Pentagonal Prism Research Articles

Structural and electronic properties of PtnSi12 (n = 1–4) clusters: Quantum chemical calculations

Pt1Si12−, Pt1Si12, and Pt1Si12+ adopt hexagonal prism- or pentagonal prism-based geometries. Pt2Si12− holds a C4v symmetric Pt-endohedral cage-like geometry with a face-capping Pt atom, while Pt2Si12 and Pt2Si12+ have a Pt-endohedral bicapped Si10 pentagonal prism with an edge-capping Pt atom. Interestingly, the C2v symmetric Pt-endohedral tritruncated trigonal bipyramid is confirmed as the global minima of Pt3Si12−, Pt3Si12, and Pt3Si12+. Both anionic and neutral Pt4Si12 clusters adopt a Pt-capped tritruncated trigonal bipyramid, whereas cationic Pt4Si12 possesses a Pt-endohedral Si12 hexagonal prism with three face-capping Pt atoms. Impressively, Pt2Si12− and Pt3Si12− exhibit σ plus π double bonding characters.

Double‐Layered Supramolecular Prisms Self‐Assembled by Geometrically Non‐equivalent Tetratopic Subunits

AbstractSupramolecular cages/vesicles in biology display sophisticated structures and functions by utilizing a few types of protein subunit quasi‐equivalently at distinct geometrical locations. However, synthetic supramolecular cages still lack comparable complexity to reach the high levels of functionality found in natural systems. Herein we report the self‐assembly of giant pentagonal supramolecular prisms (molecular weight >50 kDa) with tetratopic pyridinyl subunits serving different geometrical roles within the structures, and their packing into a novel superstructure with unexpected three‐fold rotational symmetry in a single two‐dimensional layer of crystalline state. The formation of these complicated structures is controlled by both the predetermined angles of the ligands and the mismatched structural tensions created from the multi‐layered geometry of the building blocks. Such a self‐assembly strategy is extensively used by viruses to increase the volume and complexity of capsids and would provide a new approach to construct highly sophisticated supramolecular architectures.

Double-Layered Supramolecular Prisms Self-Assembled by Geometrically Non-equivalent Tetratopic Subunits.

Supramolecular cages/vesicles in biology display sophisticated structures and functions by utilizing a few types of protein subunit quasi-equivalently at distinct geometrical locations. However, synthetic supramolecular cages still lack comparable complexity to reach the high levels of functionality found in natural systems. Herein we report the self-assembly of giant pentagonal supramolecular prisms (molecular weight >50 kDa) with tetratopic pyridinyl subunits serving different geometrical roles within the structures, and their packing into a novel superstructure with unexpected three-fold rotational symmetry in a single two-dimensional layer of crystalline state. The formation of these complicated structures is controlled by both the predetermined angles of the ligands and the mismatched structural tensions created from the multi-layered geometry of the building blocks. Such a self-assembly strategy is extensively used by viruses to increase the volume and complexity of capsids and would provide a new approach to construct highly sophisticated supramolecular architectures.

Structure, Magnetic Properties, and 151 Eu Mössbauer Spectra of the Indium‐rich Phase Eu 3 Rh 2 In 15

Structure, Magnetic Properties, and ¹⁵¹ Eu Mössbauer Spectra of the Indium‐rich Phase Eu ₃ Rh ₂ In ₁₅

The NE-SW Trending Fotouni and Fangam Basalt Cones: Evidence of Tectonic Control on Their Emplacement

The Fotouni volcanic rocks outcrop within mylonitic corridor, in the southern domain of the continental part of Cameroon Line (CL). The NE-SW shape display by these volcanic rocks within the mylonitic corridor is an uncommon case along the CL. Field and petrographic data and spaces image analysis were performed in order to understand the NE-SW shape display by these rocks. Geochemical data display two distinct volcanic compositional groups: alkaline lavas and transitional lavas. Alkaline series ranges in composition from basanite, basalt to hawaiite and transitional series range from basalt, trachy-basalt to basaltic trachy-andesite.
 Field investigations show that the Fotouni, Fangam, Song and Mbeng basalts outcrops as NE-SW trending prismatic dykes which displaying well differentiated vertical tetragonal, pentagonal and hexagonal prisms within the Fotouni-Kékem shear zone (FFSZ). The overall NE-SW orientation of hills, where these prisms outcrop suggests the tectonic control on the emplacement of these rocks. Indeed, the activation of the FFSZ developed various fracture networks that facilitate magma uplift and the emplacement of the Fomopéa and Bandja plutons during the Pan-African orogeny. These Pan-African activations of the Fotouni fault weaken the crust during the Paleozoic. These weaken zones constitute path way for emplacement of volcanic dykes during the Tertiary within the NE-SW faults, probably facilitated by the general extension at the end of Cretaceous.

