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Based on Zong's work [26] on translative packing densities of 3-dimensional convex bodies, we present a local method to estimate the density θt(C3) of the densest translative covering of an octahedron. As a consequence we prove that θt(C3) ≥ 1 + 6.6 × 10–8, which is the first non-trivial lower bound for this density. [ABSTRACT FROM AUTHOR]

Consider an arbitrary n -dimensional lattice Λ such that Z n ⊂ Λ ⊂ Q n . Such lattices are called rational and can always be obtained by adding m ≤ n rational vectors to Z n. The defect d (E , Λ) of the standard basis E of Z n (n unit vectors going in the directions of the coordinate axes) is defined as the smallest integer d such that certain (n − d) vectors from E together with some d vectors from the lattice Λ form a basis of Λ. Let ‖ ⋅ ‖ be L 1 -norm on Q n. Suppose that for each non-integer x ∈ Λ inequality ‖ x ‖ > 1 holds. Then the unit octahedron O E n = x ∈ R n : ‖ x ‖ ⩽ 1 is called admissible with respect to Λ and d (E , Λ) is also called the defect of the octahedron O E n with respect to E and is denoted by d (O E n , Λ). Let d n = max Λ ∈ A n d (O E n , Λ) , where A n is the set of all rational lattices Λ such that O E n is admissible w.r.t. Λ. In this article we show that n − d n = Θ (log n). Let d n m = max Λ ∈ A m d (O E n , Λ) , where A m is the set of all rational lattices Λ such that 1) O E n is admissible w.r.t. Λ and 2) Λ can be obtained by adding m rational vectors to Z n : Λ = Z n , a 1 , ... , a m Z for some a 1 , ... , a m ∈ Q n. In this article we show that for any 0 < ϵ < 1 and large enough n we have m < n ϵ 8 (1 ϵ + 1) ⟹ d n m < n − n 1 − ϵ. Finally we show that for any B > 0 there exists a positive constant C > 0 such that m < C n log log n log 2 n ⟹ d n m < n − B log n. [ABSTRACT FROM AUTHOR]

Single crystals of Ba2YAlO5 and of the α and β phases of Ba6Y2Al4O15 suitable for X‐ray structure analysis were obtained via grain growth of polycrystalline samples prepared by solid‐state reactions. Ba2YAlO5 was found to have a monoclinic crystal structure, with lattice parameters a = 7.2333 (7), b = 6.0254 (5), c = 7.4294 (7) Å and β = 117.249 (3)°, and to belong to the space group P21/m, while α‐Ba6Y2Al4O15 was determined to be monoclinic, with a = 5.9019 (2), b = 7.8744 (3), c = 9.6538 (3) Å and β = 107.7940 (10)°, and the space group Pm, and β‐Ba6Y2Al4O15 was found to be monoclinic, with a = 7.8310 (2), b = 5.8990 (2), c = 18.3344 (6) Å and β = 91.6065 (11)°, and the space group P2/c. In each of these compounds, BO6 octahedra in ABO3 perovskite‐type structures were replaced by AlO4 tetrahedra and YO6 octahedra. Polycrystalline samples in which some Y atoms were replaced with Eu exhibited orange–red luminescence in the range 580–730 nm in response to exposure to radiation having a wavelength of approximately 250 nm. [ABSTRACT FROM AUTHOR]

Lattice structure metamaterials offer a variety of unique and tailorable properties, yet industrial adoption is slowed by manufacturability and inspection-related difficulties. Despite recent advances in laser powder bed fusion additive manufacturing, the sub-millimeter features of lattices are at the edge of process capabilities and suffer from low geometric quality. To better understand their complex process-structure-property (PSP) relationships, octahedron structures were manufactured across a power spectrum, inspected, and mechanically tested. X-ray computed tomography was used to characterize lattice geometry, and demonstrated that lattice strut geometry measures, increased significantly as a function of laser power. Furthermore, lattices are shown to exhibit a direct correlation between laser power and mechanical performance metrics. Performance variations up to 60% are shown as a function of process parameters despite nominally identical geometry. Significant geometry variations are found to be the cause of performance variation, while material properties as measured by microindentation hardness are constant across the studied parameter range. PSP relationships are modeled, and the limitations of these models are explored. It was found that resulting models can predict mechanical performance based on geometric characteristics with R2 values of up to 0.86. Finally, mechanistic causes of observed performance changes are discussed. [ABSTRACT FROM AUTHOR]

Vanadium is the dominant trace element and chromophore in tanzanite, the most valued gemmological variety of zoisite. The structure of zoisite–tanzanite was obtained by structural refinement to assess the vanadium location in the zoisite structure. However, the small V content in tanzanite evidenced by electron microprobe and laser ablation inductively coupled plasma mass spectrometry limits the exact determination of the V position in the zoisite structure. Structural refinement revealed that the average bond length of the less distorted M 1,2O6 octahedron is below 1.90 Å, and M 3O6 has slightly longer bonds with an average of ca. 1.96 Å. The M 1,2 site is slightly overbonded with a bond-valence sum (BVS) of 3.03 vu, whereas M 3 is slightly underbonded (BVS = 2.78 vu). Optical absorption spectra revealed that most V is trivalent, but a small portion is probably in a four-valent state. Therefore, crystal field Superposition Model and Bond-Valence Model calculations were applied based on several necessary assumptions: (1) V occupies octahedral sites; and (2) it can occur in two oxidation states, V3+ or V4+. Crystal field Superposition Model calculations from the optical spectra indicated that V3+ prefers occupying the M 1,2 site; the preference of V4+ from the present data was impossible to determine. Bond-Valence Model calculations revealed no unambiguous preference for V3+, although simple bond-length calculation suggests the preference of the M 3 site. However, it is quite straightforward that the M 1,2 site is better suitable for V4+. If the possible octahedral distortion is considered, the M 1,2O6 octahedron is subject to a smaller change in distortion if occupied by V3+ than the M 3O6 octahedron. Consequently, considering the results of both the crystal field Superposition Model and Bond-Valence Model calculations, we assume that both V3+ and V4+ prefer the M 1,2 site. [ABSTRACT FROM AUTHOR]

