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Materials Data on DyGaFeCo3 by Materials Project

DyFeCo3Ga crystallizes in the monoclinic P2/m space group. The structure is three-dimensional. Dy is bonded in a 6-coordinate geometry to four equivalent Fe, ten Co, and four equivalent Ga atoms. All Dy–Fe bond lengths are 3.21 Å. There are a spread of Dy–Co bond distances ranging from 2.88–3.24 Å. All Dy–Ga bond lengths are 3.17 Å. Fe is bonded to four equivalent Dy, six Co, and two equivalent Ga atoms to form distorted FeDy4Ga2Co6 cuboctahedra that share corners with four equivalent CoDy4Ga2Fe2Co4 cuboctahedra, corners with four equivalent GaDy4Fe2Co6 cuboctahedra, corners with eight equivalent FeDy4Ga2Co6 cuboctahedra, edges with two equivalent FeDy4Ga2Co6 cuboctahedra, edges with four equivalent CoDy4Ga2Fe2Co4 cuboctahedra, edges with four equivalent GaDy4Fe2Co6 cuboctahedra, faces with two equivalent FeDy4Ga2Co6 cuboctahedra, faces with four equivalent CoDy4Ga2Fe2Co4 cuboctahedra, and faces with four equivalent GaDy4Fe2Co6 cuboctahedra. There are four shorter (2.45 Å) and two longer (2.46 Å) Fe–Co bond lengths. Both Fe–Ga bond lengths are 2.54 Å. There are two inequivalent Co sites. In the first Co site, Co is bonded in a 12-coordinate geometry to three equivalent Dy, two equivalent Fe, two equivalent Co, and two equivalent Ga atoms. Both Co–Co bond lengths are 2.44 Å. Both Co–Ga bond lengths are 2.53 Å. In the second Co site, Co is bonded to four equivalent Dy, two equivalent Fe, four equivalent Co, and two equivalent Ga atoms to form distorted CoDy4Ga2Fe2Co4 cuboctahedra that share corners with four equivalent FeDy4Ga2Co6 cuboctahedra, corners with four equivalent GaDy4Fe2Co6 cuboctahedra, corners with eight equivalent CoDy4Ga2Fe2Co4 cuboctahedra, edges with two equivalent CoDy4Ga2Fe2Co4 cuboctahedra, edges with four equivalent FeDy4Ga2Co6 cuboctahedra, edges with four equivalent GaDy4Fe2Co6 cuboctahedra, faces with two equivalent CoDy4Ga2Fe2Co4 cuboctahedra, faces with four equivalent FeDy4Ga2Co6 cuboctahedra, and faces with four equivalent GaDy4Fe2Co6 cuboctahedra. Both Co–Ga bond lengths are 2.51 Å. Ga is bonded to four equivalent Dy, two equivalent Fe, and six Co atoms to form GaDy4Fe2Co6 cuboctahedra that share corners with four equivalent FeDy4Ga2Co6 cuboctahedra, corners with four equivalent CoDy4Ga2Fe2Co4 cuboctahedra, corners with eight equivalent GaDy4Fe2Co6 cuboctahedra, edges with two equivalent GaDy4Fe2Co6 cuboctahedra, edges with four equivalent FeDy4Ga2Co6 cuboctahedra, edges with four equivalent CoDy4Ga2Fe2Co4 cuboctahedra, faces with two equivalent GaDy4Fe2Co6 cuboctahedra, faces with four equivalent FeDy4Ga2Co6 cuboctahedra, and faces with four equivalent CoDy4Ga2Fe2Co4 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on Dy2Fe4Si9 by Materials Project

Dy2Fe4Si9 crystallizes in the trigonal P-3m1 space group. The structure is three-dimensional. Dy is bonded in a 6-coordinate geometry to three equivalent Fe and eight Si atoms. All Dy–Fe bond lengths are 3.20 Å. There are a spread of Dy–Si bond distances ranging from 2.86–3.18 Å. There are two inequivalent Fe sites. In the first Fe site, Fe is bonded in a 7-coordinate geometry to ten Si atoms. There are a spread of Fe–Si bond distances ranging from 2.31–2.69 Å. In the second Fe site, Fe is bonded in a 10-coordinate geometry to three equivalent Dy and seven Si atoms. There are a spread of Fe–Si bond distances ranging from 2.31–2.46 Å. There are five inequivalent Si sites. In the first Si site, Si is bonded in a 11-coordinate geometry to one Dy, four equivalent Fe, and six Si atoms. There are three shorter (2.50 Å) and three longer (2.65 Å) Si–Si bond lengths. In the second Si site, Si is bonded in a 4-coordinate geometry to one Dy, four equivalent Fe, and six Si atoms. There are three shorter (2.64 Å) and three longer (2.66 Å) Si–Si bond lengths. In the third Si site, Si is bonded in a 10-coordinate geometry to three equivalent Dy, three equivalent Fe, and four Si atoms. The Si–Si bond length is 2.40 Å. In the fourth Si site, Si is bonded in a 6-coordinate geometry to three equivalent Dy, three equivalent Fe, and three equivalent Si atoms. In the fifth Si site, Si is bonded in a 8-coordinate geometry to six equivalent Fe and eight Si atoms.