Exploring the structural stability order and electronic properties of transition metal M@Ge12 (M = Co, Pd, Tc, and Zr) doped germanium cage clusters–A density functional simulation

In the present report, the structural stability order and electronic properties of the transition metal M@Ge12 (M = Co, Pd, Tc, and Zr) doped germanium cage has been carried out at B3LYP/LANL2DZ ECP level by using spin polarized density functional theory. Initially, we selected five lowest energy structure of neutral TM doped Ge12 cluster with high symmetry point like D6h-symmetric hexagonal prism (HP), the D6d-symmetric hexagonal anti-prism (HAP), D2d-symmetric bi-capped pentagonal prism (BPP), perfect icosahedrons (Ih) and Fullerene type structures. Further, we discussed the electronic origin of stability as well as electronic properties by calculating binding energy, HOMO-LUMO gap, charge transfer mechanism and density of states. We indentified that the Pd, Tc, and Zr encapsulated Ge12 cage with hexagonal prism [HP] structures are minimum energy structures while Co@Ge12 cage prefer HAP structure. The magnitudes of binding energy of the clusters indicate that the doping of 4d transition metal gives most stable structure rather than 3d transition metal Co atom. The large HOMO-LUMO gap and natural bond orbital analysis explain the stability of these clusters using closed shell electronic configuration and the contribution of π and σ bond. Charge transfer mechanism shows that the Tc, Pd and Zr atoms play role as an electron donor in the system whereas Co inclined to accept the electrons. The importances of “d” orbital in localized electrons near the Fermi level are also explained through partial density of states.

Estimating the strength and deformation of columnar jointed rock mass based on physical model test

The complex structure of the columnar jointed rock mass (CJRM) brings difficulty in determining its field mechanical parameters, and a reliable estimation of the strength and deformation of CJRM is crucial for engineering safety. Uniaxial compression tests were conducted on artificial CJRM specimens with columnar structures of quadrangular, pentagonal and hexagonal prisms to model the mechanical behaviour of the CJRM. The strength and deformation anisotropy were compared and analyzed on the basis of the results by combining the structural features of the three models. The failure modes and mechanisms were summarized in accordance with the failure processes and final appearances of artificial specimens. The empirical relations of predicting the field mechanical parameters were derived on the basis of the joint factor approach, the empirical gradient method and the rock quality designation (RQD). For the CJRM of the Baihetan Project, the proposed empirical correlations were used to estimate the field unaxial compression strength and elastic modulus, and the predicted values were compared with those obtained from the field tests and other empirical methods. Results revealed that the estimated values calculated by the proposed empirical equations are in good agreement with the field test results, and the three empirical relations can predict the mechanical parameters of the Baihetan CJRM effectively. The empirical relation based on RQD is extremely valuable when RQD is the only available information about discontinuities in site investigations.

Model Test Study on the Anisotropic Characteristics of Columnar Jointed Rock Mass

Because of its special structure, the anisotropic properties of columnar jointed rock mass (CJRM) are complicated, which brings difficulty to engineering construction. To comprehensively study the anisotropic characteristics of CJRM, uniaxial compression tests were conducted on artificial CJRM specimens. Quadrangular, pentagonal and hexagonal prism CJRM models were introduced, and the dip direction of the columnar joints was considered. Based on the test results and the structural features of the three CJRM models, the deformation and strength characteristics of CJRM specimens were analyzed and compared. The failure modes and mechanisms of artificial specimens with different dip directions were summarized in accordance with the failure processes and final appearances. Subsequently, the anisotropic degrees of the three CJRM models in the horizontal plane were classified, and their anisotropic characteristics were described. Finally, a simple empirical expression was adopted to estimate the strength and deformation of the CJRM, and the derived equations were used in the Baihetan Hydropower Station project. The calculated values are in good agreement with the existing research results, which reflects the engineering application value of the derived empirical equations.

