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LiNi0.5Mn1.5O4 (LNMO) is a promising next-generation cathode material for high energy density lithium-ion batteries, but the application of LNMO is blocked because of its inherent side effects with electrolytes at high voltages, namely, serious Mn dissolution and capacity attenuation. A novel LiNi0.5Mn1.5-xSrxO4 material (x = 0, 0.05, 0.1, 0.15, and 0.2) was successfully prepared using the sol-gel method, and the effect of varying in situ Sr2+-doping on the crystal structure, morphology, and electrochemical performance was researched. A series of characterizations showed that the Sr-doped LNMO structure contains less Mn3+, which enhances its cycling stability. In addition, Sr doping promotes morphological changes more remarkably. Accompanied by the appearance of (100) surfaces, the morphology of LNMO changes from an octahedron to a truncated octahedron. The (100) surface can effectively inhibit side reactions with the electrolyte and steady the structure at the working voltage, which also helps support Li+ transport kinetics. The Sr-doped LiNi0.5Mn1.4Sr0.1O4 (expressed as LNMO-Sr0.1) cathode exhibits preeminent cycling stability, after 500 cycles at 1C, the capacity retention is 86.63 %. CV and EIS results show that the right amount of Sr doping efficiently reduces electrode polarization and charge transfer resistance and increases the Li+ diffusion coefficient.

Intense orange phosphors NaY(MoO4)2: Sm3+ were successfully synthesized by means of a conventional solvothermal process in the presence of disodium ethylenediamine tetraacetate (EDTA-2Na) as a surfactant. The dependence on the phase structure, particle morphology, photoluminescence property and thermal quench behavior of the as-prepared phosphors were studied in detail. The molar ratio of EDTA-2Na/Re3+(Re = Y and Sm) played significant roles in the selective preparation of NaY(MoO4)2 microcrystals with various regular uniform shapes. With increasing molar ratios of the two composite, the morphology of the products changed from octahedron, truncated octahedron, microcube to thin plate, namely, truncation degree was positively correlated with molar ratios. The possible formation mechanism of NaY(MoO4) microplates was explained from the effects of EDTA-2Na on adsorption for (001) planes. NaY(MoO4)2: Sm3+ phosphors exhibit the orange fluorescence and the optimal single dopant contents of Sm3+ was 3.0 mol%. In addition, the markedly high enhancement of Sm3+ characteristic emission about 25.72% was achieved by co-doping with Li+ ions, and the introduction of Li+ ions had no obvious impact on the phase as well as morphology of NaY(MoO4)2: Sm3+. By optical analysis, it can be inferred that the improvement of the emission intensity was the result of the cooperative effects of ion electronegativity and the crystal field environment. The emission intensity at 543 K was as high as 60% of that at ambient temperature, meanwhile, the thermal activation energy was obtained to be 0.30344 eV on the basis of the temperature-dependent mode through means of charge transfer state, which make the phosphors a promising candidate for some temperature sensitive devices.

A conjecture is made that the weight space for 4D, $\cal N$-extended supersymmetrical representations is embedded within the permutahedra associated with permutation groups ${\mathbb{S}}{}_{d}$. Adinkras and Coxeter Groups associated with minimal representations of 4D, $\cal N$ = 1 supersymmetry provide evidence supporting this conjecture. It is shown the appearance of the mathematics of 4D, $\cal N$ = 1 minimal off-shell supersymmetry representations is equivalent to solving a four color problem on the truncated octahedron. This observation suggest an entirely new way to approach the off-shell SUSY auxiliary field problem based on IT algorithms probing the properties of ${\mathbb{S}}{}_{d}$., LaTeX twice, 39 pages, 14 figures, 28 tables (v2 added one table and associated content, v3 note added in proof comment)

Various Li-rich spinel Li1+xNi0.05Mn1.95-xO4 (0 ≤ x ≤ 0.10) cathode materials with a truncated octahedron were synthesized by a solution combustion method. The relationship of crystalline structure, particles morphology and electrochemical properties of the as-prepared samples was investigated via a series of physicochemical characterizations. The Li-Ni co-doping changes the lattice parameters and atomic configuration, whilst resulting in a contraction of unit cell dimension and giving rise to a variation of bond length. In this regard, the shrinkage of octahedral MnO6 provides a robust structure and the expansion of tetrahedral LiO4 facilitates a fast electrochemical process. Additionally, the resulted polyhedral Li1+xNi0.05Mn1.95-xO4 samples present the exposed (1 1 0), (1 0 0), and (1 1 1) crystal planes, which provide the favorable Li+ ions diffusion/transmission channel and alleviate Mn dissolution. Owing to these merits of polyhedral structure and Li-Ni co-doping, the optimized Li1.02Ni0.05Mn1.93O4 exhibits good electrochemical performance with high initial discharge capacity of 119.8, 107.1 and 97.9 mAh·g−1 at 1, 5 and 10 C, respectively. Even at a high current rate of 15 C, an excellent capacity retention of 91.7% is obtained after 1000 cycles, whilst the high temperature performance was also improved.

