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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Discrete theta angles, symmetries and anomalies

Gauge theories in various dimensions often admit discrete theta angles, that arise from gauging a global symmetry with an additional symmetry protected topological (SPT) phase. We discuss how the global symmetry and ’t Hooft anomaly depends on the discrete theta angles by coupling the gauge theory to a topological quantum field theory (TQFT). We observe that gauging an Abelian subgroup symmetry, that participates in symmetry extension, with an additional SPT phase leads to a new theory with an emergent Abelian symmetry that also participates in a symmetry extension. The symmetry extension of the gauge theory is controlled by the discrete theta angle which comes from the SPT phase. We find that discrete theta angles can lead to two-group symmetry in 4d 4 d QCD with SU(N),SU(N)/\mathbb{Z}_k S U ( N ) , S U ( N ) / ℤ k or SO(N) S O ( N ) gauge groups as well as various 3d 3 d and 2d 2 d gauge theories.

Hsin, Po-Shen↗
DOE OSTI2020

Materials Data on HoTaTiO6 by Materials Project

HoTiTaO6 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. Ho3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Ho–O bond distances ranging from 2.26–2.59 Å. Ti4+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ti–O bond distances ranging from 1.78–2.33 Å. Ta5+ is bonded to six O2- atoms to form distorted corner-sharing TaO6 octahedra. The corner-sharing octahedral tilt angles are 55°. There are a spread of Ta–O bond distances ranging from 1.87–2.22 Å. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded in a 3-coordinate geometry to two equivalent Ti4+ and one Ta5+ atom. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to one Ti4+ and two equivalent Ta5+ atoms. In the third O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Ho3+, one Ti4+, and one Ta5+ atom. In the fourth O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Ho3+, one Ti4+, and one Ta5+ atom. In the fifth O2- site, O2- is bonded in a 3-coordinate geometry to two equivalent Ho3+ and one Ti4+ atom. In the sixth O2- site, O2- is bonded in a 3-coordinate geometry to two equivalent Ho3+ and one Ta5+ atom.

36 MATERIALS SCIENCE↗
NASA NTRS1989

Introduction and data summary, chapter 5

A subset of data representing most of the participating model groups was discussed and reviewed. The results are presented for intercomparisons of that subset of data. Subsequent to the workshop, the various modeling groups had the opportunity to either update or add to the data sets discussed at the workshop. The overall revised data sets as of December 1988 are presented. Data from all the models (where available) are grouped according to: (1) photochemistry and radiation (photodissociation coefficients, and ultraviolet heating and infrared cooling); (2) transport (net radiative heating, tropospheric source tracer experiment, time-dependent source conserved tracer experiment, stratospheric source tracer experiment, and O3 column); (3) current atmosphere (integrated columns of trace gases, Cl(y) and NO(y), nitrogen gases, chlorine gases, O(x) and HO(x) gases, and source gases); and (4) perturbed circulations and temperatures. The data presented provide a detailed summary of the two-dimensional picture of the atmosphere as seen by current atmospheric models.

Source record↗
NASA NTRS2022

The reliability of the small-core Lanthanide effective core potentials

The reliability of the small-core Lanthanide effective core potentials (ECP) is tested using MF and MF(3), for M=Eu, Gd, Tb, and Yb and the atomic excitation energies for Pr, Nd, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb. In some case the ECP and all-electron (AE) results are in good agreement, while in others there are significant difference. The difference are much larger when the segmented basis set is used in conjunction with the ECP than when the atomic natural orbital (ANO) basis set is used. The study of the atoms suggests that problems for lanthanide containing molecules are associated with poor atomic excitation energies in the ECP treatment and even using the ANO basis set does not completely solve the problem. We note that the problem appears to be more severe for density functional approaches than for traditional correlation methods. We suggest that additional studies and new effective core potentials may be required for the Lanthanide atoms.

effective core potentials, atomic excitation, atom↗
DOE OSTI2020

Trivalent f-Element Squarates, Squarate-Oxalates, and Cationic Materials, and the Determination of the Nine-Coordinate Ionic Radius of Cf(III)

