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DOE OSTI2020

Materials Data on Sm6Al43W4 by Materials Project

Sm6W4Al43 crystallizes in the hexagonal P6_3/mcm space group. The structure is three-dimensional. Sm is bonded in a 6-coordinate geometry to one Sm, one W, and fifteen Al atoms. The Sm–Sm bond length is 3.46 Å. The Sm–W bond length is 3.52 Å. There are a spread of Sm–Al bond distances ranging from 3.09–3.47 Å. There are two inequivalent W sites. In the first W site, W is bonded in a distorted q6 geometry to two equivalent Sm and ten Al atoms. There are a spread of W–Al bond distances ranging from 2.60–2.73 Å. In the second W site, W is bonded in a cuboctahedral geometry to twelve Al atoms. There are six shorter (2.70 Å) and six longer (2.85 Å) W–Al bond lengths. There are seven inequivalent Al sites. In the first Al site, Al is bonded in a distorted linear geometry to one Sm, two W, and three equivalent Al atoms. There are one shorter (2.80 Å) and two longer (2.87 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a 12-coordinate geometry to four equivalent Sm and eight Al atoms. There are a spread of Al–Al bond distances ranging from 2.76–3.10 Å. In the third Al site, Al is bonded in a 1-coordinate geometry to two equivalent Sm, one W, and three Al atoms. There are one shorter (2.74 Å) and one longer (2.90 Å) Al–Al bond lengths. In the fourth Al site, Al is bonded in a distorted linear geometry to two equivalent W atoms. In the fifth Al site, Al is bonded in a 1-coordinate geometry to two equivalent Sm, one W, and nine Al atoms. Both Al–Al bond lengths are 3.01 Å. In the sixth Al site, Al is bonded to three equivalent Sm and nine Al atoms to form a mixture of corner and face-sharing AlSm3Al9 cuboctahedra. All Al–Al bond lengths are 2.84 Å. In the seventh Al site, Al is bonded in a 1-coordinate geometry to two equivalent Sm, one W, and two equivalent Al atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on TaB4W3 by Materials Project

TaW3B4 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Ta5+ is bonded in a 7-coordinate geometry to seven B3- atoms. There are a spread of Ta–B bond distances ranging from 2.36–2.53 Å. There are three inequivalent W+2.33+ sites. In the first W+2.33+ site, W+2.33+ is bonded in a 7-coordinate geometry to seven B3- atoms. There are a spread of W–B bond distances ranging from 2.35–2.53 Å. In the second W+2.33+ site, W+2.33+ is bonded in a 7-coordinate geometry to seven B3- atoms. There are a spread of W–B bond distances ranging from 2.34–2.60 Å. In the third W+2.33+ site, W+2.33+ is bonded in a 7-coordinate geometry to seven B3- atoms. There are a spread of W–B bond distances ranging from 2.36–2.50 Å. There are four inequivalent B3- sites. In the first B3- site, B3- is bonded in a 9-coordinate geometry to one Ta5+, six W+2.33+, and two equivalent B3- atoms. Both B–B bond lengths are 1.88 Å. In the second B3- site, B3- is bonded in a 9-coordinate geometry to two equivalent Ta5+, five W+2.33+, and two equivalent B3- atoms. Both B–B bond lengths are 1.86 Å. In the third B3- site, B3- is bonded in a 9-coordinate geometry to four equivalent Ta5+, three W+2.33+, and two equivalent B3- atoms. In the fourth B3- site, B3- is bonded in a 9-coordinate geometry to seven W+2.33+ and two equivalent B3- atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Na3W2(ClO)4 by Materials Project

