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Sc2Pd crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. there are two inequivalent Sc sites. In the first Sc site, Sc is bonded in a 6-coordinate geometry to six equivalent Pd atoms. All Sc–Pd bond lengths are 2.76 Å. In the second Sc site, Sc is bonded in a 2-coordinate geometry to two equivalent Pd atoms. Both Sc–Pd bond lengths are 2.85 Å. Pd is bonded in a 9-coordinate geometry to six Sc atoms.
ScNb2Ru5B2 crystallizes in the orthorhombic Cmmm space group. The structure is three-dimensional. Sc is bonded in a 7-coordinate geometry to ten Ru and three B atoms. There are a spread of Sc–Ru bond distances ranging from 2.79–3.01 Å. There are one shorter (2.72 Å) and two longer (2.84 Å) Sc–B bond lengths. There are two inequivalent Nb sites. In the first Nb site, Nb is bonded in a body-centered cubic geometry to eight Ru atoms. There are four shorter (2.65 Å) and four longer (2.66 Å) Nb–Ru bond lengths. In the second Nb site, Nb is bonded in a 11-coordinate geometry to ten Ru and three B atoms. There are six shorter (2.82 Å) and four longer (2.93 Å) Nb–Ru bond lengths. There are one shorter (2.73 Å) and two longer (2.88 Å) Nb–B bond lengths. There are four inequivalent Ru sites. In the first Ru site, Ru is bonded in a 8-coordinate geometry to four equivalent Nb and four equivalent B atoms. All Ru–B bond lengths are 2.24 Å. In the second Ru site, Ru is bonded in a distorted body-centered cubic geometry to four equivalent Sc and four equivalent B atoms. All Ru–B bond lengths are 2.21 Å. In the third Ru site, Ru is bonded in a 8-coordinate geometry to two equivalent Sc, four Nb, and two equivalent B atoms. Both Ru–B bond lengths are 2.20 Å. In the fourth Ru site, Ru is bonded in a 8-coordinate geometry to two equivalent Sc, four Nb, and two equivalent B atoms. Both Ru–B bond lengths are 2.22 Å. There are two inequivalent B sites. In the first B site, B is bonded in a 9-coordinate geometry to one Sc, two equivalent Nb, and six Ru atoms. In the second B site, B is bonded in a 9-coordinate geometry to two equivalent Sc, one Nb, and six Ru atoms.
Sc2Ir crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. there are two inequivalent Sc sites. In the first Sc site, Sc is bonded in a 6-coordinate geometry to six equivalent Ir atoms. All Sc–Ir bond lengths are 2.73 Å. In the second Sc site, Sc is bonded in a 2-coordinate geometry to four equivalent Ir atoms. There are two shorter (2.80 Å) and two longer (3.15 Å) Sc–Ir bond lengths. Ir is bonded in a 9-coordinate geometry to nine Sc atoms.
Mg2Sc is Magnesium-derived structured and crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. there are two inequivalent Mg sites. In the first Mg site, Mg is bonded to six Mg and six equivalent Sc atoms to form MgMg6Sc6 cuboctahedra that share corners with six equivalent ScMg8Sc4 cuboctahedra, corners with twelve MgMg10Sc2 cuboctahedra, edges with seven equivalent ScMg8Sc4 cuboctahedra, edges with eleven MgMg6Sc6 cuboctahedra, faces with six equivalent ScMg8Sc4 cuboctahedra, and faces with fourteen MgMg6Sc6 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.19–3.26 Å. There are four shorter (3.19 Å) and two longer (3.21 Å) Mg–Sc bond lengths. In the second Mg site, Mg is bonded to ten Mg and two equivalent Sc atoms to form MgMg10Sc2 cuboctahedra that share corners with six equivalent ScMg8Sc4 cuboctahedra, corners with twelve MgMg6Sc6 cuboctahedra, edges with seven MgMg10Sc2 cuboctahedra, edges with eleven equivalent ScMg8Sc4 cuboctahedra, faces with four equivalent ScMg8Sc4 cuboctahedra, and faces with sixteen MgMg10Sc2 cuboctahedra. There are four shorter (3.19 Å) and two longer (3.26 Å) Mg–Mg bond lengths. Both Mg–Sc bond lengths are 3.21 Å. Sc is bonded to eight Mg and four equivalent Sc atoms to form ScMg8Sc4 cuboctahedra that share corners with six equivalent ScMg8Sc4 cuboctahedra, corners with twelve MgMg6Sc6 cuboctahedra, edges with eighteen MgMg6Sc6 cuboctahedra, faces with ten MgMg6Sc6 cuboctahedra, and faces with ten equivalent ScMg8Sc4 cuboctahedra. There are two shorter (3.19 Å) and two longer (3.26 Å) Sc–Sc bond lengths.
