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NASA Langley's Formal Methods Research in Support of the Next Generation Air Transportation System

This talk will provide a brief introduction to the formal methods developed at NASA Langley and the National Institute for Aerospace (NIA) for air traffic management applications. NASA Langley's formal methods research supports the Interagency Joint Planning and Development Office (JPDO) effort to define and develop the 2025 Next Generation Air Transportation System (NGATS). The JPDO was created by the passage of the Vision 100 Century of Aviation Reauthorization Act in Dec 2003. The NGATS vision calls for a major transformation of the nation s air transportation system that will enable growth to 3 times the traffic of the current system. The transformation will require an unprecedented level of safety-critical automation used in complex procedural operations based on 4-dimensional (4D) trajectories that enable dynamic reconfiguration of airspace scalable to geographic and temporal demand. The goal of our formal methods research is to provide verification methods that can be used to insure the safety of the NGATS system. Our work has focused on the safety assessment of concepts of operation and fundamental algorithms for conflict detection and resolution (CD&R) and self- spacing in the terminal area. Formal analysis of a concept of operations is a novel area of application of formal methods. Here one must establish that a system concept involving aircraft, pilots, and ground resources is safe. The formal analysis of algorithms is a more traditional endeavor. However, the formal analysis of ATM algorithms involves reasoning about the interaction of algorithmic logic and aircraft trajectories defined over an airspace. These trajectories are described using 2D and 3D vectors and are often constrained by trigonometric relations. Thus, in many cases it has been necessary to unload the full power of an advanced theorem prover. The verification challenge is to establish that the safety-critical algorithms produce valid solutions that are guaranteed to maintain separation under all possible scenarios. Current research has assumed perfect knowledge of the location of other aircraft in the vicinity so absolute guarantees are possible, but increasingly we are relaxing the assumptions to allow incomplete, inaccurate, and/or faulty information from communication sources.

