cu4 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗

Materials Data on Sc(CuS)3 by Materials Project

Sc(CuS)3 crystallizes in the trigonal R-3 space group. The structure is three-dimensional. Sc3+ is bonded to six equivalent S2- atoms to form ScS6 octahedra that share corners with twelve equivalent CuS4 tetrahedra, edges with three equivalent ScS6 octahedra, and edges with six equivalent CuS4 tetrahedra. There are three shorter (2.62 Å) and three longer (2.63 Å) Sc–S bond lengths. Cu1+ is bonded to four equivalent S2- atoms to form CuS4 tetrahedra that share corners with four equivalent ScS6 octahedra, corners with six equivalent CuS4 tetrahedra, edges with two equivalent ScS6 octahedra, and edges with three equivalent CuS4 tetrahedra. The corner-sharing octahedra tilt angles range from 14–56°. There are a spread of Cu–S bond distances ranging from 2.30–2.42 Å. S2- is bonded in a 6-coordinate geometry to two equivalent Sc3+ and four equivalent Cu1+ atoms.

36 MATERIALS SCIENCE↗