Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “SL GROUPS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

65 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Nuclear morphometric analysis of osteoblast precursor cells in periodontal ligament, SL-3 rats

Five small (55 days old, 196 +/- 5 g) (mean +/- SE) and five large (83 days old, 382 +/- 4 g) Sprague-Dawley strain, specific pathogen-free rats were exposed to a 7-day spaceflight and 12-h postflight recovery period. As measured in 3-micron sections, periodontal ligament (PDL) fibroblastlike cells were classified according to nuclear size: A + A' (40-79), B (80-119), C (120-169), and D (greater than or equal to 170 microns 3). Since the histogenesis sequence is A----A'----C----D----osteoblast, the relative incidence of A + A' to C + D is an osteogenic index. No difference in A + A' or C + D cells in small rats may reflect partial recovery of preosteoblast formation (A----C) during the 12-h postflight period. Large flight rats demonstrated increased numbers of A + A', indicating an inhibition of preosteoblast formation (A----C). At least in the older group, a 7-day flight is adequate to reduce PDL osteogenic potential (inhibition in PDL osteoblast differentiation and/or specific attrition of C + D cells) that does not recover by 12-h postflight.

Flight Experiment↗
DOE OSTI2018

Once More on the Lattice of Subvarieties of the Wreath Product of the Variety of Semilattices and the Variety of Semigroups with Zero Multiplication

It is known that the monoid wreath product of any two semigroup varieties that are atoms in the lattice of all semigroup varieties may have a finite as well as an infinite lattice of subvarieties. If this lattice is finite, then as a rule it has at most eleven elements. This was proved in a paper of the author in 2007. The exclusion is the monoid wreath product Sl w N{sub 2} of the variety of semilattices and the variety of semigroups with zero multiplication. The number of elements of the lattice L(Sl w N{sub 2}) of subvarieties of Sl w N{sub 2} is still unknown. In a previous paper, we have shown that the lattice L(Sl w N{sub 2}) contains a sublattice having 33 elements. In the present paper, it is proved that the lattice under consideration has exactly three maximal subvarieties. As a first application of the obtained results we calculate the finite basis of the lattice union of the variety of all semilattices and the largest variety among subvarieties of our lattice having at least one heterotypic identity. As a second application we show that the considered lattice of subvarieties has at least 39 elements.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Experiment to evaluate feasibility of utilizing Skylab-EREP remote sensing data for tectonic analysis of the Bighorn Mountains region, Wyoming-Montana

The author has identified the following significant results. Excellent imagery has been obtained from SL-3 along track 5 across the Bighorn Mountains and track 19 across the northern Black Hills. The red band is by far the best of the four black and white films of S-190A. Excellent detail is visible of topography, structure, resistant lithologies, and culture with good resolution obtainable at high magnification (30X). The infrared bands do not have as good resolution and are grainy at high magnification. They are of use as a complement to the red band particularly for relief enhancement in areas of heavy green grass and forest cover. S-190B high definition black and white is comparable to the red band (S-190A) in detail. Its main advantage is larger initial scale and slightly better resolution. High resolution color transparencies along track 19 allow detailed delineation of cultivated land and strip mining. A group of folds northwest of Billings stand out clearly. Light colored units in northwestern Black Hills and in the badlands can be mapped in great detail.

Hoppin, R. A.↗
DOE OSTI2018

Entanglement entropy and the colored Jones polynomial

We study the multi-party entanglement structure of states in Chern-Simons theory created by performing the path integral on 3-manifolds with linked torus boundaries, called link complements. For gauge group SU(2), the wavefunctions of these states (in a particular basis) are the colored Jones polynomials of the corresponding links. We first review the case of U(1) Chern-Simons theory where these are stabilizer states, a fact we use to re-derive an explicit formula for the entanglement entropy across a general link bipartition. We then present the following results for SU(2) Chern-Simons theory: (i) The entanglement entropy for a bipartition of a link gives a lower bound on the genus of surfaces in the ambient S3 separating the two sublinks. (ii) All torus links (namely, links which can be drawn on the surface of a torus) have a GHZ-like entanglement structure — i.e., partial traces leave a separable state. By contrast, through explicit computation, we test in many examples that hyperbolic links (namely, links whose complements admit hyperbolic structures) have W-like entanglement — i.e., partial traces leave a non-separable state. (iii) Finally, we consider hyperbolic links in the complexified SL(2,C) Chern-Simons theory, which is closely related to 3d Einstein gravity with a negative cosmological constant. In the limit of small Newton constant, we discuss how the entanglement structure is controlled by the Neumann-Zagier potential on the moduli space of hyperbolic structures on the link complement.