Butler, Ricky W.↗

Materials Data on MnCd2TeO6 by Materials Project

MnCd2TeO6 is Ilmenite-derived structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are two inequivalent Mn2+ sites. In the first Mn2+ site, Mn2+ is bonded to six O2- atoms to form distorted MnO6 pentagonal pyramids that share corners with two TeO6 octahedra, edges with two TeO6 octahedra, and edges with two equivalent CdO6 pentagonal pyramids. The corner-sharing octahedra tilt angles range from 31–39°. There are a spread of Mn–O bond distances ranging from 2.16–2.42 Å. In the second Mn2+ site, Mn2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Mn–O bond distances ranging from 2.16–2.52 Å. There are four inequivalent Cd2+ sites. In the first Cd2+ site, Cd2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Cd–O bond distances ranging from 2.25–2.55 Å. In the second Cd2+ site, Cd2+ is bonded to six O2- atoms to form distorted CdO6 pentagonal pyramids that share corners with two TeO6 octahedra, edges with two TeO6 octahedra, and edges with two equivalent MnO6 pentagonal pyramids. The corner-sharing octahedra tilt angles range from 36–41°. There are a spread of Cd–O bond distances ranging from 2.26–2.48 Å. In the third Cd2+ site, Cd2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Cd–O bond distances ranging from 2.25–2.51 Å. In the fourth Cd2+ site, Cd2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Cd–O bond distances ranging from 2.27–2.50 Å. There are two inequivalent Te6+ sites. In the first Te6+ site, Te6+ is bonded to six O2- atoms to form TeO6 octahedra that share a cornercorner with one MnO6 pentagonal pyramid, a cornercorner with one CdO6 pentagonal pyramid, an edgeedge with one MnO6 pentagonal pyramid, and an edgeedge with one CdO6 pentagonal pyramid. There is five shorter (1.97 Å) and one longer (1.98 Å) Te–O bond length. In the second Te6+ site, Te6+ is bonded to six O2- atoms to form TeO6 octahedra that share a cornercorner with one MnO6 pentagonal pyramid, a cornercorner with one CdO6 pentagonal pyramid, an edgeedge with one MnO6 pentagonal pyramid, and an edgeedge with one CdO6 pentagonal pyramid. There is two shorter (1.96 Å) and four longer (1.97 Å) Te–O bond length. There are twelve inequivalent O2- sites. In the first O2- site, O2- is bonded to two Mn2+, one Cd2+, and one Te6+ atom to form distorted OMn2CdTe tetrahedra that share corners with five OMnCd2Te tetrahedra, corners with five OMn2CdTe trigonal pyramids, edges with three OMnCd2Te tetrahedra, and an edgeedge with one OMnCd2Te trigonal pyramid. In the second O2- site, O2- is bonded to one Mn2+, two Cd2+, and one Te6+ atom to form distorted OMnCd2Te tetrahedra that share corners with five OMnCd2Te tetrahedra, corners with seven OMn2CdTe trigonal pyramids, and edges with three OMn2CdTe tetrahedra. In the third O2- site, O2- is bonded to one Mn2+, two Cd2+, and one Te6+ atom to form distorted OMnCd2Te tetrahedra that share corners with five OMnCd2Te tetrahedra, corners with seven OMn2CdTe trigonal pyramids, edges with three OMn2CdTe tetrahedra, and an edgeedge with one OCd3Te trigonal pyramid. In the fourth O2- site, O2- is bonded to one Mn2+, two Cd2+, and one Te6+ atom to form distorted OMnCd2Te tetrahedra that share corners with five OMn2CdTe tetrahedra, corners with five OMnCd2Te trigonal pyramids, edges with three OMn2CdTe tetrahedra, and an edgeedge with one OMn2CdTe trigonal pyramid. In the fifth O2- site, O2- is bonded to three Cd2+ and one Te6+ atom to form distorted OCd3Te tetrahedra that share corners with five OMn2CdTe tetrahedra, corners with five OMnCd2Te trigonal pyramids, edges with three OMnCd2Te tetrahedra, and an edgeedge with one OMnCd2Te trigonal pyramid. In the sixth O2- site, O2- is bonded to one Mn2+, two Cd2+, and one Te6+ atom to form distorted OMnCd2Te tetrahedra that share corners with five OMn2CdTe tetrahedra, corners with six OMn2CdTe trigonal pyramids, edges with three OMnCd2Te tetrahedra, and an edgeedge with one OMnCd2Te trigonal pyramid. In the seventh O2- site, O2- is bonded to two Mn2+, one Cd2+, and one Te6+ atom to form distorted OMn2CdTe trigonal pyramids that share corners with seven OMn2CdTe tetrahedra, corners with five OMnCd2Te trigonal pyramids, an edgeedge with one OMnCd2Te tetrahedra, and edges with two OMnCd2Te trigonal pyramids. In the eighth O2- site, O2- is bonded to one Mn2+, two Cd2+, and one Te6+ atom to form distorted OMnCd2Te trigonal pyramids that share corners with seven OMn2CdTe tetrahedra, corners with four OMn2CdTe trigonal pyramids, an edgeedge with one OCd3Te tetrahedra, and edges with two OMnCd2Te trigonal pyramids. In the ninth O2- site, O2- is bonded to one Mn2+, two Cd2+, and one Te6+ atom to form distorted OMnCd2Te trigonal pyramids that share corners with seven OMn2CdTe tetrahedra, corners with five OMn2CdTe trigonal pyramids, an edgeedge with one OMnCd2Te tetrahedra, and edges with two OMnCd2Te trigonal pyramids. In the tenth O2- site, O2- is bonded to one Mn2+, two Cd2+, and one Te6+ atom to form distorted OMnCd2Te trigonal pyramids that share corners with seven OMnCd2Te tetrahedra, corners with three OMn2CdTe trigonal pyramids, an edgeedge with one OMn2CdTe tetrahedra, and edges with three OMnCd2Te trigonal pyramids. In the eleventh O2- site, O2- is bonded in a 4-coordinate geometry to one Mn2+, two Cd2+, and one Te6+ atom. In the twelfth O2- site, O2- is bonded to three Cd2+ and one Te6+ atom to form a mixture of distorted corner and edge-sharing OCd3Te trigonal pyramids.

36 MATERIALS SCIENCE↗

Materials Data on Na2CdH4(SO5)2 by Materials Project

Na2CdH4(SO5)2 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. Na1+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Na–O bond distances ranging from 2.36–2.90 Å. Cd2+ is bonded to six O2- atoms to form CdO6 octahedra that share corners with four equivalent SO4 tetrahedra. There are a spread of Cd–O bond distances ranging from 2.28–2.36 Å. There are two inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 1.00 Å. In the second H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 1.00 Å. S6+ is bonded to four O2- atoms to form SO4 tetrahedra that share corners with two equivalent CdO6 octahedra. The corner-sharing octahedra tilt angles range from 45–55°. There are a spread of S–O bond distances ranging from 1.48–1.51 Å. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted water-like geometry to one Na1+, one Cd2+, and two H1+ atoms. In the second O2- site, O2- is bonded in a distorted single-bond geometry to one Na1+ and one S6+ atom. In the third O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Na1+, one Cd2+, and one S6+ atom. In the fourth O2- site, O2- is bonded in a 1-coordinate geometry to two equivalent Na1+, one Cd2+, and one S6+ atom. In the fifth O2- site, O2- is bonded in a distorted single-bond geometry to two equivalent Na1+ and one S6+ atom.

