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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A projection method for particle resampling

Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase-space due to their better scalability than continuum approaches with respect to dimension. Complex processes collectively referred to as particle noise hamper long time simulations with particle methods. One approach to address this problem is particle mesh adaptivity, or remapping, known as particle resampling and remeshing. Here, this work introduces a resampling method that projects particles to and from a (finite element) function space. The method is simple, using standard sparse linear algebra and finite element techniques, and it preserves all moments up to the order of a polynomial represented exactly by the continuum function space. It is distinguished from most other mesh-based methods in that new particle positions and number are decoupled from the mesh, allowing particle and continuum meshes to be adapted relatively independently. While this work is developed with structured particle and continuum phase-space grids on 1X + 1V Vlasov-Poisson models of Landau damping and two-stream instability, the method is well-suited to unstructured grids. Stable long time dynamics are demonstrated up to time T = 500. Reproducibility artifacts and data are publicly available.

Kinetic methods↗
DOE OSTI2020

Materials Data on MoC by Materials Project

MoC is Molybdenum Carbide MAX Phase structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are two inequivalent Mo4+ sites. In the first Mo4+ site, Mo4+ is bonded to six C4- atoms to form a mixture of edge and corner-sharing MoC6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are three shorter (2.13 Å) and three longer (2.26 Å) Mo–C bond lengths. In the second Mo4+ site, Mo4+ is bonded to six equivalent C4- atoms to form a mixture of distorted edge and corner-sharing MoC6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 2°. All Mo–C bond lengths are 2.19 Å. There are two inequivalent C4- sites. In the first C4- site, C4- is bonded to six equivalent Mo4+ atoms to form a mixture of edge and corner-sharing CMo6 octahedra. The corner-sharing octahedral tilt angles are 5°. In the second C4- site, C4- is bonded to six Mo4+ atoms to form a mixture of face, edge, and corner-sharing CMo6 octahedra. The corner-sharing octahedra tilt angles range from 5–48°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti3AlC2 by Materials Project

Ti3AlC2 is MAX Phase-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are two inequivalent Ti sites. In the first Ti site, Ti is bonded in a 3-coordinate geometry to three equivalent Al and three equivalent C atoms. All Ti–Al bond lengths are 2.91 Å. All Ti–C bond lengths are 2.08 Å. In the second Ti site, Ti is bonded to six equivalent C atoms to form edge-sharing TiC6 octahedra. All Ti–C bond lengths are 2.20 Å. Al is bonded to six equivalent Ti atoms to form distorted AlTi6 cuboctahedra that share corners with six equivalent CTi6 octahedra, edges with six equivalent AlTi6 cuboctahedra, and edges with six equivalent CTi6 octahedra. The corner-sharing octahedral tilt angles are 21°. C is bonded to six Ti atoms to form CTi6 octahedra that share corners with three equivalent AlTi6 cuboctahedra, corners with three equivalent CTi6 octahedra, edges with three equivalent AlTi6 cuboctahedra, and edges with nine equivalent CTi6 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti3SiC2 by Materials Project

Ti3SiC2 is MAX Phase-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are two inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to six equivalent C4- atoms to form edge-sharing TiC6 octahedra. All Ti–C bond lengths are 2.19 Å. In the second Ti4+ site, Ti4+ is bonded in a 6-coordinate geometry to three equivalent Si4- and three equivalent C4- atoms. All Ti–Si bond lengths are 2.71 Å. All Ti–C bond lengths are 2.09 Å. Si4- is bonded in a 6-coordinate geometry to six equivalent Ti4+ atoms. C4- is bonded to six Ti4+ atoms to form a mixture of edge and corner-sharing CTi6 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ta3AlC2 by Materials Project

Ta3AlC2 is MAX Phase-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are two inequivalent Ta sites. In the first Ta site, Ta is bonded in a 3-coordinate geometry to three equivalent Al and three equivalent C atoms. All Ta–Al bond lengths are 2.86 Å. All Ta–C bond lengths are 2.20 Å. In the second Ta site, Ta is bonded to six equivalent C atoms to form edge-sharing TaC6 octahedra. All Ta–C bond lengths are 2.22 Å. Al is bonded in a 12-coordinate geometry to six equivalent Ta atoms. C is bonded to six Ta atoms to form a mixture of edge and corner-sharing CTa6 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Nb3AlC2 by Materials Project