The synthesis, structure, and solid-state UV–vis–NIR spectroscopy of four new f-element squarates, M 2 (C 4 O 4 ) 3 (H 2 O) 4 (M = Eu, Am, Cf) and Sm(C 4 O 4 )(C 4 O 3 OH)(H 2 O) 2 ·0.5H 2 O, four new cationic lanthanide squarate chlorides, [M 4 (C 4 O 4 ) 5 (H 2 O) 12 ]Cl 2 ·5H 2 O (M = Eu, Dy, Ho Er), and two new actinide squarate oxalates, M 2 (C 4 O 4 ) 2 (C 2 O 4 )(H 2 O) 4 (M = Am, Cf), are presented. All of the metal centers are trivalent. Single-crystal X-ray diffraction analysis reveals that M 2 (C 4 O 4 ) 3 (H 2 O) 4 and Sm(C 4 O 4 )(C 4 O 3 OH)(H 2 O) 2 ·0.5H 2 O have a two-dimensional sheet structure constructed from MO 7 (H 2 O) 2 monocapped square-antiprismatic (coordination number (CN) = 9) metal centers and SmO 6 (H 2 O) 2 square-antiprismatic (CN = 8) metal centers, respectively, whereas M 2 (C 4 O 4 ) 2 (C 2 O 4 )(H 2 O) 4 have a three-dimensional (3D) structure constructed from MO 7 (H 2 O) 2 monocapped square-antiprismatic (CN = 9) metal centers. Additionally, the cationic framework materials [M 4 (C 4 O 4 ) 5 (H 2 O) 12 ]Cl 2 ·5H 2 O have a 3D structure constructed from two crystallographically unique MO 5 (H 2 O) 3 square-antiprismatic (CN = 8) metal centers. In these structures, the squarate ligands bind to the metal centers with varying coordination modes and denticities. The results of this study provide another example of the nonparallel chemistry between the lanthanides and transplutonium elements. From the crystallographic data for the isotypic series M 2 (C 4 O 4 ) 3 (H 2 O) 4 (M = La–Nd, Sm, Eu) and the linear regression fit to a plot of the unit cell volume as a function of the cube of the ionic radius, the nine-coordinate ionic radius of Cf 3+ was determined to be 1.127 ± 0.003 Å. Lastly, computational analysis of the americium and californium complexes M 2 (C 4 O 4 ) 3 (H 2 O) 4 and M 2 (C 4 O 4 ) 2 (C 2 O 4 )(H 2 O) 4 reveals three important attributes: (i) the 5f orbitals are nonbonding in all cases, with the bonding differences occurring with the empty 6d orbitals; (ii) the Cf complexes exhibit more covalent character than their Am counterparts; and (iii) there is more covalent character in the squarate-oxalate complexes than in the squarate complexes.

Crystallography↗
DOE OSTI2021

Geometry of the charge density wave in the kagome metal A V 3 Sb 5

Kagome lattice is a fertile platform for topological and intertwined electronic excitations. Recently, experimental evidence of an unconventional charge density wave (CDW) is observed in a Z 2 kagome metal AV 3 Sb 5 (A=K, Cs, Rb). This observation triggers wide interest in the interplay between frustrated crystal structure and Fermi surface instabilities. Here, we analyze the lattice effect and its impact on CDW in AV 3 Sb 5 . Based on published experimental data, we show that the 2×2×2 CDW breaks the sixfold rotational symmetry of the crystal due to the phase shift between kagome layers and can explain the twofold symmetric CDW peak intensity observed by scanning tunneling spectroscopy. The coupling between the lattice and electronic degrees of freedom yields a weak first-order structural transition without continuous change of lattice dynamics. Our result emphasizes the fundamental role of lattice geometry in proper understanding of unconventional electronic orders in AV 3 Sb 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2000

Multi-Satellite Measurements and Model Predictions of Mesospheric and Upper Stratospheric Influences from the Very Large July 14-16, 2000, Solar Proton Event