36 MATERIALS SCIENCE↗

Materials Data on Dy2CI3 by Materials Project

Dy2CI3 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. there are four inequivalent Dy3+ sites. In the first Dy3+ site, Dy3+ is bonded in a 1-coordinate geometry to three C3- and four I1- atoms. There are a spread of Dy–C bond distances ranging from 2.27–2.61 Å. There are a spread of Dy–I bond distances ranging from 3.11–3.31 Å. In the second Dy3+ site, Dy3+ is bonded to three C3- and four I1- atoms to form distorted DyC3I4 pentagonal bipyramids that share a cornercorner with one DyCI5 octahedra, a cornercorner with one CDy4C square pyramid, edges with two equivalent DyCI5 octahedra, and an edgeedge with one DyC3I4 pentagonal bipyramid. The corner-sharing octahedral tilt angles are 48°. There are two shorter (2.50 Å) and one longer (2.63 Å) Dy–C bond lengths. There are a spread of Dy–I bond distances ranging from 3.13–3.40 Å. In the third Dy3+ site, Dy3+ is bonded in a 7-coordinate geometry to two equivalent C3- and five I1- atoms. There are one shorter (2.39 Å) and one longer (2.40 Å) Dy–C bond lengths. There are a spread of Dy–I bond distances ranging from 3.10–3.62 Å. In the fourth Dy3+ site, Dy3+ is bonded to one C3- and five I1- atoms to form a mixture of distorted edge and corner-sharing DyCI5 octahedra. The Dy–C bond length is 2.23 Å. There are a spread of Dy–I bond distances ranging from 3.07–3.23 Å. There are two inequivalent C3- sites. In the first C3- site, C3- is bonded in a 6-coordinate geometry to five Dy3+ and one C3- atom. The C–C bond length is 1.42 Å. In the second C3- site, C3- is bonded to four Dy3+ and one C3- atom to form distorted CDy4C square pyramids that share a cornercorner with one DyC3I4 pentagonal bipyramid and an edgeedge with one CDy4C square pyramid. The C–C bond length is 1.44 Å. There are six inequivalent I1- sites. In the first I1- site, I1- is bonded in a 3-coordinate geometry to three Dy3+ atoms. In the second I1- site, I1- is bonded in a distorted T-shaped geometry to three Dy3+ atoms. In the third I1- site, I1- is bonded in a distorted T-shaped geometry to three Dy3+ atoms. In the fourth I1- site, I1- is bonded in a 2-coordinate geometry to three Dy3+ atoms. In the fifth I1- site, I1- is bonded in a 3-coordinate geometry to three Dy3+ atoms. In the sixth I1- site, I1- is bonded in a distorted T-shaped geometry to three Dy3+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Dy3(Al3Ru)4 by Materials Project

Dy3Ru4Al12 crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Dy is bonded in a 5-coordinate geometry to four equivalent Ru and eleven Al atoms. All Dy–Ru bond lengths are 3.36 Å. There are a spread of Dy–Al bond distances ranging from 2.94–3.20 Å. There are two inequivalent Ru sites. In the first Ru site, Ru is bonded in a 12-coordinate geometry to four equivalent Dy and eight Al atoms. There are a spread of Ru–Al bond distances ranging from 2.54–2.68 Å. In the second Ru site, Ru is bonded in a body-centered cubic geometry to eight Al atoms. There are two shorter (2.39 Å) and six longer (2.58 Å) Ru–Al bond lengths. There are four inequivalent Al sites. In the first Al site, Al is bonded in a 2-coordinate geometry to two equivalent Dy and two equivalent Ru atoms. In the second Al site, Al is bonded in a 3-coordinate geometry to three equivalent Dy and three Ru atoms. In the third Al site, Al is bonded in a 3-coordinate geometry to three equivalent Dy and three equivalent Ru atoms. In the fourth Al site, Al is bonded in a distorted linear geometry to three equivalent Dy and two equivalent Ru atoms.