Thick β-SiC CVD-Coated SiC Die System for Dry Cold Forging of Metals

A thick β-SiC CVD (chemical vapor deposition)-coated SiC device was developed as a new punch and die system for dry, cold forging of pure titanium and austenitic stainless-steel works. This β-SiC coating thickness was 4 mm, enough to make mechanical machining of a cavity into β-SiC coating core die. These β-SiC-coated punch and core dies were fixed into the cassette die for dry, cold forging experiments. The stainless steel and titanium wires with diameters of 1.0 mm were employed as the work material. Different from the conventional metallic and ceramic die systems suffering from work material transfer, this system sustained the galling-free cold, dry forging behavior up to a higher reduction of thickness than 30%. The power to stroke the relationship was in situ monitored to describe this forging behavior up to the specified reduction of the wires together with observations on the geometric change from a circular wire to a pentagonal prism bar. Precise scanning electron microscopy-electron-dispersive X-ray spectroscopy (SEM-EDX) analyses were performed to describe the material compatibility on the contact interface between β-SiC coating and elastoplastically deforming works.

Closed-Form Solutions for the Form-Finding of Regular Tensegrity Structures by Group Elements

An analytical form-finding method for regular tensegrity structures based on the concept of force density is presented. The self-equilibrated state can be deduced linearly in terms of force densities, and then we apply eigenvalue decomposition to the force density matrix to calculate its eigenvalues. The eigenvalues are enforced to satisfy the non-degeneracy condition to fulfill the self-equilibrium condition. So the relationship between force densities can also be obtained, which is followed by the super-stability examination. The method has been developed to deal with planar tensegrity structure, prismatic tensegrity structure (triangular prism, quadrangular prism, and pentagonal prism) and star-shaped tensegrity structure by group elements to get closed-form solutions in terms of force densities, which satisfies the super stable conditions.

SrIrIn6 – An Intergrowth of SrIrIn4 with Indium Slabs

The indium‐rich intermetallic compound SrIrIn6 was synthesized from the elements in a sealed tantalum ampoule at 1173 K, followed by slow cooling for crystal growth. SrIrIn6 crystallizes with a new structure type which was characterized by X‐ray powder and single crystal diffraction: Pmma, a = 852.34(2), b = 434.54(5), c = 1059.18(6) pm, wR2 = 0.0178, 884 F2 values, and 32 variables. The SrIrIn6 structure shows two basic building units: (i) Ir@In9 tricapped trigonal prisms (261–292 pm Ir–In) and (ii) distorted bcc In@In8 cubes (301 to 329 pm In–In). The strontium cations fill cages within the complex three‐dimensional [IrIn6] network and have coordination number 13 (Sr@In13) in form of a tricapped pentagonal prism. The SrIrIn6 structure can be described as a simple intergrowth variant of SrIrIn4 (LaCoAl4 type) with indium slabs. The crystal chemical similarities with the structures of SrIrIn4, SrIr2In8 and Eu3Ir2In15 are discussed.

Constitutive Model of Stress-Dependent Seepage in Columnar Jointed Rock Mass

Columnar jointed rock mass (CJRM) is a highly symmetrical natural fractured structure. As the rock mass of the dam foundation of the Baihetan Hydropower Station, the study of its permeability anisotropy is of great significance to engineering safety. Based on the theory of composite mechanics and Goodman’s joint superposition principle, the constitutive model of joints of CJRM is derived according to the Quadrangular prism, the Pentagonal prism and the Hexagonal prism model; combined with Singh’s research results on intermittent joint stress concentration, considering column deflection angles, the joint constitutive model of CJRM in three-dimensional space is established. For the CJRM in the Baihetan dam site area, the Quadrangular prism, the Pentagonal prism and the Hexagonal prism constitutive models were used to calculate the permeability coefficients of CJRM under different deflection angles. The permeability anisotropy characteristics of the three models were compared and verified by numerical simulation results. The results show that the calculation results of the Pentagonal prism model are in good agreement with the numerical simulation results. The variation of permeability coefficient under different confining pressures is compared, and the relationship between permeability coefficient and confining pressure is obtained, which accords with the negative exponential function and conforms to the general rule of joint seepage.