A large solar flare with an associated coronal mass ejection occurred in mid-July and caused a very large solar proton event at the earth in the time period July 14-16, 2000. So far this is the largest solar storm of solar cycle 23. The solar proton fluxes were measured by instruments aboard the GOES-10 satellite and used in our proton energy deposition model to help quantify the energy input to the middle atmosphere during this large solar event. Using this computed energy deposition in the GSFC 2D atmospheric model resulted in a prediction of $>$ 20\% increases in HO$-(x)$ (H, OH, HO$-(2)$) and $>$ 100\% increases in NO$-(x)$ (N, NO, NO$-(2)$) constituents in the mesosphere and upper stratosphere at polar latitudes ($>$ 60 degrees geomagnetic). Both the HO$-(x)$ and NO$_fx)$ increases impacted ozone. Large atmospheric impacts have been measured with the NOAA 14 SBUV/2 instrument (0$_(3)$), the UARS HALOE instrument (NO, NO$-(2)$, 0$-(3)$), and the POAM III instrument (0$_{3}$, NO$-(2)$). Preliminary analysis indicates that measured (SBUV/2) and modelled 0$_{3}$ decreases from this solar event are generally in agreement in the Northern Hemisphere. Short-term ozone changes (during the event) indicate $\sim$ 15% reduction at 2 hPa ($\sim$ 45 km) up to $\sim$ 40% reduction at 0.5 hPa ($\sim$ 55 km). A longer-term ozone depletion of $\sim$ 5% is indicated between 4 and 2 hPa ($\sim$ 40-45 km). The middle atmospheric changes caused by this solar event were very large and occurred fairly quickly ($\sim$ 1-2 days). Such a significant natural perturbation provides a good test of our understanding of the middle atmosphere. The measured and modelled impacts of this solar event will be compared and discussed in this paper.

Jackman, Charles H.↗
DOE OSTI2020

Pressure-Induced Spectroscopic Changes in a Californium 1D Material Are Twice as Large as Found in the Holmium Analog

Here, in this study, the synthesis, characterization, and pressure response of a 1D californium mellitate (mellitate = 1,2,3,4,5,6-benzenehexacarboxylate) coordination polymer, Cf 2 (mell)(H 2 O) 10 ·4H 2 O (Cf-1), are reported. The Cf–O lengths within the crystal structure are compared to its gadolinium (Gd-1) and holmium (Ho-1) analogs as well. These data show that the average Cf–O bond distance is slightly longer than the average Gd–O bond, consistent with trends in effective ionic radii. UV–vis-NIR absorption spectra as a function of pressure were collected using diamond-anvil techniques for both Cf-1 and Ho-1. These experiments show that the Cf(III) f → f transitions have a stronger dependence on pressure than that of the holmium analog. In the former case, the shift is nearly linear with applied pressure and averages 6.6 cm –1 /GPa, whereas in the latter, it is <3 cm –1 /GPa.

absorption spectroscopy↗
DOE OSTI2020

Materials Data on NaLiHo2F8 by Materials Project

NaLiHo2F8 crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. Na1+ is bonded in a 7-coordinate geometry to seven F1- atoms. There are a spread of Na–F bond distances ranging from 2.21–2.55 Å. Li1+ is bonded to six F1- atoms to form distorted corner-sharing LiF6 octahedra. The corner-sharing octahedral tilt angles are 44°. There are two shorter (1.90 Å) and four longer (2.25 Å) Li–F bond lengths. Ho3+ is bonded in a 8-coordinate geometry to eight F1- atoms. There are a spread of Ho–F bond distances ranging from 2.20–2.45 Å. There are four inequivalent F1- sites. In the first F1- site, F1- is bonded in a 4-coordinate geometry to two equivalent Li1+ and two equivalent Ho3+ atoms. In the second F1- site, F1- is bonded to one Na1+, one Li1+, and two equivalent Ho3+ atoms to form a mixture of distorted corner and edge-sharing FNaLiHo2 trigonal pyramids. In the third F1- site, F1- is bonded in a trigonal planar geometry to one Na1+ and two equivalent Ho3+ atoms. In the fourth F1- site, F1- is bonded in a 3-coordinate geometry to one Na1+ and two equivalent Ho3+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ho2Sn3(PbS4)3 by Materials Project