ScIr3B2 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Sc is bonded in a 12-coordinate geometry to two equivalent Sc, twelve equivalent Ir, and six equivalent B atoms. Both Sc–Sc bond lengths are 3.06 Å. All Sc–Ir bond lengths are 3.13 Å. All Sc–B bond lengths are 3.16 Å. Ir is bonded in a distorted square co-planar geometry to four equivalent Sc and four equivalent B atoms. All Ir–B bond lengths are 2.20 Å. B is bonded in a 6-coordinate geometry to three equivalent Sc and six equivalent Ir atoms.
Sc2Au2In crystallizes in the tetragonal P4_2/mnm space group. The structure is three-dimensional. there are two inequivalent Sc sites. In the first Sc site, Sc is bonded in a 6-coordinate geometry to six equivalent Au atoms. There are two shorter (2.82 Å) and four longer (2.92 Å) Sc–Au bond lengths. In the second Sc site, Sc is bonded in a 6-coordinate geometry to six equivalent Au atoms. There are two shorter (2.81 Å) and four longer (2.89 Å) Sc–Au bond lengths. Au is bonded in a 8-coordinate geometry to six Sc and two equivalent In atoms. Both Au–In bond lengths are 3.04 Å. In is bonded in a 4-coordinate geometry to four equivalent Au atoms.
Sc3P is Cementite structured and crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. there are two inequivalent Sc sites. In the first Sc site, Sc is bonded in a 3-coordinate geometry to three equivalent P atoms. There are two shorter (2.69 Å) and one longer (2.85 Å) Sc–P bond lengths. In the second Sc site, Sc is bonded in a distorted bent 150 degrees geometry to two equivalent P atoms. There are one shorter (2.67 Å) and one longer (2.70 Å) Sc–P bond lengths. P is bonded in a 8-coordinate geometry to eight Sc atoms.
Steel Plate Concrete (SC) composite members have been widely adopted because of its cost-efficiency and enhanced structural behavior. While researchers have attempted to study its in-plane shear behavior in the past twenty years, very limited number of large-scale pure shear tests were performed due to the challenge of experimental set-up and the availability of facilities. In this paper, a series of uniaxial loading tests and two full-scale pure shear panel tests of SC members were reported, on which the “mechanics-based Membrane Model of SC elements (MM-SC)” is developed. The MM-SC model is based on the fixed-angle crack formulation and the smeared-crack formulation, in which the experimental-based uniaxial constitutive models are implemented, considering the local buckling of faceplate, the tension stiffening of steel plate, the strength degradation of cracked concrete and the confinement effect of concrete. The proposed MM-SC model is subsequently incorporated into the object-oriented software OpenSEES. Finally, the simulation results of proposed model well predict the SC test observations in terms of critical branch points and structural behaviors, including initial stiffness, cracking strength, post-crack stiffness, yield strength, maximum strength, and failure modes.