Nb3AlC2 is MAX Phase-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are two inequivalent Nb sites. In the first Nb site, Nb is bonded in a 3-coordinate geometry to three equivalent Al and three equivalent C atoms. All Nb–Al bond lengths are 2.88 Å. All Nb–C bond lengths are 2.19 Å. In the second Nb site, Nb is bonded to six equivalent C atoms to form edge-sharing NbC6 octahedra. All Nb–C bond lengths are 2.25 Å. Al is bonded to six equivalent Nb atoms to form distorted AlNb6 cuboctahedra that share corners with six equivalent CNb6 octahedra, edges with six equivalent AlNb6 cuboctahedra, and edges with six equivalent CNb6 octahedra. The corner-sharing octahedral tilt angles are 17°. C is bonded to six Nb atoms to form CNb6 octahedra that share corners with three equivalent AlNb6 cuboctahedra, corners with three equivalent CNb6 octahedra, edges with three equivalent AlNb6 cuboctahedra, and edges with nine equivalent CNb6 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Co3H by Materials Project

Co3H is H-Phase-derived structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are two inequivalent Co sites. In the first Co site, Co is bonded in a 3-coordinate geometry to three equivalent Co and three equivalent H atoms. All Co–Co bond lengths are 2.47 Å. All Co–H bond lengths are 1.83 Å. In the second Co site, Co is bonded to twelve Co atoms to form CoCo12 cuboctahedra that share corners with six equivalent CoCo12 cuboctahedra, corners with six equivalent HCo6 octahedra, edges with six equivalent CoCo12 cuboctahedra, edges with six equivalent HCo6 octahedra, and faces with six equivalent CoCo12 cuboctahedra. The corner-sharing octahedral tilt angles are 17°. All Co–Co bond lengths are 2.55 Å. H is bonded to six equivalent Co atoms to form HCo6 octahedra that share corners with six equivalent CoCo12 cuboctahedra, edges with six equivalent CoCo12 cuboctahedra, and edges with six equivalent HCo6 octahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on InBi3Te4 by Materials Project