Ho2Pb3Sn3S12 crystallizes in the orthorhombic Pmc2_1 space group. The structure is three-dimensional. there are two inequivalent Ho3+ sites. In the first Ho3+ site, Ho3+ is bonded to seven S2- atoms to form distorted HoS7 pentagonal bipyramids that share corners with two equivalent SnS6 octahedra, edges with four SnS6 octahedra, and edges with two equivalent HoS7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 49°. There are a spread of Ho–S bond distances ranging from 2.77–2.84 Å. In the second Ho3+ site, Ho3+ is bonded in a 8-coordinate geometry to eight S2- atoms. There are a spread of Ho–S bond distances ranging from 2.82–3.08 Å. There are three inequivalent Pb2+ sites. In the first Pb2+ site, Pb2+ is bonded in a 8-coordinate geometry to eight S2- atoms. There are a spread of Pb–S bond distances ranging from 2.97–3.29 Å. In the second Pb2+ site, Pb2+ is bonded in a 7-coordinate geometry to seven S2- atoms. There are a spread of Pb–S bond distances ranging from 2.93–3.27 Å. In the third Pb2+ site, Pb2+ is bonded in a 8-coordinate geometry to eight S2- atoms. There are a spread of Pb–S bond distances ranging from 2.91–3.23 Å. There are three inequivalent Sn4+ sites. In the first Sn4+ site, Sn4+ is bonded to six S2- atoms to form SnS6 octahedra that share corners with two equivalent HoS7 pentagonal bipyramids, edges with two equivalent SnS6 octahedra, and edges with two equivalent HoS7 pentagonal bipyramids. There are a spread of Sn–S bond distances ranging from 2.54–2.63 Å. In the second Sn4+ site, Sn4+ is bonded to six S2- atoms to form SnS6 octahedra that share edges with two equivalent SnS6 octahedra and edges with two equivalent HoS7 pentagonal bipyramids. There are a spread of Sn–S bond distances ranging from 2.54–2.65 Å. In the third Sn4+ site, Sn4+ is bonded to five S2- atoms to form corner-sharing SnS5 trigonal bipyramids. There are a spread of Sn–S bond distances ranging from 2.45–2.58 Å. There are twelve inequivalent S2- sites. In the first S2- site, S2- is bonded in a 4-coordinate geometry to one Ho3+, one Pb2+, and two equivalent Sn4+ atoms. In the second S2- site, S2- is bonded in a 3-coordinate geometry to two equivalent Ho3+, two equivalent Pb2+, and one Sn4+ atom. In the third S2- site, S2- is bonded in a distorted single-bond geometry to four Pb2+ and one Sn4+ atom. In the fourth S2- site, S2- is bonded in a 3-coordinate geometry to two equivalent Ho3+, two equivalent Pb2+, and one Sn4+ atom. In the fifth S2- site, S2- is bonded in a 4-coordinate geometry to one Ho3+, one Pb2+, and two equivalent Sn4+ atoms. In the sixth S2- site, S2- is bonded in a 3-coordinate geometry to two equivalent Ho3+, two equivalent Pb2+, and one Sn4+ atom. In the seventh S2- site, S2- is bonded to one Ho3+, one Pb2+, and two equivalent Sn4+ atoms to form distorted corner-sharing SHoSn2Pb trigonal pyramids. In the eighth S2- site, S2- is bonded in a 5-coordinate geometry to four Pb2+ and one Sn4+ atom. In the ninth S2- site, S2- is bonded in a 2-coordinate geometry to one Ho3+, one Pb2+, and two equivalent Sn4+ atoms. In the tenth S2- site, S2- is bonded in a 5-coordinate geometry to two equivalent Ho3+, two equivalent Pb2+, and one Sn4+ atom. In the eleventh S2- site, S2- is bonded in a 3-coordinate geometry to two equivalent Ho3+, two equivalent Pb2+, and one Sn4+ atom. In the twelfth S2- site, S2- is bonded in a 4-coordinate geometry to one Ho3+, one Pb2+, and two equivalent Sn4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HoTa3O9 by Materials Project