Na3W2(OCl)4 crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are three inequivalent Na1+ sites. In the first Na1+ site, Na1+ is bonded in a 9-coordinate geometry to four equivalent O2- and five Cl1- atoms. All Na–O bond lengths are 2.84 Å. There are a spread of Na–Cl bond distances ranging from 2.85–3.04 Å. In the second Na1+ site, Na1+ is bonded in a 9-coordinate geometry to four equivalent O2- and five Cl1- atoms. All Na–O bond lengths are 2.76 Å. There are a spread of Na–Cl bond distances ranging from 2.85–3.05 Å. In the third Na1+ site, Na1+ is bonded in a 9-coordinate geometry to four equivalent O2- and five Cl1- atoms. All Na–O bond lengths are 2.75 Å. There are a spread of Na–Cl bond distances ranging from 2.87–3.12 Å. There are two inequivalent W+4.50+ sites. In the first W+4.50+ site, W+4.50+ is bonded to four equivalent O2- and two Cl1- atoms to form distorted corner-sharing WCl2O4 octahedra. The corner-sharing octahedral tilt angles are 5°. All W–O bond lengths are 2.04 Å. There are one shorter (2.45 Å) and one longer (2.56 Å) W–Cl bond lengths. In the second W+4.50+ site, W+4.50+ is bonded to four equivalent O2- and two Cl1- atoms to form distorted corner-sharing WCl2O4 octahedra. The corner-sharing octahedral tilt angles are 5°. All W–O bond lengths are 1.97 Å. There are one shorter (2.43 Å) and one longer (2.51 Å) W–Cl bond lengths. O2- is bonded to three Na1+ and two W+4.50+ atoms to form distorted ONa3W2 square pyramids that share corners with three equivalent ClNa5W octahedra, corners with two equivalent ClNa4W square pyramids, corners with three equivalent ONa3W2 square pyramids, edges with three equivalent ONa3W2 square pyramids, a faceface with one ClNa5W octahedra, a faceface with one ClNa4W square pyramid, and faces with two equivalent ONa3W2 square pyramids. The corner-sharing octahedra tilt angles range from 45–51°. There are four inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded to five Na1+ and one W+4.50+ atom to form distorted ClNa5W octahedra that share corners with four equivalent ClNa5W octahedra, corners with twelve equivalent ONa3W2 square pyramids, edges with four equivalent ClNa4W square pyramids, and faces with four equivalent ONa3W2 square pyramids. The corner-sharing octahedra tilt angles range from 22–23°. In the second Cl1- site, Cl1- is bonded to four Na1+ and one W+4.50+ atom to form distorted ClNa4W square pyramids that share corners with four equivalent ClNa4W square pyramids, corners with eight equivalent ONa3W2 square pyramids, edges with four equivalent ClNa5W octahedra, and faces with four equivalent ONa3W2 square pyramids. In the third Cl1- site, Cl1- is bonded in a distorted square co-planar geometry to three Na1+ and one W+4.50+ atom. In the fourth Cl1- site, Cl1- is bonded in a distorted square co-planar geometry to three Na1+ and one W+4.50+ atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on AlW3C4 by Materials Project

W3AlC4 is Tungsten Carbide-derived structured and crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. there are three inequivalent W+4.33+ sites. In the first W+4.33+ site, W+4.33+ is bonded to six C4- atoms to form distorted WC6 pentagonal pyramids that share corners with four equivalent AlC6 pentagonal pyramids, corners with eight WC6 pentagonal pyramids, edges with two equivalent AlC6 pentagonal pyramids, edges with four WC6 pentagonal pyramids, and faces with two equivalent WC6 pentagonal pyramids. There are four shorter (2.19 Å) and two longer (2.20 Å) W–C bond lengths. In the second W+4.33+ site, W+4.33+ is bonded to six C4- atoms to form a mixture of distorted corner, edge, and face-sharing WC6 pentagonal pyramids. There are two shorter (2.20 Å) and four longer (2.21 Å) W–C bond lengths. In the third W+4.33+ site, W+4.33+ is bonded to six C4- atoms to form distorted WC6 pentagonal pyramids that share corners with four equivalent AlC6 pentagonal pyramids, corners with eight WC6 pentagonal pyramids, edges with two equivalent AlC6 pentagonal pyramids, edges with four WC6 pentagonal pyramids, and faces with two equivalent WC6 pentagonal pyramids. There are two shorter (2.15 Å) and four longer (2.21 Å) W–C bond lengths. Al3+ is bonded to six C4- atoms to form distorted AlC6 pentagonal pyramids that share corners with four equivalent AlC6 pentagonal pyramids, corners with eight WC6 pentagonal pyramids, edges with two equivalent AlC6 pentagonal pyramids, edges with four WC6 pentagonal pyramids, and faces with two equivalent AlC6 pentagonal pyramids. There are four shorter (2.19 Å) and two longer (2.36 Å) Al–C bond lengths. There are four inequivalent C4- sites. In the first C4- site, C4- is bonded to six W+4.33+ atoms to form a mixture of distorted corner, edge, and face-sharing CW6 pentagonal pyramids. In the second C4- site, C4- is bonded to six W+4.33+ atoms to form a mixture of distorted corner, edge, and face-sharing CW6 pentagonal pyramids. In the third C4- site, C4- is bonded in a 6-coordinate geometry to two equivalent W+4.33+ and four equivalent Al3+ atoms. In the fourth C4- site, C4- is bonded to four equivalent W+4.33+ and two equivalent Al3+ atoms to form distorted CAl2W4 pentagonal pyramids that share corners with eight CW6 pentagonal pyramids, edges with four CW6 pentagonal pyramids, and faces with two equivalent CAl2W4 pentagonal pyramids.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on La4Al51W7 by Materials Project