Mn(II)-based perovskite materials are being intensively explored for lighting applications; understanding the role of ligands regarding their photobehavior is fundamental for their development. Herein, we report on two Mn (II) bromide perovskites using monovalent (perovskite 1, P1) and bivalent (perovskite 2, P2) alkyl interlayer spacers. The perovskites were characterized with powder X-ray diffraction (PXRD), electron spin paramagnetic resonance (EPR), steady-state, and time-resolved emission spectroscopy. The EPR experiments suggest octahedral coordination in P1 and tetrahedral coordination for P2, while the PXRD results demonstrate the presence of a hydrated phase in P2 when exposed to ambient conditions. P1 exhibits an orange-red emission, while P2 shows a green photoluminescence, as a result of the different types of coordination of Mn(II) ions. Furthermore, the P2 photoluminescence quantum yield (26%) is significantly higher than that of P1 (3.6 %), which we explain in terms of different electron-phonon couplings and Mn-Mn interactions. The encapsulation of both perovskites into a PMMA film largely increases their stability against moisture, being more than 1000 h for P2. Upon increasing the temperature, the emission intensity of both perovskites decreases without a significant shift in the emission spectrum, which is explained in terms of an increase in the electron-phonon interactions. The photoluminescence decays fit two components in the microsecond regime—the shortest lifetime for hydrated phases and the longest one for non-hydrated phases. Our findings provide insights into the effects of linear mono- and bivalent organic interlayer spacer cations on the photophysics of these kinds of Mn (II)-based perovskites. The results will help in better designs of Mn(II)-perovskites, to increase their lighting performance. [ABSTRACT FROM AUTHOR]

Fractal structures with self‐similarity are of fundamental importance in the fields of aesthetic, chemistry and mathematics. Here, by taking advantage of constructs the rational geometry‐directed precursor design, we report the construction of two fascinating Platonic solids, the Sierpiński tetrahedron ST‐T and the Sierpiński octahedron ST‐O, in which each possesses a fractal Sierpiński triangle on their independent faces. These two discrete complexes are formed in near‐quantitative yield from the multi‐component self‐assembly of truncated Sierpiński triangular kernel L1 with tribenzotriquinacene‐based hexatopic and anthracene‐based tetratopic terpyridine ligands (L3 and L4) in the presence of metal ions, respectively. The enhanced stabilities of the 3D discrete structures were investigated by gradient tandem mass spectrometry (gMS2). This work provides new constructs for the imitation of complex virus assemblies and for the molecular encapsulation of giant guest molecules. [ABSTRACT FROM AUTHOR]

Fractal structures with self‐similarity are of fundamental importance in the fields of aesthetic, chemistry and mathematics. Here, by taking advantage of constructs the rational geometry‐directed precursor design, we report the construction of two fascinating Platonic solids, the Sierpiński tetrahedron ST‐T and the Sierpiński octahedron ST‐O, in which each possesses a fractal Sierpiński triangle on their independent faces. These two discrete complexes are formed in near‐quantitative yield from the multi‐component self‐assembly of truncated Sierpiński triangular kernel L1 with tribenzotriquinacene‐based hexatopic and anthracene‐based tetratopic terpyridine ligands (L3 and L4) in the presence of metal ions, respectively. The enhanced stabilities of the 3D discrete structures were investigated by gradient tandem mass spectrometry (gMS2). This work provides new constructs for the imitation of complex virus assemblies and for the molecular encapsulation of giant guest molecules. [ABSTRACT FROM AUTHOR]

A mononuclear Dy(III)-based complex constructed from a phosphine oxide ligand and light halogen Cl donor displays octahedral geometry and field-induced single-molecule magnet behavior. [Display omitted] • A new Dy(III)-containing complex has been constructed from a phosphine oxide ligand and halogen Cl ligand. • The hexa -coordinated Dy(III) ions with a octahedral geometry are well-isolated in the complex. • The complex presents the field-induced single-molecule magnet behavior. We have synthesized a mononuclear Dy(III)-based complex, [Dy(CyPh 2 PO) 3 Cl 3)] (1) (CyPh 2 PO = cyclohexylbisphenylphosphine oxide), constructed from a phosphine oxide ligand and a light halogen Cl donor. The Dy(III) ion presents an octahedral geometry where two O atoms from two phosphine ligands locate at two vertexes, while the equatorial positions are completed by three Cl anions and a O atom from another phosphine ligand. Magnetism results reveal that slow relaxation of the magnetizations exists in 1 under an extra dc field because of the significant quantum tunnelling of magnetization (QTM) at 0 Oe dc field. The lighter Cl ions in equatorial plane result in a larger effect to QTM, and thus smaller contribution to slow magnetic relaxation. [ABSTRACT FROM AUTHOR]

The sintering mechanisms and temperature dependence of coalescence of colliding cubic boron nitride (c-BN) nanoparticles are investigated using classical molecular dynamics (MD) simulation. Particle-particle collisions of 2.55-nm octahedral c-BN nanoparticles, consisting solely of the most stable {111} facets, with half of the surface terminations being boron and the other half nitrogen, are analyzed statistically and evaluated to assess the initial temperature range (2500 K – 3100 K) for sintering and its effect on grain growth. At these temperatures, the collision process maximizes contact surface area through interfacial sliding, thereby minimizing free energy and accommodating dangling bonds. Moreover, the exothermic formation of bonds of the coalescing nanoparticles increases the temperature. The alignment of the {111} orientation of the two collided nanoparticles occurs at a temperature slightly above the melting point, and rapid grain growth happens when the temperature is a few hundred degrees higher than that. However, phase separation also takes place at the corners away from the collision plane of the merging nanoparticles. Between 3100 K and 3250 K, crystalline alignment occurs, which aids the sintering process and allows for the formation of a well-structured nanocluster. However, above 3300 K, phase separation dominates and drives the melting of the entire sintered nanocluster. • Initial contact of vertex-to-surface rapidly converts to edge-to-surface followed by surface-to-surface. • Two nanoparticles can slide at sufficiently high temperatures to maximize the contact area for B–N bond formation. • Crystallographic alignment of {111} facets of two nanoparticles can occur upon exceeding the melting temperature at 3000 K. • Coalescence can result in the evolvement of a good mono-crystalline {111} surface, forming a well-structured nanocluster. • Phase segregation engulfs the entire cluster when the temperature exceeds 3200 K. [ABSTRACT FROM AUTHOR]

Let Oct 1 + and Oct 2 + be the planar and non-planar graphs, respectively, obtained from the Octahedron by 3-splitting a vertex. For Oct 1 + , we prove that if a 4-connected graph is Oct 1 + -minor-free, then it is C 6 2 , C 2 k + 1 2 (k ≥ 2) or it is obtained from C 5 2 by repeatedly 4-splitting vertices. We also show that a planar graph is Oct 1 + -minor-free if and only if it is constructed by repeatedly taking 0-, 1-, 2-sums starting from { K 1 , K 2 , K 3 } ∪ κ ∪ { O c t a h e d r o n , L 5 } , where κ is the set of graphs obtained by repeatedly taking the special 3-sums of K 4 and L 5 is the graph obtained from two 5-cycles a 1 a 2 ... a 5 a 1 , b 1 b 2 ... b 5 b 1 by adding the five edges a i b i for all 1 ≤ i ≤ 5. For Oct 2 + , we prove that if a 4-connected graph is Oct 2 + -minor-free, then it is planar, C 2 k + 1 2 (k ≥ 2) , the line graph of K 3 , 3 or it is obtained from C 5 2 by repeatedly 4-splitting vertices. [ABSTRACT FROM AUTHOR]