36 MATERIALS SCIENCE↗

Materials Data on Cd3H2CSeO8 by Materials Project

Cd3CH2SeO8 crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. there are two inequivalent Cd2+ sites. In the first Cd2+ site, Cd2+ is bonded to six O2- atoms to form a mixture of distorted edge and corner-sharing CdO6 octahedra. The corner-sharing octahedra tilt angles range from 45–68°. There are a spread of Cd–O bond distances ranging from 2.25–2.46 Å. In the second Cd2+ site, Cd2+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Cd–O bond distances ranging from 2.33–2.69 Å. C4+ is bonded in a trigonal planar geometry to three O2- atoms. There is two shorter (1.30 Å) and one longer (1.31 Å) C–O bond length. H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. Se4+ is bonded in a trigonal non-coplanar geometry to three O2- atoms. There is one shorter (1.72 Å) and two longer (1.74 Å) Se–O bond length. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to three Cd2+ and one Se4+ atom. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to two equivalent Cd2+ and one C4+ atom. In the third O2- site, O2- is bonded in a distorted single-bond geometry to three Cd2+ and one H1+ atom. In the fourth O2- site, O2- is bonded in a distorted single-bond geometry to two Cd2+ and one C4+ atom. In the fifth O2- site, O2- is bonded in a distorted trigonal planar geometry to two equivalent Cd2+ and one Se4+ atom.

36 MATERIALS SCIENCE↗

Materials Data on Na2CdH4(SeO5)2 by Materials Project

Na2CdH4(SeO5)2 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. Na1+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Na–O bond distances ranging from 2.42–2.75 Å. Cd2+ is bonded to six O2- atoms to form CdO6 octahedra that share corners with four equivalent SeO4 tetrahedra. There are four shorter (2.31 Å) and two longer (2.39 Å) Cd–O bond lengths. There are two inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to two O2- atoms. There is one shorter (1.00 Å) and one longer (1.69 Å) H–O bond length. In the second H1+ site, H1+ is bonded in a single-bond geometry to two O2- atoms. There is one shorter (1.00 Å) and one longer (1.76 Å) H–O bond length. Se6+ is bonded to four O2- atoms to form SeO4 tetrahedra that share corners with two equivalent CdO6 octahedra. The corner-sharing octahedra tilt angles range from 47–55°. There are a spread of Se–O bond distances ranging from 1.66–1.69 Å. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted water-like geometry to one Na1+, one Cd2+, and two H1+ atoms. In the second O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one H1+, and one Se6+ atom. In the third O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Na1+, one Cd2+, and one Se6+ atom. In the fourth O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Cd2+, and one Se6+ atom. In the fifth O2- site, O2- is bonded in a 1-coordinate geometry to two equivalent Na1+, one H1+, and one Se6+ atom.

36 MATERIALS SCIENCE↗

Materials Data on Mn3Cd3(TeO6)2 by Materials Project

Mn3Cd3(TeO6)2 is Ilmenite-derived structured and crystallizes in the trigonal R3 space group. The structure is three-dimensional. Mn2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Mn–O bond distances ranging from 2.14–2.53 Å. Cd2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Cd–O bond distances ranging from 2.26–2.52 Å. There are two inequivalent Te6+ sites. In the first Te6+ site, Te6+ is bonded in an octahedral geometry to six O2- atoms. There is three shorter (1.96 Å) and three longer (1.97 Å) Te–O bond length. In the second Te6+ site, Te6+ is bonded in an octahedral geometry to six O2- atoms. There is three shorter (1.96 Å) and three longer (1.97 Å) Te–O bond length. There are four inequivalent O2- sites. In the first O2- site, O2- is bonded to one Mn2+, two equivalent Cd2+, and one Te6+ atom to form distorted OMnCd2Te tetrahedra that share corners with five equivalent OMn2CdTe tetrahedra, corners with two equivalent OMn2CdTe trigonal pyramids, edges with three OMnCd2Te tetrahedra, and an edgeedge with one OMn2CdTe trigonal pyramid. In the second O2- site, O2- is bonded to two equivalent Mn2+, one Cd2+, and one Te6+ atom to form distorted OMn2CdTe trigonal pyramids that share corners with seven OMnCd2Te tetrahedra, corners with four equivalent OMn2CdTe trigonal pyramids, and an edgeedge with one OMnCd2Te tetrahedra. In the third O2- site, O2- is bonded in a 4-coordinate geometry to one Mn2+, two equivalent Cd2+, and one Te6+ atom. In the fourth O2- site, O2- is bonded to two equivalent Mn2+, one Cd2+, and one Te6+ atom to form distorted OMn2CdTe tetrahedra that share corners with five equivalent OMnCd2Te tetrahedra, corners with five equivalent OMn2CdTe trigonal pyramids, and edges with three OMnCd2Te tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on CdTeO3 by Materials Project