A new method for the manufacturing of pre-determined open porosity Al foams is presented in this work. Starting from a 3D foam model designed with CAD and printed with fused deposition modeling (FDM), a porous structure of poly lactic acid (PLA) has been replicated. The choice of this material has been driven by the properties in terms of recyclability and low cost. The truncated octahedron for the porosity shape has been selected due to benefit and properties ascribable to its morphology. After creating the 3D PLA model, it has been filled with liquid plaster. After its solidification, PLA is removed in oven at 600 °C so that a negative-shaped plaster mold is obtained. Successively liquid Al at 750 °C is poured in the mold inside the oven. After Al solidification, plaster can be easily removed in ultrasonic bath thus obtaining Al foam with the same morphology of the starting PLA model. This process shows great flexibility allowing to manufacture different kind of elementary cell types. Tailoring of the selected properties of the manufactured foams, e.g. the morphology, the density or the surface/volume ratio may be obtained. With this technique many other metals and alloys can be manufactured too. The potential of this production technique can be successfully employed in many application fields of metal foam. Light-weight 3D lattice structures are widely employed for multifunctional applications such as loading bearing, negative and zero thermal-expansion structures, vibration attenuation, impact and blast proof structures.

The controllable synthesis and customized design of micro/nanomotors represents a highly desired paradigm in the field of intelligent nanovehicles. Exploiting asymmetrical structures and geometry-dependent propulsion are the two main strategies for achieving light-driven micro/nanomotors. However, inherent crystal-structure differences in a single colloidal motor have rarely been explored. Here, we propose the first surface-heterojunction-induced propulsion methodology for cuprous oxide (Cu2O) nanomotors, by tailoring the crystal morphology of a Cu2O crystalloid from a sphere into a truncated octahedron and preserving the controllable-index crystal facets of {100} and {111} in a single colloid. Due to the high crystallinity and distinct activity of the exposed crystal facets, a surface heterojunction between the {100} and {111} facets is formed to enhance electron-hole separation, as confirmed by density functional theory (DFT) calculations, thus endowing the truncated octahedral Cu2O nanomotors with autonomous and vigorous movement in biocompatible fuels under visible light. These Cu2O nanomotors can reach a propulsion speed in water of over two times faster than that of polycrystalline spherical motors with low crystallinity. The efficient Cu2O nanomotors offer a promising guideline not only for the synthesis of novel light-driven motors with desired structures, but also for potential applications in biocompatible environments.

Polyhedral shapes can be found in crystalline materials ranging from macroscopic natural mineral solids to microscopic or nanoscopic particles. These shapes originate from the crystallographic properties of the constituting material, and the outer shape depends on several unique habit planes. In this study, polyhedral crystal growth was simulated considering the surface energy and crystallographic characteristics. A series of polyhedrons, including cube, truncated hexahedron, cuboctahedron, truncated octahedron, and regular octahedron, was targeted. First, the polyhedron’s static surface energy and dynamic energy variation during crystal growth were computed. Then, the crystal-growth process was simulated based on the energy minimization policy. Interestingly, when the simulation began with truncated hexahedral nucleus, the shape changed to a cuboctahedron; however, a certain type of truncated octahedron was obtained when starting with different types of truncated octahedrons. In addition, once converged cuboctahedron abruptly changed the shape to a truncated octahedron as the crystal became larger. These results were supported by the static and dynamic energy curves. Furthermore, the method was applied to different materials by assuming virtual parameters, yielding various morphologies.

The aim of this work is to investigate some properties of the truncated octahedron metric introduced in the space in further studies on metric geometry. With this metric, the 3-dimensional analytical space is a Minkowski geometry which is a non-Euclidean geometry in a finite number of dimensions. In a Minkowski geometry, the unit ball is a certain symmetric closed convex set instead of the usual sphere in Euclidean space. The unit ball of the truncated octahedron geometry is a truncated octahedron which is an Archimedean solid. In this study, first, metric properties of truncated octahedron distance, d_TO, in R^2 has been examined by metric approach. Then, by using synthetic approach some distance formulae in R_TO^3, 3-dimensional analytical space furnished with the truncated octahedron metric has been found.