't Hooft and Polyakov loops↗
DOE OSTI2016

Understanding ligand effects in gold clusters using mass spectrometry

This review summarizes recent research on the influence of phosphine ligands on the size, stability, and reactivity of gold clusters synthesized in solution. Sub-nanometer clusters exhibit size- and composition-dependent properties that are unique from those of larger nanoparticles. The highly tunable properties of clusters and their high surface-to-volume ratio make them promising candidates for a variety of technological applications. However, because “each-atom-counts” toward defining cluster properties it is critically important to develop robust synthesis methods to efficiently prepare clusters of predetermined size. For decades phosphines have been known to direct the size-selected synthesis of gold clusters. Despite the preparation of numerous species it is still not understood how different functional groups at phosphine centers affect the size and properties of gold clusters. Using electrospray ionization mass spectrometry (ESI-MS) it is possible to characterize the effect of ligand substitution on the distribution of clusters formed in solution at defined reaction conditions. In addition, ligand exchange reactions on preformed clusters may be monitored using ESI-MS. Collision induced dissociation (CID) may also be employed to obtain qualitative insight into the fragmentation of mixed ligand clusters and the relative binding energies of differently substituted phosphines. Quantitative ligand binding energies and cluster stability may be determined employing surface induced dissociation (SID) in a custom-built Fourier transform ion cyclotron resonance mass spectrometer (FT-ICR-MS). Rice-Ramsperger-Kassel-Marcus (RRKM) based modeling of the SID data allows dissociation energies and entropy values to be extracted that may be compared with the results of high-level theoretical calculations. The charge reduction and reactivity of atomically precise gold clusters, including partially ligated species generated in the gas-phase by in source CID, on well-defined surfaces may be explored using ion soft landing (SL) in a custom-built instrument combined with in situ time of flight secondary ion mass spectrometry (TOF-SIMS). Jointly, this multipronged experimental approach allows characterization of the full spectrum of relevant phenomena including cluster synthesis, ligand exchange, thermochemistry, surface immobilization, and reactivity. The fundamental insights obtained from this work will facilitate the directed synthesis of gold clusters with predetermined size and properties for specific applications.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2015

Complex Chern–Simons Theory at Level k via the 3d–3d Correspondence

Herein, we use the 3d–3d correspondence together with the DGG construction of theories T n [ M ] labelled by 3-manifolds M to define a non-perturbative state-integral model for \({SL(n,\mathbb{C})}\) Chern–Simons theory at any level k , based on ideal triangulations. The resulting partition functions generalize a widely studied k = 1 state-integral, as well as the 3d index, which is k = 0. The Chern–Simons partition functions correspond to partition functions of T n [ M ] on squashed lens spaces L ( k , 1). At any k , they admit a holomorphic-antiholomorphic factorization, corresponding to the decomposition of L ( k , 1) into two solid tori, and the associated holomorphic block decomposition of the partition functions of T n [ M ]. A generalization to L ( k , p ) is also introduced. Convergence of the state integrals, for any k , requires triangulations to admit a positive angle structure; we propose that this is also necessary for the DGG gauge theory T n [ M ] to flow to a desired IR SCFT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRSDate not supplied

