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Atomic structure and Mott nature of the insulating charge density wave phase of 1T-TaS 2

Here, using x-ray pair distribution function (PDF) analysis and computer modeling, we explore structure models for the complex charge density wave (CDW) phases of layered 1T-TaS 2 that both well capture their atomic-level features and are amenable to electronic structure calculations. The models give the most probable position of constituent atoms in terms of 3D repetitive unit cells comprising a minimum number of Ta–S layers. Structure modeling results confirm the emergence of star-of-David (SD) like clusters of Ta atoms in the high-temperature incommensurate (IC) CDW phase and show that, contrary to the suggestions of recent studies, the low-temperature commensurate (C) CDW phase expands upon cooling thus reducing lattice strain. The C-CDW phase is also found to preserve the stacking sequence of Ta–S layers found in the room temperature, nearly commensurate (NC) CDW phase to a large extent. DFT based on the PDF refined model shows that bulk C-CDW 1T-TaS 2 also preserves the insulating state of individual layers of SD clusters, favoring the Mott physics description of the metal-to-insulator (NC-CDW to C-CDW) phase transition in 1T-TaS 2 . Our work highlights the importance of using precise crystal structure models in determining the nature of electronic phases in complex materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Materials Data on TaP2NCl12 by Materials Project

TaCl6P2NCl6 crystallizes in the monoclinic C2/c space group. The structure is zero-dimensional and consists of four P2NCl6 clusters and four TaCl6 clusters. In each P2NCl6 cluster, P5+ is bonded to one N3- and three Cl1- atoms to form corner-sharing PNCl3 tetrahedra. The P–N bond length is 1.57 Å. There is one shorter (1.97 Å) and two longer (1.98 Å) P–Cl bond length. N3- is bonded in a bent 150 degrees geometry to two equivalent P5+ atoms. There are three inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a single-bond geometry to one P5+ atom. In the second Cl1- site, Cl1- is bonded in a single-bond geometry to one P5+ atom. In the third Cl1- site, Cl1- is bonded in a single-bond geometry to one P5+ atom. In each TaCl6 cluster, Ta5+ is bonded in an octahedral geometry to six Cl1- atoms. There are two shorter (2.37 Å) and four longer (2.38 Å) Ta–Cl bond lengths. There are three inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a single-bond geometry to one Ta5+ atom. In the second Cl1- site, Cl1- is bonded in a single-bond geometry to one Ta5+ atom. In the third Cl1- site, Cl1- is bonded in a single-bond geometry to one Ta5+ atom.

36 MATERIALS SCIENCE↗

Materials Data on SbAsH6(CF4)2 by Materials Project

AsH6(CF)2SbF6 crystallizes in the orthorhombic Ibca space group. The structure is zero-dimensional and consists of eight AsH6(CF)2 clusters and eight SbF6 clusters. In each AsH6(CF)2 cluster, C4+ is bonded to one As3- and three H1+ atoms to form distorted corner-sharing CAsH3 tetrahedra. The C–As bond length is 1.91 Å. There is one shorter (1.09 Å) and two longer (1.10 Å) C–H bond length. As3- is bonded in a distorted tetrahedral geometry to two equivalent C4+ and two equivalent F1- atoms. Both As–F bond lengths are 1.73 Å. There are three inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one C4+ atom. In the second H1+ site, H1+ is bonded in a single-bond geometry to one C4+ atom. In the third H1+ site, H1+ is bonded in a single-bond geometry to one C4+ atom. F1- is bonded in a single-bond geometry to one As3- atom. In each SbF6 cluster, Sb3- is bonded in an octahedral geometry to six F1- atoms. There are a spread of Sb–F bond distances ranging from 1.91–1.94 Å. There are three inequivalent F1- sites. In the first F1- site, F1- is bonded in a single-bond geometry to one Sb3- atom. In the second F1- site, F1- is bonded in a single-bond geometry to one Sb3- atom. In the third F1- site, F1- is bonded in a single-bond geometry to one Sb3- atom.

36 MATERIALS SCIENCE↗

Materials Data on Os2Xe(O3F5)2 by Materials Project

XeF5Os2O6F5 crystallizes in the orthorhombic Pnma space group. The structure is zero-dimensional and consists of four Os2O6F5 clusters and four XeF5 clusters. In each Os2O6F5 cluster, Os is bonded to three O and three F atoms to form distorted corner-sharing OsO3F3 octahedra. The corner-sharing octahedral tilt angles are 24°. There is two shorter (1.71 Å) and one longer (1.72 Å) Os–O bond length. There are a spread of Os–F bond distances ranging from 2.00–2.17 Å. There are three inequivalent O sites. In the first O site, O is bonded in a single-bond geometry to one Os atom. In the second O site, O is bonded in a single-bond geometry to one Os atom. In the third O site, O is bonded in a single-bond geometry to one Os atom. There are three inequivalent F sites. In the first F site, F is bonded in a bent 150 degrees geometry to two equivalent Os atoms. In the second F site, F is bonded in a single-bond geometry to one Os atom. In the third F site, F is bonded in a single-bond geometry to one Os atom. In each XeF5 cluster, Xe is bonded in a distorted square pyramidal geometry to five F atoms. There is three shorter (1.98 Å) and two longer (1.99 Å) Xe–F bond length. There are four inequivalent F sites. In the first F site, F is bonded in a single-bond geometry to one Xe atom. In the second F site, F is bonded in a single-bond geometry to one Xe atom. In the third F site, F is bonded in a single-bond geometry to one Xe atom. In the fourth F site, F is bonded in a single-bond geometry to one Xe atom.