HoTa3O9 crystallizes in the monoclinic P2_1/m space group. The structure is three-dimensional. Ho3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Ho–O bond distances ranging from 2.30–2.51 Å. There are two inequivalent Ta5+ sites. In the first Ta5+ site, Ta5+ is bonded to six O2- atoms to form corner-sharing TaO6 octahedra. The corner-sharing octahedra tilt angles range from 32–50°. There are a spread of Ta–O bond distances ranging from 1.96–2.05 Å. In the second Ta5+ site, Ta5+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TaO6 octahedra. The corner-sharing octahedra tilt angles range from 34–50°. There are a spread of Ta–O bond distances ranging from 1.86–2.19 Å. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded in a bent 150 degrees geometry to two equivalent Ta5+ atoms. In the second O2- site, O2- is bonded in a 3-coordinate geometry to one Ho3+ and two Ta5+ atoms. In the third O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Ho3+ and two equivalent Ta5+ atoms. In the fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Ho3+ and two equivalent Ta5+ atoms. In the fifth O2- site, O2- is bonded in a bent 150 degrees geometry to two Ta5+ atoms. In the sixth O2- site, O2- is bonded in a 3-coordinate geometry to one Ho3+ and two equivalent Ta5+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HoTa7O19 by Materials Project

HoTa7O19 crystallizes in the hexagonal P-6c2 space group. The structure is three-dimensional. Ho3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are six shorter (2.40 Å) and two longer (2.63 Å) Ho–O bond lengths. There are two inequivalent Ta5+ sites. In the first Ta5+ site, Ta5+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Ta–O bond distances ranging from 1.93–2.46 Å. In the second Ta5+ site, Ta5+ is bonded in an octahedral geometry to six equivalent O2- atoms. All Ta–O bond lengths are 2.01 Å. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal planar geometry to one Ho3+ and two Ta5+ atoms. In the second O2- site, O2- is bonded in a trigonal planar geometry to three equivalent Ta5+ atoms. In the third O2- site, O2- is bonded in a distorted bent 150 degrees geometry to three equivalent Ta5+ atoms. In the fourth O2- site, O2- is bonded in a bent 150 degrees geometry to two equivalent Ta5+ atoms. In the fifth O2- site, O2- is bonded in a 3-coordinate geometry to one Ho3+ and three equivalent Ta5+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ho2PbS4 by Materials Project

Ho2PbS4 is Orthorhombic Perovskite-like structured and crystallizes in the orthorhombic Cmc2_1 space group. The structure is three-dimensional. there are six inequivalent Ho3+ sites. In the first Ho3+ site, Ho3+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing HoS6 octahedra. The corner-sharing octahedra tilt angles range from 46–62°. There are a spread of Ho–S bond distances ranging from 2.70–2.77 Å. In the second Ho3+ site, Ho3+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing HoS6 octahedra. The corner-sharing octahedra tilt angles range from 47–62°. There are a spread of Ho–S bond distances ranging from 2.71–2.77 Å. In the third Ho3+ site, Ho3+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing HoS6 octahedra. The corner-sharing octahedra tilt angles range from 47–65°. There are a spread of Ho–S bond distances ranging from 2.72–2.77 Å. In the fourth Ho3+ site, Ho3+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing HoS6 octahedra. The corner-sharing octahedra tilt angles range from 50–62°. There are a spread of Ho–S bond distances ranging from 2.69–2.79 Å. In the fifth Ho3+ site, Ho3+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing HoS6 octahedra. The corner-sharing octahedra tilt angles range from 46–62°. There are a spread of Ho–S bond distances ranging from 2.70–2.77 Å. In the sixth Ho3+ site, Ho3+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing HoS6 octahedra. The corner-sharing octahedra tilt angles range from 47–65°. There are a spread of Ho–S bond distances ranging from 2.71–2.75 Å. There are three inequivalent Pb2+ sites. In the first Pb2+ site, Pb2+ is bonded in a 7-coordinate geometry to seven S2- atoms. There are a spread of Pb–S bond distances ranging from 2.85–3.42 Å. In the second Pb2+ site, Pb2+ is bonded in a 7-coordinate geometry to seven S2- atoms. There are a spread of Pb–S bond distances ranging from 2.80–3.48 Å. In the third Pb2+ site, Pb2+ is bonded in a 8-coordinate geometry to eight S2- atoms. There are a spread of Pb–S bond distances ranging from 3.05–3.53 Å. There are twelve inequivalent S2- sites. In the first S2- site, S2- is bonded in a 5-coordinate geometry to three Ho3+ and two equivalent Pb2+ atoms. In the second S2- site, S2- is bonded in a 4-coordinate geometry to three Ho3+ and two Pb2+ atoms. In the third S2- site, S2- is bonded in a 3-coordinate geometry to three Ho3+ and two equivalent Pb2+ atoms. In the fourth S2- site, S2- is bonded to three Ho3+ and one Pb2+ atom to form distorted corner-sharing SHo3Pb trigonal pyramids. In the fifth S2- site, S2- is bonded in a 3-coordinate geometry to three Ho3+ and two Pb2+ atoms. In the sixth S2- site, S2- is bonded in a 3-coordinate geometry to three Ho3+ and two Pb2+ atoms. In the seventh S2- site, S2- is bonded to three Ho3+ and one Pb2+ atom to form distorted corner-sharing SHo3Pb trigonal pyramids. In the eighth S2- site, S2- is bonded in a 3-coordinate geometry to three Ho3+ and two equivalent Pb2+ atoms. In the ninth S2- site, S2- is bonded in a 3-coordinate geometry to three Ho3+ and two equivalent Pb2+ atoms. In the tenth S2- site, S2- is bonded in a 5-coordinate geometry to three Ho3+ and two equivalent Pb2+ atoms. In the eleventh S2- site, S2- is bonded in a 3-coordinate geometry to three Ho3+ and two equivalent Pb2+ atoms. In the twelfth S2- site, S2- is bonded in a 3-coordinate geometry to three Ho3+ and two equivalent Pb2+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ho3TaO7 by Materials Project