Next Generation Thermal Protection System for Outer Planet Probes and Orbiter

Saturn Probe and Ice Giant Orbiter along with in-situ Probe Missions continue to be very high priority mis-sions. A result of the advocacy by OPAG and other Analysis Groups, the 3D Woven, Dual-Layer HEEET thermal protection system, mature at TRL 6, has closed the TPS gap for extreme environment missions. A mid density follow on to DL HEEET, developed to meet earth entry requirements, is a Single Layer vari-ant of the 3D woven TPS, which provides a mass effi-cient single layer 3D Mid-Density TPS (3MDCP) that has been baselined as the heatshield for MSR EEV. Continued development of 3MDCP will elevate it to TRL 6 by 2025. Conformal-PICA (C-PICA) devel-opment was pursued to establish a more efficient and robust alternate to PICA, and it is at TRL 4+. Our rationale for the next generation of TPS de-velopment is based on the on the missions needs of the next decade Outer Planet missions that are unique and more demanding than any other destinations. Taking advantage of the recent planned development of sev-eral materials, the next generation of TPS offers a much more mass efficient option for small, medium, and large class Outer Planet missions. Saturn Probes: While mission designers are gen-erally interested in shallow entry to maintain the g-load during entry around 50g, the heat-load for shallow entry can range between (100 kJ/cm2 – 300 kJ/cm2), two orders of magnitude higher than Venus or Sample Return missions. TPS must not only offer protection but must be mass efficient to perform reasonable sci-ence. TPS mass can quickly become 50% or more of the mass of the entire entry system. Recent analysis performed shows Saturn Probe missions could signifi-cantly benefit from the single layer HEEET (SL-HEEET/3MDCP). A DL-HEEET based heatshield mass could be ~ (40% -50%), SL-HEEET can provide additional (30% - 50%) mass savings. At the same time, C-PICA can provide (30% - 50%) mass savings on the backshell. The combined mass savings can be significant enough to carry an additional probe, if de-sired. Ice Giant Aerocapture Missions: Aerocapture mission architectures can provide significant ad-vantage over traditional propulsive insertion missions in multiple ways. 1) Reduced trip time ~ (4- 6) years (30% -40%), 2) Enables placing the orbiter, probe, and lander, all together and 3) Allows for greater science mass (probes and landers) due to mass efficiency. The delivery of a probe from orbit makes it easier and eliminates mission design constraints by HEEET for direct entry [4] of probes and allows for more targeted in-situ science once the Orbiter is able to collect data. In the past 20 years, progress made in GN&C for lift-guided entry missions (MSL, Orion EFT1, Mars 2020) and the expertise in blunt body aerodynamics at large scale (~ 5m) has led the EDL community to conclude that aerocapture is a “go do” engineering activity. An aerocapture mission that will deplete the excess energy of a fast arrival mission will require a mass efficient TPS that can handle extreme heat-load, ~ (100 kJ/cm2 – 500 kJ/cm2). Hence TPS, feasibility as well as mass efficiency requires assessment. Utilizing the recent developments, a comprehensive, bounding analysis was done to establish the potential for SOA (HEEET) system as well as emerging new TPS such as SL-HEEET and C-PICA. In this proposed poster, we will outline the process by which we establish bounding aerocapture trajecto-ries for hyperbolic excess velocities ranging from 27 km/s to 35 km/s, for low L/D (~ 0.4) configurations and determine conservative/bounding estimate of aer-othermal environment by using a combination of CFD simulations and stagnation point heating estimates [7]. This engineering approach allows us to assess the TPS need vs. TPS capability and determine the applicability of existing TPS. Once an applicable suite of TPS is determined, the TPS thickness and mass are comput-ed. We show that the TPS mass fraction can be as low as 5% to as high as 20%, depending on the use of ad-vanced TPS, while HEEET is sufficient but will require 50% of the entry mass.

E Venkatapathy↗
NASA NTRS2002

Iridium and Spherules in Late Eocene Impact Deposits

We have been independently examining the Ir (FTK) and spherule (SL) contents of recently discovered late Eocene impact deposits from the south Atlantic and western Indian oceans. These include ODP Sites 1090 [14,15], 709 [lo], and 699 [Liu in prep.]. Iridium abundances at these sites are within the typical range reported for late Eocene deposits, with peak concentrations between 100 and 1000 pg/g. In Table 1 we present estimated net Ir fluences (in ng Ir/cm ) for these and nine other sites. Although there are fewer sites than the K/T boundary, the average of 9 ng Ir/cm2 is probably a good estimate of the late Eocene global flux. This is enough Ir for a 6 km comet (assuming 250 ng/g Ir, p=1.5), is sufficient to produce the Popigai or Chesapeake Bay structures, and is 16% of the flux estimated for the K/T boundary (55 ng/cm2 [ 161). Figure 1 shows the relative abundances of Ir, glassy microtektites and cpx-bearing spherules in sediments from Sites 699 and 1090, which are separated by only 3100 km. Although these two sites have similar Ir anomalies, the abundances of spherules are quite different. Site 1090 has well-defined peaks for both types of spherules, with a peak of 562 cpx spheruledg, while Site 699 contains only a few glassy microtektites and no cpx spherules. While the different abundances of spherules may reflect a heterogeneous distribution of spherules on the Earth s surface, an equally likely cause of this difference may be differential preservation of spherules in the sediment. recovered are only a trace residue of the initial impact deposit. Earlier work found 0.22 ng/g Ir in glassy microtektites from Site 689 [17], an insufficient concentration to support 0.16 ng/g in the bulk sediment at this site. We measured 15 ng/g Ir in a group of 95 cpx spherules from Site 1090 with sizes from 63 to -200 pm, a set typical of the size distribution at this site. Although this is a significant concentration it also cannot support the Ir peak. We presently lack quantitative data on the mass concentration of cpx spherules in Site 1090 sediments, but it is certainly <1 mg/g in The impact record in the late Eocene is very different from that at the Cretaceous-Tertiary In contrast, the late Eocene probably experienced multiple impact events.