36 MATERIALS SCIENCE↗

Materials Data on AsS by Materials Project

SAs crystallizes in the triclinic P1 space group. The structure is zero-dimensional and consists of two $l^{1}-arsanylsulfanylarsenic molecules, two arsenic molecules, two arsinothious acid (9ci) molecules, two As4S5 clusters, one As5S7 cluster, and one SAs cluster. In each As4S5 cluster, there are four inequivalent As2+ sites. In the first As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.23 Å. In the second As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.31 Å. In the third As2+ site, As2+ is bonded in a distorted linear geometry to two S2- atoms. There are one shorter (2.38 Å) and one longer (2.85 Å) As–S bond lengths. In the fourth As2+ site, As2+ is bonded in an L-shaped geometry to two S2- atoms. There are one shorter (2.29 Å) and one longer (2.31 Å) As–S bond lengths. There are five inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted bent 120 degrees geometry to one As2+ and one S2- atom. The S–S bond length is 2.00 Å. In the second S2- site, S2- is bonded in a bent 120 degrees geometry to two As2+ atoms. In the third S2- site, S2- is bonded in a water-like geometry to one As2+ and one S2- atom. The S–S bond length is 2.03 Å. In the fourth S2- site, S2- is bonded in a distorted L-shaped geometry to one As2+ and one S2- atom. In the fifth S2- site, S2- is bonded in a distorted water-like geometry to one As2+ and one S2- atom. In the As5S7 cluster, there are five inequivalent As2+ sites. In the first As2+ site, As2+ is bonded in an L-shaped geometry to two S2- atoms. There are one shorter (2.27 Å) and one longer (2.41 Å) As–S bond lengths. In the second As2+ site, As2+ is bonded in a distorted single-bond geometry to two S2- atoms. There are one shorter (2.35 Å) and one longer (2.98 Å) As–S bond lengths. In the third As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.30 Å. In the fourth As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.31 Å. In the fifth As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.35 Å. There are seven inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted bent 120 degrees geometry to one As2+ and one S2- atom. The S–S bond length is 1.99 Å. In the second S2- site, S2- is bonded in a distorted water-like geometry to one As2+ and one S2- atom. The S–S bond length is 2.04 Å. In the third S2- site, S2- is bonded in a water-like geometry to one As2+ and one S2- atom. In the fourth S2- site, S2- is bonded in a bent 120 degrees geometry to one As2+ and one S2- atom. The S–S bond length is 2.01 Å. In the fifth S2- site, S2- is bonded in a distorted water-like geometry to one As2+ and one S2- atom. In the sixth S2- site, S2- is bonded in a 3-coordinate geometry to two As2+ and one S2- atom. The S–S bond length is 2.18 Å. In the seventh S2- site, S2- is bonded in a water-like geometry to two S2- atoms. In the SAs cluster, there are three inequivalent As2+ sites. In the first As2+ site, As2+ is bonded in an L-shaped geometry to two S2- atoms. There are one shorter (2.29 Å) and one longer (2.32 Å) As–S bond lengths. In the second As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.30 Å. In the third As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.23 Å. There are three inequivalent S2- sites. In the first S2- site, S2- is bonded in a bent 120 degrees geometry to two As2+ atoms. In the second S2- site, S2- is bonded in a distorted water-like geometry to one As2+ and one S2- atom. The S–S bond length is 2.03 Å. In the third S2- site, S2- is bonded in a distorted water-like geometry to one As2+ and one S2- atom.