Dynamical fluxionality, multiplicity of geometrical forms, and electronic properties of anionic, neutral, and cationic Ta n Si12 (n = 1–3) clusters: quantum chemical calculations

ABSTRACT The dynamical fluxionality, multiplicity of geometrical forms, and electronic properties of anionic, neutral, and cationic Ta n Si12 (n = 1–3) clusters are studied by quantum chemical calculations. The results show that (n = 1–3) clusters are dominated by prism-based geometries. Impressively, neutral and cationic Ta n Si12 (n = 1–3) clusters have multiple geometrical forms and their low-lying isomers exhibit dynamical fluxionality. is a D 6h symmetric Ta-endohedral Si12 hexagonal prism with highly electronically stability because of satisfying the 18-electrons rule, and having a closing-shell electronic configuration with a large HOMO–LUMO gap of 2.81 eV and delocalised Ta-Si12 ligand interactions. clusters have a C 2v symmetric Ta-endohedral bicapped pentagonal prism. In , a Si5 pentagonal ring and a Si7 heptagonal ring are bridged by the Ta−Ta bonding axis, which is perpendicular to the Si5 and Si7 frameworks. adopts a bicapped hexagonal antiprism with one Ta atom encapsulated into the TaSi11 hexagonal antiprism, whereas neutral and cationic Ta3Si12 hold a TaSi5 hexagon and a Si7 heptagon penetrated by the vertical Ta−Ta bond. The Ta atoms in (n = 2–3) clusters have strong bonding interactions and the charges are transferred from the Si12 frameworks to the Ta atoms.

B3Ge12: a aromatic molecular sandwich-shaped structure with short B−B single bonds coordinated by a Ge12 hexagonal prism and reinforced by σ + π double delocalised bonding patterns

The geometrical structures and bonding properties of anionic, neutral, and cationic B3Ge12 clusters are investigated by quantum chemical calculations. The lowest-lying isomer of anion is found to have a distorted B-endohedral pentagonal prism with two face-capping B atoms and two face-capping Si atoms. In particular, anion is an outstanding superatom cluster with closed-shell electronic configuration of 1S21P61D102S21F142P61G18 on the principle of jellium model. Global minimum of B3Ge12 neutral adopts a D 3h symmetric hexagonal prismatic structure with a B3 triangle at the centre being parallel to the two hexagons and has strong B–B bonding interactions, being very close to the typical B−B single bond. cation has a similar structural feature with its neutral corresponding counterpart. Moreover, the nucleus-independent chemical shift (NICS), aromatic stabilisation energy (ASE), and multicenter bond index calculations suggest B3Ge12 neutral to be aromatic. Furthermore, the molecular orbitals reveal that B3Ge12 neutral exhibits σ plus π double bonding characters. Electrons are transferred from Ge12 framework to B atoms in terms of natural population analysis (NPA), atoms in molecules (AIM), and atomic dipole moment corrected Hirshfeld (ADCH) population analyses.

Quantum chemical calculation studies of PdnSi12 (n = 1–3) clusters: effects of doping Pd atoms on the structural and electronic properties

ABSTRACTStructural and electronic properties of silicon clusters doped with different number of palladium atoms, PdnSi12 (n = 1–3), are investigated using quantum chemical calculations. The most stable structures of , PdSi12, and are found to be a distorted Si12 hexagonal prism with a Pd atom encapsulated into Si12 cage. Further addition of the second and third Pd atoms leads to different structural evolutions for anionic, neutral, and cationic Pd2Si12 (n = 2–3) clusters. The most stable structures of both and Pd2Si12 adopt a Si12 bicapped pentagonal prism with an edge-capping Pd atom and another Pd atom at the centre, while that of has a distorted Si12 hexagonal prism with a Pd atom at the centre and another Pd atom edge-capping one vertical Si−Si bonds of Si12 cage. Interestingly, the most stable structure of adopts a D3h symmetric tritruncated trigonal bipyramid. Pd atoms in anionic, neutral, and cationic PdnSi12 (n = 2–3) clusters are found to have very weak interactions. Natural population analysis suggests that negative charges transfer from Si12 frameworks to Pd atoms. Furthermore, the D3h symmetric tritruncated trigonal bipyramid of exhibits significant aromaticity and σ plus π double bonding characters.

Fabrication of innocuous gold nanoparticles using plant cells in culture

Plant extracts and their different growth phases have been manipulated for the fabrication of nanomaterials, which can be an eco-friendly alternative to the chemical methods that produce hazardous by-products. However, practical difficulties in isolation of the nanoparticles obtained through biological methods and the scanty control that these methods allow over their shapes and sizes impose limitations in their utility. For the first time, we report here a versatile system using cell suspension culture of Medicago sativa, which ensures control over the reaction to regulate size of the particles as well as their easier recovery afterwards. Isolated nanoparticles were characterized for their shape, size and functions. The particles varied in shapes from isodiametric spheres to exotic tetrahedrons, pentagons and pentagonal prisms. They clearly demonstrated catalytic activity in the reduction reaction of methylene blue by stannous chloride. Interestingly, the cell culture-derived particles were found less cytotoxic to healthy human cell line HEp-2 while more cytotoxic to the cancer cell line 4T-1 in comparison to those synthesized through citrate method. However, when administered in mice, these nanoparticles elicited similar inflammatory responses as those produced by chemically synthesized counterparts. These results envisage the utility of these particles for various biological applications.