Kyte, F. T.↗
DOE OSTI2015

Inflation in maximal gauged supergravities

We discuss the dynamics of multiple scalar fields and the possibility of realistic inflation in the maximal gauged supergravity. In this paper, we address this problem in the framework of recently discovered 1-parameter deformation of SO(4,4) and SO(5,3) dyonic gaugings, for which the base point of the scalar manifold corresponds to an unstable de Sitter critical point. In the gauge-field frame where the embedding tensor takes the value in the sum of the 36 and 36’ representations of SL(8), we present a scheme that allows us to derive an analytic expression for the scalar potential. With the help of this formalism, we derive the full potential and gauge coupling functions in analytic forms for the SO(3)×SO(3)-invariant subsectors of SO(4,4) and SO(5,3) gaugings, and argue that there exist no new critical points in addition to those discovered so far. For the SO(4,4) gauging, we also study the behavior of 6-dimensional scalar fields in this sector near the Dall’Agata-Inverso de Sitter critical point at which the negative eigenvalue of the scalar mass square with the largest modulus goes to zero as the deformation parameter s approaches a critical value s{sub c}. We find that when the deformation parameter s is taken sufficiently close to the critical value, inflation lasts more than 60 e-folds even if the initial point of the inflaton allows an O(0.1) deviation in Planck units from the Dall’Agata-Inverso critical point. It turns out that the spectral index n{sub s} of the curvature perturbation at the time of the 60 e-folding number is always about 0.96 and within the 1σ range n{sub s}=0.9639±0.0047 obtained by Planck, irrespective of the value of the η parameter at the critical saddle point. The tensor-scalar ratio predicted by this model is around 10{sup −3} and is close to the value in the Starobinsky model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1993

