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DOE OSTI2020

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↗
DOE OSTI2020

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↗
DOE OSTI2020

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↗
DOE OSTI2020

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↗
DOE OSTI2020

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↗
DOE OSTI2020

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↗
DOE OSTI2020

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↗
DOE OSTI2020

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↗
DOE OSTI2020

Materials Data on Dy2Si3Ni by Materials Project

Dy2NiSi3 is hexagonal omega structure-derived structured and crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. Dy is bonded to three equivalent Ni and nine Si atoms to form a mixture of edge and face-sharing DySi9Ni3 cuboctahedra. There are one shorter (2.99 Å) and two longer (3.00 Å) Dy–Ni bond lengths. There are a spread of Dy–Si bond distances ranging from 2.99–3.12 Å. Ni is bonded in a 9-coordinate geometry to six equivalent Dy and three equivalent Si atoms. All Ni–Si bond lengths are 2.32 Å. There are three inequivalent Si sites. In the first Si site, Si is bonded in a 9-coordinate geometry to six equivalent Dy and three equivalent Si atoms. There are one shorter (2.31 Å) and two longer (2.33 Å) Si–Si bond lengths. In the second Si site, Si is bonded in a 9-coordinate geometry to six equivalent Dy and three equivalent Ni atoms. In the third Si site, Si is bonded in a 9-coordinate geometry to six equivalent Dy and three equivalent Si atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Dy2Cu(SO6)2 by Materials Project

Dy2Cu(SO6)2 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. Dy is bonded in a 9-coordinate geometry to nine O atoms. There are a spread of Dy–O bond distances ranging from 2.32–2.53 Å. Cu is bonded in a square co-planar geometry to four O atoms. There is two shorter (1.81 Å) and two longer (1.85 Å) Cu–O bond length. S is bonded in a tetrahedral geometry to four O atoms. There are a spread of S–O bond distances ranging from 1.44–1.54 Å. There are six inequivalent O sites. In the first O site, O is bonded in a distorted trigonal non-coplanar geometry to two equivalent Dy and one Cu atom. In the second O site, O is bonded in a distorted trigonal non-coplanar geometry to two equivalent Dy and one Cu atom. In the third O site, O is bonded in a distorted single-bond geometry to two equivalent Dy and one S atom. In the fourth O site, O is bonded in a bent 150 degrees geometry to one Dy and one S atom. In the fifth O site, O is bonded in a 3-coordinate geometry to two equivalent Dy and one S atom. In the sixth O site, O is bonded in a single-bond geometry to one S atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on DyNiGe3 by Materials Project

DyNiGe3 crystallizes in the orthorhombic Cmmm space group. The structure is three-dimensional. Dy is bonded in a 4-coordinate geometry to four equivalent Ni and ten Ge atoms. All Dy–Ni bond lengths are 3.17 Å. There are a spread of Dy–Ge bond distances ranging from 3.08–3.21 Å. Ni is bonded in a 9-coordinate geometry to four equivalent Dy and five Ge atoms. There are a spread of Ni–Ge bond distances ranging from 2.30–2.35 Å. There are three inequivalent Ge sites. In the first Ge site, Ge is bonded in a 1-coordinate geometry to six equivalent Dy, one Ni, and two equivalent Ge atoms. Both Ge–Ge bond lengths are 2.52 Å. In the second Ge site, Ge is bonded in a 2-coordinate geometry to two equivalent Dy, two equivalent Ni, and five Ge atoms. There are one shorter (2.48 Å) and four longer (2.90 Å) Ge–Ge bond lengths. In the third Ge site, Ge is bonded in a 2-coordinate geometry to two equivalent Dy, two equivalent Ni, and five Ge atoms. The Ge–Ge bond length is 2.48 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Dy7BP2O17 by Materials Project