In this work, fabrication of Cu2O@Cu1.75S core‐shell octahedrons was achieved through a facile water bath stirring process. Compared with pure Cu2O, the composite showed enhanced sensing performance for NO2. The response value of Cu2O@Cu1.75S to 5 ppm NO2 at 40 °C is seven times that of Cu2O to 5 ppm NO2 at 75 °C. Moreover, Cu2O@Cu1.75S has the ability to detect 100 ppb NO2 and has good NO2 sensing selectivity and long‐term stability. This study shows that Cu2O@Cu1.75S hybrid is a type of outstanding NO2 gas sensing material on account of its low working temperature and high sensing sensitivity. [ABSTRACT FROM AUTHOR]

GLO:1CJF/01may21:bkcs12183-fig-0003.jpg PHOTO (COLOR): 3 Electrochemical characterization of the Pd octahedra/C, PdH octahedra/C, Pd cubes/C, and PdH cubes/C catalysts. The ORR mass activities for Pd octahedra/C, PdH octahedra/C, Pd cubes/C, and PdH cubes/C were 0.007, 0.014, 0.124, and 0.041 A mg SB Pd sb SP -1 sp at 0.9 V (vs. The measured ECSA SB CO sb s were 58.34, 57.51, 61.83, and 57.2 m SP 2 sp g SP -1 sp SB Pd sb for Pd octahedra/C, PdH octahedra/C, Pd cubes/C, and PdH cubes/C, respectively. Keywords: Palladium hydride; Oxygen reduction reaction; Catalyst; Octahedron; Cube EN Palladium hydride Oxygen reduction reaction Catalyst Octahedron Cube 802 805 4 05/27/21 20210501 NES 210501 Oxygen reduction reaction (ORR) performances of palladium nanocubes and octahedra and their hydride forms were investigated. [Extracted from the article]

Significant efforts have been dedicated to boosting the electrocatalytic activity of Co9S8 for the oxygen evolution reaction (OER); however, with limited improvement in its intrinsic activity, which relies on careful band engineering. Fe possesses one less 3d electron and lower electronegativity than Co, suggesting a higher d‐band center when forming polyhedron with S anions. Here, to improve the intrinsic activity by elevating the d‐band center, the six‐coordinated octahedrons in Co9S8 are redesigned utilizing an Fe‐incorporated topochemical deintercalation method. Through substituting partial Co octahedrons by Fe octahedrons with higher d‐band, the overall d‐band center is regulated to achieve optimized adsorption and thus superior OER activity. With a reduction of 95 mV on the overpotential (at 10 mA cm−2), this work sheds lights on the design of OER catalysts through polyhedron engineering using topochemical deintercalation. [ABSTRACT FROM AUTHOR]

Transition metal (TM)‐based bimetallic spinel oxides can efficiently activate peroxymonosulfate (PMS) presumably attributed to enhanced electron transfer between TMs, but the existing model cannot fully explain the efficient TM redox cycling. Here, we discover a critical role of TM−O covalency in governing the intrinsic catalytic activity of Co3−xMnxO4 spinel oxides. Experimental and theoretical analysis reveals that the Co sites significantly raises the Mn valence and enlarges Mn−O covalency in octahedral configuration, thereby lowering the charge transfer energy to favor MnOh–PMS interaction. With appropriate MnIV/MnIII ratio to balance PMS adsorption and MnIV reduction, the Co1.1Mn1.9O4 exhibits remarkable catalytic activities for PMS activation and pollutant degradation, outperforming all the reported TM spinel oxides. The improved understandings on the origins of spinel oxides activity for PMS activation may inspire the development of more active and robust metal oxide catalysts. [ABSTRACT FROM AUTHOR]

Transition metal (TM)‐based bimetallic spinel oxides can efficiently activate peroxymonosulfate (PMS) presumably attributed to enhanced electron transfer between TMs, but the existing model cannot fully explain the efficient TM redox cycling. Here, we discover a critical role of TM−O covalency in governing the intrinsic catalytic activity of Co3−xMnxO4 spinel oxides. Experimental and theoretical analysis reveals that the Co sites significantly raises the Mn valence and enlarges Mn−O covalency in octahedral configuration, thereby lowering the charge transfer energy to favor MnOh–PMS interaction. With appropriate MnIV/MnIII ratio to balance PMS adsorption and MnIV reduction, the Co1.1Mn1.9O4 exhibits remarkable catalytic activities for PMS activation and pollutant degradation, outperforming all the reported TM spinel oxides. The improved understandings on the origins of spinel oxides activity for PMS activation may inspire the development of more active and robust metal oxide catalysts. [ABSTRACT FROM AUTHOR]

Consider an arbitrary n -dimensional lattice Λ such that Z n ⊂ Λ ⊂ Q n . Such lattices are called rational and can always be obtained by adding m ⩽ n rational vectors to Z n. The defect d (E , Λ) of the standard basis E of Z n (n unit vectors going in the directions of the coordinate axes) is defined as the smallest integer d such that certain (n − d) vectors from E together with some d vectors from the lattice Λ form a basis of Λ. Let | | ⋅ | | be L 1 -norm on Q n. Suppose that for each non-integer x ∈ Λ inequality | | x | | > 1 holds. Then the unit octahedron O n = x ∈ R n : | | x | | ⩽ 1 is called admissible with respect to Λ and d (E , Λ) is also called the defect of the octahedron O n with respect to E and is denoted by d (O E n , Λ). Let d n m = max Λ ∈ A m d (O E n , Λ) , where A m is the set of all rational lattices Λ such that (1) O n is admissible w.r.t. Λ and (2) Λ can be obtained by adding m rational vectors to Z n : Λ = Z n , a 1 , ... , a m Z for some a 1 , ... , a m ∈ Q n. In this article we show that there exists an absolute positive constant C such that for any m < n d n m ⩽ C n ln (m + 1) ln n m ln ln n m m 2 This bound was also claimed in [2] and [1] , however the proof was incorrect. In this article along with giving correct proof we highlight substantial inaccuracies in those articles. [ABSTRACT FROM AUTHOR]