36 MATERIALS SCIENCE↗

Materials Data on AsS by Materials Project

SAs crystallizes in the triclinic P1 space group. The structure is one-dimensional and consists of two arsenic compounds molecules; one As4S3 cluster; one SAs cluster; one SSAs cluster; one As3S4 ribbon oriented in the (1, 0, 0) direction; and two SAs ribbons oriented in the (1, 0, 0) direction. In the As4S3 cluster, there are four inequivalent As2+ sites. In the first As2+ site, As2+ is bonded in a water-like geometry to two S2- atoms. There are one shorter (2.26 Å) and one longer (2.27 Å) As–S bond lengths. In the second As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.28 Å. In the third As2+ site, As2+ is bonded in a water-like geometry to two S2- atoms. There are one shorter (2.28 Å) and one longer (2.29 Å) As–S bond lengths. In the fourth As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.26 Å. There are three inequivalent S2- sites. In the first S2- site, S2- is bonded in a 3-coordinate geometry to two As2+ atoms. In the second S2- site, S2- is bonded in a bent 120 degrees geometry to two As2+ atoms. In the third S2- site, S2- is bonded in a bent 120 degrees geometry to two As2+ atoms. In the SAs cluster, there are two inequivalent As2+ sites. In the first As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.31 Å. In the second As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.32 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted water-like geometry to one As2+ and one S2- atom. The S–S bond length is 2.09 Å. In the second S2- site, S2- is bonded in a distorted water-like geometry to one As2+ and one S2- atom. In the SSAs cluster, there are two inequivalent As2+ sites. In the first As2+ site, As2+ is bonded in a water-like geometry to two S2- atoms. There are one shorter (2.30 Å) and one longer (2.35 Å) As–S bond lengths. In the second As2+ site, As2+ is bonded in a water-like geometry to two S2- atoms. There are one shorter (2.29 Å) and one longer (2.35 Å) As–S bond lengths. There are four inequivalent S2- sites. In the first S2- site, S2- is bonded in a water-like geometry to two As2+ atoms. In the second S2- site, S2- is bonded in a water-like geometry to two S2- atoms. There are one shorter (2.05 Å) and one longer (2.06 Å) S–S bond lengths. In the third S2- site, S2- is bonded in a distorted water-like geometry to one As2+ and one S2- atom. In the fourth S2- site, S2- is bonded in a distorted water-like geometry to one As2+ and one S2- atom. In the As3S4 ribbon, there are three inequivalent As2+ sites. In the first As2+ site, As2+ is bonded in a trigonal non-coplanar geometry to three S2- atoms. There are a spread of As–S bond distances ranging from 2.25–2.36 Å. In the second As2+ site, As2+ is bonded in a water-like geometry to two S2- atoms. There are one shorter (2.26 Å) and one longer (2.33 Å) As–S bond lengths. In the third As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.28 Å. There are four inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted water-like geometry to one As2+ and one S2- atom. The S–S bond length is 2.04 Å. In the second S2- site, S2- is bonded in a distorted water-like geometry to one As2+ and one S2- atom. In the third S2- site, S2- is bonded in a water-like geometry to two As2+ atoms. In the fourth S2- site, S2- is bonded in a water-like geometry to two As2+ atoms. In one of the SAs ribbons, there are five inequivalent As2+ sites. In the first As2+ site, As2+ is bonded in a water-like geometry to two S2- atoms. There are one shorter (2.26 Å) and one longer (2.30 Å) As–S bond lengths. In the second As2+ site, As2+ is bonded in a 3-coordinate geometry to three S2- atoms. There are a spread of As–S bond distances ranging from 2.11–2.86 Å. In the third As2+ site, As2+ is bonded in a distorted T-shaped geometry to three S2- atoms. There are a spread of As–S bond distances ranging from 2.28–2.32 Å. In the fourth As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.31 Å. In the fifth As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.28 Å. There are five inequivalent S2- sites. In the first S2- site, S2- is bonded in a single-bond geometry to one As2+ atom. In the second S2- site, S2- is bonded in a water-like geometry to two As2+ atoms. In the third S2- site, S2- is bonded in a water-like geometry to two As2+ atoms. In the fourth S2- site, S2- is bonded in a water-like geometry to two As2+ atoms. In the fifth S2- site, S2- is bonded in a 3-coordinate geometry to three As2+ atoms. In one of the SAs ribbons, there are six inequivalent As2+ sites. In the first As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.31 Å. In the second As2+ site, As2+ is bonded in a water-like geometry to two S2- atoms. There are one shorter (2.27 Å) and one longer (2.34 Å) As–S bond lengths. In the third As2+ site, As2+ is bonded in a distorted trigonal non-coplanar geometry to three S2- atoms. There are a spread of As–S bond distances ranging from 2.28–2.33 Å. In the fourth As2+ site, As2+ is bonded in a single-bond geometry to one S2- atom. The As–S bond length is 2.27 Å. In the fifth As2+ site, As2+ is bonded in a water-like geometry to two S2- atoms. There are one shorter (2.25 Å) and one longer (2.27 Å) As–S bond lengths. In the sixth As2+ site, As2+ is bonded in a trigonal non-coplanar geometry to three S2- atoms. There are a spread of As–S bond distances ranging from 2.28–2.30 Å. There are six inequivalent S2- sites. In the first S2- site, S2- is bonded in a bent 120 degrees geometry to two As2+ atoms. In the second S2- site, S2- is bonded in a water-like geometry to two As2+ atoms. In the third S2- site, S2- is bonded in a water-like geometry to two As2+ atoms. In the fourth S2- site, S2- is bonded in a bent 120 degrees geometry to two As2+ atoms. In the fifth S2- site, S2- is bonded in a water-like geometry to two As2+ atoms. In the sixth S2- site, S2- is bonded in a water-like geometry to two As2+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on H9BrO4 by Materials Project