CdTeO3 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. there are two inequivalent Cd2+ sites. In the first Cd2+ site, Cd2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Cd–O bond distances ranging from 2.23–2.55 Å. In the second Cd2+ site, Cd2+ is bonded to six O2- atoms to form distorted corner-sharing CdO6 octahedra. The corner-sharing octahedral tilt angles are 72°. There are a spread of Cd–O bond distances ranging from 2.32–2.42 Å. There are two inequivalent Te4+ sites. In the first Te4+ site, Te4+ is bonded in a 3-coordinate geometry to four O2- atoms. There are a spread of Te–O bond distances ranging from 1.90–2.81 Å. In the second Te4+ site, Te4+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Te–O bond distances ranging from 1.91–2.78 Å. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to two Cd2+ and two equivalent Te4+ atoms. In the second O2- site, O2- is bonded in a 1-coordinate geometry to one Cd2+ and two Te4+ atoms. In the third O2- site, O2- is bonded in a 3-coordinate geometry to two Cd2+ and one Te4+ atom. In the fourth O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent Cd2+ and two equivalent Te4+ atoms. In the fifth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to two Cd2+ and one Te4+ atom. In the sixth O2- site, O2- is bonded to three Cd2+ and one Te4+ atom to form distorted corner-sharing OCd3Te tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on Cd3Pb2Se4(IO6)2 by Materials Project

Cd3Pb2Se4(O6I)2 crystallizes in the monoclinic P2/c space group. The structure is three-dimensional. there are two inequivalent Cd2+ sites. In the first Cd2+ site, Cd2+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Cd–O bond distances ranging from 2.30–2.71 Å. In the second Cd2+ site, Cd2+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Cd–O bond distances ranging from 2.30–2.86 Å. Pb2+ is bonded in a 7-coordinate geometry to four O2- and three equivalent I1- atoms. There are a spread of Pb–O bond distances ranging from 2.46–2.64 Å. There are a spread of Pb–I bond distances ranging from 3.47–3.54 Å. There are two inequivalent Se4+ sites. In the first Se4+ site, Se4+ is bonded in a distorted trigonal non-coplanar geometry to three O2- atoms. There are a spread of Se–O bond distances ranging from 1.72–1.76 Å. In the second Se4+ site, Se4+ is bonded in a trigonal non-coplanar geometry to three O2- atoms. There are a spread of Se–O bond distances ranging from 1.70–1.79 Å. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded to two Cd2+, one Pb2+, and one Se4+ atom to form distorted corner-sharing OCd2PbSe tetrahedra. In the second O2- site, O2- is bonded in a 4-coordinate geometry to two Cd2+, one Pb2+, one Se4+, and one I1- atom. The O–I bond length is 3.79 Å. In the third O2- site, O2- is bonded in a 2-coordinate geometry to two Cd2+ and one Se4+ atom. In the fourth O2- site, O2- is bonded in a 3-coordinate geometry to two Cd2+ and one Se4+ atom. In the fifth O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Cd2+, one Pb2+, one Se4+, and one I1- atom. The O–I bond length is 3.78 Å. In the sixth O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent Cd2+, one Pb2+, and one Se4+ atom. I1- is bonded in a 3-coordinate geometry to three equivalent Pb2+ and two O2- atoms.