Wastewater treatment plants (WWTPs) consume significant amount of energy to sustain their operation. From this point, the current study aims to enhance the capacity of these facilities to meet their energy needs by integrating renewable energy sources. The study focused on the investigation of two primary solar energy systems in As Samra WWTP in Jordan. The first system combines parabolic trough collectors (PTCs) with thermal energy storage (TES). This system primarily serves to fulfill the thermal energy demands of the plant by reducing the demands from boiler units, which allows more biogas for electricity generation. The second system is a photovoltaic (PV) system with Lithium-Ion batteries, which directly produces electricity that will be used to cover part of the electrical energy demands of plant. To assess the optimal configuration, two distinct scenarios have been formulated and compared to the current case scenario (SC#1). The first scenario focuses on maximizing the net present value (NPV) and minimizing the levelized cost of electricity (LCOE). The second scenario is centred on minimizing the levelized cost of heat (LCOH). The findings indicate that both scenarios succeeded in reducing the reliance on the grid to a value that reach 1 %. Moreover, they both reduced biogas percentage in energy production from 88 % to approximately 65 % through the integration of the PV system. In terms of thermal demand, SC#2 reduced the reliance on biogas boiler units from 100 % to 25 %, while SC#3 achieved an even more impressive reduction to just 8 %. The best LCOE value was attained in SC#2, at 0.0895 USD/kWh, with an NPV of 10.54 million USD. Conversely, SC# 3 yielded an LCOH value of 0.0432 USD/kWh th compared to 0.0534 USD/kWh th USD for SC#2. In conclusion, despite their relatively high capital and operating costs, SC#2 and SC#3 managed to substantially decrease the annual electricity expenditure from approximately 2 million USD to 86,000 USD and 0 USD, respectively.
At temperatures T much lower than its superconducting critical temperature T c = 2.1 K, the heavy fermion superconductor UTe 2 has a unique phase diagram of magnetic field H vs. φ and θ, angles H is tilted from the b-axis toward the a- and c-axes, respectively, of its orthorhombic unit cell. The phase diagram contains three distinct superconducting phases: SC1 in which φ and θ extend from 0 to 90° and H ≤ ~15 T; SC 2 for φ ≤ ~7°, θ ≤ ~4° and ~15 T ≤ H ≤ H m = ~35 T, the onset of the magnetic field polarized (FP) phase, and SC FP which resides entirely within the FP phase in a pocket of superconductivity extending from θ ≈ 20° to 40° and from ~40 T to above 60 T. We studied the evolution of the H vs. θ phase diagram for Th concentrations 0.005 ≤ x ≤ 0.047 in the U 1-x Th x Te 2 system at ~0.6 K. Within this range of x values, SC 1 extends over 0 ≤ θ ≤ 90° and H ≤ ~10 T for x = 0.047, while SC 2 is suppressed. The SC FP and FP phases are unaffected to x = 0.02 but are completely suppressed in the region x = 0.025 to 0.047 where the residual resistance ratio RRR ~3 indicates a significant amount of disorder. In conclusion, these results complement recent studies of nonsuperconducting disordered UTe 2 single crystals in which the SC 1 and SC 2 phases are absent, but the FP and so-called “orphan” SC FP phases are retained.
Using high-energy x-ray scattering and large-scale three-dimensional (3D) structure modeling, in this study we investigate the relationship between the crystal lattice, charge density wave (CDW), and superconducting (SC) orders in transition metal dichalcogenides (TMDs). In particular, we systematically substitute Te for Se in Ta-Se-Te solid solutions, determine changes in their crystal lattice, and relate them to changes in the CDW transition temperature, $T_{CDW}$, and SC critical temperature, $T_c$ . We find that strong lattice distortions such as buckling of Ta layers are detrimental to the CDW and SC orders. The presence of a perfect lattice order in two dimensions is a prerequisite to the emergence of CDWs but insufficient to achieve a SC ordered state. For the SC order to emerge, the Ta sublattice should also appear periodic in 3D. Local chemical disorder may promote the SC order, and the perfectness of Ta coordination polyhedra is a factor contributing to its strength. A hierarchical relationship among the crystal lattice, CDW, and SC orders thus appears to exist in TMDs in a sense that different degrees of crystal lattice order-disorder promote and maintain the CDW and SC orders to a different extent, offering an opportunity to control the latter through modifying the former by rational design. Our findings are a step towards a better understanding of the correlation between lattice and electronic degrees of freedom in TMDs. We also demonstrate an efficient experimental approach to study them in fine detail.