Dy7BP2O17 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. there are seven inequivalent Dy3+ sites. In the first Dy3+ site, Dy3+ is bonded to seven O2- atoms to form distorted DyO7 pentagonal bipyramids that share corners with three PO4 tetrahedra and an edgeedge with one DyO7 pentagonal bipyramid. There are a spread of Dy–O bond distances ranging from 2.22–2.45 Å. In the second 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 2.18–2.77 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 2.24–2.54 Å. In the fourth 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 2.23–2.68 Å. In the fifth 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 2.15–2.82 Å. In the sixth Dy3+ site, Dy3+ is bonded to seven O2- atoms to form distorted DyO7 pentagonal bipyramids that share corners with two equivalent PO4 tetrahedra and an edgeedge with one DyO7 pentagonal bipyramid. There are a spread of Dy–O bond distances ranging from 2.23–2.49 Å. 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 2.21–2.65 Å. B3+ is bonded in a trigonal planar geometry to three O2- atoms. There are a spread of B–O bond distances ranging from 1.37–1.42 Å. There are two inequivalent P5+ sites. In the first P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two equivalent DyO7 pentagonal bipyramids. There are a spread of P–O bond distances ranging from 1.54–1.57 Å. In the second P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with three DyO7 pentagonal bipyramids. There are a spread of P–O bond distances ranging from 1.53–1.57 Å. There are seventeen inequivalent O2- sites. In the first O2- site, O2- is bonded in a 1-coordinate geometry to two Dy3+ and one P5+ atom. In the second O2- site, O2- is bonded in a 1-coordinate geometry to three Dy3+ and one B3+ atom. In the third O2- site, O2- is bonded to four Dy3+ atoms to form a mixture of edge and corner-sharing ODy4 tetrahedra. In the fourth O2- site, O2- is bonded to four Dy3+ atoms to form a mixture of edge and corner-sharing ODy4 tetrahedra. In the fifth O2- site, O2- is bonded in a 1-coordinate geometry to three Dy3+ and one P5+ atom. In the sixth O2- site, O2- is bonded in a distorted single-bond geometry to two Dy3+ and one P5+ atom. In the seventh O2- site, O2- is bonded to four Dy3+ atoms to form a mixture of edge and corner-sharing ODy4 tetrahedra. In the eighth O2- site, O2- is bonded in a 1-coordinate geometry to three Dy3+ and one P5+ atom. In the ninth O2- site, O2- is bonded to four Dy3+ atoms to form a mixture of edge and corner-sharing ODy4 tetrahedra. In the tenth O2- site, O2- is bonded in a 1-coordinate geometry to three Dy3+ and one P5+ atom. In the eleventh O2- site, O2- is bonded in a distorted single-bond geometry to two Dy3+ and one P5+ atom. In the twelfth O2- site, O2- is bonded to four Dy3+ atoms to form a mixture of edge and corner-sharing ODy4 tetrahedra. In the thirteenth O2- site, O2- is bonded in a 1-coordinate geometry to two Dy3+ and one P5+ atom. In the fourteenth O2- site, O2- is bonded in a distorted single-bond geometry to three Dy3+ and one B3+ atom. In the fifteenth O2- site, O2- is bonded in a distorted single-bond geometry to three Dy3+ and one B3+ atom. In the sixteenth O2- site, O2- is bonded in a 4-coordinate geometry to four Dy3+ atoms. In the seventeenth O2- site, O2- is bonded in a 3-coordinate geometry to two Dy3+ and one P5+ atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on GdDy by Materials Project

Gd(Dy) is Magnesium-derived structured and crystallizes in the hexagonal P-6m2 space group. The structure is three-dimensional. Dy is bonded to six equivalent Dy and six equivalent Gd atoms to form DyGd6Dy6 cuboctahedra that share corners with eighteen equivalent DyGd6Dy6 cuboctahedra, edges with six equivalent DyGd6Dy6 cuboctahedra, edges with twelve equivalent GdGd6Dy6 cuboctahedra, faces with eight equivalent DyGd6Dy6 cuboctahedra, and faces with twelve equivalent GdGd6Dy6 cuboctahedra. All Dy–Dy bond lengths are 3.58 Å. All Dy–Gd bond lengths are 3.53 Å. Gd is bonded to six equivalent Dy and six equivalent Gd atoms to form GdGd6Dy6 cuboctahedra that share corners with eighteen equivalent GdGd6Dy6 cuboctahedra, edges with six equivalent GdGd6Dy6 cuboctahedra, edges with twelve equivalent DyGd6Dy6 cuboctahedra, faces with eight equivalent GdGd6Dy6 cuboctahedra, and faces with twelve equivalent DyGd6Dy6 cuboctahedra. All Gd–Gd bond lengths are 3.58 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on DyMoO5 by Materials Project

DyMoO5 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. Dy is bonded in a 8-coordinate geometry to eight O atoms. There are a spread of Dy–O bond distances ranging from 2.28–2.43 Å. Mo is bonded in a tetrahedral geometry to five O atoms. There are a spread of Mo–O bond distances ranging from 1.76–2.72 Å. There are five inequivalent O sites. In the first O site, O is bonded in a 4-coordinate geometry to two equivalent Dy, one Mo, and one O atom. The O–O bond length is 1.52 Å. In the second O site, O is bonded in a distorted trigonal planar geometry to two equivalent Dy and one Mo atom. In the third O site, O is bonded in a distorted trigonal planar geometry to two equivalent Dy and one Mo atom. In the fourth O site, O is bonded in a distorted bent 150 degrees geometry to one Dy and one Mo atom. In the fifth O site, O is bonded in a distorted bent 150 degrees geometry to one Dy and one Mo atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on LaDy by Materials Project