Ho3TaO7 crystallizes in the orthorhombic C222_1 space group. The structure is three-dimensional. there are two inequivalent Ho3+ sites. In the first Ho3+ site, Ho3+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ho–O bond distances ranging from 2.32–2.39 Å. In the second Ho3+ site, Ho3+ is bonded to seven O2- atoms to form distorted HoO7 pentagonal bipyramids that share corners with two equivalent TaO6 octahedra, a cornercorner with one HoO7 pentagonal bipyramid, edges with two equivalent TaO6 octahedra, and edges with three equivalent HoO7 pentagonal bipyramids. The corner-sharing octahedra tilt angles range from 38–50°. There are a spread of Ho–O bond distances ranging from 2.21–2.45 Å. Ta5+ is bonded to six O2- atoms to form TaO6 octahedra that share corners with two equivalent TaO6 octahedra, corners with four equivalent HoO7 pentagonal bipyramids, and edges with four equivalent HoO7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 43°. There are a spread of Ta–O bond distances ranging from 1.93–2.05 Å. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Ho3+ and two equivalent Ta5+ atoms. In the second O2- site, O2- is bonded to four Ho3+ atoms to form a mixture of edge and corner-sharing OHo4 tetrahedra. In the third O2- site, O2- is bonded to four Ho3+ atoms to form a mixture of edge and corner-sharing OHo4 tetrahedra. In the fourth O2- site, O2- is bonded to three Ho3+ and one Ta5+ atom to form a mixture of distorted edge and corner-sharing OHo3Ta tetrahedra. In the fifth O2- site, O2- is bonded in a 3-coordinate geometry to two equivalent Ho3+ and one Ta5+ atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ho2Zr2O7 by Materials Project