LiNi0.5Mn1.5O4 materials with different crystal surface proportions are synthesized by graphite-assisted calcination method. Scanning electron microscopy (SEM) reveals homogeneous microsized polyhedral morphology with different proportions of exposed {100} and {111} surfaces. The most highlighted result is that LiNi0.5Mn1.5O4 with appropriate proportion exposed {100} and {111} surfaces can achieve both high power and long lifetime simultaneously. The LiNi0.5Mn1.5O4 with appropriate proportion exposed {100} and {111} surfaces can provide a large capacity of 74.8 mAh g−1 even at a discharge rate as high as 20 C. Besides, the capacity retentions of the LiNi0.5Mn1.5O4 with appropriate proportion exposed {100} and {111} surfaces are found to be 93.33% at 1 C after 100 cycles. These results represent the experimental evidence for lattice-plane anisotropy in LiNi0.5Mn1.5O4 crystals. Moreover, the LiNi0.5Mn1.5O4 with appropriate proportion exposed {100} and {111} surface structure is beneficial for obtaining high volumetric energy density and excellent processability in practical applications.

The metal-organic framework (MOF) HKUST-1 with a tbo topology serves as an archetypal tunable and isoreticular framework platform for targeting desired applications, but the design and synthesis of tbo-covalent organic frameworks (COFs) remains a formidable challenge. Here we demonstrate the successful use of reticular chemistry as an appropriate strategy for the design and deliberate construction of COFs with a tbo topology. The judicious selection of the perquisite planar building blocks, 4-connected square tetramine of porphyrin and 3-connected trigonal trialdehydes of triphenylamine, allows the condensation of two tbo-COFs, the first examples of COFs with a tbo topology. The resulting COFs both crystallize in the cubic Pm3 space group and adopt a non-interpenetrated open framework, in which each tritopic linker connects to three square units forming a truncated Td-octahedron and occupies the alternating triangular faces of the truncated octahedron. Owing to the presence of two different types of photoredox-active moieties, the two COFs can be efficient heterogeneous photocatalysts for the oxidative hydroxylation of arylboronic acids and the reductive defluoroalkylation of trifluoromethyl aromatics with alkenes. The present finding will provide an impetus to examine the potential of tbo-COFs as a new platform for engineering multifunctional materials via expansion and functionalization of building blocks.

In this article, five fundamental unit cells namely BCC, hexagonal packing, rhombicuboctahedron, diamond, and truncated octahedron, for which there was a lack of accurate analytical yield stress re...

Shape-controlled Pt-Ni alloys usually offer an exceptional electrocatalytic activity toward the oxygen reduction reaction (ORR) of polymer electrolyte membrane fuel cells (PEMFCs), whose tricks lie in well-designed structures and surface morphologies. In this paper, a novel synthesis of truncated octahedral PtNi35 alloy catalysts that consist of homogeneous Pt-Ni alloy cores enclosed by NiO-Pt double shells through thermally annealing defective heterogeneous PtNi3.5 alloys is reported. By tracking the evolution of both compositions and morphologies, the outward segregation of both PtOx and NiO are first observed in Pt-Ni alloys. It is speculated that the diffusion of low-coordination atoms results in the formation of an energetically favorable truncated octahedron while the outward segregation of oxides leads to the formation of NiO-Pt double shells. It is very attractive that after gently removing the NiO outer shell, the dealloyed truncated octahedral core-shell structure demonstrates a greatly enhanced ORR activity. The as-obtained truncated octahedral Pt21Ni core-shell alloy presents a 3.4-folds mass-specific activity of that for unannealed sample, and its activity preserves 45.4% after 30000 potential cycles of accelerated degradation test (ADT). The peak power density of the dealloyed truncated octahedral Pt2.1Ni core-shell alloy catalyst based membrane electrolyte assembly (MEA) reaches 679.8 mW/cm2, increased by 138.4 mW/cm2 relative to that based on commercial Pt/C.

Polyhedra are ubiquitous in chemistry, biology, mathematics and other disciplines. Coordination-driven self-assembly has created molecules mimicking Platonic, Archimedean and even Goldberg polyhedra, however, nesting multiple polyhedra in one cluster is challenging, not only for synthesis but also for determining the alignment of the polyhedra. Here, we synthesize a nested Ag90 nanocluster under solvothermal condition. This pseudo-Th symmetric Ag90 ball contains three concentric Ag polyhedra with apparently incompatible symmetry. Specifically, the inner (Ag6) and middle (Ag24) shells are octahedral (Oh), an octahedron (a Platonic solid with six 3.3.3.3 vertices) and a truncated octahedron (an Archimedean solid with twenty-four 4.6.6 vertices), whereas the outer (Ag60) shell is icosahedral (Ih), a rhombicosidodecahedron (an Archimedean solid with sixty 3.4.5.4 vertices). The Ag90 nanocluster solves the apparent incompatibility with the most symmetric arrangement of 2- and 3-fold rotational axes, similar to the arrangement in the model called Kepler’s Kosmos, devised by the mathematician John Conway.