36 MATERIALS SCIENCE↗

Materials Data on Dy3Mn3Ga2Si by Materials Project

Dy3Mn3SiGa2 crystallizes in the hexagonal P-6 space group. The structure is three-dimensional. Dy is bonded in a 5-coordinate geometry to six equivalent Mn, three Ga, and two equivalent Si atoms. There are a spread of Dy–Mn bond distances ranging from 3.17–3.35 Å. There are one shorter (2.93 Å) and two longer (2.96 Å) Dy–Ga bond lengths. Both Dy–Si bond lengths are 2.93 Å. Mn is bonded in a 12-coordinate geometry to six equivalent Dy, two equivalent Mn, three Ga, and one Si atom. Both Mn–Mn bond lengths are 2.85 Å. There are two shorter (2.65 Å) and one longer (2.78 Å) Mn–Ga bond lengths. The Mn–Si bond length is 2.68 Å. There are two inequivalent Ga sites. In the first Ga site, Ga is bonded in a distorted q6 geometry to three equivalent Dy and six equivalent Mn atoms. In the second Ga site, Ga is bonded in a 9-coordinate geometry to six equivalent Dy and three equivalent Mn atoms. Si is bonded in a 9-coordinate geometry to six equivalent Dy and three equivalent Mn atoms.

36 MATERIALS SCIENCE↗

Materials Data on Dy5Ge3 by Materials Project

Dy5Ge3 crystallizes in the hexagonal P6_3/mcm space group. The structure is three-dimensional. there are two inequivalent Dy sites. In the first Dy site, Dy is bonded in a 6-coordinate geometry to six equivalent Ge atoms. All Dy–Ge bond lengths are 3.07 Å. In the second Dy site, Dy is bonded in a 5-coordinate geometry to five equivalent Ge atoms. There are a spread of Dy–Ge bond distances ranging from 2.93–3.45 Å. Ge is bonded in a 9-coordinate geometry to nine Dy atoms.

36 MATERIALS SCIENCE↗

Materials Data on DyMnFe by Materials Project

DyMnFe crystallizes in the orthorhombic Imma space group. The structure is three-dimensional. Dy is bonded in a 12-coordinate geometry to four equivalent Dy, six equivalent Mn, and six equivalent Fe atoms. There are two shorter (3.13 Å) and two longer (3.16 Å) Dy–Dy bond lengths. There are four shorter (2.99 Å) and two longer (3.03 Å) Dy–Mn bond lengths. There are two shorter (3.00 Å) and four longer (3.04 Å) Dy–Fe bond lengths. Mn is bonded to six equivalent Dy, two equivalent Mn, and four equivalent Fe atoms to form MnDy6Mn2Fe4 cuboctahedra that share corners with eight equivalent FeDy6Mn4Fe2 cuboctahedra, corners with ten equivalent MnDy6Mn2Fe4 cuboctahedra, edges with six equivalent MnDy6Mn2Fe4 cuboctahedra, faces with six equivalent MnDy6Mn2Fe4 cuboctahedra, and faces with twelve equivalent FeDy6Mn4Fe2 cuboctahedra. Both Mn–Mn bond lengths are 2.60 Å. All Mn–Fe bond lengths are 2.57 Å. Fe is bonded to six equivalent Dy, four equivalent Mn, and two equivalent Fe atoms to form FeDy6Mn4Fe2 cuboctahedra that share corners with eight equivalent MnDy6Mn2Fe4 cuboctahedra, corners with ten equivalent FeDy6Mn4Fe2 cuboctahedra, edges with six equivalent FeDy6Mn4Fe2 cuboctahedra, faces with six equivalent FeDy6Mn4Fe2 cuboctahedra, and faces with twelve equivalent MnDy6Mn2Fe4 cuboctahedra. Both Fe–Fe bond lengths are 2.54 Å.

36 MATERIALS SCIENCE↗

Materials Data on Dy2Ge5Ru3 by Materials Project

Dy2Ru3Ge5 crystallizes in the orthorhombic Ibam space group. The structure is three-dimensional. Dy is bonded in a 1-coordinate geometry to six Ru and ten Ge atoms. There are a spread of Dy–Ru bond distances ranging from 3.20–3.47 Å. There are a spread of Dy–Ge bond distances ranging from 2.99–3.45 Å. There are two inequivalent Ru sites. In the first Ru site, Ru is bonded in a 6-coordinate geometry to four equivalent Dy and six Ge atoms. There are four shorter (2.51 Å) and two longer (2.62 Å) Ru–Ge bond lengths. In the second Ru site, Ru is bonded in a 9-coordinate geometry to four equivalent Dy and five Ge atoms. There are a spread of Ru–Ge bond distances ranging from 2.41–2.51 Å. There are three inequivalent Ge sites. In the first Ge site, Ge is bonded in a 4-coordinate geometry to four equivalent Dy and four equivalent Ru atoms. In the second Ge site, Ge is bonded in a 11-coordinate geometry to four equivalent Dy, three Ru, and four Ge atoms. There are two shorter (2.69 Å) and two longer (2.90 Å) Ge–Ge bond lengths. In the third Ge site, Ge is bonded in a 4-coordinate geometry to four equivalent Dy, three Ru, and two equivalent Ge atoms.