(InBi2Te3)2InBi5Te6 is MAX Phase-like structured and crystallizes in the triclinic P1 space group. The structure is two-dimensional and consists of one InBi2Te3 sheet oriented in the (0, 0, 1) direction and one InBi5Te6 sheet oriented in the (0, 0, 1) direction. In the InBi2Te3 sheet, there are two inequivalent In1+ sites. In the first In1+ site, In1+ is bonded to six Te2- atoms to form InTe6 octahedra that share corners with three equivalent BiTe6 octahedra, edges with three BiTe6 octahedra, and edges with six InTe6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of In–Te bond distances ranging from 2.95–3.29 Å. In the second In1+ site, In1+ is bonded to six Te2- atoms to form InTe6 octahedra that share corners with three equivalent BiTe6 octahedra, edges with three BiTe6 octahedra, and edges with six InTe6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of In–Te bond distances ranging from 2.95–3.29 Å. There are four inequivalent Bi+2.33+ sites. In the first Bi+2.33+ site, Bi+2.33+ is bonded in a 3-coordinate geometry to three Te2- atoms. There are a spread of Bi–Te bond distances ranging from 3.57–3.61 Å. In the second Bi+2.33+ site, Bi+2.33+ is bonded in a 3-coordinate geometry to three Te2- atoms. There are two shorter (3.57 Å) and one longer (3.61 Å) Bi–Te bond lengths. In the third Bi+2.33+ site, Bi+2.33+ is bonded to six Te2- atoms to form BiTe6 octahedra that share corners with three equivalent InTe6 octahedra, edges with three InTe6 octahedra, and edges with six BiTe6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Bi–Te bond distances ranging from 3.11–3.30 Å. In the fourth Bi+2.33+ site, Bi+2.33+ is bonded to six Te2- atoms to form BiTe6 octahedra that share corners with three equivalent InTe6 octahedra, edges with three InTe6 octahedra, and edges with six BiTe6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Bi–Te bond distances ranging from 3.12–3.29 Å. There are six inequivalent Te2- sites. In the first Te2- site, Te2- is bonded to three In1+ and three Bi+2.33+ atoms to form TeIn3Bi3 octahedra that share corners with three equivalent TeBi6 octahedra and edges with nine TeIn3Bi3 octahedra. The corner-sharing octahedral tilt angles are 4°. In the second Te2- site, Te2- is bonded to three In1+ and three Bi+2.33+ atoms to form TeIn3Bi3 octahedra that share corners with three equivalent TeBi6 octahedra and edges with nine TeIn3Bi3 octahedra. The corner-sharing octahedral tilt angles are 4°. In the third Te2- site, Te2- is bonded in a 3-coordinate geometry to three In1+ atoms. In the fourth Te2- site, Te2- is bonded in a 3-coordinate geometry to three In1+ atoms. In the fifth Te2- site, Te2- is bonded to six Bi+2.33+ atoms to form TeBi6 octahedra that share corners with three equivalent TeIn3Bi3 octahedra and edges with nine TeBi6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the sixth Te2- site, Te2- is bonded to six Bi+2.33+ atoms to form TeBi6 octahedra that share corners with three equivalent TeIn3Bi3 octahedra and edges with nine TeBi6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the InBi5Te6 sheet, In1+ is bonded to six Te2- atoms to form InTe6 octahedra that share corners with three equivalent BiTe6 octahedra, edges with two equivalent InTe6 octahedra, and edges with seven BiTe6 octahedra. The corner-sharing octahedral tilt angles are 2°. There are a spread of In–Te bond distances ranging from 2.97–3.30 Å. There are five inequivalent Bi+2.33+ sites. In the first Bi+2.33+ site, Bi+2.33+ is bonded to six Te2- atoms to form BiTe6 octahedra that share corners with three equivalent BiTe6 octahedra, edges with four equivalent InTe6 octahedra, and edges with five BiTe6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. There are a spread of Bi–Te bond distances ranging from 3.06–3.32 Å. In the second Bi+2.33+ site, Bi+2.33+ is bonded in a 3-coordinate geometry to three Te2- atoms. There are two shorter (3.58 Å) and one longer (3.60 Å) Bi–Te bond lengths. In the third Bi+2.33+ site, Bi+2.33+ is bonded in a 3-coordinate geometry to three Te2- atoms. There are two shorter (3.57 Å) and one longer (3.61 Å) Bi–Te bond lengths. In the fourth Bi+2.33+ site, Bi+2.33+ is bonded to six Te2- atoms to form BiTe6 octahedra that share corners with three equivalent BiTe6 octahedra, edges with two equivalent InTe6 octahedra, and edges with seven BiTe6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. There are a spread of Bi–Te bond distances ranging from 3.11–3.25 Å. In the fifth Bi+2.33+ site, Bi+2.33+ is bonded to six Te2- atoms to form BiTe6 octahedra that share corners with three equivalent InTe6 octahedra, an edgeedge with one InTe6 octahedra, and edges with eight BiTe6 octahedra. The corner-sharing octahedral tilt angles are 2°. There are a spread of Bi–Te bond distances ranging from 3.11–3.31 Å. There are six inequivalent Te2- sites. In the first Te2- site, Te2- is bonded to one In1+ and five Bi+2.33+ atoms to form TeInBi5 octahedra that share corners with three equivalent TeBi6 octahedra and edges with nine TeInBi5 octahedra. The corner-sharing octahedra tilt angles range from 3–4°. In the second Te2- site, Te2- is bonded to two equivalent In1+ and four Bi+2.33+ atoms to form TeIn2Bi4 octahedra that share corners with three equivalent TeBi6 octahedra and edges with nine TeInBi5 octahedra. The corner-sharing octahedra tilt angles range from 4–5°. In the third Te2- site, Te2- is bonded in a 3-coordinate geometry to two equivalent In1+ and one Bi+2.33+ atom. In the fourth Te2- site, Te2- is bonded in a 3-coordinate geometry to one In1+ and two equivalent Bi+2.33+ atoms. In the fifth Te2- site, Te2- is bonded to six Bi+2.33+ atoms to form a mixture of corner and edge-sharing TeBi6 octahedra. The corner-sharing octahedra tilt angles range from 3–4°. In the sixth Te2- site, Te2- is bonded to six Bi+2.33+ atoms to form TeBi6 octahedra that share corners with three equivalent TeIn2Bi4 octahedra and edges with nine TeInBi5 octahedra. The corner-sharing octahedra tilt angles range from 4–5°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on SnBi3Te4 by Materials Project