Generation of propagation-invariant vector beams with square array by use of 2D binary phase mask and pentagonal prism.

In this paper, we realize the generation of propagation-invariant vector beams with square array by use of a 2D binary phase mask and pentagonal prism in a typical Mach-Zehnder optical system. The binary phase mask set in the optical system is perpendicular to the optical axis, and its periodic orientation is 45° relative to the horizontal and vertical directions. One polarizer was used to produce the linearly polarized beam with the angle of 45° relative to the horizontal and vertical directions. One mirror in the Mach-Zehnder optical system was replaced by a pentagonal prism, as the light will be reflected twice inside the pentagonal prism. The intensity distribution of the two branches with the mirror and pentagonal prism have mirror symmetry, and the output optical field of the two branches has an orthogonal polarization state. By adjusting the position of the phase plate accordingly, the total optical field of the two branches can form a vector beam with a square array. The experimental results coincide with the simulation results very well and demonstrate the feasibility of this method.

Anisotropic constitutive model of pentagonal prism columnar jointed rock mass

The pentagonal prism is the dominant structural shape in the columnar jointed rock mass (CJRM) structure, and its anisotropic mechanical properties are crucial for engineering safety. In this paper, we propose an anisotropic constitutive model to accurately describe the anisotropic behavior of the CJRM. First, a generalized model of a pentagonal prism column with variable angle θ was established according to the basic structural features of the CJRM. Based on this model, the constitutive relationship space was derived in three dimensions and then improved through analysis of the influence of the inner disturbed belt and coordinate deflection. Subsequently, considering the CJRM at the Baihetan Hydropower Station in China, we determined the optimal value of θ using one set of in situ test results, thereby obtaining the constitutive relationship for this structure. Finally, the optimal constitutive model of the pentagonal prism was verified by the remaining test results, and its anisotropic characteristics were compared with the existing quadrangular and hexagonal prism constitutive models. The results revealed that the calculated elastic parameters of the pentagonal prism model are in good agreement with the test results and that the curve of the horizontal elastic modulus is approximately circular, which reflects the quasi-transverse isotropy of the proposed model. We found that the calculated results of the three models exhibit different deviations from the test results, owing to the different structural characteristics, and that the deviation in the pentagonal prism model is the smallest.

Three-Dimensional Right-Angled Polytopes of Finite Volume in the Lobachevsky Space: Combinatorics and Constructions

We study combinatorial properties of polytopes realizable in the Lobachevsky space $$\mathbb{L}^{3}$$ as polytopes of finite volume with right dihedral angles. On the basis of E. M. An-dreev’s theorem we prove that cutting off ideal vertices of right-angled polytopes defines a one-to-one correspondence with strongly cyclically four-edge-connected polytopes different from the cube and the pentagonal prism. We show that any polytope of the latter family can be obtained by cutting off a matching of a polytope from the same family or of the cube with at most two nonadjacent orthogonal edges cut, in such a way that each quadrangle results from cutting off an edge. We refine D. Barnette’s construction of this family of polytopes and present its application to right-angled polytopes. We refine the known construction of ideal right-angled polytopes using edge twists and describe its connection with D. Barnette’s construction via perfect matchings. We make a conjecture on the behavior of the volume under operations and give arguments to support it.

Sr4Pt10In21 – the first representative of the Ho4Ni10In21 type with a divalent cation

Abstract Rod-shaped single crystals of Sr4Pt10In21 were prepared from the elements in glassy-carbon crucibles in a high-frequency furnace. The structure of Sr4Pt10In21 was refined from single-crystal X-ray diffractometer data: C2/m, Ho4Ni10Ga21 type, a = 2322.62(7), b = 450.27(2), c = 1958.09(7) pm, β = 133.191(3)°, wR = 0.0464, 3200 F 2 values and 107 variables. The three-dimensional [Pt10In21]δ− polyanionic network is stabilized through substantial Pt–In (269–313 pm Pt–In) and In–In (294–362 pm In–In) bonding. All platinum atoms have slightly distorted tri-capped trigonal prismatic coordination and the two crystallographically independent strontium atoms are located in penta-capped pentagonal prisms.