36 MATERIALS SCIENCE↗

Materials Data on TlV3CdCu4O13 by Materials Project

V3Cu4CdTlO13 crystallizes in the monoclinic P2_1/m space group. The structure is three-dimensional. there are three inequivalent V5+ sites. In the first V5+ site, V5+ is bonded to four O2- atoms to form VO4 tetrahedra that share corners with three equivalent CdO6 octahedra and corners with four equivalent CuO6 octahedra. The corner-sharing octahedra tilt angles range from 49–76°. There are a spread of V–O bond distances ranging from 1.69–1.94 Å. In the second V5+ site, V5+ is bonded to four O2- atoms to form VO4 tetrahedra that share a cornercorner with one CdO6 octahedra, corners with two equivalent CuO6 octahedra, and corners with four CuO5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 51°. There are a spread of V–O bond distances ranging from 1.70–1.78 Å. In the third V5+ site, V5+ is bonded to four O2- atoms to form VO4 tetrahedra that share corners with two equivalent CdO6 octahedra, corners with four equivalent CuO6 octahedra, and corners with four CuO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 36–66°. There are a spread of V–O bond distances ranging from 1.70–1.82 Å. There are three inequivalent Cu2+ sites. In the first Cu2+ site, Cu2+ is bonded to six O2- atoms to form distorted CuO6 octahedra that share corners with five VO4 tetrahedra, a cornercorner with one CuO5 trigonal bipyramid, an edgeedge with one CdO6 octahedra, edges with two equivalent CuO6 octahedra, and edges with two CuO5 trigonal bipyramids. There are a spread of Cu–O bond distances ranging from 1.94–2.62 Å. In the second Cu2+ site, Cu2+ is bonded to five O2- atoms to form CuO5 trigonal bipyramids that share corners with two equivalent CuO6 octahedra, corners with four VO4 tetrahedra, an edgeedge with one CdO6 octahedra, edges with two equivalent CuO6 octahedra, and an edgeedge with one CuO5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 60°. There are a spread of Cu–O bond distances ranging from 1.95–2.24 Å. In the third Cu2+ site, Cu2+ is bonded to five O2- atoms to form distorted CuO5 trigonal bipyramids that share corners with four VO4 tetrahedra, edges with two equivalent CuO6 octahedra, and an edgeedge with one CuO5 trigonal bipyramid. There are a spread of Cu–O bond distances ranging from 1.92–2.07 Å. Cd2+ is bonded to six O2- atoms to form distorted CdO6 octahedra that share corners with six VO4 tetrahedra, edges with two equivalent CuO6 octahedra, and an edgeedge with one CuO5 trigonal bipyramid. There are a spread of Cd–O bond distances ranging from 2.24–2.51 Å. Tl1+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Tl–O bond distances ranging from 2.82–3.28 Å. There are ten inequivalent O2- sites. In the first O2- site, O2- is bonded to one V5+, two equivalent Cu2+, and one Cd2+ atom to form distorted corner-sharing OVCdCu2 trigonal pyramids. In the second O2- site, O2- is bonded in a 1-coordinate geometry to one V5+, one Cd2+, and two equivalent Tl1+ atoms. In the third O2- site, O2- is bonded in a 2-coordinate geometry to one V5+, one Cd2+, and three equivalent Tl1+ atoms. In the fourth O2- site, O2- is bonded in a 3-coordinate geometry to one V5+, two Cu2+, and one Tl1+ atom. In the fifth O2- site, O2- is bonded in a distorted linear geometry to one V5+, one Cu2+, and one Tl1+ atom. In the sixth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one V5+ and three Cu2+ atoms. In the seventh O2- site, O2- is bonded in a 3-coordinate geometry to one V5+ and two Cu2+ atoms. In the eighth O2- site, O2- is bonded in a 4-coordinate geometry to one V5+, two Cu2+, and one Cd2+ atom. In the ninth O2- site, O2- is bonded to four Cu2+ atoms to form corner-sharing OCu4 trigonal pyramids. In the tenth O2- site, O2- is bonded in a distorted single-bond geometry to one V5+ and two equivalent Cu2+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on K2CdSiO4 by Materials Project

K2CdSiO4 crystallizes in the orthorhombic Pca2_1 space group. The structure is three-dimensional. there are four inequivalent K1+ sites. In the first K1+ site, K1+ is bonded to five O2- atoms to form distorted KO5 square pyramids that share corners with three CdO4 tetrahedra, corners with five SiO4 tetrahedra, and an edgeedge with one CdO4 tetrahedra. There are a spread of K–O bond distances ranging from 2.64–3.04 Å. In the second K1+ site, K1+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of K–O bond distances ranging from 2.69–3.15 Å. In the third K1+ site, K1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of K–O bond distances ranging from 2.63–2.91 Å. In the fourth K1+ site, K1+ is bonded in a 4-coordinate geometry to eight O2- atoms. There are a spread of K–O bond distances ranging from 2.75–3.41 Å. There are two inequivalent Cd2+ sites. In the first Cd2+ site, Cd2+ is bonded to four O2- atoms to form CdO4 tetrahedra that share corners with two equivalent KO5 square pyramids and corners with four SiO4 tetrahedra. There are a spread of Cd–O bond distances ranging from 2.19–2.21 Å. In the second Cd2+ site, Cd2+ is bonded to four O2- atoms to form CdO4 tetrahedra that share a cornercorner with one KO5 square pyramid, corners with four SiO4 tetrahedra, and an edgeedge with one KO5 square pyramid. There are a spread of Cd–O bond distances ranging from 2.18–2.22 Å. There are two inequivalent Si4+ sites. In the first Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two equivalent KO5 square pyramids and corners with four CdO4 tetrahedra. There is three shorter (1.66 Å) and one longer (1.67 Å) Si–O bond length. In the second Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with three equivalent KO5 square pyramids and corners with four CdO4 tetrahedra. There is three shorter (1.66 Å) and one longer (1.67 Å) Si–O bond length. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a 1-coordinate geometry to three K1+, one Cd2+, and one Si4+ atom. In the second O2- site, O2- is bonded in a 1-coordinate geometry to three K1+, one Cd2+, and one Si4+ atom. In the third O2- site, O2- is bonded in a 1-coordinate geometry to three K1+, one Cd2+, and one Si4+ atom. In the fourth O2- site, O2- is bonded in a 1-coordinate geometry to three K1+, one Cd2+, and one Si4+ atom. In the fifth O2- site, O2- is bonded in a 1-coordinate geometry to three K1+, one Cd2+, and one Si4+ atom. In the sixth O2- site, O2- is bonded in a 1-coordinate geometry to three K1+, one Cd2+, and one Si4+ atom. In the seventh O2- site, O2- is bonded in a 1-coordinate geometry to three K1+, one Cd2+, and one Si4+ atom. In the eighth O2- site, O2- is bonded in a 1-coordinate geometry to three K1+, one Cd2+, and one Si4+ atom.