(SnBi2Te3)2SnBi5Te6 is MAX Phase-like structured and crystallizes in the triclinic P1 space group. The structure is two-dimensional and consists of one SnBi2Te3 sheet oriented in the (0, 0, 1) direction and one SnBi5Te6 sheet oriented in the (0, 0, 1) direction. In the SnBi2Te3 sheet, there are two inequivalent Sn2+ sites. In the first Sn2+ site, Sn2+ is bonded to six Te2- atoms to form SnTe6 octahedra that share corners with three equivalent BiTe6 octahedra, edges with three BiTe6 octahedra, and edges with six SnTe6 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. There are a spread of Sn–Te bond distances ranging from 3.00–3.37 Å. In the second Sn2+ site, Sn2+ is bonded to six Te2- atoms to form SnTe6 octahedra that share corners with three equivalent BiTe6 octahedra, edges with three BiTe6 octahedra, and edges with six SnTe6 octahedra. The corner-sharing octahedral tilt angles are 3°. There are a spread of Sn–Te bond distances ranging from 3.02–3.36 Å. There are four inequivalent Bi2+ sites. In the first Bi2+ site, Bi2+ is bonded in a 3-coordinate geometry to three Te2- atoms. There are a spread of Bi–Te bond distances ranging from 3.57–3.63 Å. In the second Bi2+ site, Bi2+ is bonded in a 3-coordinate geometry to three Te2- atoms. There are a spread of Bi–Te bond distances ranging from 3.56–3.61 Å. In the third Bi2+ site, Bi2+ is bonded to six Te2- atoms to form BiTe6 octahedra that share corners with three equivalent SnTe6 octahedra, edges with three SnTe6 octahedra, and edges with six BiTe6 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. There are a spread of Bi–Te bond distances ranging from 3.13–3.22 Å. In the fourth Bi2+ site, Bi2+ is bonded to six Te2- atoms to form BiTe6 octahedra that share corners with three equivalent SnTe6 octahedra, edges with three SnTe6 octahedra, and edges with six BiTe6 octahedra. The corner-sharing octahedral tilt angles are 3°. There are a spread of Bi–Te bond distances ranging from 3.14–3.23 Å. There are six inequivalent Te2- sites. In the first Te2- site, Te2- is bonded to three Sn2+ and three Bi2+ atoms to form TeSn3Bi3 octahedra that share corners with three equivalent TeBi6 octahedra and edges with nine TeSn3Bi3 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. In the second Te2- site, Te2- is bonded to three Sn2+ and three Bi2+ atoms to form TeSn3Bi3 octahedra that share corners with three equivalent TeBi6 octahedra and edges with nine TeSn3Bi3 octahedra. The corner-sharing octahedral tilt angles are 2°. In the third Te2- site, Te2- is bonded in a 3-coordinate geometry to three Sn2+ atoms. In the fourth Te2- site, Te2- is bonded in a 3-coordinate geometry to three Sn2+ atoms. In the fifth Te2- site, Te2- is bonded to six Bi2+ atoms to form distorted TeBi6 octahedra that share corners with three equivalent TeSn3Bi3 octahedra and edges with nine TeBi6 octahedra. The corner-sharing octahedral tilt angles are 2°. In the sixth Te2- site, Te2- is bonded to six Bi2+ atoms to form distorted TeBi6 octahedra that share corners with three equivalent TeSn3Bi3 octahedra and edges with nine TeBi6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. In the SnBi5Te6 sheet, Sn2+ is bonded to six Te2- atoms to form SnTe6 octahedra that share corners with three equivalent BiTe6 octahedra, edges with two equivalent SnTe6 octahedra, and edges with seven BiTe6 octahedra. The corner-sharing octahedra tilt angles range from 3–4°. There are a spread of Sn–Te bond distances ranging from 3.03–3.36 Å. There are five inequivalent Bi2+ sites. In the first Bi2+ site, Bi2+ is bonded to six Te2- atoms to form BiTe6 octahedra that share corners with three equivalent BiTe6 octahedra, edges with four equivalent SnTe6 octahedra, and edges with five BiTe6 octahedra. The corner-sharing octahedral tilt angles are 2°. There are a spread of Bi–Te bond distances ranging from 3.05–3.35 Å. In the second Bi2+ site, Bi2+ is bonded in a 3-coordinate geometry to three Te2- atoms. There are a spread of Bi–Te bond distances ranging from 3.57–3.63 Å. In the third Bi2+ site, Bi2+ is bonded in a 3-coordinate geometry to three Te2- atoms. There are a spread of Bi–Te bond distances ranging from 3.59–3.65 Å. In the fourth Bi2+ site, Bi2+ is bonded to six Te2- atoms to form BiTe6 octahedra that share corners with three equivalent BiTe6 octahedra, edges with two equivalent SnTe6 octahedra, and edges with seven BiTe6 octahedra. The corner-sharing octahedral tilt angles are 2°. There are a spread of Bi–Te bond distances ranging from 3.10–3.26 Å. In the fifth Bi2+ site, Bi2+ is bonded to six Te2- atoms to form BiTe6 octahedra that share corners with three equivalent SnTe6 octahedra, an edgeedge with one SnTe6 octahedra, and edges with eight BiTe6 octahedra. The corner-sharing octahedra tilt angles range from 3–4°. There are a spread of Bi–Te bond distances ranging from 3.15–3.21 Å. There are six inequivalent Te2- sites. In the first Te2- site, Te2- is bonded to two equivalent Sn2+ and four Bi2+ atoms to form TeSn2Bi4 octahedra that share corners with three equivalent TeBi6 octahedra and edges with nine TeSn2Bi4 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the second Te2- site, Te2- is bonded to one Sn2+ and five Bi2+ atoms to form TeSnBi5 octahedra that share corners with three equivalent TeBi6 octahedra and edges with nine TeSn2Bi4 octahedra. The corner-sharing octahedra tilt angles range from 2–3°. In the third Te2- site, Te2- is bonded in a 6-coordinate geometry to one Sn2+ and two equivalent Bi2+ atoms. In the fourth Te2- site, Te2- is bonded in a 3-coordinate geometry to two equivalent Sn2+ and one Bi2+ atom. In the fifth Te2- site, Te2- is bonded to six Bi2+ atoms to form a mixture of distorted edge and corner-sharing TeBi6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the sixth Te2- site, Te2- is bonded to six Bi2+ atoms to form distorted TeBi6 octahedra that share corners with three equivalent TeSnBi5 octahedra and edges with nine TeSn2Bi4 octahedra. The corner-sharing octahedra tilt angles range from 2–3°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Nb4AlN3 by Materials Project