(H2O)3H7O3H11O5BrH12O5Br2Br crystallizes in the triclinic P1 space group. The structure is zero-dimensional and consists of one hydrobromic acid molecule, three water molecules, one H11O5Br cluster, one H12O5Br2 cluster, and one H7O3 cluster. In the H11O5Br cluster, there are eleven 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 distorted single-bond geometry to one O2- atom. The H–O bond length is 1.01 Å. In the third H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the fourth 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 fifth H1+ site, H1+ is bonded in a linear geometry to two O2- atoms. There is one shorter (1.06 Å) and one longer (1.47 Å) H–O bond length. In the sixth H1+ site, H1+ is bonded in a linear geometry to two O2- atoms. There is one shorter (1.03 Å) and one longer (1.58 Å) H–O bond length. In the seventh H1+ site, H1+ is bonded in a linear geometry to two O2- atoms. There is one shorter (1.03 Å) and one longer (1.58 Å) H–O bond length. In the eighth H1+ site, H1+ is bonded in a linear geometry to two O2- atoms. There is one shorter (1.04 Å) and one longer (1.55 Å) H–O bond length. In the ninth 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 tenth H1+ site, H1+ is bonded in a single-bond geometry to one O2- and one Br1- atom. The H–O bond length is 1.01 Å. The H–Br bond length is 2.20 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. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three H1+ atoms. In the second O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three H1+ atoms. In the third O2- site, O2- is bonded in a trigonal non-coplanar geometry to three H1+ atoms. In the fourth O2- site, O2- is bonded in a 3-coordinate geometry to three H1+ atoms. In the fifth O2- site, O2- is bonded in a distorted water-like geometry to three H1+ atoms. Br1- is bonded in a 1-coordinate geometry to one H1+ atom. In the H12O5Br2 cluster, there are twelve inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one O2- and one Br1- atom. The H–O bond length is 1.01 Å. The H–Br bond length is 2.12 Å. In the second H1+ site, H1+ is bonded in a linear geometry to two O2- atoms. There is one shorter (1.21 Å) and one longer (1.22 Å) H–O bond length. In the third H1+ site, H1+ is bonded in a distorted single-bond geometry to one O2- atom. The H–O bond length is 1.01 Å. In the fourth H1+ site, H1+ is bonded in a single-bond geometry to one O2- and one Br1- atom. The H–O bond length is 1.02 Å. The H–Br bond length is 2.12 Å. In the fifth 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 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 1.00 Å. In the eighth 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 ninth 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 tenth H1+ site, H1+ is bonded in a linear geometry to two O2- atoms. There is one shorter (1.03 Å) and one longer (1.59 Å) H–O bond length. In the eleventh H1+ site, H1+ is bonded in a linear geometry to two O2- atoms. There is one shorter (1.08 Å) and one longer (1.38 Å) H–O bond length. In the twelfth H1+ site, H1+ is bonded in a single-bond geometry to one O2- and one Br1- atom. The H–O bond length is 1.03 Å. The H–Br bond length is 2.08 Å. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded in a trigonal non-coplanar geometry to three H1+ atoms. In the second O2- site, O2- is bonded in a trigonal non-coplanar geometry to three H1+ atoms. In the third O2- site, O2- is bonded in a distorted water-like geometry to three H1+ atoms. In the fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to three H1+ atoms. In the fifth O2- site, O2- is bonded in a trigonal non-coplanar geometry to three H1+ atoms. There are two inequivalent Br1- sites. In the first Br1- site, Br1- is bonded in an L-shaped geometry to two H1+ atoms. In the second Br1- site, Br1- is bonded in a distorted single-bond geometry to one H1+ atom. In the H7O3 cluster, there are seven 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 linear geometry to two O2- atoms. There is one shorter (1.08 Å) and one longer (1.41 Å) H–O bond length. 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 1.00 Å. In the fifth H1+ site, H1+ is bonded in a distorted single-bond geometry to one O2- atom. The H–O bond length is 1.01 Å. In the sixth H1+ site, H1+ is bonded in a linear geometry to two O2- atoms. There is one shorter (1.05 Å) and one longer (1.50 Å) H–O bond length. In the seventh H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded in a 3-coordinate geometry to three H1+ atoms. In the second O2- site, O2- is bonded in a trigonal non-coplanar geometry to three H1+ atoms. In the third O2- site, O2- is bonded in a trigonal non-coplanar geometry to three H1+ atoms.