The square-lattice Hubbard and closely related t-J models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group simulations on the extended t-J model have identified d-wave SC on the electron-doped side (with the next-nearest-neighbor hopping t 2 > 0) but a dominant charge density wave (CDW) order on the hole-doped side (t 2 < 0), which is inconsistent with the SC of hole-doped cuprate compounds. We re-examine the ground-state phase diagram of the extended t-J model by employing the state-of-the-art density matrix renormalization group calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state. On six-leg cylinders, while different CDW phases are identified on the hole-doped side for the doping range δ = 1/16 – 1/8, a SC phase emerges at a lower doping regime, with algebraically decaying pairing correlations and d-wave symmetry. On the wider eight-leg systems, the d-wave SC also emerges on the hole-doped side at the optimal 1=8 doping, demonstrating the winning of SC over CDW by increasing the system width. Furthermore, our results not only suggest a new path to SC in general t-J model through weakening the competing charge orders, but also provide a unified understanding on the SC of both hole- and electron-doped cuprate superconductors.
Abstract We explore the decoupling physics of a stratocumulus-topped boundary layer (STBL) moving over cooler water, a situation mimicking warm-air advection (WADV). We simulate an initially well-mixed STBL over a doubly periodic domain with the sea surface temperature decreasing linearly over time using the System for Atmospheric Modeling large-eddy model. Due to the surface cooling, the STBL becomes increasingly stably stratified, manifested as a near-surface temperature inversion topped by a well-mixed cloud-containing layer. Unlike the stably stratified STBL in cold-air advection (CADV) that is characterized by cumulus coupling, the stratocumulus deck in the WADV is unambiguously decoupled from the sea surface, manifested as weakly negative buoyancy flux throughout the subcloud layer. Without the influxes of buoyancy from the surface, the convective circulation in the well-mixed cloud-containing layer is driven by cloud-top radiative cooling. In such a regime, the downdrafts propel the circulation, in contrast to that in CADV regime for which the cumulus updrafts play a more determinant role. Such a contrast in convection regime explains the difference in many aspects of the STBLs including the entrainment rate, cloud homogeneity, vertical exchanges of heat and moisture, and lifetime of the stratocumulus deck, with the last being subject to a more thorough investigation in Part II. Finally, we investigate under what conditions a secondary stratus near the surface (or fog) can form in the WADV. We found that weaker subsidence favors the formation of fog whereas a more rapid surface cooling rate does not. Significant Statement The low-lying blanketlike clouds, called stratocumulus (Sc), reflect much incoming sunlight, substantially modulating Earth’s temperature. While much is known about how the Sc evolves when it moves over warmer water, few studies examine the opposite situation of Sc moving over colder water. We used a high-resolution numerical model to simulate such a case. When moving over cold water, the Sc becomes unambiguously decoupled from the water surface, distinctive from its warm counterpart in which the Sc interacts with the water surface via intermittent cauliflower-like clouds called cumulus clouds. Such decoupling influences many aspects of the Sc–sea surface system, which combine to alter the ability of the Sc to reflect sunlight, thereby influencing the climate. This work laid the foundation for future work that quantifies the contribution of such a decoupled Sc regime to Earth’s radiative budget and climate change.