36 MATERIALS SCIENCE↗

Materials Data on Dy2AlCo3 by Materials Project

Dy2Co3Al crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Dy is bonded in a 9-coordinate geometry to four equivalent Dy, nine equivalent Co, and three equivalent Al atoms. There are one shorter (3.02 Å) and three longer (3.20 Å) Dy–Dy bond lengths. There are three shorter (2.82 Å) and six longer (3.07 Å) Dy–Co bond lengths. All Dy–Al bond lengths are 3.12 Å. Co is bonded to six equivalent Dy, four equivalent Co, and two equivalent Al atoms to form distorted CoDy6Al2Co4 cuboctahedra that share corners with four equivalent AlDy6Co6 cuboctahedra, corners with fourteen equivalent CoDy6Al2Co4 cuboctahedra, edges with six equivalent CoDy6Al2Co4 cuboctahedra, faces with six equivalent AlDy6Co6 cuboctahedra, and faces with twelve equivalent CoDy6Al2Co4 cuboctahedra. All Co–Co bond lengths are 2.67 Å. Both Co–Al bond lengths are 2.47 Å. Al is bonded to six equivalent Dy and six equivalent Co atoms to form distorted AlDy6Co6 cuboctahedra that share corners with six equivalent AlDy6Co6 cuboctahedra, corners with twelve equivalent CoDy6Al2Co4 cuboctahedra, edges with six equivalent AlDy6Co6 cuboctahedra, and faces with eighteen equivalent CoDy6Al2Co4 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on Dy2FeCo3 by Materials Project

Dy2FeCo3 is Hexagonal Laves-derived structured and crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Dy is bonded in a 12-coordinate geometry to four equivalent Dy, three equivalent Fe, and nine equivalent Co atoms. There are one shorter (3.05 Å) and three longer (3.16 Å) Dy–Dy bond lengths. All Dy–Fe bond lengths are 3.05 Å. There are three shorter (2.90 Å) and six longer (3.02 Å) Dy–Co bond lengths. Fe is bonded to six equivalent Dy and six equivalent Co atoms to form FeDy6Co6 cuboctahedra that share corners with six equivalent FeDy6Co6 cuboctahedra, corners with twelve equivalent CoDy6Fe2Co4 cuboctahedra, edges with six equivalent FeDy6Co6 cuboctahedra, and faces with eighteen equivalent CoDy6Fe2Co4 cuboctahedra. All Fe–Co bond lengths are 2.50 Å. Co is bonded to six equivalent Dy, two equivalent Fe, and four equivalent Co atoms to form CoDy6Fe2Co4 cuboctahedra that share corners with four equivalent FeDy6Co6 cuboctahedra, corners with fourteen equivalent CoDy6Fe2Co4 cuboctahedra, edges with six equivalent CoDy6Fe2Co4 cuboctahedra, faces with six equivalent FeDy6Co6 cuboctahedra, and faces with twelve equivalent CoDy6Fe2Co4 cuboctahedra. All Co–Co bond lengths are 2.60 Å.

36 MATERIALS SCIENCE↗

Monte Carlo Global QCD Analyses of the Pion Parton Distribution Functions

As the lightest hadron, the pion presents itself as a dichotomy. While being the pseudo Goldstone boson associated with chiral symmetry breaking, it is simultaneously regarded as the lightest pseudoscalar meson typically composed of constituent quark and antiquark. As the chiral symmetry shares the same global symmetry as QCD, studying the pion and its internal structure is key in understanding one of the four fundamental forces of nature, namely the quantum chromodynamic strong interaction. We study the pion's parton distribution functions (PDFs), which are universal quantities that describe the structure of the pion in terms of its constituent quarks, antiquarks, and gluons. Our goal is to discover what the available data reveal for these universal quantities, namely the PDFs. Through the use of factorization theorems and perturbative QCD, we use Monte Carlo (MC) methods to extract the PDFs from the available Drell-Yan (DY) and leading neutron (LN) data. While the DY process involves two hadrons colliding, the LN electroproduction involves an electron beam incident on a target nucleon. We can constrain well the pion PDFs at large momentum fraction using DY data, and at low momentum fraction using LN data. We also use threshold resummation in the DY process to gather predictable higher order terms associated with the soft gluon radiation because their contributions to the cross section are nontrivial. In this dissertation, we parametrize the pion PDFs and fit those parameters to the available data. We make use of Bayesian inference and use MC techniques to sample the parameter space. Three sets of results are presented. We first extract the pion PDFs by fitting the DY and LN data. Then, we include transverse momentum dependent DY data in conjunction with the DY and LN data to extract the pion PDFs. Finally, we apply various methods of threshold resummation to the DY cross section and extract pion PDFs. The pion PDFs presented here are the first global QCD analyses performed as well as the first MC extracted pion PDFs, which are at the forefront of the pion PDF community.