La4W7Al51 crystallizes in the trigonal P-3m1 space group. The structure is three-dimensional. there are two inequivalent La sites. In the first La site, La is bonded in a 9-coordinate geometry to fifteen Al atoms. There are a spread of La–Al bond distances ranging from 3.21–3.46 Å. In the second La site, La is bonded in a 3-coordinate geometry to fifteen Al atoms. There are a spread of La–Al bond distances ranging from 3.20–3.30 Å. There are two inequivalent W sites. In the first W site, W is bonded in a 10-coordinate geometry to ten Al atoms. There are a spread of W–Al bond distances ranging from 2.49–2.74 Å. In the second W site, W is bonded in a cuboctahedral geometry to twelve Al atoms. There are six shorter (2.59 Å) and six longer (2.87 Å) W–Al bond lengths. There are eight inequivalent Al sites. In the first Al site, Al is bonded in a distorted linear geometry to two equivalent La atoms. In the second Al site, Al is bonded in a distorted bent 150 degrees geometry to two equivalent W atoms. In the third Al site, Al is bonded in a 1-coordinate geometry to two La, one W, and one Al atom. The Al–Al bond length is 2.85 Å. In the fourth Al site, Al is bonded in a distorted linear geometry to one La and two equivalent W atoms. In the fifth Al site, Al is bonded in a 12-coordinate geometry to one La, one W, and eight Al atoms. There are a spread of Al–Al bond distances ranging from 2.70–3.01 Å. In the sixth Al site, Al is bonded in a distorted bent 120 degrees geometry to two equivalent La and two equivalent W atoms. In the seventh Al site, Al is bonded in a distorted linear geometry to two W and three equivalent Al atoms. In the eighth Al site, Al is bonded in a 1-coordinate geometry to one La, one W, and one Al atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Dy6Al43W4 by Materials Project

Dy6W4Al43 crystallizes in the hexagonal P6_3/mcm space group. The structure is three-dimensional. Dy is bonded in a 6-coordinate geometry to one Dy, one W, and fifteen Al atoms. The Dy–Dy bond length is 3.44 Å. The Dy–W bond length is 3.49 Å. There are a spread of Dy–Al bond distances ranging from 3.06–3.44 Å. There are two inequivalent W sites. In the first W site, W is bonded in a distorted q6 geometry to two equivalent Dy and ten Al atoms. There are a spread of W–Al bond distances ranging from 2.60–2.73 Å. In the second W site, W is bonded in a cuboctahedral geometry to twelve Al atoms. There are six shorter (2.68 Å) and six longer (2.86 Å) W–Al bond lengths. There are seven inequivalent Al sites. In the first Al site, Al is bonded in a 2-coordinate geometry to one Dy, two W, and three equivalent Al atoms. There are one shorter (2.77 Å) and two longer (2.87 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a 12-coordinate geometry to four equivalent Dy and eight Al atoms. There are a spread of Al–Al bond distances ranging from 2.75–3.06 Å. In the third Al site, Al is bonded in a 1-coordinate geometry to two equivalent Dy, one W, and three Al atoms. There are one shorter (2.72 Å) and one longer (2.87 Å) Al–Al bond lengths. In the fourth Al site, Al is bonded in a distorted linear geometry to two equivalent W atoms. In the fifth Al site, Al is bonded in a 1-coordinate geometry to two equivalent Dy, one W, and nine Al atoms. Both Al–Al bond lengths are 3.01 Å. In the sixth Al site, Al is bonded to three equivalent Dy and nine Al atoms to form a mixture of face and corner-sharing AlDy3Al9 cuboctahedra. All Al–Al bond lengths are 2.83 Å. In the seventh Al site, Al is bonded in a 1-coordinate geometry to two equivalent Dy, one W, and two equivalent Al atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Na4W4O15 by Materials Project