A Committee on Satellite Communication (COSC) was formed under the auspices of the Space Applications Board (SAB) in order to study Federal research and development on satellite communications (SC). Discussion on whether to continue the research and development and the proper role of the Federal Government are addressed. Discussion focussed on six possible options for a Federal role in SC research and development: (1) the current NASA SC program; (2) an expanded NASA SC technology program; (3) a SC technology flight test support program; (4) an experimental SC technology flight program; (5) an experimental public service SC system program; and (6) an operational public service SC system program. Decision criteria and recommendations are presented.
In several papers, the solar cycle (SC) effect in the lower atmosphere has been linked to the Quasi-biennial Oscillation (QBO), which is generated primarily by small-scale gravity waves. Salby and Callaghan (2000) analyzed the observed zonal winds of the QBO over more than 40 years and found that it contains a relatively large SC signature at 20 km. Following up on an earlier 2D study with our global-scale Numerical Spectral Model (NSM), we discuss here a 3D study with the QBO under the influence of the SC. For a SC period of 10 years, the amplitude of the relative variations of radiative forcing is taken to vary for simplicity from 0.2% at the surface to 2% at 50 km to 20% at 100 km and above. Covering a limited time span of 40 years, this model produces in the lower stratosphere a relatively large modulation of the QBO, which appears to be related to the SC and is in qualitative agreement with the observations. Some of the energy in the QBO, confined to low latitudes primarily, is redistributed globally by the meridional circulation and planetary waves presumably, so that a measurable SC modulation is generated in the tropospheric temperatures of the polar regions. Further studies are needed, (1) to determine whether the effect is real and prevails in more extensive simulations and whether the results are robust when shorter integration steps are employed, and (2) to explore the mechanism(s) that may ample the apparent SC influence of the UV radiation extending into the lower atmosphere. Quasi-decadal oscillations, generated internally by the QBO interacting with the seasonal cycles, may interfere with or aid the SC effect.
ScZn2 is Hexagonal Laves structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Sc is bonded in a 12-coordinate geometry to four equivalent Sc and twelve Zn atoms. There are one shorter (3.20 Å) and three longer (3.22 Å) Sc–Sc bond lengths. There are three shorter (3.03 Å) and nine longer (3.09 Å) Sc–Zn bond lengths. There are two inequivalent Zn sites. In the first Zn site, Zn is bonded to six equivalent Sc and six equivalent Zn atoms to form a mixture of face, edge, and corner-sharing ZnSc6Zn6 cuboctahedra. All Zn–Zn bond lengths are 2.64 Å. In the second Zn site, Zn is bonded to six equivalent Sc and six Zn atoms to form a mixture of face, edge, and corner-sharing ZnSc6Zn6 cuboctahedra. There are two shorter (2.57 Å) and two longer (2.71 Å) Zn–Zn bond lengths.
Sc(H2O)7Sc(H2O)9(CF3)6(SO3)6 crystallizes in the monoclinic Pm space group. The structure is zero-dimensional and consists of six fluoroform molecules, six sulfur trioxide molecules, one Sc(H2O)7 cluster, and one Sc(H2O)9 cluster. In the Sc(H2O)7 cluster, Sc3+ is bonded in a distorted pentagonal bipyramidal geometry to seven O2- atoms. There are a spread of Sc–O bond distances ranging from 2.15–2.31 Å. There are seven 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 0.99 Å. In the second H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the third H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the fourth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the fifth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the sixth 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 seventh H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. There are four inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted water-like geometry to one Sc3+ and two H1+ atoms. In the second O2- site, O2- is bonded in a distorted water-like geometry to one Sc3+ and two H1+ atoms. In the third O2- site, O2- is bonded in a distorted water-like geometry to one Sc3+ and two equivalent H1+ atoms. In the fourth O2- site, O2- is bonded in a distorted water-like geometry to one Sc3+ and two H1+ atoms. In the Sc(H2O)9 cluster, Sc3+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sc–O bond distances ranging from 2.21–2.60 Å. There are nine 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 0.98 Å. In the second H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the third H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the fourth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the fifth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the sixth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the seventh H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the eighth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the ninth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted water-like geometry to one Sc3+ and two H1+ atoms. In the second O2- site, O2- is bonded in a water-like geometry to one Sc3+ and two equivalent H1+ atoms. In the third O2- site, O2- is bonded in a water-like geometry to one Sc3+ and two equivalent H1+ atoms. In the fourth O2- site, O2- is bonded in a distorted water-like geometry to one Sc3+ and two H1+ atoms. In the fifth O2- site, O2- is bonded in a distorted water-like geometry to one Sc3+ and two H1+ atoms. In the sixth O2- site, O2- is bonded in a water-like geometry to one Sc3+ and two equivalent H1+ atoms.