Making consistent and precise octahedral pressure media is crucial for reproducible high-pressure experiments in the multi-anvil press. Here we report a new approach of casting octahedra using 3D-printed molds, and pressure calibrations for octahedra both with and without pre-existing gaskets ("fins"). The 3D-printed molds for casting octahedra from either Ceramacast 584-OF or 646 cement improve the reproducibility of the octahedra and allow for a pre-existing central hole (for the high-pressure cell assembly) in the final cast product. Pressure and temperature calibrations of the octahedra have been performed based on phase transitions in bismuth (Bi) and silica (SiO2), respectively, in order to determine the efficiency and reproducibility of pressure generation and thermal insulation for cast octahedra designed for use with 18/12, 14/8, and 10/5 multi-anvil assemblies. The pressure-generating efficiency of the 14/8 and 10/5 octahedra with pre-existing gaskets, cast from the 584-OF cement, is similar to that of the corresponding COMPRES (Consortium for Materials Properties Research in Earth Sciences) octahedra, and more efficient than pre-cast octahedra made from the same material but lacking pre-existing gaskets. The efficiency of pre-gasketed 18/12 octahedra made of the 646 cement is markedly lower than those of the 584 cement. However, the 18/12 large-volume octahedra, cast (with fins) from the ZrO2-based 646 cement, also provides efficient thermal insulation. Casting octahedral solid pressure media for multi-anvil experiments using 3D-printed "injection" molds is a low-cost and low failure-rate alternative for conducting reproducible experiments at high pressure in the multi-anvil apparatus. [ABSTRACT FROM AUTHOR]

Octahedral core-shell ZIF-67a/b@CuOx (a/b=4/1,2/1,1/1,1/1.5) coated with nano particle ZIF-67 catalyst for low temperature denitrification was prepared by encapsulation method at room temperature and characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (IR), scanning electron microscopy (SEM), specific surface area analyzer (BET). The effect of different amounts of ZIF-67 on the morphology, composition, specific surface area of catalysts and the catalytic reduction performance was studied. The results showed that octahedral CuOx derived by HKUST-1 sintered had good carrying capacity, and the morphology, crystal structure and great BET value of ZIF-67 were kept. When a/b was 4/1, better uniformity and higher dispersion of ZIF-67 and larger specific surface area of catalyst, and the best catalytic low-temperature denitrification were obtained. The catalysts activity of CO-SCR results showed that denitrification rate of ZIF-674/1@CuOx was 86.5% and 95% at 150 and 225°C respectively. The temperature of ZIF-674/1@CuOx was 50°C lower than that of ZIF-67 at the same denitrification rate (86%). Specific surface area of ZIF-674/1@CuOx was largest, 1168.410 m²/g, which provided more reaction interfaces and effective contacts and improved the catalytic denitrification rate. [ABSTRACT FROM AUTHOR]

• A novel NiSe 2 @MXene/rGO aerogel (NSMGA) was fabricated with different mass loading of Ti 3 C 2 MXene. • NSMGA applied as multifunctional electrode material for supercapacitor study and overall water splitting. • The optimal electrode (NSMGA-40) exhibited excellent electrochemical performance. • NSMGA-40 showed remarkable stability during electrochemical applications. In this research, we have designed novel three-dimensional (3D) Ti 3 C 2 MXene/rGO composite aerogels (MGA) integrated with octahedron-like NiSe 2 (NS), with different mass loadings of MXene (20 wt% and 40 wt%). Resultant aerogels developed into a cellular lattice like network that significantly improved the contact area among active material and electrolyte. 3D spongy scaffold of MGA boosted the mass diffusion rate, and good electrical conductivity of MXene and rGO provided fast transport of charges during the electrochemical tests, which endowed superior supercapacitor and water splitting performances. Electrode with optimized MXene/rGO ratio i.e., NSMGA-40, exhibited a remarkable specific capacity of 289.7 mAh g−1 at current density of 1 A g−1 and excellent durability of 92.5% over 5000 charge/discharge cycles at 12 A g−1 in a three electrode system for supercapacitor. Meanwhile, as a bifunctional electrocatalyst, NSMGA-40 required a low overpotential of 97 mV and 262 mV to reach 10 mA cm−2 for HER and OER activity, respectively, in alkaline media. The values of Tafel slopes were as small as 89 mV dec−1 (HER) and 75 mV dec−1 (OER), signifying accelerated electron-transfer kinetics. Furthermore, in both cases, NSMGA-40 electrocatalyst withstood a long-term stability test of 10 h. Hence, the obtained results can be manifested for the structural and componential engineering that maximizes the synergetic effects from Ti 3 C 2 MXene, rGO, and NS. Indeed, our fabricated aerogels offer a valuable reference for the fabrication of 3D multicomponent electrode materials for energy storage and conversion applications. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a facile molten-salt strategy is developed for controllably synthesizing LiNbO 3 microcrystals shaped as octahedrons and cubes in molten LiNO 3 and LiCl salts without using any capping agents. The as-prepared LiNbO 3 micro-octahedrons and micro-cubes are characterized by means of X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and selected area electron diffraction (SAED). Our results show that the formation of LiNbO 3 micro-octahedrons and micro-cubes can be attributed to a dissolution-nucleation-aggregation-recrystallization process. Furthermore, in order to minimize the surface and interface energies between the constituents and the salts, octahedral and cubic morphology forms under different molten-salt conditions, which shows the anion may play a crucial role in tuning the product morphology. [ABSTRACT FROM AUTHOR]

Zinc stannate (Zn 2 SnO 4 ) that used for detecting traces of H 2 S was less concerned. In this work, Zn 2 SnO 4 octahedra with the average size of 0.18 μm were prepared through a facile hydrothermal method followed by an annealing process in air atmosphere. The fabricated sensor shows excellent selectivity and sensitivity to H 2 S at working temperature of 170 °C. The gas response exhibits good linear relationship with the increasing of concentrations in the range of 5 –10 ppm. The response to 100 ppm H 2 S can reach up to 172.5 and the lowest detection limit is down to 5 ppb. Such outstanding gas property might be attributed to the morphology of the octahedra and the increased contact area between Zn 2 SnO 4 and target gas, which may has potential applications in detecting traces of H 2 S. [ABSTRACT FROM AUTHOR]

A promising class of mixed transition-metal oxides (MTMOs) with stoichiometric or non-stoichiometric ratios has recently received notable attention worldwide. Benefiting from their excellent electrochemical properties, these MTMOs will play a substantial role for low-cost and ecologically responsive energy storage/conversion technologies. In this work, we have developed highly crystalline octahedron 3D-Zn 2 SnO 4 by hydrothermal synthesis and evaluated their application in Li-ion batteries (LIBs). Several characterization techniques have been used to analyze structural, compositional, and morphological features of the material. The highly crystalline octahedron 3D-Zn 2 SnO 4 micro-particle attained a specific discharge capacity of 739 mAh g −1 with a coulombic efficiency of 99% after 100 cycles at a current density of 100 mA g −1 . These attractive results suggest that 3D-Zn 2 SnO 4 shows good performance as a negative electrode material for high-performance LIBs. [ABSTRACT FROM AUTHOR]