36 MATERIALS SCIENCE↗

The effect of composition on helium bubble nucleation in complex concentrated alloys

Molecular dynamics simulations of helium implantation have been performed in the MoNbTaTi complex concentrated alloy (CCA) to determine the impact of composition on helium clustering and bubble nucleation. It was found that compositions with lower interstitial atomic volume resulted in smaller cluster sizes, higher helium-to-vacancy ratios, and larger migration barriers. As the atomic volume decreases, it is harder to accommodate additional helium in the lattice and for helium to diffuse between interstitial sites, resulting in smaller cluster sizes. In particular, increasing molybdenum directly correlated with a decreased interstitial atomic volume and increased migration barrier. Niobium exhibited the opposite trend, where more niobium in the material resulted in larger interstitial atomic volumes and cluster sizes but lower migration barriers. The atomic volume was determined to be an indicator of the susceptibility of the material to helium bubble growth and could potentially be used as a metric to screen compositions for resistance to helium damage. In this way, properties such as available interstitial volumes could be used to screen materials more rapidly given the vast compositional space of CCAs.

McCarthy, Megan Jeanne [Sandia National Laboratori↗

Oxygen Defect Configurations in Single-Phase UO 2.15

Hyperstoichiometric UO 2.15 was characterized by neutron total scattering at high temperature in the single-phase UO 2+x region of the U/O phase diagram. The diffraction data confirmed a single-phase fluorite structure at high temperature. Analysis of the short-range data showed that the same structural model does not fit the pair distribution functions well. Instead, structural models containing specific configurations of oxygen defect clusters best represent the local atomic arrangement. In conclusion, prevalent defect clusters previously proposed were fit to the experimental data, and moderately distorted oxygen cuboctahedra hypothesized by recent molecular dynamics simulations fit the data most accurately.

neutron pair-distribution function analysis↗

Materials Data on NbP2NCl12 by Materials Project

NbCl6P2NCl6 crystallizes in the monoclinic C2/c space group. The structure is zero-dimensional and consists of four NbCl6 clusters and four P2NCl6 clusters. In each NbCl6 cluster, Nb5+ is bonded in an octahedral geometry to six Cl1- atoms. There are a spread of Nb–Cl bond distances ranging from 2.38–2.40 Å. There are three inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a single-bond geometry to one Nb5+ atom. In the second Cl1- site, Cl1- is bonded in a single-bond geometry to one Nb5+ atom. In the third Cl1- site, Cl1- is bonded in a single-bond geometry to one Nb5+ atom. In each P2NCl6 cluster, P5+ is bonded to one N3- and three Cl1- atoms to form corner-sharing PNCl3 tetrahedra. The P–N bond length is 1.56 Å. There are a spread of P–Cl bond distances ranging from 1.97–1.99 Å. N3- is bonded in a bent 150 degrees geometry to two equivalent P5+ atoms. There are three inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a single-bond geometry to one P5+ atom. In the second Cl1- site, Cl1- is bonded in a single-bond geometry to one P5+ atom. In the third Cl1- site, Cl1- is bonded in a single-bond geometry to one P5+ atom.

36 MATERIALS SCIENCE↗

Sub-Nanometer Nanoclusters of Copper Atop Single-Atom Copper Moieties toward Electrochemical CO 2 Hydrogenation to Methane

The electrochemical CO 2 reduction (eCO 2 R) offers a compelling route for converting CO 2 into value-added fuels and chemicals. Among CO 2 -derived products, methane (CH 4 ) occupies a distinct position, serving both as a key intermediate for emerging cascade electro-oxidation to oxygenates and as a strategically important extraterrestrial fuel that can be generated in situ from off-planet CO 2 resources. Although Cu-based catalysts capable of selectively producing CH 4 have been reported, they seldom sustain high selectivity at practically relevant current densities. Here, we created a single-step co-pyrolysis strategy toward generating and anchoring Cu sub-nanometer clusters (Cu SNC ) atop Cu-N x single-atom (SA) motifs embedded within N-doped carbon (NC), with controllable nanostructures through tuning of the synthesis parameters. Complementary spectroscopic analyses and density functional theory (DFT) calculations help reveal a structure−activity correlation that could guide the catalyst design. The Cu SNC @NC sample synthesized at 550 °C pyrolysis temperature (best described and modeled as Cu 3 -CuN 4 domains) represents the most effective combination of cluster size, metal-nitrogen coordination, and adsorption energetics needed to selectively promote CH 4 generation versus other eCO 2 R products. Incorporating pulsed electrolysis and hydrophobicity-modulated transport tuning at the triple-phase boundary (TPB) further enhanced CH 4 production achieving a partial CH 4 current density of ∼321 mA cm −2 , 53% Faradaic efficiency (FECH 4 ), and less than 4% combined FE for other eCO 2 R products, simplifying downstream CH 4 purification or upgrading. This work establishes generalizable principles for controlling Cu cluster atomicity and metal−nitrogen coordination, both of which are recognized determinants of CH 4 -efficient eCO 2 R.