Li11Sc7Ti(PO4)12 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are eleven inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded in a 4-coordinate geometry to five O2- atoms. There are a spread of Li–O bond distances ranging from 1.94–2.61 Å. In the second Li1+ site, Li1+ is bonded to four O2- atoms to form distorted LiO4 trigonal pyramids that share corners with two PO4 tetrahedra and a cornercorner with one TiO5 trigonal bipyramid. There are a spread of Li–O bond distances ranging from 1.94–2.22 Å. In the third Li1+ site, Li1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Li–O bond distances ranging from 1.92–2.47 Å. In the fourth Li1+ site, Li1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Li–O bond distances ranging from 1.89–2.59 Å. In the fifth Li1+ site, Li1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Li–O bond distances ranging from 2.02–2.26 Å. In the sixth Li1+ site, Li1+ is bonded in a 3-coordinate geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.82–2.55 Å. In the seventh Li1+ site, Li1+ is bonded to five O2- atoms to form distorted LiO5 trigonal bipyramids that share an edgeedge with one PO4 tetrahedra. There are a spread of Li–O bond distances ranging from 1.97–2.27 Å. In the eighth Li1+ site, Li1+ is bonded in a 1-coordinate geometry to five O2- atoms. There are a spread of Li–O bond distances ranging from 2.06–2.56 Å. In the ninth Li1+ site, Li1+ is bonded in a 4-coordinate geometry to six O2- atoms. There are a spread of Li–O bond distances ranging from 1.90–2.77 Å. In the tenth Li1+ site, Li1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Li–O bond distances ranging from 1.89–2.54 Å. In the eleventh Li1+ site, Li1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Li–O bond distances ranging from 1.97–2.52 Å. There are seven inequivalent Sc3+ sites. In the first Sc3+ site, Sc3+ is bonded to five O2- atoms to form distorted ScO5 trigonal bipyramids that share a cornercorner with one PO4 tetrahedra and a cornercorner with one TiO5 trigonal bipyramid. There are a spread of Sc–O bond distances ranging from 1.94–2.41 Å. In the second Sc3+ site, Sc3+ is bonded in a 4-coordinate geometry to five O2- atoms. There are a spread of Sc–O bond distances ranging from 1.82–2.50 Å. In the third Sc3+ site, Sc3+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Sc–O bond distances ranging from 2.00–2.38 Å. In the fourth Sc3+ site, Sc3+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Sc–O bond distances ranging from 2.07–2.30 Å. In the fifth Sc3+ site, Sc3+ is bonded in a 1-coordinate geometry to seven O2- atoms. There are a spread of Sc–O bond distances ranging from 1.81–2.63 Å. In the sixth Sc3+ site, Sc3+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Sc–O bond distances ranging from 1.94–2.58 Å. In the seventh Sc3+ site, Sc3+ is bonded to five O2- atoms to form distorted ScO5 trigonal bipyramids that share corners with two PO4 tetrahedra. There are a spread of Sc–O bond distances ranging from 2.04–2.19 Å. Ti4+ is bonded to five O2- atoms to form distorted TiO5 trigonal bipyramids that share a cornercorner with one PO4 tetrahedra, a cornercorner with one ScO5 trigonal bipyramid, and a cornercorner with one LiO4 trigonal pyramid. There are a spread of Ti–O bond distances ranging from 1.75–2.20 Å. There are twelve inequivalent P5+ sites. In the first P5+ site, P5+ is bonded to four O2- atoms to form corner-sharing PO4 tetrahedra. There are a spread of P–O bond distances ranging from 1.51–1.65 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, a