Unique Co 3 O 4 nano-octahedrons for modifying electrode were synthesized through simple chemical reaction. This versatile Co 3 O 4 nanostructure possesses the combined advantages of morphological stability and high porosity that can buffer volume change during electrochemical cycles, shorten diffusion path of electron transport, and exhibit remarkable overall electrochemical performance. Samples were characterized by field transmission electron microscopy, transmission electron microscopy, energy dispersive X-ray spectroscopy, X-ray diffractometry, Fourier transform infrared spectroscopy and electrochemical impedance spectroscopy. An electrode modified by this material was used for detection of benzobicyclon. Square wave voltammetry showed that there was a linear relationship between peak current and concentration in the range of 10.00–582.96 μmol L −1 with a detection limit (S/N = 3) of 0.38 μmol L −1 . The modified electrode was used for detection of benzobicyclon in brown rice and rice straw samples with satisfactory recovery, reproducibility and stability. Modified electrodes reported in the literature that were prepared by different methods resulted in other kinds of surface morphologies that did not exhibit the same level of performance. [ABSTRACT FROM AUTHOR]

The syntheses, structural characterization, and magnetic properties of three lanthanide complexes with formulas [Ln(L¹)3] (Ln = Dy (1Dy); Er (1Er)); and [Dy(L²)2] (2Dy) were reported. Complexes 1Dy and 1Er are isostructural with the metal ion in distorted trigonal-prismatic coordination geometry, but exhibit distinct magnetic properties due to the different shapes of electron density for DyIII (oblate) and ErIII (prolate) ions. Complex 1Dy shows obvious SMM behavior under a zero direct current (dc) field with an effective energy barrier of 31.4 K, while complex 1Er only features SMM behavior under a 400 Oe external field with an effective energy barrier of 23.96 K. In stark contrast, complex 2Dy with the octahedral geometry only exhibits the frequency dependence of alternating current (ac) susceptibility signals without χ" peaks under a zero dc field. [ABSTRACT FROM AUTHOR]

Understanding and designing versatile electrocatalysts for the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) in alkaline electrolyte is of great interest and importance towards overall water splitting. Here we investigated the crystal-plane-dependent electrocatalytic activity of NiCo 2 O 4 crystals by combining experimental studies and theoretical calculations for the first time. It is revealed that NiCo 2 O 4 nanosheet exposing {1 1 0} crystal planes shows higher catalytic activity for both HER and OER than that of NiCo 2 O 4 octahedron exposing {1 1 1} crystal planes and NiCo 2 O 4 truncated octahedron exposing {1 1 1} and {1 0 0} crystal planes. Furthermore, we grew the nanosheet with {1 1 0} planes on nickel foam (NF), which could guarantee fast electron and ion transport, rapid release of evolved bubbles and good structural stability, leading to the improved electrochemical performance. Acting as both anode and cathode electrocatalysts with a two-electrode electrolyzer in alkaline medium, NiCo 2 O 4 nanosheet array produced a small cell voltage of 1.59 V to drive a current density of 10 mA cm −2 . The research presented here is of both fundamental and instructional significance because it unveils that selectively exposing specific crystal planes is very effective to receive promising catalysts for overall water splitting. [ABSTRACT FROM AUTHOR]

Recently, spinel cobalt oxide (Co 3 O 4 ) structure has been widely investigated due to its excellent sensitivity towards various noxious gases and good response/recovery speed at low concentration. In this work, we designed and synthesized two kinds of different Co 3 O 4 micro-structure (cube and octahedron) with a similar size. After fabricating them into gas sensors, we found that the crystal plane structure of Co 3 O 4 has an important effect on its gas sensing performance. Furthermore, the {111} planes of Co 3 O 4 may be more sensitive than {100} planes to various testing gases. Co 3 O 4 octahedrons micro-structure exhibits an excellent sensitivity (about 12.6), good response/recovery speed and cycling stability (no decline even after 2 days) under 50 ppm ethanol gases at working temperature of 200 °C. As such, thisCo 3 O 4 octahedrons micro-structure is a promising candidate for a high-performance gas sensing material. [ABSTRACT FROM AUTHOR]

[Display omitted] • We have grown the first octahedral NiSe 2 on one-dimensional NiTiO 3 NFs using a one-pot solvothermal method. • The composite NiTiO 3 NFs/NiSe 2 presented an improved CO 2 photoreduction efficiency compared to the pristine NiTiO 3 NFs photocatalyst. • The optimal sample (0.09 wt% NTNs) can perform UV–vis light-driven CO 2 reduction to CO and CH 4 with a selectivity of 88.8% at a rate of 459.96, 269.02 μmol g−1h−1 respectively. • The high CO 2 photoreduction is attributed to the improved light absorbance and prolonged lifetime of photogenerated carriers due to metallic NiSe 2. • In situ FT-IR (DRIFT) revealed the selective CO 2 → COOH ∗ → CO ∗ / C O → CHO ∗ → CH 3 O ∗ → CH 4 conversion on the optimal sample. Excessive CO 2 concentrations in the atmosphere have a range of adverse effects, including climate change and the rise in sea levels. One approach to mitigate these issues is to utilize artificial photosynthesis, which transforms CO 2 into valuable fuels. In this study, a unique octahedral nickel selenide (NiSe 2) structure supported on one-dimensional (1D) nickel titanate nanofibers (NiTiO 3 NFs) was created through a one-pot solvothermal process. The optimized NiTiO 3 NFs/NiSe 2 nanostructure exhibits exceptional CO 2 photoreduction performance across a broader range of the solar spectrum (UV–vis). At a 0.09 wt% NiSe 2 concentration, the yields of CH 4 and CO were 3.14 and 1.47 times higher, respectively, than those produced by pure NiTiO 3 NFs. The exceptional photocatalytic activity can be attributed to the efficient electron extraction and transfer from NiTiO 3 NFs to NiSe 2 , as well as the enhanced light harvesting capacity. Furthermore, the introduction of NiSe 2 generates more oxygen vacancies (O V) that can promote the adsorption and activation of CO 2 and water, considerably reducing the free energy barrier for COOH* formation and accelerating the reaction kinetics. The results of this study are expected to create new opportunities for synthesizing efficient photocatalysts based on transition metal dichalcogenides that can be utilized in energy conversion applications. [ABSTRACT FROM AUTHOR]