Na4W4O15 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are two inequivalent Na sites. In the first Na site, Na is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Na–O bond distances ranging from 2.37–2.82 Å. In the second Na site, Na is bonded to six O atoms to form NaO6 octahedra that share a cornercorner with one NaO6 octahedra, corners with three equivalent WO6 octahedra, and an edgeedge with one NaO6 octahedra. The corner-sharing octahedra tilt angles range from 0–62°. There are a spread of Na–O bond distances ranging from 2.28–2.68 Å. There are two inequivalent W sites. In the first W site, W is bonded in a 6-coordinate geometry to six O atoms. There are a spread of W–O bond distances ranging from 1.79–2.28 Å. In the second W site, W is bonded to six O atoms to form distorted WO6 octahedra that share corners with three equivalent NaO6 octahedra and an edgeedge with one WO6 octahedra. The corner-sharing octahedra tilt angles range from 49–62°. There are a spread of W–O bond distances ranging from 1.80–2.15 Å. There are eight inequivalent O sites. In the first O site, O is bonded in a linear geometry to two equivalent Na atoms. In the second O site, O is bonded in a distorted T-shaped geometry to two Na and one W atom. In the third O site, O is bonded to three Na and one W atom to form a mixture of distorted edge and corner-sharing ONa3W trigonal pyramids. In the fourth O site, O is bonded in a trigonal planar geometry to one Na and two W atoms. In the fifth O site, O is bonded in a distorted T-shaped geometry to three W atoms. In the sixth O site, O is bonded to two equivalent Na and two W atoms to form distorted ONa2W2 trigonal pyramids that share a cornercorner with one ONa3W trigonal pyramid and edges with two ONa2W2 trigonal pyramids. In the seventh O site, O is bonded in a 3-coordinate geometry to one Na and two W atoms. In the eighth O site, O is bonded in a distorted T-shaped geometry to two Na and one W atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Yb6Al43W4 by Materials Project

Yb6W4Al43 crystallizes in the hexagonal P6_3/mcm space group. The structure is three-dimensional. Yb is bonded in a 6-coordinate geometry to one Yb, one W, and fifteen Al atoms. The Yb–Yb bond length is 3.41 Å. The Yb–W bond length is 3.51 Å. There are a spread of Yb–Al bond distances ranging from 3.09–3.43 Å. There are two inequivalent W sites. In the first W site, W is bonded in a distorted q6 geometry to two equivalent Yb and ten Al atoms. There are a spread of W–Al bond distances ranging from 2.60–2.73 Å. In the second W site, W is bonded in a cuboctahedral geometry to twelve Al atoms. There are six shorter (2.69 Å) and six longer (2.86 Å) W–Al bond lengths. There are seven inequivalent Al sites. In the first Al site, Al is bonded in a 2-coordinate geometry to one Yb, two W, and three equivalent Al atoms. There are one shorter (2.78 Å) and two longer (2.86 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a 12-coordinate geometry to four equivalent Yb and eight Al atoms. There are a spread of Al–Al bond distances ranging from 2.77–3.09 Å. In the third Al site, Al is bonded in a 1-coordinate geometry to two equivalent Yb, one W, and three Al atoms. There are one shorter (2.75 Å) and one longer (2.87 Å) Al–Al bond lengths. In the fourth Al site, Al is bonded in a distorted linear geometry to two equivalent W atoms. In the fifth Al site, Al is bonded in a 1-coordinate geometry to two equivalent Yb, one W, and nine Al atoms. Both Al–Al bond lengths are 3.01 Å. In the sixth Al site, Al is bonded to three equivalent Yb and nine Al atoms to form a mixture of face and corner-sharing AlYb3Al9 cuboctahedra. All Al–Al bond lengths are 2.82 Å. In the seventh Al site, Al is bonded in a 1-coordinate geometry to two equivalent Yb, one W, and two equivalent Al atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on LiMg3(WO4)3 by Materials Project