Nb4AlN3 is MAX Phase-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are two inequivalent Nb sites. In the first Nb site, Nb is bonded to six N atoms to form a mixture of distorted corner and edge-sharing NbN6 pentagonal pyramids. There are three shorter (2.21 Å) and three longer (2.24 Å) Nb–N bond lengths. In the second Nb site, Nb is bonded in a 3-coordinate geometry to three equivalent Al and three equivalent N atoms. All Nb–Al bond lengths are 2.83 Å. All Nb–N bond lengths are 2.23 Å. Al is bonded to six equivalent Nb and six equivalent Al atoms to form AlNb6Al6 cuboctahedra that share corners with six equivalent AlNb6Al6 cuboctahedra, corners with six equivalent NNb6 octahedra, edges with six equivalent AlNb6Al6 cuboctahedra, edges with six equivalent NNb6 octahedra, and faces with six equivalent AlNb6Al6 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. All Al–Al bond lengths are 3.01 Å. There are two inequivalent N sites. In the first N site, N is bonded to six equivalent Nb atoms to form a mixture of corner, edge, and face-sharing NNb6 octahedra. The corner-sharing octahedral tilt angles are 46°. In the second N site, N is bonded to six Nb atoms to form NNb6 octahedra that share corners with three equivalent AlNb6Al6 cuboctahedra, corners with six equivalent NNb6 octahedra, edges with three equivalent AlNb6Al6 cuboctahedra, edges with six equivalent NNb6 octahedra, and a faceface with one NNb6 octahedra. The corner-sharing octahedral tilt angles are 46°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ta4AlN3 by Materials Project