A new indium(III) fluoride complex Cu(InF)·10HO with the divalent Cu cation is synthesized for first time, and its crystal structure, which is a new type of the structure of complex fluorides of trivalent metals with divalent cations, obtained from a hydrofluoric acid solution, is studied. The structure of Cu(InF)·10HO is monoclinic, space group P2/a. The structure is formed by isolated centrosymmetric distorted octahedral complex [Cu(HO)] cations and isolated distorted octahedral complex [InF(HO)] anions with the cis arrangement of coordinated water molecules. The branched system of O-H·F hydrogen bonds, which is formed by the coordinated HO molecules with the F atoms of anions, combines the structural elements of the compound to form a three-dimensional framework. [ABSTRACT FROM AUTHOR]

The crystal structures of isostructural fluoride complexes of indium(III) M[InF(HO)] (M = Rb, Cs) crystallizing in the monoclinic system, space group I2/ a, are studied. The structures of M[InF(HO)] (M = Rb, Cs) are formed of isolated centrosymmetric complex [InF(HO)] anions with the trans-position of coordinated HO molecules and Rb, respectively Cs, cations. The In atom in the complex [InF(HO)] anion is surrounded by four F atoms and two oxygen atoms of coordinated HO molecules, forming the coordination polyhedron as a slightly distorted octahedron. Via a system of hydrogen O-H⋯F bonds the polyhedra of In atoms are arranged in a three-dimensional framework with the cations located in its channels. [ABSTRACT FROM AUTHOR]

• Two new octahedral compounds were synthesized. • Crystal structures were elucidated by X-ray analysis. • Octahedron was formed by intramolecular hydrogen bonds. • Emission properties were studied by experimental measurement and DFT calculation. Two new octahedral compounds, [(phenH)(phen)]PF 6 (phen = 1,10-phenanthroline) and [(ClterpyH 2)(Clterpy)(H 2 O)](PF 6) 2 (Clterpy = 4′‑chloro-2,2′:6′,2″-terpyridine) were synthesized. Their light emission properties were investigated by experimental measurements and theoretical calculations, and the relationship between the emission and structure of the protonated compounds was studied. Time-dependent density functional theory calculations revealed that [(phenH)(phen)]PF 6 and [(ClterpyH 2)(Clterpy)(H 2 O)](PF 6) 2 exhibit hydrogen-bonded octahedrons, even in the excited states. In [(phenH)(phen)]PF 6 , an octahedron was formed by three hydrogen bonds and the dihedral angle between phenH+ and phen was 78° In [(ClterpyH 2)(Clterpy)(H 2 O)](PF 6) 2 , four hydrogen bonds were detected forming an octahedron with the angle between ClterpyH 2 2+ and Clterpy being nearly 90° [(ClterpyH 2)(Clterpy)(H 2 O)](PF 6) 2 also exhibited a unique configuration attributed to the attachment of a proton to the nitrogen, which causes an intense emission (Φ = 0.290). NMR analyses revealed that the presence of phenH+, phen, ClterpyH 2 2+, and Clterpy did not present any additional peaks to the spectra, indicating that the H signals were averaged. We newly prepared two octahedrons of [(phenH)(phen)]PF 6 and [(ClterpyH 2)(Clterpy)(H 2 O)](PF 6) 2 and their structures were calculated using DFT. In [(ClterpyH 2)(Clterpy)(H 2 O)](PF 6) 2 , this unique configuration caused an intense emission (Φ = 0.290). [Display omitted] [ABSTRACT FROM AUTHOR]

We study polyiamonds (polygons arising from the triangular grid) that fold into the smallest yet unstudied platonic solid – the octahedron. We show a number of results. Firstly, we characterize foldable polyiamonds containing a hole of positive area, namely each but one polyiamond is foldable. Secondly, we show that a convex polyiamond folds into the octahedron if and only if it contains one of five polyiamonds. We thirdly present a sharp size bound: While there exist unfoldable polyiamonds of size 14, every polyiamond of size at least 15 folds into the octahedron. This clearly implies that one can test in polynomial time whether a given polyiamond folds into the octahedron. Lastly, we show that for any assignment of positive integers to the faces, there exists a polyiamond that folds into the octahedron such that the number of triangles covering a face is equal to the assigned number. [ABSTRACT FROM AUTHOR]

Complex [Cu( μ -Gly)Im(ClO 4 )] n (Im = imidazole, and Gly = glycine) with μ -glycine-briged copper (II) chain, containing six-coordination distorted elongated octahedron, was synthesized and characterized. The complex belongs to space group P 21/ c measured by X-ray single crystal diffraction. In the cluster, each Cu 2+ ion are six-coordination by one nitrogen atom and two oxygen atoms of glycine, one nitrogen atoms of imidazole, and two of oxygen atoms of two perchlorate. Each Cu 2+ ion has an N 2 O 4 donor set, which forms the distorted elongated octahedron due to the Jahn–Teller (JT) effect. The magnetic and thermodynamic properties were researched. Magnetic susceptibilities of the complex showed that ferromagnetic interactions occurred between the Cu (II) atoms. The Curie–Weiss constant C = 0.565 cm 3 K·mol −1 and the Weiss constant θ = 1.0585 K were given by the Curie-Weiss law The ferromagnetic nature of the interaction could be deduced as the exchange pathway of Cu O C O Cu, which involved an equatorial position at one copper (II) ion and an axial position of the nearest copper (II). The complex decomposed from 511 to 538 K as two steps. [ABSTRACT FROM AUTHOR]

In this article, a method for constructing an approximate equal area grid based on the octahedron and Snyder projection is introduced. An octahedron that has equal surface area to a sphere is built; each face of this octahedron is considered as initial subdivision surface. Then, each initial sur­face is subdivided into hierarchical triangles using a quaternary triangular subdivision scheme, which are projected onto the surface of sphere using Snyder projection. The arc projecting polyhedron trian­gles onto the spherical surface is modified by using great circle line instead of Snyder projection arc. A new approximate equal area global discrete grid system is constructed. Based on the analysis of differ­ence between the great circle arc and Snyder projection arc. the values of area, edge length, and angle of different subdivision level grids are calculated according lo corresponding spherical calculation equa­tion. Based the calculation results, different levels of approximately equidistant grid areas-lengths. angles, and spatial distributions of the deformation are analyzed. Results indicate that with increasing osubdivision levels, 1) the difference in grid areas is very little; area errors of 99. 8% of the grids are between -10% and 10%. The girds with heavy area distortion are near the lines between the middle point and three vertexes of octahedron surface, when subdivision level is equal to 10; 2) the ratio in­crements of the maximum and minimum values of grid areas and edge length show a trend toward con­vergence, converging lo 1. 73 and 3. 03 respectively. [ABSTRACT FROM AUTHOR]