LiMg3(WO4)3 crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. Li1+ is bonded to six O2- atoms to form distorted LiO6 pentagonal pyramids that share corners with two equivalent MgO6 octahedra, corners with two equivalent WO5 trigonal bipyramids, edges with two equivalent LiO6 pentagonal pyramids, and edges with four equivalent WO5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 66°. There are a spread of Li–O bond distances ranging from 2.13–2.29 Å. There are two inequivalent Mg2+ sites. In the first Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent WO4 tetrahedra, corners with four equivalent WO5 trigonal bipyramids, and faces with two equivalent MgO6 octahedra. There are a spread of Mg–O bond distances ranging from 2.03–2.09 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share a cornercorner with one MgO6 octahedra, a cornercorner with one LiO6 pentagonal pyramid, corners with three equivalent WO4 tetrahedra, corners with three equivalent WO5 trigonal bipyramids, and edges with two equivalent MgO6 octahedra. The corner-sharing octahedral tilt angles are 54°. There are a spread of Mg–O bond distances ranging from 2.03–2.19 Å. There are two inequivalent W+5.67+ sites. In the first W+5.67+ site, W+5.67+ is bonded to four O2- atoms to form WO4 tetrahedra that share corners with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 28–64°. There is three shorter (1.81 Å) and one longer (1.84 Å) W–O bond length. In the second W+5.67+ site, W+5.67+ is bonded to five O2- atoms to form distorted WO5 trigonal bipyramids that share corners with five MgO6 octahedra, a cornercorner with one LiO6 pentagonal pyramid, corners with two equivalent WO5 trigonal bipyramids, and edges with two equivalent LiO6 pentagonal pyramids. The corner-sharing octahedra tilt angles range from 28–55°. There are a spread of W–O bond distances ranging from 1.84–2.37 Å. There are seven inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to two equivalent Li1+ and two equivalent W+5.67+ atoms. In the second O2- site, O2- is bonded in a trigonal planar geometry to one Li1+, one Mg2+, and one W+5.67+ atom. In the third O2- site, O2- is bonded in a trigonal planar geometry to two equivalent Mg2+ and one W+5.67+ atom. In the fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to two equivalent Mg2+ and one W+5.67+ atom. In the fifth O2- site, O2- is bonded in a distorted trigonal planar geometry to two equivalent Mg2+ and one W+5.67+ atom. In the sixth O2- site, O2- is bonded in a 3-coordinate geometry to two equivalent Mg2+ and one W+5.67+ atom. In the seventh O2- site, O2- is bonded in a 3-coordinate geometry to two equivalent Mg2+ and one W+5.67+ atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Er6Al43W4 by Materials Project

Er6W4Al43 crystallizes in the hexagonal P6_3/mcm space group. The structure is three-dimensional. Er is bonded in a 6-coordinate geometry to one Er, one W, and fifteen Al atoms. The Er–Er bond length is 3.43 Å. The Er–W bond length is 3.48 Å. There are a spread of Er–Al bond distances ranging from 3.06–3.43 Å. There are two inequivalent W sites. In the first W site, W is bonded in a distorted q6 geometry to two equivalent Er and ten Al atoms. There are a spread of W–Al bond distances ranging from 2.60–2.73 Å. In the second W site, W is bonded in a cuboctahedral geometry to twelve Al atoms. There are six shorter (2.68 Å) and six longer (2.87 Å) W–Al bond lengths. There are seven inequivalent Al sites. In the first Al site, Al is bonded in a 2-coordinate geometry to one Er, two W, and three equivalent Al atoms. There are one shorter (2.76 Å) and two longer (2.87 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a 12-coordinate geometry to four equivalent Er and eight Al atoms. There are a spread of Al–Al bond distances ranging from 2.74–3.06 Å. In the third Al site, Al is bonded in a 1-coordinate geometry to two equivalent Er, one W, and three Al atoms. There are one shorter (2.72 Å) and one longer (2.86 Å) Al–Al bond lengths. In the fourth Al site, Al is bonded in a distorted linear geometry to two equivalent W atoms. In the fifth Al site, Al is bonded in a 1-coordinate geometry to two equivalent Er, one W, and nine Al atoms. Both Al–Al bond lengths are 3.01 Å. In the sixth Al site, Al is bonded to three equivalent Er and nine Al atoms to form a mixture of corner and face-sharing AlEr3Al9 cuboctahedra. All Al–Al bond lengths are 2.83 Å. In the seventh Al site, Al is bonded in a 1-coordinate geometry to two equivalent Er, one W, and two equivalent Al atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on TiP4W3 by Materials Project