Barry, Patrick↗

Materials Data on Dy3Mn3Ga2Si by Materials Project

Dy3Mn3SiGa2 crystallizes in the hexagonal P-62m space group. The structure is three-dimensional. Dy is bonded in a 5-coordinate geometry to six equivalent Mn, four equivalent Ga, and one Si atom. There are four shorter (3.17 Å) and two longer (3.31 Å) Dy–Mn bond lengths. All Dy–Ga bond lengths are 2.92 Å. The Dy–Si bond length is 2.88 Å. Mn is bonded in a 12-coordinate geometry to six equivalent Dy, two equivalent Mn, two equivalent Ga, and two equivalent Si atoms. Both Mn–Mn bond lengths are 2.73 Å. Both Mn–Ga bond lengths are 2.86 Å. Both Mn–Si bond lengths are 2.51 Å. Ga is bonded in a 9-coordinate geometry to six equivalent Dy and three equivalent Mn atoms. Si is bonded in a 9-coordinate geometry to three equivalent Dy and six equivalent Mn atoms.

36 MATERIALS SCIENCE↗

Materials Data on DyAl4Ni by Materials Project

DyNiAl4 crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. Dy is bonded in a 11-coordinate geometry to two equivalent Ni and thirteen Al atoms. Both Dy–Ni bond lengths are 3.15 Å. There are a spread of Dy–Al bond distances ranging from 2.99–3.37 Å. Ni is bonded in a 7-coordinate geometry to two equivalent Dy and seven Al atoms. There are a spread of Ni–Al bond distances ranging from 2.32–2.48 Å. There are three inequivalent Al sites. In the first Al site, Al is bonded in a distorted q6 geometry to four equivalent Dy and six Al atoms. There are four shorter (2.87 Å) and two longer (2.93 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a 1-coordinate geometry to three equivalent Dy, one Ni, and four equivalent Al atoms. In the third Al site, Al is bonded in a 3-coordinate geometry to three equivalent Dy, three equivalent Ni, and one Al atom.