Two approaches to predict the overall elastic properties of solids with regularly and irregularly shaped pores are compared. The first approach involves direct finite element simulations of periodic representative volume elements containing arrangements of pores. A simplified algorithm of collective rearrangement type is developed for generating microstructures with the desired density of randomly distributed pores of regular and irregular shapes. Homogeneity and isotropy (where appropriate) of the microstructures are confirmed by generating two-point statistics functions. The second approach utilizes Mori-Tanaka and Maxwell micromechanical models implemented via the cavity compliance contribution tensor (H-tensor) formalism. The effects of pore shape and matrix Poisson's ratio on compliance contribution parameters of different shapes are discussed. H-tensors of cubical, octahedral and tetrahedral pores for several values of matrix Poisson's ratio are published in explicit form for the first time. Good correspondence between the direct finite element simulations and micromechanical homogenization is observed for randomly oriented and parallel pores of the same shape, as well as mixtures of pores of various shapes up to 0.25 pore volume fractions. [ABSTRACT FROM AUTHOR]

Control over the shape of platinum nanocrystals has received great interests owing to their correlations with structure sensitive catalytic reactions such as CO/HC oxidation, NO x reduction, H 2 oxidation, O 2 reduction, and petroleum reforming. Pt octahedra and cubes are the well-known model catalysts for the low-index {1 1 1} and {1 0 0} faceted nanocrystals, respectively. In this work, a facile synthesis of Pt octahedra and cubes was conducted by manipulating the reduction kinetics. The reduction kinetics for the Pt precursor was altered by adjusting the volume ratio of oleylamine (OAm) and oleic acid (OAc) as the co-stabilizers and the coordination ligands in the reaction mixture. The morphologies of well-controlled Pt octahedra and cubes were observed by typical transmission electron microscopy. [ABSTRACT FROM AUTHOR]

The platinum nanocrystals with truncated octahedral, spherical and cubic morphologies were synthesized and well dispersed onto the ZSM-22 support, in order to investigate the shape effect of Pt crystals on n -hexadecane hydroconversion. It is found that the crystal facets of Pt nanoparticles play more profound roles in determining the catalytic properties. The reaction test shows that both the conversion of n -hexadecane and selectivity of iso-hydrocarbons are higher for the catalysts with octahedron nanoparticles of Pt that are predominantly enclosed by Pt {111} crystal facets than those with spherical and cubic morphologies of Pt, whose surfaces consist of more Pt {100} facets. Combined with the results of CO-IR and TPHD, it is suggested that the activity and selectivity of the reaction are well correlated to the fractions of exposed Pt {111} crystal facets, which possess more activated surface defect sites and higher amounts of activated hydrogens either on the Pt surface or in the Pt phase. Meanwhile, the catalyst activity and selectivity are found to be highly sensitive to the Pt particle size. Smaller Pt particles have higher activity and lower isomerization selectivity. [ABSTRACT FROM AUTHOR]

In this work, we have carried out a systematic study on the optical properties of gold nano-octahedra via numerical simulations. We obtained broadening scattering spectra dominated by a hybridized bonding mode originated from the interaction between intrinsic plasmon modes when increasing the size of gold nano-octahedra in vacuum. Once placing the nano-octahedra on a high refractive index dielectric substrate, a Fano dip can be induced in the scattering spectra due to the mutual interference between a dipolar mode and a quadrupolar mode. Moreover, we found that the interference become stronger by increasing the refractive index in substrate, and the broadening scattering spectra split into two hybridized modes in a single gold nano-octahedron: the anti-bonding mode and the bonding mode. Our results for the first time give a clear description of the complex plasmonic properties of a gold nano-octahedron and provide insights in designing appropriate nano-octahedral structures for applications. [ABSTRACT FROM AUTHOR]

Two new cadmium(II) complexes with the formula of CdL 2 (NCS) 2 and CdL 2 (N 3 ) 2 (in which L is 2,2-dimethyl- N , N ′-bis-(3-phenyl-allylidene)-propane-1,3-diamine) have been synthesized and characterized by elemental analysis, molar conductivity measurements, FT/IR, UV–Visible, 1 H and 13 C NMR spectra and X-ray studies. The crystal structure analysis of CdL 2 (NCS) 2 indicated that it crystallizes in orthorhombic system with space group of Pbca . Two Schiff base ligands are bonded to cadmium(II) ion as N 2 -donor chelate. Coordination geometry around the cadmium ion was found to be partially distorted octahedron. The Cd–N imine bond distances are found in the range of 2.363(2)–2.427(2) Å while the Cd–N isothiocyanate bond distances are 2.287(2) Å and 2.310(2) Å. The existence of C–H⋯π and C–H⋯S interactions in the CdL 2 (NCS) 2 crystal leads to a supramolecular structure in its network. Then cadmium complexes were screened in vitro for their antibacterial and antifungal activities against two Gram-negative and two Gram-positive bacteria and also against Candida albicans as a fungus. Moreover, the compounds were subjected for DNA-cleavage potential by gel electrophoresis method. Finally thermo-gravimetric analysis of the complexes was applied for thermal behavior studies and then some thermo-kinetics activation parameters were evaluated. [ABSTRACT FROM AUTHOR]

A new indium(III) fluoride complex with the ammonium cation (NH)[InF] is synthesized and its crystal structure is studied. The structure of (NH)[InF] is formed of NH cations and complex [InF] anions. The In atom in the complex anion surrounded by four terminal and two bridging F atoms forms an almost regular octahedral coordination polyhedron (CN 6) with two terminal F atoms in the axial positions and two terminal and two bridging F atoms in the equatorial plane. Through bridging F atoms, the InF6 polyhedra are arranged in polymer trans- vertex-connected corrugated anion chains (InF) directed along the c axis. The N-H⋯F hydrogen bonds organize the chains in a three-dimensional framework. [ABSTRACT FROM AUTHOR]

Abstract: In this work, a continuous two-step route consisting of ammonolysis and re-oxidation process was developed for the growth of a novel In2O3 truncated octahedron string morphology. The as-synthesized products were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM), results of which indicated that the truncated octahedron strings were self-assembled by In2O3 crystals, and several tens of micrometers along their longitudinal axes. In addition, a gas sensor based on as-synthesized In2O3 truncated octahedron strings was fabricated using a ceramic tube as substrate in an in situ deposition manner. The sensor exhibited good selectivity toward formaldehyde, and showed a significant response for formaldehyde at a concentration lower to 5ppm. The present study may serve as a basis for designing other novel morphology from semiconductor oxides for gas-sensing applications. [Copyright &y& Elsevier]

To the best of our knowledge, this is the first report of the synthesis and characterization of tetramethylammonium fluoridotitanate(IV) [N(CH)][TiF][TiF(HO)] with two dimeric complex anions of different compositions. The disordered crystal structure of [N(CH)][TiF][TiF(HO)] is formed by dimeric complex anions [TiF] and [TiF(HO)] in a 1:1 ratio and tetramethylammonium cations N(CH), each with an occupancy factor of 0.5. The dimeric complex anions, which structurally alternate with an occupancy factor of 0.5, form a pseudodimeric anion {(TiF)(TiF(HO))} whose charge is compensated by the disordered cations N(CH). The hydrogen bonds O-H⋯F link the dimeric complex anions [TiF] and [TiF(HO)] into polymeric ribbons, with the N(CH) cations being located between the ribbons. [ABSTRACT FROM AUTHOR]