Amphibian fertilization and development in microgravity

During the year before launch, female frogs will be tested every 3 months for the quantity and quality of eggs produced. Two weeks or more prior to launch, male and female frogs will be transported to the John F. Kennedy Space Center (KSC). During the few weeks before launch, groups will be periodically tested for egg quality to assure that the frogs have adapted to the KSC laboratory environment. About 27 hours before launch, four females will be placed in a damp foam-lined box, called the Adult Frog Box (AFB), through which 100 cc/min of air wil be circulated. The AFB will be lowered into the Spacelab and loaded into the Frog Environmental Unit (FEU) during the final pre-launch preparations. A sperm suspension, for use in flight to fertilize the eggs, will also be prepared and loaded during the pre-launch period. The sperm suspension, together with a kit of syringes containing Human Chorionic Gonadotropin (HCG), will be stored in a refrigerator aboard the shuttle until needed in flight. On the first day of flight, the AFB will be transferred from the FEU to the General Purpose Work Station (GPWS), which is a type of glove box specially designed to allow the crew to use chemicals and biological materials during the flight without contaminating the shuttle/Spacelab environment. Inside the GPWS the four adult frogs will be injected with the HCG hormone and returned to the FEU. Approximately 16 hours after injection, ovulation should have taken place and 15 to 20 eggs from each frog will be placed on each of two egg baskets and covered with sperm for 10 minutes. The egg baskets are inserted into acrylic egg chambers and 50 ml of 'pond water' (20 percent strength Modified Ringers solution (is added. One of the chambers from each frog will be placed on a centrifuge within the FEU and rotated to simulate normal terrestrial gravity (1 g). The remaining chambers are incubated under microgravity conditions within the FEU. Forty minutes after fertilization, the four chambers exposed to 1 g will be removed and observed within the GPWS using a dissecting microscope and camera system. On the basis of egg rotation and egg appearance, the 'best' and 'second best' frogs will be selected to contribute additional eggs. Using the two best frogs, 22 egg chambers will be loaded with eggs and fertilized. Eleven chambers wil be incubated at microgravity and eleven will be incubated on the centrifuge. At various times during the flight, chambers will be removed from the FEU and transferred to the GPWS where a formaldehyde-based fixative will be injected in order to preserve important developmental stages for in depth study following the flight. Five of the 22 chambers plus the eight fertilization test chambers will be returned to Earth with live tadpoles. The swimming behavior of these free swimming tadpoles will be examined within several hours of landing and some will be fixed for a detailed analysis of their inner ear, the otolity, the animals 'balance system.' Lychakov and Vinikov reported an increase in otolith size in tadpoles that developed (but were not fertilized) in space. Live tadpoles from the SL-J flight will be raised through metamorphsis for studies of maturation including an analysis of the effects of space flight on their ability to produce normal progency. Following the flight, the fixed embryos will be serially sectioned and stained using procedures that were developed for this experiment. The embroys fixed at the 2-4 cell stage will be examined for the distribution of cytoplasmic contents, including the various classes of yolk platelets, and the location and shape of the cleavage furrows. The gastrulae will be assessed for the normality of the complex cellular rearrangements that constitute blastopore formation and involution, i.e., the differentiation of the embryo into its specialized body parts. Using a new procedure, the gastrulae will be bleached which will enable the initial sperm entry point (SEP) to be located. The correlation between the SEP and the dorsal lip of the blastopore will be determined. Under normal terrestrial conditions it was shown that the SEP typically is located on the side of the egg opposite the future dorsal side of the embryo. The neurulae will be examined for the normality and completeness of the neural plate and archenteron expansion. The tadpole stages will be used to study the allometry and morphology of the various organ systems.