CH4 production↗

Materials Data on Re3Se2Br5 by Materials Project

ReBr2Re2SeBr4Re3Se3Br4(Re3Se2Br5)2 crystallizes in the triclinic P1 space group. The structure is zero-dimensional and consists of one dibromorhenium molecule, one Re2SeBr4 cluster, one Re3Se2Br5 cluster, and one Re3Se3Br4 cluster. In the Re2SeBr4 cluster, there are two inequivalent Re3+ sites. In the first Re3+ site, Re3+ is bonded in a trigonal non-coplanar geometry to one Se2- and two Br1- atoms. The Re–Se bond length is 2.25 Å. There are one shorter (2.41 Å) and one longer (2.52 Å) Re–Br bond lengths. In the second Re3+ site, Re3+ is bonded in a distorted trigonal non-coplanar geometry to three Br1- atoms. There are a spread of Re–Br bond distances ranging from 2.40–2.76 Å. Se2- is bonded in a single-bond geometry to one Re3+ atom. There are four inequivalent Br1- sites. In the first Br1- site, Br1- is bonded in a 1-coordinate geometry to two Re3+ atoms. In the second Br1- site, Br1- is bonded in a single-bond geometry to one Re3+ atom. In the third Br1- site, Br1- is bonded in a single-bond geometry to one Re3+ atom. In the fourth Br1- site, Br1- is bonded in a single-bond geometry to one Re3+ atom. In the Re3Se2Br5 cluster, there are six inequivalent Re3+ sites. In the first Re3+ site, Re3+ is bonded to two Se2- and three Br1- atoms to form edge-sharing ReSe2Br3 square pyramids. Both Re–Se bond lengths are 2.55 Å. There are a spread of Re–Br bond distances ranging from 2.52–2.62 Å. In the second Re3+ site, Re3+ is bonded to two Se2- and three Br1- atoms to form edge-sharing ReSe2Br3 square pyramids. There are one shorter (2.50 Å) and one longer (2.51 Å) Re–Se bond lengths. There are a spread of Re–Br bond distances ranging from 2.52–2.72 Å. In the third Re3+ site, Re3+ is bonded in a see-saw-like geometry to two Se2- and two Br1- atoms. There are one shorter (2.46 Å) and one longer (2.49 Å) Re–Se bond lengths. There are one shorter (2.67 Å) and one longer (2.69 Å) Re–Br bond lengths. In the fourth Re3+ site, Re3+ is bonded to two Se2- and three Br1- atoms to form edge-sharing ReSe2Br3 square pyramids. There are one shorter (2.49 Å) and one longer (2.52 Å) Re–Se bond lengths. There are one shorter (2.52 Å) and two longer (2.67 Å) Re–Br bond lengths. In the fifth Re3+ site, Re3+ is bonded in a rectangular see-saw-like geometry to one Se2- and three Br1- atoms. The Re–Se bond length is 2.50 Å. There are a spread of Re–Br bond distances ranging from 2.46–2.77 Å. In the sixth Re3+ site, Re3+ is bonded in a see-saw-like geometry to one Se2- and three Br1- atoms. The Re–Se bond length is 2.56 Å. There are a spread of Re–Br bond distances ranging from 2.48–2.60 Å. There are four inequivalent Se2- sites. In the first Se2- site, Se2- is bonded in a 7-coordinate geometry to three Re3+ atoms. In the second Se2- site, Se2- is bonded in a 3-coordinate geometry to three Re3+ atoms. In the third Se2- site, Se2- is bonded in a 4-coordinate geometry to three Re3+ atoms. In the fourth Se2- site, Se2- is bonded in a distorted bent 120 degrees geometry to one Re3+ and one Br1- atom. The Se–Br bond length is 2.36 Å. There are ten inequivalent Br1- sites. In the first Br1- site, Br1- is bonded in a single-bond geometry to one Re3+ atom. In the second Br1- site, Br1- is bonded in a 7-coordinate geometry to three Re3+ atoms. In the third Br1- site, Br1- is bonded in a single-bond geometry to one Re3+ atom. In the fourth Br1- site, Br1- is bonded in a single-bond geometry to one Re3+ atom. In the fifth Br1- site, Br1- is bonded in a 1-coordinate geometry to three Re3+ atoms. In the sixth Br1- site, Br1- is bonded in a single-bond geometry to one Re3+ atom. In the seventh Br1- site, Br1- is bonded in a 7-coordinate geometry to three Re3+ atoms. In the eighth Br1- site, Br1- is bonded in a single-bond geometry to one Re3+ atom. In the ninth Br1- site, Br1- is bonded in a single-bond geometry to one Se2- atom. In the tenth Br1- site, Br1- is bonded in a 5-coordinate geometry to three Re3+ atoms. In the Re3Se3Br4 cluster, there are three inequivalent Re3+ sites. In the first Re3+ site, Re3+ is bonded in a see-saw-like geometry to two Se2- and two Br1- atoms. There are one shorter (2.43 Å) and one longer (2.45 Å) Re–Se bond lengths. There are one shorter (2.48 Å) and one longer (2.61 Å) Re–Br bond lengths. In the second Re3+ site, Re3+ is bonded in a distorted rectangular see-saw-like geometry to two Se2- and two Br1- atoms. There are one shorter (2.35 Å) and one longer (2.46 Å) Re–Se bond lengths. There are one shorter (2.46 Å) and one longer (2.59 Å) Re–Br bond lengths. In the third Re3+ site, Re3+ is bonded in a distorted rectangular see-saw-like geometry to three Se2- and one Br1- atom. There are a spread of Re–Se bond distances ranging from 2.44–2.52 Å. The Re–Br bond length is 2.46 Å. There are three inequivalent Se2- sites. In the first Se2- site, Se2- is bonded in a 6-coordinate geometry to three Re3+ atoms. In the second Se2- site, Se2- is bonded in a 2-coordinate geometry to two Re3+ atoms. In the third Se2- site, Se2- is bonded in a 2-coordinate geometry to two Re3+ atoms. There are four inequivalent Br1- sites. In the first Br1- site, Br1- is bonded in a single-bond geometry to one Re3+ atom. In the second Br1- site, Br1- is bonded in a single-bond geometry to one Re3+ atom. In the third Br1- site, Br1- is bonded in a 3-coordinate geometry to two Re3+ atoms. In the fourth Br1- site, Br1- is bonded in a single-bond geometry to one Re3+ atom.