36 MATERIALS SCIENCE↗

Materials Data on Dy2Ti2O7 by Materials Project

Dy2Ti2O7 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. there are seven inequivalent Dy3+ sites. In the first Dy3+ site, Dy3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Dy–O bond distances ranging from 2.27–2.88 Å. In the second Dy3+ site, Dy3+ is bonded to six O2- atoms to form distorted DyO6 octahedra that share corners with four equivalent TiO6 octahedra and edges with two equivalent TiO6 octahedra. The corner-sharing octahedral tilt angles are 68°. There are two shorter (2.27 Å) and four longer (2.39 Å) Dy–O bond lengths. In the third Dy3+ site, Dy3+ is bonded to seven O2- atoms to form DyO7 pentagonal bipyramids that share corners with four TiO6 octahedra and edges with two equivalent TiO6 octahedra. The corner-sharing octahedra tilt angles range from 49–66°. There are a spread of Dy–O bond distances ranging from 2.19–2.39 Å. In the fourth Dy3+ site, Dy3+ is bonded to eight O2- atoms to form distorted DyO8 hexagonal bipyramids that share edges with six DyO8 hexagonal bipyramids and edges with six TiO6 octahedra. There are a spread of Dy–O bond distances ranging from 2.21–2.54 Å. In the fifth Dy3+ site, Dy3+ is bonded to eight O2- atoms to form distorted DyO8 hexagonal bipyramids that share edges with six DyO8 hexagonal bipyramids and edges with six TiO6 octahedra. There are a spread of Dy–O bond distances ranging from 2.20–2.52 Å. In the sixth Dy3+ site, Dy3+ is bonded to eight O2- atoms to form distorted DyO8 hexagonal bipyramids that share edges with six DyO8 hexagonal bipyramids and edges with six TiO6 octahedra. There are a spread of Dy–O bond distances ranging from 2.20–2.53 Å. In the seventh Dy3+ site, Dy3+ is bonded to eight O2- atoms to form distorted DyO8 hexagonal bipyramids that share edges with three DyO8 hexagonal bipyramids and edges with six TiO6 octahedra. There are a spread of Dy–O bond distances ranging from 2.15–2.67 Å. There are eight inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Ti–O bond distances ranging from 1.88–2.45 Å. In the second Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two equivalent DyO6 octahedra, corners with four TiO6 octahedra, and edges with two equivalent DyO7 pentagonal bipyramids. The corner-sharing octahedra tilt angles range from 40–68°. There are a spread of Ti–O bond distances ranging from 1.91–2.01 Å. In the third Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four equivalent TiO6 octahedra, corners with two equivalent DyO7 pentagonal bipyramids, and edges with two equivalent DyO6 octahedra. The corner-sharing octahedral tilt angles are 50°. There is two shorter (1.92 Å) and four longer (2.03 Å) Ti–O bond length. In the fourth Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five TiO6 octahedra, a cornercorner with one DyO7 pentagonal bipyramid, and edges with four DyO8 hexagonal bipyramids. The corner-sharing octahedra tilt angles range from 47–52°. There are a spread of Ti–O bond distances ranging from 1.89–2.06 Å. In the fifth Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five TiO6 octahedra, a cornercorner with one DyO7 pentagonal bipyramid, and edges with four DyO8 hexagonal bipyramids. The corner-sharing octahedra tilt angles range from 47–52°. There are a spread of Ti–O bond distances ranging from 1.91–2.07 Å. In the sixth Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and edges with six DyO8 hexagonal bipyramids. The corner-sharing octahedral tilt angles are 49°. There are a spread of Ti–O bond distances ranging from 1.97–1.99 Å. In the seventh Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and edges with six DyO8 hexagonal bipyramids. The corner-sharing octahedra tilt angles range from 47–52°. There are a spread of Ti–O bond distances ranging from 1.94–2.00 Å. In the eighth Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and edges with six DyO8 hexagonal bipyramids. The corner-sharing octahedra tilt angles range from 47–49°. There is two shorter (1.96 Å) and four longer (1.98 Å) Ti–O bond length. There are twenty inequivalent O2- sites. In the first O2- site, O2- is bonded to three Dy3+ and one Ti4+ atom to form a mixture of edge and corner-sharing ODy3Ti tetrahedra. In the second O2- site, O2- is bonded in a 3-coordinate geometry to one Dy3+ and two equivalent Ti4+ atoms. In the third O2- site, O2- is bonded in a 2-coordinate geometry to two Dy3+ and two Ti4+ atoms. In the fourth O2- site, O2- is bonded in a 4-coordinate geometry to two Dy3+ and two Ti4+ atoms. In the fifth O2- site, O2- is bonded to three Dy3+ and one Ti4+ atom to form ODy3Ti tetrahedra that share corners with six ODy3Ti tetrahedra and edges with two ODyTi3 tetrahedra. In the sixth O2- site, O2- is bonded to three Dy3+ and one Ti4+ atom to form a mixture of distorted edge and corner-sharing ODy3Ti tetrahedra. In the seventh O2- site, O2- is bonded in a 2-coordinate geometry to two Dy3+ and two equivalent Ti4+ atoms. In the eighth O2- site, O2- is bonded in a 4-coordinate geometry to two Dy3+ and two Ti4+ atoms. In the ninth O2- site, O2- is bonded in a 4-coordinate geometry to two Dy3+ and two Ti4+ atoms. In the tenth O2- site, O2- is bonded to four Dy3+ atoms to form corner-sharing ODy4 tetrahedra. In the eleventh O2- site, O2- is bonded to three Dy3+ and one Ti4+ atom to form a mixture of edge and corner-sharing ODy3Ti tetrahedra. In the twelfth O2- site, O2- is bonded in a 4-coordinate geometry to two Dy3+ and two Ti4+ atoms. In the thirteenth O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Dy3+ and two Ti4+ atoms. In the fourteenth O2- site, O2- is bonded in a 4-coordinate geometry to two Dy3+ and two Ti4+ atoms. In the fifteenth O2- site, O2- is bonded in a 4-coordinate geometry to two Dy3+ and two equivalent Ti4+ atoms. In the sixteenth O2- site, O2- is bonded to four Dy3+ atoms to form corner-sharing ODy4 tetrahedra. In the seventeenth O2- site, O2- is bonded in a 4-coordinate geometry to two Dy3+ and two Ti4+ atoms. In the eighteenth O2- site, O2- is bonded in a 4-coordinate geometry to two Dy3+ and two Ti4+ atoms. In the nineteenth O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Dy3+ and two Ti4+ atoms. In the twentieth O2- site, O2- is bonded to one Dy3+ and three Ti4+ atoms to form a mixture of distorted edge and corner-sharing ODyTi3 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on Dy2Sb2O7 by Materials Project