36 MATERIALS SCIENCE↗

Evaluation of Lunar Dark Mantle Deposits as Key to Future Human Missions

I proposed to continue detailed mapping, analysis and assessment of the lunar pyroclastic dark mantle deposits in support of the Human Exploration and Development of Space (HEDS) initiative. Specifically: (1) I continued gathering data via the Internet and mailable media, and a variety of other digital lunar images including; high resolution digital images of the new Apollo masters from JSC, images from Clementine and Galileo, and recent telescopic images from Hawaii; (2) continued analyses on these images using sophisticated hardware and software at JSC and the College of Charleston to determine and map composition using returned sample data for calibration; (3) worked closely with Dr. David McKay and others at JSC to relate sample data to image data using laboratory spectra from JSC and Brown University; (4) mapped the extent, thickness, and composition of important dark mantle deposits in selected study areas; and (5) began composing a geographically referenced database of lunar pyroclastic materials in the Apollo 17 area. The results have been used to identify and evaluate several candidate landing sites in dark mantle terrains. Additional work spawned from this effort includes the development of an educational CD-Rom on exploring the Moon: Contact Light. Throughout the whole process I have been in contact with the JSC HEDS personnel.

Coombs, Cassandra↗

Materials Data on CdH18Se4(N2O7)2 by Materials Project

CdH2(Se2O7)2(NH4)4 crystallizes in the triclinic P-1 space group. The structure is two-dimensional and consists of four ammonium molecules and one CdH2(Se2O7)2 sheet oriented in the (0, 0, 1) direction. In the CdH2(Se2O7)2 sheet, Cd2+ is bonded to six O2- atoms to form CdO6 octahedra that share corners with two equivalent SeO4 tetrahedra. There are a spread of Cd–O bond distances ranging from 2.33–2.36 Å. H1+ is bonded in a linear geometry to two O2- atoms. There is one shorter (1.03 Å) and one longer (1.53 Å) H–O bond length. There are two inequivalent Se2- sites. In the first Se2- site, Se2- is bonded in a trigonal non-coplanar geometry to three O2- atoms. There are a spread of Se–O bond distances ranging from 1.71–1.78 Å. In the second Se2- site, Se2- is bonded to four O2- atoms to form SeO4 tetrahedra that share a cornercorner with one CdO6 octahedra. The corner-sharing octahedral tilt angles are 50°. There are a spread of Se–O bond distances ranging from 1.66–1.69 Å. There are seven inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Cd2+ and one Se2- atom. In the second O2- site, O2- is bonded in a bent 120 degrees geometry to one Cd2+ and one Se2- atom. In the third O2- site, O2- is bonded in a bent 120 degrees geometry to one Cd2+ and one Se2- atom. In the fourth O2- site, O2- is bonded in a distorted water-like geometry to one H1+ and one Se2- atom. In the fifth O2- site, O2- is bonded in a single-bond geometry to one Se2- atom. In the sixth O2- site, O2- is bonded in a bent 120 degrees geometry to one H1+ and one Se2- atom. In the seventh O2- site, O2- is bonded in a single-bond geometry to one Se2- atom.

36 MATERIALS SCIENCE↗

Materials Data on Ca2Cd3(Cl5O9)2 by Materials Project

Ca2Cd3(OCl)10(O2)4 crystallizes in the triclinic P-1 space group. The structure is three-dimensional and consists of four hydrogen peroxide molecules and one Ca2Cd3(OCl)10 framework. In the Ca2Cd3(OCl)10 framework, Ca is bonded in a 5-coordinate geometry to five O atoms. There are a spread of Ca–O bond distances ranging from 2.19–2.50 Å. There are two inequivalent Cd sites. In the first Cd site, Cd is bonded in a square co-planar geometry to four Cl atoms. There are two shorter (2.46 Å) and two longer (2.72 Å) Cd–Cl bond lengths. In the second Cd site, Cd is bonded to six Cl atoms to form edge-sharing CdCl6 octahedra. There are a spread of Cd–Cl bond distances ranging from 2.59–2.79 Å. There are five inequivalent O sites. In the first O site, O is bonded in a bent 150 degrees geometry to one Ca and one O atom. The O–O bond length is 1.24 Å. In the second O site, O is bonded in a bent 150 degrees geometry to one Ca and one Cl atom. The O–Cl bond length is 1.62 Å. In the third O site, O is bonded in a trigonal planar geometry to two equivalent Ca and one Cl atom. The O–Cl bond length is 1.66 Å. In the fourth O site, O is bonded in a bent 120 degrees geometry to one Ca and one Cl atom. The O–Cl bond length is 1.64 Å. In the fifth O site, O is bonded in a distorted water-like geometry to two O atoms. The O–O bond length is 1.97 Å. There are five inequivalent Cl sites. In the first Cl site, Cl is bonded in a water-like geometry to one Cd and one O atom. In the second Cl site, Cl is bonded in a bent 120 degrees geometry to one Cd and one O atom. In the third Cl site, Cl is bonded in a distorted T-shaped geometry to three Cd atoms. In the fourth Cl site, Cl is bonded in a water-like geometry to two Cd atoms. In the fifth Cl site, Cl is bonded in a water-like geometry to one Cd and one O atom.