Souza, Kenneth A.↗
DOE OSTI2016

Materials Data on Li48P16S61 by Materials Project

Li48P16S61 crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are twenty-four inequivalent Li sites. In the first Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share corners with three LiS5 square pyramids, corners with two PS4 tetrahedra, corners with three LiS4 tetrahedra, an edgeedge with one LiS5 square pyramid, and an edgeedge with one PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.44–2.50 Å. In the second Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share a cornercorner with one LiS5 square pyramid, corners with three LiS4 tetrahedra, and an edgeedge with one PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.42–2.54 Å. In the third Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share corners with two LiS5 square pyramids, corners with two PS4 tetrahedra, corners with four LiS4 tetrahedra, an edgeedge with one LiS5 square pyramid, and an edgeedge with one PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.44–2.52 Å. In the fourth Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share a cornercorner with one LiS5 square pyramid, a cornercorner with one PS4 tetrahedra, corners with four LiS4 tetrahedra, and an edgeedge with one PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.43–2.51 Å. In the fifth Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share a cornercorner with one LiS5 square pyramid, corners with two PS4 tetrahedra, corners with four LiS4 tetrahedra, and an edgeedge with one PS4 tetrahedra. There are one shorter (2.46 Å) and three longer (2.48 Å) Li–S bond lengths. In the sixth Li site, Li is bonded in a distorted trigonal planar geometry to three S atoms. There are a spread of Li–S bond distances ranging from 2.35–2.46 Å. In the seventh Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share corners with two LiS5 square pyramids, corners with two PS4 tetrahedra, corners with four LiS4 tetrahedra, and an edgeedge with one PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.47–2.49 Å. In the eighth Li site, Li is bonded in a distorted trigonal planar geometry to three S atoms. There are a spread of Li–S bond distances ranging from 2.35–2.46 Å. In the ninth Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share a cornercorner with one LiS5 square pyramid, corners with two PS4 tetrahedra, corners with three LiS4 tetrahedra, and an edgeedge with one PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.45–2.48 Å. In the tenth Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share a cornercorner with one LiS5 square pyramid, corners with two PS4 tetrahedra, corners with four LiS4 tetrahedra, and an edgeedge with one PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.46–2.49 Å. In the eleventh Li site, Li is bonded in a distorted trigonal planar geometry to three S atoms. There are a spread of Li–S bond distances ranging from 2.36–2.47 Å. In the twelfth Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share corners with two LiS5 square pyramids, corners with two PS4 tetrahedra, corners with four LiS4 tetrahedra, and an edgeedge with one PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.47–2.49 Å. In the thirteenth Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share corners with two LiS5 square pyramids, corners with two PS4 tetrahedra, corners with three LiS4 tetrahedra, an edgeedge with one LiS5 square pyramid, and an edgeedge with one PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.45–2.49 Å. In the fourteenth Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share a cornercorner with one LiS5 square pyramid, corners with three LiS4 tetrahedra, and an edgeedge with one PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.42–2.53 Å. In the fifteenth Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share corners with two LiS5 square pyramids, corners with two PS4 tetrahedra, corners with three LiS4 tetrahedra, and an edgeedge with one PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.45–2.48 Å. In the sixteenth Li site, Li is bonded to four S atoms to form LiS4 tetrahedra that share a cornercorner with one PS4 tetrahedra, corners with three LiS4 tetrahedra, and an edgeedge with one PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.42–2.51 Å. In the seventeenth Li site, Li is bonded to five S atoms to form distorted LiS5 square pyramids that share a cornercorner with one LiS5 square pyramid, a cornercorner with one PS4 tetrahedra, corners with seven LiS4 tetrahedra, an edgeedge with one LiS4 tetrahedra, and edges with two PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.48–2.84 Å. In the eighteenth Li site, Li is bonded in a distorted square co-planar geometry to four S atoms. There are a spread of Li–S bond distances ranging from 2.45–2.66 Å. In the nineteenth Li site, Li is bonded in a distorted square co-planar geometry to four S atoms. There are a spread of Li–S bond distances ranging from 2.48–2.60 Å. In the twentieth Li site, Li is bonded in a distorted square co-planar geometry to four S atoms. There are a spread of Li–S bond distances ranging from 2.49–2.60 Å. In the twenty-first Li site, Li is bonded to five S atoms to form distorted LiS5 square pyramids that share a cornercorner with one LiS5 square pyramid, a cornercorner with one PS4 tetrahedra, corners with six LiS4 tetrahedra, an edgeedge with one LiS5 square pyramid, an edgeedge with one LiS4 tetrahedra, and edges with two PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.47–2.83 Å. In the twenty-second Li site, Li is bonded in a distorted square co-planar geometry to four S atoms. There are a spread of Li–S bond distances ranging from 2.45–2.65 Å. In the twenty-third Li site, Li is bonded to five S atoms to form distorted