The signed volume function for polyhedra can be generalized to a mean volume function for volume elements by averaging over the triangulations of the underlying polyhedron. If we consider these up to translation and scaling, the resulting quotient space is diffeomorphic to a sphere. The mean volume function restricted to this sphere is a quality measure for volume elements. We show that the gradient ascent of this map regularizes the building blocks of hybrid meshes consisting of tetrahedra, hexahedra, prisms, pyramids, and octahedra, that is, the optimization process converges to regular polyhedra. We show that the (normalized) gradient flow of the mean volume yields a fast and efficient optimization scheme for the finite element method known as the geometric element transformation method. Furthermore, we shed some light on the dynamics of this method and the resulting smoothing procedure both theoretically and experimentally. [ABSTRACT FROM AUTHOR]

Octahedron-like \Au/\Fe3{\O}4 magnetic nanoparticles are synthesized using decomposition of FeO(OH) and \HAuCl4 with the presence of oleic acid in 1-octadecene solvent. In the octahedron-like hybrid particles, \Fe3{\O}4 mainly displayed the octahedral morphology and spherical Au nanoparticles partially embedded into one side of \Fe3{\O}4 octahedron. The size of particle could be tuned from 25  to 240 nm for the whole particle (mainly for \Fe3{\O}4) and 10  to 40 nm for Au by changing the proportion of the starting materials. The hybrid particles showed the magnetic properties of \Fe3{\O}4 with dependence on the size of \Fe3{\O}4 octahedron composite and the proportion of \Fe3{\O}4 to Au. Coercivity is observed in the hybrid \Au/\Fe3{\O}4 octahedron-like nanoparticles (55 Oe for 25 nm, 135 Oe for 100 nm, and 159 Oe for 240 nm) at room temperature. These size-controllable hybrid \Au/\Fe3{\O}4 magnetic octahedron-like particles, inheriting the advantages of Au and \Fe3{\O}4 nanoparticles, may evolve as useful building blocks for nano- and micro-electronic applications. [ABSTRACT FROM PUBLISHER]

An effective strategy was developed to control molecular space configurations and ZIFs' growth on PAN nanofibers precisely. ZIFs' size was controlled by regulating pH and N elemens' coordination environment. Molecular space configurations were controlled by N elemens' coordination environment. And the well-designed catalyst was applied on the oxidation of toluene. [Display omitted] • A new strategy was proposed to control ZIFs' growth on PAN precisely. • N elements coordination microenvironment could effectively control the molecular space configurations of Co complexes. • The TEA-induced Co 3 O 4 generated more octahedral structure, which is beneficial for the catalytic oxidation of VOCs. Selective exposure of dominant molecular space configurations and controllable synthesis of nanocomposites microstructure are full of challenge in improving the catalyst activity and designing materials. Herein, we precisely designed the size of ZIFs growing on nanofibers by changing the distribution of surface N elements. N elements microenvironment of nanofibers surface influenced not only ZIFs' growth mechanism, but also its derivatives' molecular space configurations (octahedral and tetrahedral structure of Co 3 O 4). To verify the influence of N element on space configurations, DFT were used to investigate structure preference energy (SPE). The result showed that the TEA (triethylamine)-induced method showed a big difference between octahedral and tetrahedral structure, indicating that this method was easier to generate octahedral complexes. Its derived Co 3 O 4 catalysts with more Co3+ spieces showed the best catalytic performance (T 90 only 220 °C). Based on this, exposure of molecular space configurations will no longer be random but manipulable. The establishment of this new strategy will play an important role in the future catalyst design and realize the adjustable and controllable catalyst. [ABSTRACT FROM AUTHOR]

Abstract: In this letter, the formation of the hierarchical SnO2 hollow octahedra was achieved by thermal treatment of ZnSn(OH)6 precursors in ammonia solution. The synthesized SnO2 was characterized by X-ray powder diffraction (XRD), field emission scanning electron microscopy (FE-SEM), and high resolution transmission electron microscopy (HR-TEM). The XRD pattern indicated the formation of well crystallized SnO2. The FE-SEM and HR-TEM images showed that the hollow octahedra were built by SnO2 nanorod arrays. A possible formation mechanism for this kind of hollow octahedron structure was proposed. Room temperature photoluminescence shows that hierarchical SnO2 hollow octahedra have two prominent emission bands at 575 and 625nm. [Copyright &y& Elsevier]

It is proved that a graph does not contain an octahedron minor if and only if it is constructed from [ABSTRACT FROM AUTHOR]

Abstract: Well-defined Mn3O4 octahedrons were synthesized by a facile triethanolamine (TEA)-assisted route under mild hydrothermal conditions. The chemical compositions and morphologies of the as-prepared samples were characterized in detail by power X-ray diffraction (XRD), fourier transform infrared spectra (FT-IR), transmission electron microscopy (TEM), energy dispersive X-ray spectrometry (EDS), and field emission scanning electron microscopy (FE-SEM). The possible reaction mechanism and growth mechanism was discussed to elucidate the formation of the single-crystalline Mn3O4 octahedrons. The amounts of TEA and NaOH played important roles in controlling the morphology of the final products. Besides, the magnetic property was tested by a vibrating sample magnetometer (VSM), and the as-obtained sample exhibit ferrimagnetic behavior at low temperature and normal paramagnetic behavior at room temperature. The method can be easily controlled and expected to be applicable for the large-scale preparation of the Mn3O4 octahedrons. [Copyright &y& Elsevier]

Aristotle contended that (regular) tetrahedra tile space, an opinion that remained widespread until it was observed that non-overlapping tetrahedra cannot subtend a solid angle of 4 π around a point if this point lies on a tetrahedron edge. From this 15th century argument, we can deduce that tetrahedra do not tile space but, more than 500 years later, we are unaware of any known non-trivial upper bound to the packing density of tetrahedra. In this article, we calculate such a bound. To this end, we show the existence, in any packing of regular tetrahedra, of a set of disjoint spheres centered on tetrahedron edges, so that each sphere is not fully covered by the packing. The bound on the amount of space that is not covered in each sphere is obtained in a recursive way by building on the solid angle argument. The argument can be readily modified to apply to other polyhedra. The resulting lower bound on the fraction of empty space in a packing of regular tetrahedra is 2.6...×10 and reaches 1.4...×10 for regular octahedra. [ABSTRACT FROM AUTHOR]