cornercorner with one ScO5 trigonal bipyramid, and a cornercorner with one LiO4 trigonal pyramid. There are a spread of P–O bond distances ranging from 1.50–1.70 Å. In the third P5+ site, P5+ is bonded in a 3-coordinate geometry to three O2- atoms. There are a spread of P–O bond distances ranging from 1.51–2.04 Å. In the fourth P5+ site, P5+ is bonded in a trigonal non-coplanar geometry to three O2- atoms. There are a spread of P–O bond distances ranging from 1.54–1.60 Å. In the fifth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one TiO5 trigonal bipyramid and an edgeedge with one LiO5 trigonal bipyramid. There are a spread of P–O bond distances ranging from 1.54–1.59 Å. In the sixth P5+ site, P5+ is bonded in a trigonal non-coplanar geometry to three O2- atoms. There are a spread of P–O bond distances ranging from 1.52–1.58 Å. In the seventh P5+ site, P5+ is bonded in a trigonal non-coplanar geometry to three O2- atoms. There are a spread of P–O bond distances ranging from 1.57–1.72 Å. In the eighth P5+ site, P5+ is bonded in a tetrahedral geometry to four O2- atoms. There are a spread of P–O bond distances ranging from 1.50–1.67 Å. In the ninth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one ScO5 trigonal bipyramid. There are a spread of P–O bond distances ranging from 1.50–1.67 Å. In the tenth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one ScO5 trigonal bipyramid and a cornercorner with one LiO4 trigonal pyramid. There are a spread of P–O bond distances ranging from 1.51–1.68 Å. In the eleventh P5+ site, P5+ is bonded in a trigonal non-coplanar geometry to three O2- atoms. There are a spread of P–O bond distances ranging from 1.55–1.58 Å. In the twelfth P5+ site, P5+ is bonded in a distorted trigonal non-coplanar geometry to three O2- atoms. There are a spread of P–O bond distances ranging from 1.56–1.59 Å. There are forty-eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a trigonal planar geometry to one Li1+, one Sc3+, and one P5+ atom. In the second O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one Sc3+, and one P5+ atom. In the third O2- site, O2- is bonded in a T-shaped geometry to two Li1+ and one P5+ atom. In the fourth O2- site, O2- is bonded in a 3-coordinate geometry to two Li1+, one Ti4+, and one P5+ atom. In the fifth O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+ and two P5+ atoms. In the sixth O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+ and two P5+ atoms. In the seventh O2- site, O2- is bonded in a 2-coordinate geometry to one Sc3+ and one Ti4+ atom. In the eighth O2- site, O2- is bonded in a 2-coordinate geometry to one Li1+, one Sc3+, and one P5+ atom. In the ninth O2- site, O2- is bonded in a distorted T-shaped geometry to one Li1+, one Sc3+, and one P5+ atom. In the tenth O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one Sc3+, and one Ti4+ atom. In the eleventh O2- site, O2- is bonded in a 1-coordinate geometry to one Sc3+, one P5+, and one O2- atom. The O–O bond length is 1.50 Å. In the twelfth O2- site, O2- is bonded in a 4-coordinate geometry to two Li1+, one Sc3+, and one P5+ atom. In the thirteenth O2- site, O2- is bonded in a distorted trigonal pyramidal geometry to three Li1+ and one Sc3+ atom. In the fourteenth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Ti4+ and one P5+ atom. In the fifteenth O2- site, O2- is bonded in a 3-coordinate geometry to two Sc3+ and one P5+ atom. In the sixteenth O2- site, O2- is bonded in a 3-coordinate geometry to two Li1+ and one P5+ atom. In