36 MATERIALS SCIENCE↗

Materials Data on Cd5Ge(PO6)2 by Materials Project

Cd5Ge(PO6)2 crystallizes in the orthorhombic P2_12_12_1 space group. The structure is three-dimensional. there are five inequivalent Cd2+ sites. In the first Cd2+ site, Cd2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Cd–O bond distances ranging from 2.26–2.50 Å. In the second Cd2+ site, Cd2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Cd–O bond distances ranging from 2.23–2.65 Å. In the third Cd2+ site, Cd2+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Cd–O bond distances ranging from 2.26–2.84 Å. In the fourth Cd2+ site, Cd2+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Cd–O bond distances ranging from 2.28–2.86 Å. In the fifth Cd2+ site, Cd2+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Cd–O bond distances ranging from 2.21–2.92 Å. Ge4+ is bonded in a tetrahedral geometry to four O2- atoms. There are a spread of Ge–O bond distances ranging from 1.76–1.80 Å. There are two inequivalent P5+ sites. In the first P5+ site, P5+ is bonded in a tetrahedral geometry to four O2- atoms. There is one shorter (1.55 Å) and three longer (1.56 Å) P–O bond length. In the second P5+ site, P5+ is bonded in a tetrahedral geometry to four O2- atoms. There are a spread of P–O bond distances ranging from 1.55–1.58 Å. There are twelve inequivalent O2- sites. In the first O2- site, O2- is bonded to three Cd2+ and one Ge4+ atom to form distorted corner-sharing OCd3Ge tetrahedra. In the second O2- site, O2- is bonded in a 1-coordinate geometry to two Cd2+ and one P5+ atom. In the third O2- site, O2- is bonded in a 1-coordinate geometry to three Cd2+ and one P5+ atom. In the fourth O2- site, O2- is bonded in a distorted single-bond geometry to three Cd2+ and one P5+ atom. In the fifth O2- site, O2- is bonded to three Cd2+ and one Ge4+ atom to form distorted corner-sharing OCd3Ge tetrahedra. In the sixth O2- site, O2- is bonded in a 3-coordinate geometry to three Cd2+ and one Ge4+ atom. In the seventh O2- site, O2- is bonded in a 1-coordinate geometry to three Cd2+ and one P5+ atom. In the eighth O2- site, O2- is bonded in a 1-coordinate geometry to two Cd2+ and one P5+ atom. In the ninth O2- site, O2- is bonded in a 1-coordinate geometry to three Cd2+ and one P5+ atom. In the tenth O2- site, O2- is bonded in a 4-coordinate geometry to three Cd2+ and one Ge4+ atom. In the eleventh O2- site, O2- is bonded in a 1-coordinate geometry to three Cd2+ and one P5+ atom. In the twelfth O2- site, O2- is bonded in a 3-coordinate geometry to two Cd2+ and one P5+ atom.

36 MATERIALS SCIENCE↗

Materials Data on Rb2CdP2O7 by Materials Project

Rb2CdP2O7 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. there are two inequivalent Rb1+ sites. In the first Rb1+ site, Rb1+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Rb–O bond distances ranging from 2.93–3.28 Å. In the second Rb1+ site, Rb1+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Rb–O bond distances ranging from 2.77–3.38 Å. Cd2+ is bonded to five O2- atoms to form CdO5 trigonal bipyramids that share corners with five PO4 tetrahedra. There are a spread of Cd–O bond distances ranging from 2.21–2.33 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 a cornercorner with one PO4 tetrahedra and corners with three equivalent CdO5 trigonal bipyramids. There are a spread of P–O bond distances ranging from 1.53–1.64 Å. In the second P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one PO4 tetrahedra and corners with two equivalent CdO5 trigonal bipyramids. There are a spread of P–O bond distances ranging from 1.52–1.68 Å. There are seven inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two equivalent Rb1+ and two P5+ atoms. In the second O2- site, O2- is bonded in a 1-coordinate geometry to two Rb1+, one Cd2+, and one P5+ atom. In the third O2- site, O2- is bonded in a 1-coordinate geometry to two equivalent Rb1+, one Cd2+, and one P5+ atom. In the fourth O2- site, O2- is bonded in a distorted single-bond geometry to three Rb1+ and one P5+ atom. In the fifth O2- site, O2- is bonded in a 4-coordinate geometry to two Rb1+, one Cd2+, and one P5+ atom. In the sixth O2- site, O2- is bonded in a 1-coordinate geometry to two equivalent Rb1+, one Cd2+, and one P5+ atom. In the seventh O2- site, O2- is bonded in a 1-coordinate geometry to two Rb1+, one Cd2+, and one P5+ atom.