Ho2Zr2O7 crystallizes in the monoclinic P2_1 space group. The structure is three-dimensional. there are four inequivalent Ho3+ sites. In the first Ho3+ site, Ho3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Ho–O bond distances ranging from 2.22–2.63 Å. In the second Ho3+ site, Ho3+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ho–O bond distances ranging from 2.23–2.46 Å. In the third Ho3+ site, Ho3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Ho–O bond distances ranging from 2.26–2.61 Å. In the fourth Ho3+ site, Ho3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Ho–O bond distances ranging from 2.26–2.93 Å. There are four inequivalent Zr4+ sites. In the first Zr4+ site, Zr4+ is bonded to six O2- atoms to form corner-sharing ZrO6 octahedra. The corner-sharing octahedra tilt angles range from 41–49°. There are a spread of Zr–O bond distances ranging from 2.03–2.18 Å. In the second Zr4+ site, Zr4+ is bonded to six O2- atoms to form corner-sharing ZrO6 octahedra. The corner-sharing octahedra tilt angles range from 35–49°. There are a spread of Zr–O bond distances ranging from 2.01–2.30 Å. In the third Zr4+ site, Zr4+ is bonded to six O2- atoms to form corner-sharing ZrO6 octahedra. The corner-sharing octahedra tilt angles range from 42–54°. There are a spread of Zr–O bond distances ranging from 2.00–2.25 Å. In the fourth Zr4+ site, Zr4+ is bonded to six O2- atoms to form distorted corner-sharing ZrO6 octahedra. The corner-sharing octahedra tilt angles range from 33–54°. There are a spread of Zr–O bond distances ranging from 2.01–2.40 Å. There are fourteen inequivalent O2- sites. In the first O2- site, O2- is bonded to three Ho3+ and one Zr4+ atom to form distorted corner-sharing OHo3Zr tetrahedra. In the second O2- site, O2- is bonded in a 4-coordinate geometry to two Ho3+ and two Zr4+ atoms. In the third O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Ho3+ and two Zr4+ atoms. In the fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Ho3+ and two Zr4+ atoms. In the fifth O2- site, O2- is bonded in a 4-coordinate geometry to three Ho3+ and one Zr4+ atom. In the sixth O2- site, O2- is bonded in a 4-coordinate geometry to two Ho3+ and two equivalent Zr4+ atoms. In the seventh O2- site, O2- is bonded in a 3-coordinate geometry to two Ho3+ and two Zr4+ atoms. In the eighth O2- site, O2- is bonded in a distorted trigonal planar geometry to two Ho3+ and one Zr4+ atom. In the ninth O2- site, O2- is bonded in a 4-coordinate geometry to two Ho3+ and two Zr4+ atoms. In the tenth O2- site, O2- is bonded in a distorted tetrahedral geometry to two Ho3+ and two Zr4+ atoms. In the eleventh O2- site, O2- is bonded in a distorted see-saw-like geometry to two Ho3+ and two Zr4+ atoms. In the twelfth O2- site, O2- is bonded in a 4-coordinate geometry to three Ho3+ and one Zr4+ atom. In the thirteenth O2- site, O2- is bonded in a 4-coordinate geometry to two Ho3+ and two equivalent Zr4+ atoms. In the fourteenth O2- site, O2- is bonded in a 3-coordinate geometry to two Ho3+ and two Zr4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ho2TiO5 by Materials Project

Ho2TiO5 crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. there are two inequivalent Ho3+ sites. In the first Ho3+ site, Ho3+ is bonded to six O2- atoms to form distorted HoO6 octahedra that share corners with two equivalent HoO6 octahedra, corners with four equivalent TiO6 octahedra, and edges with six HoO6 octahedra. The corner-sharing octahedra tilt angles range from 58–65°. There are a spread of Ho–O bond distances ranging from 2.28–2.32 Å. In the second Ho3+ site, Ho3+ is bonded to six O2- atoms to form HoO6 octahedra that share corners with four HoO6 octahedra, corners with four equivalent TiO6 octahedra, and edges with four HoO6 octahedra. The corner-sharing octahedra tilt angles range from 51–65°. There are a spread of Ho–O bond distances ranging from 2.20–2.34 Å. Ti4+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with two equivalent TiO6 octahedra, corners with eight HoO6 octahedra, and edges with two equivalent TiO6 octahedra. The corner-sharing octahedra tilt angles range from 34–65°. There are a spread of Ti–O bond distances ranging from 1.85–2.36 Å. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded to four Ho3+ atoms to form OHo4 tetrahedra that share corners with ten OHo4 tetrahedra and edges with three OHo3Ti tetrahedra. In the second O2- site, O2- is bonded in a 2-coordinate geometry to three equivalent Ti4+ atoms. In the third O2- site, O2- is bonded to three Ho3+ and one Ti4+ atom to form a mixture of distorted edge and corner-sharing OHo3Ti tetrahedra. In the fourth O2- site, O2- is bonded to three equivalent Ho3+ and one Ti4+ atom to form a mixture of distorted edge and corner-sharing OHo3Ti tetrahedra. In the fifth O2- site, O2- is bonded in a 3-coordinate geometry to two equivalent Ho3+ and one Ti4+ atom.

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