LiS5 square pyramids that share a cornercorner with one LiS5 square pyramid, a cornercorner with one PS4 tetrahedra, corners with six LiS4 tetrahedra, an edgeedge with one LiS5 square pyramid, an edgeedge with one LiS4 tetrahedra, and edges with two PS4 tetrahedra. There are a spread of Li–S bond distances ranging from 2.47–2.83 Å. In the twenty-fourth Li site, Li is bonded in a distorted square co-planar geometry to four S atoms. There are a spread of Li–S bond distances ranging from 2.46–2.65 Å. There are twelve inequivalent P sites. In the first P site, P is bonded to four S atoms to form PS4 tetrahedra that share corners with four LiS4 tetrahedra, edges with two equivalent LiS5 square pyramids, and edges with two equivalent LiS4 tetrahedra. There are a spread of P–S bond distances ranging from 2.04–2.09 Å. In the second P site, P is bonded in a distorted trigonal non-coplanar geometry to three S atoms. There are two shorter (2.12 Å) and one longer (2.15 Å) P–S bond lengths. In the third P site, P is bonded to four S atoms to form PS4 tetrahedra that share corners with four LiS4 tetrahedra and edges with two equivalent LiS4 tetrahedra. There are a spread of P–S bond distances ranging from 2.04–2.10 Å. In the fourth P site, P is bonded to four S atoms to form PS4 tetrahedra that share corners with four LiS4 tetrahedra and edges with two equivalent LiS4 tetrahedra. There are a spread of P–S bond distances ranging from 2.05–2.09 Å. In the fifth P site, P is bonded to four S atoms to form PS4 tetrahedra that share corners with three LiS4 tetrahedra, an edgeedge with one LiS5 square pyramid, and edges with two LiS4 tetrahedra. There are a spread of P–S bond distances ranging from 2.03–2.10 Å. In the sixth P site, P is bonded to four S atoms to form PS4 tetrahedra that share a cornercorner with one LiS5 square pyramid, corners with two LiS4 tetrahedra, and edges with two LiS4 tetrahedra. There are a spread of P–S bond distances ranging from 2.05–2.08 Å. In the seventh P site, P is bonded to four S atoms to form PS4 tetrahedra that share corners with two LiS5 square pyramids, corners with three LiS4 tetrahedra, and edges with two LiS4 tetrahedra. There are a spread of P–S bond distances ranging from 2.05–2.08 Å. In the eighth P site, P is bonded to four S atoms to form PS4 tetrahedra that share corners with two LiS4 tetrahedra, edges with two LiS5 square pyramids, and edges with two LiS4 tetrahedra. There are a spread of P–S bond distances ranging from 2.03–2.11 Å. In the ninth P site, P is bonded to four S atoms to form PS4 tetrahedra that share corners with four LiS4 tetrahedra, edges with two equivalent LiS5 square pyramids, and edges with two equivalent LiS4 tetrahedra. There are a spread of P–S bond distances ranging from 2.04–2.10 Å. In the tenth P site, P is bonded in a distorted trigonal non-coplanar geometry to three S atoms. There are two shorter (2.12 Å) and one longer (2.15 Å) P–S bond lengths. In the eleventh P site, P is bonded to four S atoms to form PS4 tetrahedra that share corners with four LiS4 tetrahedra, edges with two equivalent LiS5 square pyramids, and edges with two equivalent LiS4 tetrahedra. There are a spread of P–S bond distances ranging from 2.04–2.09 Å. In the twelfth P site, P is bonded in a distorted trigonal non-coplanar geometry to three S atoms. There are two shorter (2.12 Å) and one longer (2.16 Å) P–S bond lengths. There are thirty-seven inequivalent S sites. In the first S site, S is bonded in a distorted T-shaped geometry to two equivalent Li and one P atom. In the second S site, S is bonded in a distorted T-shaped geometry to two equivalent Li and one P atom. In the third S site, S is bonded in a distorted T-shaped geometry to two equivalent Li and one P atom. In the fourth S site, S is bonded in a distorted rectangular see-saw-like geometry to three Li and one P atom. In the fifth S site, S is bonded in a distorted T-shaped geometry to two Li and one P atom. In the sixth S site, S is bonded in a distorted pentagonal planar geometry to four Li and one P atom. In the seventh S site, S is bonded in a distorted T-shaped geometry to two Li and one P atom. In the eighth S site, S is bonded in a distorted T-shaped geometry to two equivalent Li and one P atom. In the ninth S site, S is bonded in a distorted T-shaped geometry to two equivalent Li and one P atom. In the tenth S site, S is bonded to four Li and one P atom to form distorted SLi4P trigonal bipyramids that share corners with two equivalent SLi4P trigonal bipyramids, corners with six SLi3P trigonal pyramids, and edges with two equivalent SLi3P trigonal pyramids. In the eleventh S site, S is bonded to four Li and one P atom to form distorted SLi4P trigonal bipyramids that share corners with two equivalent SLi4P trigonal bipyramids, corners with six SLi3P trigonal pyramids, and edges with two equivalent SLi3P trigonal pyramids. In the twelfth S site, S is bonded to four Li and one P atom to form distorted SLi4P trigonal bipyramids that share corners with two equivalent SLi4P trigonal bipyramids, corners with six SLi3P trigonal pyramids, and edges with two equivalent SLi3P trigonal pyramids. In the thirteenth S site, S is bonded to four Li and one P atom to form distorted SLi4P trigonal bipyramids that share corners with two equivalent SLi4P trigonal bipyramids, corners with six SLi3P trigonal pyramids, and edges with two equivalent SLi3P trigonal pyramids. In the fourteenth S site, S is bonded to four Li and one P atom to form distorted SLi4P trigonal bipyramids that share corners with two SLi4P trigonal bipyramids, corners with six SLi3P trigonal pyramids, and edges with two SLi3P trigonal pyramids. In the fifteenth S site, S is bonded to four Li and one P atom to form distorted SL

36 MATERIALS SCIENCE↗