36 MATERIALS SCIENCE↗

Materials Data on SrCdAs2O7 by Materials Project

SrCdAs2O7 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.55–3.21 Å. Cd2+ is bonded to six O2- atoms to form distorted CdO6 octahedra that share corners with six AsO4 tetrahedra and an edgeedge with one CdO6 octahedra. There are a spread of Cd–O bond distances ranging from 2.27–2.51 Å. There are two inequivalent As5+ sites. In the first As5+ site, As5+ is bonded to four O2- atoms to form AsO4 tetrahedra that share corners with two equivalent CdO6 octahedra and a cornercorner with one AsO4 tetrahedra. The corner-sharing octahedra tilt angles range from 61–63°. There are a spread of As–O bond distances ranging from 1.69–1.80 Å. In the second As5+ site, As5+ is bonded to four O2- atoms to form AsO4 tetrahedra that share corners with four equivalent CdO6 octahedra and a cornercorner with one AsO4 tetrahedra. The corner-sharing octahedra tilt angles range from 56–63°. There are a spread of As–O bond distances ranging from 1.69–1.80 Å. There are seven inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal planar geometry to one Sr2+, one Cd2+, and one As5+ atom. In the second O2- site, O2- is bonded in a 1-coordinate geometry to three equivalent Sr2+ and one As5+ atom. In the third O2- site, O2- is bonded in a bent 120 degrees geometry to two As5+ atoms. In the fourth O2- site, O2- is bonded in a 1-coordinate geometry to two equivalent Sr2+, one Cd2+, and one As5+ atom. In the fifth O2- site, O2- is bonded in a 4-coordinate geometry to one Sr2+, two equivalent Cd2+, and one As5+ atom. In the sixth O2- site, O2- is bonded in a 1-coordinate geometry to one Sr2+, one Cd2+, and one As5+ atom. In the seventh O2- site, O2- is bonded in a 3-coordinate geometry to one Sr2+, one Cd2+, and one As5+ atom.

36 MATERIALS SCIENCE↗

Materials Data on KCdC3(NO)3 by Materials Project

KCdC3(NO)3 crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. K1+ is bonded in a 7-coordinate geometry to three N3- and five O2- atoms. There are two shorter (2.89 Å) and one longer (3.33 Å) K–N bond lengths. There are a spread of K–O bond distances ranging from 2.78–2.99 Å. Cd2+ is bonded to six N3- atoms to form edge-sharing CdN6 octahedra. There are a spread of Cd–N bond distances ranging from 2.27–2.54 Å. There are three inequivalent C4+ sites. In the first C4+ site, C4+ is bonded in a linear geometry to one N3- and one O2- atom. The C–N bond length is 1.22 Å. The C–O bond length is 1.20 Å. In the second C4+ site, C4+ is bonded in a linear geometry to one N3- and one O2- atom. The C–N bond length is 1.21 Å. The C–O bond length is 1.21 Å. In the third C4+ site, C4+ is bonded in a linear geometry to one N3- and one O2- atom. The C–N bond length is 1.21 Å. The C–O bond length is 1.21 Å. There are three inequivalent N3- sites. In the first N3- site, N3- is bonded in a 4-coordinate geometry to two equivalent K1+, one Cd2+, and one C4+ atom. In the second N3- site, N3- is bonded in a 3-coordinate geometry to one K1+, two equivalent Cd2+, and one C4+ atom. In the third N3- site, N3- is bonded in a 4-coordinate geometry to three equivalent Cd2+ and one C4+ atom. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted single-bond geometry to two equivalent K1+ and one C4+ atom. In the second O2- site, O2- is bonded in a distorted single-bond geometry to two equivalent K1+ and one C4+ atom. In the third O2- site, O2- is bonded in a distorted single-bond geometry to one K1+ and one C4+ atom.

36 MATERIALS SCIENCE↗

Unexplained Fe, Ni and S anomalies in CV chondrite components

Large negative anomalies in Fe, Co, Ni, S and Se are present in Allende Type B Ca-Al-rich inclusions (CAI's). Based on compilations of all the known published analyses, Allende chondrules, aggregates and other types of CAI's also display anomalies. These observations show that: (1) since Fe, Co, Ni, S and Se are more depleted than elements bracketing them in volatility (such as Pt and Au, and Su and Cd), the anomalies were not produced during the volatility dependent, high temperature CAI forming processes; (2) since Pt, Au, Ge and other siderophiles are not as depleted as Fe, Co and Ni, the anomalies are not due to a metal/silicate fractionation; (3) the association of Fe, Co, and Ni anomalies with S and Se anomalies suggests that the anomalies are due to the removal of FeNi sulfide; and (4) since these anomalies occur in all types of Allende inclusions, aggregates and chondrules, the Allende parental material must have undergone sulfide loss before the formation of these components.

Wark, D. A.↗