Dy2Sb2O7 crystallizes in the monoclinic C2 space group. The structure is three-dimensional. there are seven inequivalent Dy3+ sites. In the first Dy3+ site, Dy3+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are a spread of Dy–O bond distances ranging from 2.34–2.63 Å. In the second Dy3+ site, Dy3+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Dy–O bond distances ranging from 2.19–2.39 Å. In the third Dy3+ site, Dy3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Dy–O bond distances ranging from 2.21–2.57 Å. In the fourth Dy3+ site, Dy3+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are a spread of Dy–O bond distances ranging from 2.34–2.62 Å. In the fifth Dy3+ site, Dy3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Dy–O bond distances ranging from 2.21–2.56 Å. In the sixth Dy3+ site, Dy3+ is bonded in a 6-coordinate geometry to six O2- atoms. There are two shorter (2.20 Å) and four longer (2.38 Å) Dy–O bond lengths. In the seventh Dy3+ site, Dy3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Dy–O bond distances ranging from 2.21–2.57 Å. There are seven inequivalent Sb4+ sites. In the first Sb4+ site, Sb4+ is bonded to six O2- atoms to form distorted corner-sharing SbO6 octahedra. The corner-sharing octahedra tilt angles range from 58–61°. There are a spread of Sb–O bond distances ranging from 2.25–2.38 Å. In the second Sb4+ site, Sb4+ is bonded in a 2-coordinate geometry to four O2- atoms. There are a spread of Sb–O bond distances ranging from 2.05–2.53 Å. In the third Sb4+ site, Sb4+ is bonded to six O2- atoms to form corner-sharing SbO6 octahedra. The corner-sharing octahedra tilt angles range from 38–61°. There are a spread of Sb–O bond distances ranging from 1.99–2.03 Å. In the fourth Sb4+ site, Sb4+ is bonded to six O2- atoms to form corner-sharing SbO6 octahedra. The corner-sharing octahedra tilt angles range from 38–61°. There are a spread of Sb–O bond distances ranging from 1.99–2.02 Å. In the fifth Sb4+ site, Sb4+ is bonded to six O2- atoms to form corner-sharing SbO6 octahedra. The corner-sharing octahedra tilt angles range from 38–61°. There are a spread of Sb–O bond distances ranging from 1.99–2.03 Å. In the sixth Sb4+ site, Sb4+ is bonded to six O2- atoms to form distorted corner-sharing SbO6 octahedra. The corner-sharing octahedra tilt angles range from 58–61°. There are a spread of Sb–O bond distances ranging from 2.25–2.38 Å. In the seventh Sb4+ site, Sb4+ is bonded in a 2-coordinate geometry to four O2- atoms. There are two shorter (2.05 Å) and two longer (2.52 Å) Sb–O bond lengths. There are twenty-one inequivalent O2- sites. In the first O2- site, O2- is bonded to three Dy3+ and one Sb4+ atom to form ODy3Sb tetrahedra that share corners with six ODy2Sb2 tetrahedra and edges with four ODy3Sb tetrahedra. In the second O2- site, O2- is bonded to two Dy3+ and two Sb4+ atoms to form distorted ODy2Sb2 tetrahedra that share corners with ten ODy2Sb2 tetrahedra and edges with three ODy3Sb tetrahedra. In the third O2- site, O2- is bonded in a 4-coordinate geometry to two Dy3+ and two Sb4+ atoms. In the fourth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two Sb4+ atoms. In the fifth O2- site, O2- is bonded to three Dy3+ and one Sb4+ atom to form a mixture of corner and edge-sharing ODy3Sb tetrahedra. In the sixth O2- site, O2- is bonded in a 3-coordinate geometry to two Dy3+ and one Sb4+ atom. In the seventh O2- site, O2- is bonded to three Dy3+ and one Sb4+ atom to form a mixture of corner and edge-sharing ODy3Sb tetrahedra. In the eighth O2- site, O2- is bonded to two Dy3+ and two Sb4+ atoms to form a mixture of distorted corner and edge-sharing ODy2Sb2 tetrahedra. In the ninth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two equivalent Sb4+ atoms. In the tenth O2- site, O2- is bonded in a 3-coordinate geometry to two Dy3+ and one Sb4+ atom. In the eleventh O2- site, O2- is bonded to two Dy3+ and two Sb4+ atoms to form a mixture of distorted corner and edge-sharing ODy2Sb2 tetrahedra. In the twelfth O2- site, O2- is bonded in a 4-coordinate geometry to two Dy3+ and two Sb4+ atoms. In the thirteenth O2- site, O2- is bonded to three Dy3+ and one Sb4+ atom to form a mixture of corner and edge-sharing ODy3Sb tetrahedra. In the fourteenth O2- site, O2- is bonded to two Dy3+ and two Sb4+ atoms to form distorted ODy2Sb2 tetrahedra that share corners with eight ODy2Sb2 tetrahedra and edges with three ODy3Sb tetrahedra. In the fifteenth O2- site, O2- is bonded to two Dy3+ and two Sb4+ atoms to form distorted ODy2Sb2 tetrahedra that share corners with ten ODy3Sb tetrahedra and edges with three ODy2Sb2 tetrahedra. In the sixteenth O2- site, O2- is bonded in a 3-coordinate geometry to two Dy3+ and one Sb4+ atom. In the seventeenth O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Dy3+ and two Sb4+ atoms. In the eighteenth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two Sb4+ atoms. In the nineteenth O2- site, O2- is bonded to two Dy3+ and two Sb4+ atoms to form a mixture of distorted corner and edge-sharing ODy2Sb2 tetrahedra. In the twentieth O2- site, O2- is bonded to three Dy3+ and one Sb4+ atom to form a mixture of corner and edge-sharing ODy3Sb tetrahedra. In the twenty-first O2- site, O2- is bonded to three Dy3+ and one Sb4+ atom to form a mixture of corner and edge-sharing ODy3Sb tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on Dy3(SbPd2)4 by Materials Project