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Materials Data on SbAs2Cl13 by Materials Project

SbCl6AsCl3AsCl4 crystallizes in the orthorhombic Cmc2_1 space group. The structure is zero-dimensional and consists of four trichloroarsine molecules, four AsCl4 clusters, and four SbCl6 clusters. In each AsCl4 cluster, As5+ is bonded in a tetrahedral geometry to four Cl1- atoms. There are two shorter (2.10 Å) and two longer (2.11 Å) As–Cl bond lengths. There are three inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a single-bond geometry to one As5+ atom. In the second Cl1- site, Cl1- is bonded in a single-bond geometry to one As5+ atom. In the third Cl1- site, Cl1- is bonded in a single-bond geometry to one As5+ atom. In each SbCl6 cluster, Sb3+ is bonded in an octahedral geometry to six Cl1- atoms. There are four shorter (2.41 Å) and two longer (2.43 Å) Sb–Cl bond lengths. There are four inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a single-bond geometry to one Sb3+ atom. In the second Cl1- site, Cl1- is bonded in a single-bond geometry to one Sb3+ atom. In the third Cl1- site, Cl1- is bonded in a single-bond geometry to one Sb3+ atom. In the fourth Cl1- site, Cl1- is bonded in a single-bond geometry to one Sb3+ atom.

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Materials Data on SbI5F6 by Materials Project

SbF6(Sb(IF3)2)2(I)11 crystallizes in the triclinic P-1 space group. The structure is zero-dimensional and consists of eleven hydriodic acid molecules, two Sb(IF3)2 clusters, and one SbF6 cluster. In each Sb(IF3)2 cluster, Sb5+ is bonded in an octahedral geometry to six F1- atoms. There are a spread of Sb–F bond distances ranging from 1.91–1.95 Å. There are two inequivalent I+0.20+ sites. In the first I+0.20+ site, I+0.20+ is bonded in a single-bond geometry to one F1- atom. The I–F bond length is 2.80 Å. In the second I+0.20+ site, I+0.20+ is bonded in a single-bond geometry to one F1- atom. The I–F bond length is 2.81 Å. There are six inequivalent F1- sites. In the first F1- site, F1- is bonded in a single-bond geometry to one Sb5+ atom. In the second F1- site, F1- is bonded in a single-bond geometry to one Sb5+ atom. In the third F1- site, F1- is bonded in a single-bond geometry to one Sb5+ and one I+0.20+ atom. In the fourth F1- site, F1- is bonded in a single-bond geometry to one Sb5+ and one I+0.20+ atom. In the fifth F1- site, F1- is bonded in a single-bond geometry to one Sb5+ atom. In the sixth F1- site, F1- is bonded in a single-bond geometry to one Sb5+ atom. In the SbF6 cluster, Sb5+ is bonded in an octahedral geometry to six F1- atoms. There are a spread of Sb–F bond distances ranging from 1.91–1.94 Å. There are three inequivalent F1- sites. In the first F1- site, F1- is bonded in a single-bond geometry to one Sb5+ atom. In the second F1- site, F1- is bonded in a single-bond geometry to one Sb5+ atom. In the third F1- site, F1- is bonded in a single-bond geometry to one Sb5+ atom.