TiW3P4 is Modderite-derived structured and crystallizes in the monoclinic Pm space group. The structure is three-dimensional. Ti4+ is bonded to six P3- atoms to form distorted TiP6 pentagonal pyramids that share corners with twelve WP6 pentagonal pyramids, edges with two equivalent TiP6 pentagonal pyramids, edges with four equivalent WP6 pentagonal pyramids, and faces with two equivalent WP6 pentagonal pyramids. There are a spread of Ti–P bond distances ranging from 2.44–2.60 Å. There are three inequivalent W+2.67+ sites. In the first W+2.67+ site, W+2.67+ is bonded to six P3- atoms to form distorted WP6 pentagonal pyramids that share corners with four equivalent TiP6 pentagonal pyramids, corners with eight equivalent WP6 pentagonal pyramids, edges with six WP6 pentagonal pyramids, and faces with two equivalent TiP6 pentagonal pyramids. There are a spread of W–P bond distances ranging from 2.46–2.60 Å. In the second W+2.67+ site, W+2.67+ is bonded to six P3- atoms to form distorted WP6 pentagonal pyramids that share corners with twelve WP6 pentagonal pyramids, edges with two equivalent WP6 pentagonal pyramids, edges with four equivalent TiP6 pentagonal pyramids, and faces with two equivalent WP6 pentagonal pyramids. There are a spread of W–P bond distances ranging from 2.44–2.59 Å. In the third W+2.67+ site, W+2.67+ is bonded to six P3- atoms to form distorted WP6 pentagonal pyramids that share corners with four equivalent WP6 pentagonal pyramids, corners with eight equivalent TiP6 pentagonal pyramids, edges with six WP6 pentagonal pyramids, and faces with two equivalent WP6 pentagonal pyramids. There are a spread of W–P bond distances ranging from 2.45–2.57 Å. There are four inequivalent P3- sites. In the first P3- site, P3- is bonded in a 6-coordinate geometry to one Ti4+ and five W+2.67+ atoms. In the second P3- site, P3- is bonded in a 1-coordinate geometry to one Ti4+ and five W+2.67+ atoms. In the third P3- site, P3- is bonded in a 6-coordinate geometry to two equivalent Ti4+ and four W+2.67+ atoms. In the fourth P3- site, P3- is bonded in a 6-coordinate geometry to two equivalent Ti4+ and four W+2.67+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on MnB4W3 by Materials Project

W3MnB4 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. there are three inequivalent W+3.33+ sites. In the first W+3.33+ site, W+3.33+ is bonded in a 7-coordinate geometry to seven B3- atoms. There are a spread of W–B bond distances ranging from 2.32–2.55 Å. In the second W+3.33+ site, W+3.33+ is bonded in a 7-coordinate geometry to seven B3- atoms. There are a spread of W–B bond distances ranging from 2.29–2.34 Å. In the third W+3.33+ site, W+3.33+ is bonded in a 7-coordinate geometry to seven B3- atoms. There are a spread of W–B bond distances ranging from 2.33–2.54 Å. Mn2+ is bonded in a 7-coordinate geometry to seven B3- atoms. There are a spread of Mn–B bond distances ranging from 2.17–2.46 Å. There are four inequivalent B3- sites. In the first B3- site, B3- is bonded in a 9-coordinate geometry to six W+3.33+, one Mn2+, and two equivalent B3- atoms. Both B–B bond lengths are 1.85 Å. In the second B3- site, B3- is bonded in a 9-coordinate geometry to five W+3.33+, two equivalent Mn2+, and two equivalent B3- atoms. Both B–B bond lengths are 1.81 Å. In the third B3- site, B3- is bonded in a 9-coordinate geometry to three W+3.33+, four equivalent Mn2+, and two equivalent B3- atoms. In the fourth B3- site, B3- is bonded in a 9-coordinate geometry to seven W+3.33+ and two equivalent B3- atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2024

The vertical-velocity skewness in the atmospheric boundary layer without buoyancy and Coriolis effects

One of the main features of near-neutral atmospheric boundary layer (ABL) turbulence is the positive vertical velocity skewness $Sk_w$ above the roughness sublayer or the buffer region in smooth-walls. The $Sk_w$ variations are receiving renewed interest in many climate-related parameterizations of the ABL given their significance to cloud formation and to testing sub-grid schemes for Large Eddy Simulations (LES). The vertical variations of $Sk_w$ are explored here using wind tunnel and flume experiments collected above smooth, rough, and permeable-walls in the absence of buoyancy and Coriolis effects. These laboratory experiments form a necessary starting point to probe the canonical structure of $Sk_w$ as they deal with a key limiting case (i.e., near-neutral conditions). Diagnostic models based on cumulant expansions, realizability constraints, and constant mass flux approach routinely employed in the convective boundary layer as well as prognostic models based on third-order budgets are used to explain variations in $Sk_w$ for the idealized laboratory conditions. The failure of flux-gradient relations to model $Sk_w$ from the gradients of the vertical velocity variance σ$_w^2$ are explained and corrections based on models of energy transport offered. Novel links between the diagnostic and prognostic models are also featured, especially for the inertial term in the third-order budget of the vertical velocity fluctuation. The co-spectral properties of w′/σ w vs w′ 2 /σ$_w^2$ are also presented for the first time to assess the dominant scales governing $Sk_w$ in the inner and outer layers, where w′ is the fluctuating vertical velocity and σ w is the vertical velocity standard deviation.>