La(Dy) crystallizes in the hexagonal P-6m2 space group. The structure is three-dimensional. Dy is bonded to six equivalent Dy and six equivalent La atoms to form DyLa6Dy6 cuboctahedra that share corners with eighteen equivalent DyLa6Dy6 cuboctahedra, edges with six equivalent DyLa6Dy6 cuboctahedra, edges with twelve equivalent LaLa6Dy6 cuboctahedra, faces with eight equivalent DyLa6Dy6 cuboctahedra, and faces with twelve equivalent LaLa6Dy6 cuboctahedra. All Dy–Dy bond lengths are 3.66 Å. All Dy–La bond lengths are 3.66 Å. La is bonded to six equivalent Dy and six equivalent La atoms to form LaLa6Dy6 cuboctahedra that share corners with eighteen equivalent LaLa6Dy6 cuboctahedra, edges with six equivalent LaLa6Dy6 cuboctahedra, edges with twelve equivalent DyLa6Dy6 cuboctahedra, faces with eight equivalent LaLa6Dy6 cuboctahedra, and faces with twelve equivalent DyLa6Dy6 cuboctahedra. All La–La bond lengths are 3.66 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on DyMn2SiGe by Materials Project

DyMn2GeSi crystallizes in the tetragonal I4mm space group. The structure is three-dimensional. Dy is bonded in a 8-coordinate geometry to eight equivalent Mn, four equivalent Ge, and four equivalent Si atoms. There are four shorter (3.23 Å) and four longer (3.34 Å) Dy–Mn bond lengths. All Dy–Ge bond lengths are 3.04 Å. All Dy–Si bond lengths are 3.05 Å. Mn is bonded to four equivalent Dy, two equivalent Ge, and two equivalent Si atoms to form a mixture of corner, edge, and face-sharing MnDy4Si2Ge2 tetrahedra. Both Mn–Ge bond lengths are 2.44 Å. Both Mn–Si bond lengths are 2.35 Å. Ge is bonded in a 9-coordinate geometry to four equivalent Dy, four equivalent Mn, and one Si atom. The Ge–Si bond length is 2.53 Å. Si is bonded in a 9-coordinate geometry to four equivalent Dy, four equivalent Mn, and one Ge atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Dy3(In2Co)2 by Materials Project

Dy3(CoIn2)2 crystallizes in the hexagonal P-6 space group. The structure is three-dimensional. Dy is bonded in a 2-coordinate geometry to three Co and eight In atoms. There are two shorter (2.81 Å) and one longer (3.14 Å) Dy–Co bond lengths. There are a spread of Dy–In bond distances ranging from 3.15–3.42 Å. There are two inequivalent Co sites. In the first Co site, Co is bonded in a 9-coordinate geometry to three equivalent Dy and six equivalent In atoms. All Co–In bond lengths are 2.69 Å. In the second Co site, Co is bonded in a 6-coordinate geometry to six equivalent Dy and three equivalent In atoms. All Co–In bond lengths are 3.00 Å. There are two inequivalent In sites. In the first In site, In is bonded in a 10-coordinate geometry to six equivalent Dy, three Co, and one In atom. The In–In bond length is 2.98 Å. In the second In site, In is bonded in a 9-coordinate geometry to six equivalent Dy and three equivalent In atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on DyMg3 by Materials Project

Mg3Dy is beta Cu3Ti-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are three inequivalent Mg sites. In the first Mg site, Mg is bonded to eight Mg and four equivalent Dy atoms to form MgDy4Mg8 cuboctahedra that share corners with four equivalent DyMg12 cuboctahedra, corners with fourteen MgDy4Mg8 cuboctahedra, edges with six equivalent DyMg12 cuboctahedra, edges with twelve MgDy4Mg8 cuboctahedra, faces with four equivalent DyMg12 cuboctahedra, and faces with sixteen MgDy4Mg8 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.21–3.39 Å. There are two shorter (3.25 Å) and two longer (3.33 Å) Mg–Dy bond lengths. In the second Mg site, Mg is bonded to eight Mg and four equivalent Dy atoms to form MgDy4Mg8 cuboctahedra that share corners with four equivalent DyMg12 cuboctahedra, corners with fourteen MgDy4Mg8 cuboctahedra, edges with six equivalent DyMg12 cuboctahedra, edges with twelve MgDy4Mg8 cuboctahedra, faces with four equivalent DyMg12 cuboctahedra, and faces with sixteen MgDy4Mg8 cuboctahedra. Both Mg–Mg bond lengths are 3.21 Å. There are two shorter (3.25 Å) and two longer (3.33 Å) Mg–Dy bond lengths. In the third Mg site, Mg is bonded to eight Mg and four equivalent Dy atoms to form MgDy4Mg8 cuboctahedra that share corners with four equivalent DyMg12 cuboctahedra, corners with fourteen MgDy4Mg8 cuboctahedra, edges with six equivalent DyMg12 cuboctahedra, edges with twelve MgDy4Mg8 cuboctahedra, faces with four equivalent DyMg12 cuboctahedra, and faces with sixteen MgDy4Mg8 cuboctahedra. There are two shorter (3.25 Å) and two longer (3.33 Å) Mg–Dy bond lengths. Dy is bonded to twelve Mg atoms to form DyMg12 cuboctahedra that share corners with six equivalent DyMg12 cuboctahedra, corners with twelve MgDy4Mg8 cuboctahedra, edges with eighteen MgDy4Mg8 cuboctahedra, faces with eight equivalent DyMg12 cuboctahedra, and faces with twelve MgDy4Mg8 cuboctahedra.

36 MATERIALS SCIENCE↗