Ta4AlN3 is MAX Phase-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are two inequivalent Ta sites. In the first Ta site, Ta is bonded to six N atoms to form a mixture of distorted edge and corner-sharing TaN6 pentagonal pyramids. There are three shorter (2.21 Å) and three longer (2.23 Å) Ta–N bond lengths. In the second Ta site, Ta is bonded in a 3-coordinate geometry to three equivalent Al and three equivalent N atoms. All Ta–Al bond lengths are 2.81 Å. All Ta–N bond lengths are 2.23 Å. Al is bonded to six equivalent Ta and six equivalent Al atoms to form distorted AlTa6Al6 cuboctahedra that share corners with six equivalent AlTa6Al6 cuboctahedra, corners with six equivalent NTa6 octahedra, edges with six equivalent AlTa6Al6 cuboctahedra, edges with six equivalent NTa6 octahedra, and faces with six equivalent AlTa6Al6 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. All Al–Al bond lengths are 2.98 Å. There are two inequivalent N sites. In the first N site, N is bonded to six equivalent Ta atoms to form a mixture of edge, face, and corner-sharing NTa6 octahedra. The corner-sharing octahedral tilt angles are 46°. In the second N site, N is bonded to six Ta atoms to form NTa6 octahedra that share corners with three equivalent AlTa6Al6 cuboctahedra, corners with six equivalent NTa6 octahedra, edges with three equivalent AlTa6Al6 cuboctahedra, edges with six equivalent NTa6 octahedra, and a faceface with one NTa6 octahedra. The corner-sharing octahedral tilt angles are 46°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on LiSi by Materials Project

Si(Li) is Zintl Phase structured and crystallizes in the cubic Fd-3m space group. The structure is three-dimensional and consists of two Si(Li) frameworks. Li is bonded to four equivalent Si atoms to form distorted corner-sharing LiSi4 tetrahedra. All Li–Si bond lengths are 2.69 Å. Si is bonded to four equivalent Li atoms to form distorted corner-sharing SiLi4 tetrahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on TaS2N by Materials Project

TaNS2 is H-Phase-like structured and crystallizes in the hexagonal P6_3mc space group. The structure is three-dimensional. Ta5+ is bonded to six equivalent S2- atoms to form distorted TaS6 pentagonal pyramids that share corners with nine equivalent NS6 cuboctahedra, edges with three equivalent NS6 cuboctahedra, edges with six equivalent TaS6 pentagonal pyramids, and a faceface with one NS6 cuboctahedra. All Ta–S bond lengths are 2.49 Å. N1- is bonded to six equivalent S2- atoms to form distorted NS6 cuboctahedra that share corners with nine equivalent TaS6 pentagonal pyramids, edges with six equivalent NS6 cuboctahedra, edges with three equivalent TaS6 pentagonal pyramids, and a faceface with one TaS6 pentagonal pyramid. There are three shorter (3.44 Å) and three longer (3.45 Å) N–S bond lengths. S2- is bonded in a 3-coordinate geometry to three equivalent Ta5+ and three equivalent N1- atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on NbHSe2 by Materials Project

(NbSe2)2H2 is H-Phase structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is two-dimensional and consists of two hydrogen molecules and two NbSe2 sheets oriented in the (0, 0, 1) direction. In each NbSe2 sheet, Nb3+ is bonded to six equivalent Se2- atoms to form distorted edge-sharing NbSe6 pentagonal pyramids. All Nb–Se bond lengths are 2.62 Å. Se2- is bonded in a 3-coordinate geometry to three equivalent Nb3+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Mn10C3N by Materials Project