Dy3(Pd2Sb)4 crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Dy is bonded in a 1-coordinate geometry to eight Pd and five Sb atoms. There are four shorter (3.05 Å) and four longer (3.23 Å) Dy–Pd bond lengths. There are one shorter (2.98 Å) and four longer (3.34 Å) Dy–Sb bond lengths. There are two inequivalent Pd sites. In the first Pd site, Pd is bonded in a 6-coordinate geometry to three equivalent Dy and three equivalent Sb atoms. All Pd–Sb bond lengths are 2.71 Å. In the second Pd site, Pd is bonded in a 7-coordinate geometry to three equivalent Dy and four Sb atoms. There are one shorter (2.73 Å) and three longer (2.93 Å) Pd–Sb bond lengths. There are three inequivalent Sb sites. In the first Sb site, Sb is bonded in a body-centered cubic geometry to eight equivalent Pd atoms. In the second Sb site, Sb is bonded to four equivalent Dy and eight Pd atoms to form SbDy4Pd8 cuboctahedra that share corners with four equivalent SbDy4Pd8 cuboctahedra, edges with two equivalent SbDy6 octahedra, and faces with eight equivalent SbDy4Pd8 cuboctahedra. In the third Sb site, Sb is bonded to six equivalent Dy atoms to form edge-sharing SbDy6 octahedra.

36 MATERIALS SCIENCE↗

Materials Data on Dy2Ga5Cu12 by Materials Project

Dy2Cu12Ga5 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Dy is bonded in a 10-coordinate geometry to fifteen Cu and four Ga atoms. There are a spread of Dy–Cu bond distances ranging from 3.01–3.35 Å. There are one shorter (3.11 Å) and three longer (3.39 Å) Dy–Ga bond lengths. There are two inequivalent Cu sites. In the first Cu site, Cu is bonded in a 12-coordinate geometry to two equivalent Dy, six Cu, and four Ga atoms. There are a spread of Cu–Cu bond distances ranging from 2.56–2.72 Å. There are two shorter (2.51 Å) and two longer (3.00 Å) Cu–Ga bond lengths. In the second Cu site, Cu is bonded to three equivalent Dy, six Cu, and three Ga atoms to form a mixture of distorted edge, face, and corner-sharing CuDy3Ga3Cu6 cuboctahedra. Both Cu–Cu bond lengths are 2.47 Å. There are two shorter (2.55 Å) and one longer (2.75 Å) Cu–Ga bond lengths. There are two inequivalent Ga sites. In the first Ga site, Ga is bonded in a 12-coordinate geometry to two equivalent Dy, eight Cu, and two equivalent Ga atoms. Both Ga–Ga bond lengths are 2.65 Å. In the second Ga site, Ga is bonded in a 8-coordinate geometry to one Dy, nine Cu, and four Ga atoms. The Ga–Ga bond length is 2.52 Å.

36 MATERIALS SCIENCE↗

Materials Data on DyIn5Co by Materials Project

DyCoIn5 crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Dy is bonded to twelve In atoms to form DyIn12 cuboctahedra that share corners with four equivalent DyIn12 cuboctahedra, faces with four equivalent DyIn12 cuboctahedra, and faces with four equivalent InDy4In8 cuboctahedra. All Dy–In bond lengths are 3.23 Å. Co is bonded in a body-centered cubic geometry to eight In atoms. All Co–In bond lengths are 2.71 Å. There are five inequivalent In sites. In the first In site, In is bonded to four equivalent Dy and eight In atoms to form distorted InDy4In8 cuboctahedra that share corners with four equivalent InDy4In8 cuboctahedra, faces with four equivalent DyIn12 cuboctahedra, and faces with four equivalent InDy4In8 cuboctahedra. All In–In bond lengths are 3.23 Å. In the second In site, In is bonded in a 4-coordinate geometry to two equivalent Dy, two equivalent Co, and seven In atoms. There are one shorter (2.91 Å) and four longer (3.23 Å) In–In bond lengths. In the third In site, In is bonded in a 4-coordinate geometry to two equivalent Dy, two equivalent Co, and seven In atoms. The In–In bond length is 2.91 Å. In the fourth In site, In is bonded in a 4-coordinate geometry to two equivalent Dy, two equivalent Co, and seven In atoms. All In–In bond lengths are 3.23 Å. In the fifth In site, In is bonded in a 4-coordinate geometry to two equivalent Dy, two equivalent Co, and seven In atoms.

36 MATERIALS SCIENCE↗