Boundary layer flow↗
DOE OSTI2021

Twisted bilayer graphene. I. Matrix elements, approximations, perturbation theory, and a k · p two-band model

We investigate the twisted bilayer graphene (TBG) model of Bistritzer and MacDonald (BM) [Bistritzer and MacDonald, Proc. Natl. Acad. Sci. 108, 12233 (2011)] to obtain an analytic understanding of its energetics and wave functions needed for many-body calculations. We provide an approximation scheme for the wave functions of the BM model, which first elucidates why the BM K M -point centered original calculation containing only four plane waves provides a good analytical value for the first magic angle (θ M ≈ 1°). The approximation scheme also elucidates why most of the many-body matrix elements in the Coulomb Hamiltonian projected to the active bands can be neglected. By applying our approximation scheme at the first magic angle to a Γ M -point centered model of six plane waves, we analytically understand the reason for the small Γ M -point gap between the active and passive bands in the isotropic limit w 0 = w 1 . Furthermore, we analytically calculate the group velocities of the passive bands in the isotropic limit, and show that they are almost doubly degenerate, even away from the Γ M point, where no symmetry forces them to be. Furthermore, moving away from the Γ M and K M points, we provide an explicit analytical perturbative understanding as to why the TBG bands are flat at the first magic angle, despite the first magic angle is defined by only requiring a vanishing K M -point Dirac velocity. We derive analytically a connected “magic manifold” w 1 = $2\sqrt{1 + w^{2}_{0}}$ $-\sqrt{2 + 3w^2_0}$, on which the bands remain extremely flat as w 0 is tuned between the isotropic (w 0 = w 1 ) and chiral (w 0 = 0) limits. We analytically show why going away from the isotropic limit by making w 0 less (but not larger) than w 1 increases the Γ M -point gap between the active and the passive bands. Finally, by perturbation theory, we provide an analytic Γ M point k ∙ p two-band model that reproduces the TBG band structure and eigenstates within a certain w 0 , w 1 parameter range. Further refinement of this model are discussed, which suggest a possible faithful representation of the TBG bands by a two-band Γ M point k ∙ p model in the full w 0 , w 1 parameter range.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Superposition principle and nonlinear response in spin glasses

The extended principle of superposition has been a touchstone of spin-glass dynamics for almost 30 years. Here the Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields H up to 10 Oe at the reduced temperature T r = T/T g = 0.95, where T g is the spin-glass condensation temperature. For H > 10 Oe, they observe a departure from linear response which they ascribe to the development of nonlinear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin-glass correlation length, ξ(t, t w ; H). Here, t is the time after H changes, and t w is the time from the quench for T > T g to the working temperature T until H changes. We connect the growth of ξ(t, t w ; H) to the barrier heights Δ(t w ) that set the dynamics. The effect of H on the magnitude of Δ (t w ) is responsible for affecting differently the two dynamical protocols associated with turning H off (TRM, or thermoremanent magnetization) or on (ZFC, or zero-field-cooled magnetization). This difference is a consequence of nonlinearity based on the effect of H on Δ (t w ). Superposition is preserved if Δ(t w ) is linear in the Hamming distance Hd (proportional to the difference between the self-overlap q EA and the overlap q[Δ(t w )]). However, superposition is violated if Δ(t w ) increases faster than linear in Hd. We have previously shown, through experiment and simulation, that the barriers Δ(t w ) do increase more rapidly than linearly with Hd through the observation that the growth of ξ(t,t w ;H) slows down as ξ(t,t w ; H) increases. In this paper, we display the difference between the zero-field-cooled ξ ZFC (t, t w ; H) and the thermoremanent magnetization ξ TRM (t, t w ; H) correlation lengths as H increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Toward Robust and Routine Determination of Mw for Small Earthquakes: Application to the 2020 Mw 5.7 Magna, Utah, Seismic Sequence