(Mn2C)2Mn6CN is H-Phase-like structured and crystallizes in the trigonal P3m1 space group. The structure is two-dimensional and consists of two Mn2C sheets oriented in the (0, 0, 1) direction and one Mn6CN sheet oriented in the (0, 0, 1) direction. In each Mn2C sheet, there are two inequivalent Mn sites. In the first Mn site, Mn is bonded in a distorted T-shaped geometry to three equivalent C atoms. All Mn–C bond lengths are 1.96 Å. In the second Mn site, Mn is bonded in a distorted T-shaped geometry to three equivalent C atoms. All Mn–C bond lengths are 1.96 Å. C is bonded to six Mn atoms to form edge-sharing CMn6 octahedra. In the Mn6CN sheet, there are six inequivalent Mn sites. In the first Mn site, Mn is bonded to twelve Mn atoms to form MnMn12 cuboctahedra that share corners with six equivalent MnMn12 cuboctahedra, corners with three equivalent CMn6 octahedra, edges with twelve MnMn12 cuboctahedra, edges with three equivalent CMn6 octahedra, and faces with twelve MnMn12 cuboctahedra. The corner-sharing octahedral tilt angles are 19°. There are a spread of Mn–Mn bond distances ranging from 2.70–2.81 Å. In the second Mn site, Mn is bonded in a distorted T-shaped geometry to three equivalent C atoms. All Mn–C bond lengths are 1.96 Å. In the third Mn site, Mn is bonded in a distorted T-shaped geometry to three equivalent Mn and three equivalent N atoms. All Mn–Mn bond lengths are 2.69 Å. All Mn–N bond lengths are 1.98 Å. In the fourth Mn site, Mn is bonded in a distorted T-shaped geometry to three equivalent Mn and three equivalent C atoms. All Mn–C bond lengths are 1.97 Å. In the fifth Mn site, Mn is bonded in a distorted T-shaped geometry to three equivalent N atoms. All Mn–N bond lengths are 1.96 Å. In the sixth Mn site, Mn is bonded to twelve Mn atoms to form MnMn12 cuboctahedra that share corners with six equivalent MnMn12 cuboctahedra, corners with three equivalent NMn6 octahedra, edges with twelve MnMn12 cuboctahedra, edges with three equivalent NMn6 octahedra, and faces with twelve MnMn12 cuboctahedra. The corner-sharing octahedral tilt angles are 18°. All Mn–Mn bond lengths are 2.81 Å. C is bonded to six Mn atoms to form CMn6 octahedra that share corners with three equivalent MnMn12 cuboctahedra, edges with three equivalent MnMn12 cuboctahedra, and edges with six equivalent CMn6 octahedra. N is bonded to six Mn atoms to form NMn6 octahedra that share corners with three equivalent MnMn12 cuboctahedra, edges with three equivalent MnMn12 cuboctahedra, and edges with six equivalent NMn6 octahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on AlV4N3 by Materials Project

V4AlN3 is MAX Phase-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are two inequivalent V sites. In the first V site, V is bonded to six N atoms to form a mixture of distorted edge and corner-sharing VN6 pentagonal pyramids. There are three shorter (2.06 Å) and three longer (2.07 Å) V–N bond lengths. In the second V site, V is bonded in a 3-coordinate geometry to three equivalent Al and three equivalent N atoms. All V–Al bond lengths are 2.68 Å. All V–N bond lengths are 2.03 Å. Al is bonded to six equivalent V and six equivalent Al atoms to form AlAl6V6 cuboctahedra that share corners with six equivalent AlAl6V6 cuboctahedra, corners with six equivalent NV6 octahedra, edges with six equivalent AlAl6V6 cuboctahedra, edges with six equivalent NV6 octahedra, and faces with six equivalent AlAl6V6 cuboctahedra. The corner-sharing octahedral tilt angles are 16°. All Al–Al bond lengths are 2.80 Å. There are two inequivalent N sites. In the first N site, N is bonded to six equivalent V atoms to form a mixture of edge, face, and corner-sharing NV6 octahedra. The corner-sharing octahedral tilt angles are 46°. In the second N site, N is bonded to six V atoms to form NV6 octahedra that share corners with three equivalent AlAl6V6 cuboctahedra, corners with six equivalent NV6 octahedra, edges with three equivalent AlAl6V6 cuboctahedra, edges with six equivalent NV6 octahedra, and a faceface with one NV6 octahedra. The corner-sharing octahedral tilt angles are 46°.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Macromolecular phasing using diffraction from multiple crystal forms

A phasing algorithm for macromolecular crystallography is proposed that utilizes diffraction data from multiple crystal forms – crystals of the same molecule with different unit-cell packings (different unit-cell parameters or space-group symmetries). The approach is based on the method of iterated projections, starting with no initial phase information. The practicality of the method is demonstrated by simulation using known structures that exist in multiple crystal forms, assuming some information on the molecular envelope and positional relationships between the molecules in the different unit cells. With incorporation of new or existing methods for determination of these parameters, the approach has potential as a method for ab initio phasing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

High-dimensional maximum-entropy phase space tomography using normalizing flows

Particle accelerators generate charged-particle beams with tailored distributions in six-dimensional position-momentum space (phase space). Knowledge of the phase space distribution enables model-based beam optimization and control. In the absence of direct measurements, the distribution must be tomographically reconstructed from its projections. In this paper, we highlight that such problems can be severely underdetermined and that entropy maximization is the most conservative solution strategy. We leverage —invertible generative models—to extend maximum-entropy tomography to six-dimensional phase space and perform numerical experiments to validate the model's performance. Our numerical experiments demonstrate consistency with exact two-dimensional maximum-entropy solutions and the ability to fit complicated six-dimensional distributions to large measurement sets in reasonable time. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