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Materials Data on Te4As2S(OF6)2 by Materials Project

(Te)2AsTe2F6AsF6SO2 crystallizes in the orthorhombic Pnma space group. The structure is zero-dimensional and consists of four sulfur dioxide molecules, eight tellurium molecules, four AsF6 clusters, and four AsTe2F6 clusters. In each AsF6 cluster, As1+ is bonded in an octahedral geometry to six F1- atoms. There are a spread of As–F bond distances ranging from 1.77–1.79 Å. There are four inequivalent F1- sites. In the first F1- site, F1- is bonded in a single-bond geometry to one As1+ atom. In the second F1- site, F1- is bonded in a single-bond geometry to one As1+ atom. In the third F1- site, F1- is bonded in a single-bond geometry to one As1+ atom. In the fourth F1- site, F1- is bonded in a single-bond geometry to one As1+ atom. In each AsTe2F6 cluster, As1+ is bonded in an octahedral geometry to six F1- atoms. There are a spread of As–F bond distances ranging from 1.77–1.80 Å. Te4+ is bonded in a 1-coordinate geometry to one F1- atom. The Te–F bond length is 2.97 Å. There are four inequivalent F1- sites. In the first F1- site, F1- is bonded in a single-bond geometry to one As1+ atom. In the second F1- site, F1- is bonded in a single-bond geometry to one As1+ atom. In the third F1- site, F1- is bonded in a single-bond geometry to one As1+ and two equivalent Te4+ atoms. In the fourth F1- site, F1- is bonded in a single-bond geometry to one As1+ atom.

36 MATERIALS SCIENCE↗

Materials Data on AlS2NCl4 by Materials Project

AlCl4NS2 is Modderite structured and crystallizes in the orthorhombic Pnma space group. The structure is zero-dimensional and consists of four AlCl4 clusters and four NS2 clusters. In each AlCl4 cluster, Al3+ is bonded in a tetrahedral geometry to four Cl1- atoms. All Al–Cl bond lengths are 2.16 Å. There are three inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ atom. In the second Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Al3+ atom. In the third Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ atom. In each NS2 cluster, N5+ is bonded in a linear geometry to two S2- atoms. Both N–S bond lengths are 1.50 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a single-bond geometry to one N5+ atom. In the second S2- site, S2- is bonded in a distorted single-bond geometry to one N5+ atom.

36 MATERIALS SCIENCE↗

Materials Data on CuSb2(XeF4)6 by Materials Project

Cu(XeF2)6(SbF6)2 is Fluorite structured and crystallizes in the trigonal R-3 space group. The structure is zero-dimensional and consists of three Cu(XeF2)6 clusters and six SbF6 clusters. In each Cu(XeF2)6 cluster, Xe is bonded in a linear geometry to two F atoms. There are one shorter (2.03 Å) and one longer (2.17 Å) Xe–F bond lengths. Cu is bonded in an octahedral geometry to six equivalent F atoms. All Cu–F bond lengths are 2.02 Å. There are two inequivalent F sites. In the first F site, F is bonded in a bent 120 degrees geometry to one Xe and one Cu atom. In the second F site, F is bonded in a single-bond geometry to one Xe atom. In each SbF6 cluster, Sb is bonded in an octahedral geometry to six F atoms. There is three shorter (1.92 Å) and three longer (1.93 Å) Sb–F bond length. There are two inequivalent F sites. In the first F site, F is bonded in a single-bond geometry to one Sb atom. In the second F site, F is bonded in a single-bond geometry to one Sb atom.

36 MATERIALS SCIENCE↗

Materials Data on Sb2OsC6(OF2)6 by Materials Project

Os(CO)6(SbF6)2 is Fluorite structured and crystallizes in the tetragonal P4/mnc space group. The structure is zero-dimensional and consists of two Os(CO)6 clusters and four SbF6 clusters. In each Os(CO)6 cluster, Os2- is bonded in an octahedral geometry to six C4+ atoms. There are two shorter (2.01 Å) and four longer (2.02 Å) Os–C bond lengths. There are two inequivalent C4+ sites. In the first C4+ site, C4+ is bonded in a distorted single-bond geometry to one Os2- and one O2- atom. The C–O bond length is 1.14 Å. In the second C4+ site, C4+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.14 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a single-bond geometry to one C4+ atom. In the second O2- site, O2- is bonded in a single-bond geometry to one C4+ atom. In each SbF6 cluster, Sb1+ is bonded in an octahedral geometry to six F1- atoms. All Sb–F bond lengths are 1.92 Å. There are two inequivalent F1- sites. In the first F1- site, F1- is bonded in a single-bond geometry to one Sb1+ atom. In the second F1- site, F1- is bonded in a single-bond geometry to one Sb1+ atom.

36 MATERIALS SCIENCE↗