To better characterize seismic hazard, particularly, for induced seismicity, there is an increasing interest in methods to estimate moment magnitude (M w ) for small earthquakes. M w is generally preferred over other magnitude types, but, it is difficult to estimate M w for earthquakes with local magnitude (M L ) <3-3.5, using conventional moment tensor (MT) inversion. The 2020 M ww 5.7 Magna, Utah, seismic sequence provides an opportunity to illustrate and evaluate the value of spectral methods for this purpose. Starting with a high-quality seismic catalog of 2103 earthquakes (M L <5.6), we estimate M w using two independent spectral methods—one based on direct waves, yielding M w,direct , and the other based on coda waves, yielding M w,coda . For the direct-wave method, we present a non-parametric (NP) inversion scheme that solves for apparent geometrical spreading, G(R), and site effects (S), similar to other NP procedures that have been used to calibrate regional M L scales. The NP inversion is constrained using M ws derived from MTs for nine events in the Magna sequence. We recover statistically robust and physically reasonable G(R) and S and compute M w,direct for 635 Magna earthquakes down to M L 0.7. For the coda-wave method, we consider two separate calibration schemes involving previous MT solutions and compute M w,coda for 311 earthquakes down to M L 1.0. For 280 of the events that were processed with both methods—M w,direct and M w,coda —are strongly correlated (r = 0.98), with a mean difference of only 0.05. We compare M w,direct and M w,coda with M L and find reasonably good agreement for M L <3.6 with the theoretically predicted relationship of M w =(2/3)M L +C, in which C is a regional constant. Our results imply that seismic network operators can use spectral-based M w estimates to replace M L estimates for events with M L ≥1.0, and possibly smaller. The main requirement is the existence of a small number of MT solutions for calibration purposes.

58 GEOSCIENCES↗
DOE OSTI2026

Frequentist cosmological constraints from full-shape clustering measurements in DESI DR1

We present a frequentist analysis of clustering measurements from Data Release 1 of the Dark Energy Spectroscopic Instrument (DESI) using the standard profile likelihood method. While Bayesian inferences for effective field theory models of galaxy clustering can be highly sensitive to prior choices for extended cosmological models, frequentist inferences are not susceptible to such effects. We compare frequentist and Bayesian constraints for the parameter set {σ 8 , H 0 , Ω m , w 0 , w a } using the full-shape power spectrum multipoles, post-reconstruction baryon acoustic oscillation (BAO) measurements, and external datasets from the CMB and type Ia supernovae measurements. The frequentist confidence intervals are significantly shifted relative to the Bayesian credible intervals for the w 0 w a CDM model, unless supernovae data are included. When DESI full-shape and BAO data are fit jointly, we obtain the following 1σ frequentist confidence intervals for ΛCDM (w 0 w a CDM): σ 8 = 0.863 +0.048 -0.040 , H 0 = 68.96 +0.81 -0.80 km s -1 Mpc -1 , Ω m = 0.3034 ± 0.0110 (σ 8 = 0.782 +0.060 -0.036 , H 0 = 63.7 +4.2 -2.0 km s -1 Mpc -1 , Ω m = 0.378 +0.024 -0.047 , w 0 = -0.16 +0.10 -0.50 , w a = -3.0 +1.7 ), corresponding to 0.8σ, 0.3σ, 0.7σ (2.1σ, 4.1σ, 6.5σ, 6.3σ, 6.6σ) shifts between the maximum likelihood estimate and the Bayesian posterior mean for ΛCDM (w 0 w a CDM) respectively.

Bayesian reasoning↗
DOE OSTI2020

Materials Data on Rb(WO3)6 by Materials Project

Rb(WO3)6 crystallizes in the orthorhombic Pnnm space group. The structure is three-dimensional. Rb1+ is bonded to twelve O2- atoms to form RbO12 cuboctahedra that share edges with twelve WO6 octahedra. All Rb–O bond lengths are 3.36 Å. There are two inequivalent W+5.83+ sites. In the first W+5.83+ site, W+5.83+ is bonded to six O2- atoms to form WO6 octahedra that share corners with six WO6 octahedra and edges with two equivalent RbO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–30°. There are a spread of W–O bond distances ranging from 1.92–1.97 Å. In the second W+5.83+ site, W+5.83+ is bonded to six O2- atoms to form WO6 octahedra that share corners with six WO6 octahedra and edges with two equivalent RbO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–30°. There are a spread of W–O bond distances ranging from 1.92–1.97 Å. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded in a linear geometry to two equivalent W+5.83+ atoms. In the second O2- site, O2- is bonded in a bent 150 degrees geometry to one Rb1+ and two W+5.83+ atoms. In the third O2- site, O2- is bonded in a bent 150 degrees geometry to one Rb1+ and two W+5.83+ atoms. In the fourth O2- site, O2- is bonded in a bent 150 degrees geometry to one Rb1+ and two equivalent W+5.83+ atoms. In the fifth O2- site, O2- is bonded in a linear geometry to two equivalent W+5.83+ atoms. In the sixth O2- site, O2- is bonded in a linear geometry to two equivalent W+5.83+ atoms.

36 MATERIALS SCIENCE↗