the seventeenth O2- site, O2- is bonded in a 3-coordinate geometry to three Li1+, one Sc3+, and one O2- atom. In the eighteenth O2- site, O2- is bonded in a bent 120 degrees geometry to one Sc3+ and one P5+ atom. In the nineteenth O2- site, O2- is bonded in a 1-coordinate geometry to one Sc3+ and one P5+ atom. In the twentieth O2- site, O2- is bonded in a distorted trigonal planar geometry to two Li1+ and one P5+ atom. In the twenty-first O2- site, O2- is bonded in a 3-coordinate geometry to two Li1+ and one P5+ atom. In the twenty-second O2- site, O2- is bonded in a distorted T-shaped geometry to two Li1+ and one P5+ atom. In the twenty-third O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Sc3+ and one P5+ atom. In the twenty-fourth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Ti4+ and one P5+ atom. In the twenty-fifth O2- site, O2- is bonded in a trigonal planar geometry to one Li1+, one Sc3+, and one P5+ atom. In the twenty-sixth O2- site, O2- is bonded in a 2-coordinate geometry to one Li1+, one Sc3+, and one P5+ atom. In the twenty-seventh O2- site, O2- is bonded in a 2-coordinate geometry to two Li1+, one Sc3+, and one P5+ atom. In the twenty-eighth O2- site, O2- is bonded in a 4-coordinate geometry to two Li1+, one Sc3+, and one P5+ atom. In the twenty-ninth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one Li1+ and two P5+ atoms. In the thirtieth O2- site, O2- is bonded in a 2-coordinate geometry to one Li1+, one Sc3+, and one P5+ atom. In the thirty-first O2- site, O2- is bonded in a distorted T-shaped geometry to one Li1+, one Sc3+, and one P5+ atom. In the thirty-second O2- site, O2- is bonded in a 4-coordinate geometry to one Li1+, two Sc3+, and one O2- atom. The O–O bond length is 1.52 Å. In the thirty-third O2- site, O2- is bonded in a distorted T-shaped geometry to one Li1+, one Sc3+, and one P5+ atom. In the thirty-fourth O2- site, O2- is bonded in a distorted T-shaped geometry to two Li1+ and one Sc3+ atom. In the thirty-fifth O2- site, O2- is bonded in a 2-coordinate geometry to one Li1+, one Sc3+, one P5+, and one O2- atom. The O–O bond length is 1.50 Å. In the thirty-sixth O2- site, O2- is bonded in a 1-coordinate geometry to one Li1+, one Sc3+, one P5+, and one O2- atom. The O–O bond length is 1.49 Å. In the thirty-seventh O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one Sc3+, and one P5+ atom. In the thirty-eighth O2- site, O2- is bonded in a 1-coordinate geometry to one Sc3+, one P5+, and one O2- atom. In the thirty-ninth O2- site, O2- is bonded in a 2-coordinate geometry to one Li1+, one Sc3+, and one P5+ atom. In the fortieth O2- site, O2- is bonded in a distorted tetrahedral geometry to two Li1+ and two Sc3+ atoms. In the forty-first O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one Sc3+, and one O2- atom. In the forty-second O2- site, O2- is bonded in a 2-coordinate geometry to one Li1+, one Sc3+, and one O2- atom. In the forty-third O2- site, O2- is bonded in a 1-coordinate geometry to one Li1+, one Sc3+, and one P5+ atom. In the forty-fourth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Li1+, one Sc3+, and one P5+ atom. In the forty-fifth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Li1+ and one P5+ atom. In the forty-sixth O2- site, O2- is bonded in a bent 120 degrees geometry to one Li1+ and one P5+ atom. In the forty-seventh O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one Sc3+, and one P5+ atom. In the forty-eighth O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one Sc3+, and one P5+ atom.