The experimental shape control of metallic Co nanoparticles (NPs) remains a great challenge in terms of their direct characterization for the further rational design and optimization of efficient nanocatalysts nowadays, especially when a low promoter content is involved. Thus, spin-polarized density functional theory (DFT) and ab initio molecular dynamics (AIMD) simulations have been carried out to investigate the adsorption configurations and growth trend of Run clusters on Co surfaces to systemically explore the surface morphology of Co NPs induced by Ru promotion in Co-based Fischer–Tropsch synthesis (FTS). The predicted Run aggregation adsorption patterns on Co(100) and Co(110) surfaces combined with the recent results for Co(111) and Co(311) surfaces show the thermodynamic growth tendency that Run aggregates are favorable for planar layered growth on Co surfaces under realistic FTS reaction conditions, which is consistent with the experimental EELS spectral results. The addition of Ru promoter has an important role in tuning the stability of the exposed facets of face-centered-cubic (FCC) Co NPs, accompanied by the change from truncated octahedron to rhombic dodecahedron morphology. At high Ru content, the increased high index Co(311) and Co(110) surfaces, including more active step and kink sites, are desirable for the enhanced activity of FCC Co NPs.

A metal-organic framework (MOF), namely SCNU-Z3, based on an imidazole-tetrazole tripodal ligand and Mn(ii), has been constructed. It exhibits a porous 3D framework composed of truncated octahedron cage subunits. Unexpected ligand-induced missing metal-ion defects were observed in the framework. In addition, the application of SCNU-Z3 in a supercapacitor was performed.

Spinel LiMn2O4 has been widely investigated as a cathode material for lithium-ion batteries, but it suffers from a limited cycle life due to the dissolution of Mn and structural distortion. Herein, a facile solution combustion approach was used to prepare a spinel LiCu0.05Mn1.95O4 cathode material with truncated octahedron morphology. This unique octahedral structure endowed LiCu0.05Mn1.95O4 with a small portion of orientated {110} and {100} surfaces aligned to the favorable diffusion channels of Li ions, resulting in enhanced kinetics. Moreover, Cu-doping increased the average oxidation state of manganese, which effectively restrained the Jahn–Teller distortion. Consequently, the obtained sample showed improved electrochemical cyclability and structural stability. The initial discharge capacities of 110.2 and 90.2 mA h g−1 were delivered at 1C and 10C, with the corresponding capacity retentions of 66.1% and 81.5% after 1000 cycles, respectively. Additionally, enhanced high-temperature electrochemical properties were achieved at 1C and 55 °C after 500 cycles. These excellent electrochemical performances are also ascribed to the low activation energy (22.57 kJ mol−1) and a relatively high Li+ diffusion coefficient (1.84 × 10−15 cm2 s−1).

Hierarchical lattices are structures composed of self-similar or dissimilar architected metamaterials that span multiple length scales. Hierarchical lattices have superior and tunable properties when compared to conventional lattices, and thus, open the door for a wide range of material property manipulation and optimization. Using finite element analysis, we investigate the energy absorption capabilities of 3D hierarchical lattices for various unit cells under low strain rates and loads. In this study, we use fused deposition modeling (FDM) 3D printing to fabricate a dog bone specimen and extract the mechanical properties of thermoplastic polyurethane (TPU) 85A with a hundred percent infill printed along the direction of tensile loading. With the numerical results, we observed that the energy absorption performance of the octet lattice can be enhanced four to five times by introducing a hierarchy in the structure. Conventional energy absorption structures such as foams and lattices have demonstrated their effectiveness and strengths, this research aims at expanding the design domain of energy absorption structures by exploiting 3D hierarchical lattices. The result of introducing a hierarchy to a lattice on the energy absorption performance is investigated by varying the hierarchical order from a first-order octet to a second-order octet. In addition, the effect of relative density on the energy absorption is isolated by creating a comparison between a first-order octet lattice with an equivalent relative density as a second-order octet lattice. The compression behaviors for the second order octet, dodecahedron, and truncated octahedron are studied. The effect of changing the cross-sectional geometry of the lattice members with respect to the energy absorption performance is investigated. Changing the orientation of the second-order cells from 0 to 45 degrees has a considerable impact on the force–displacement curve, providing a 20% increase in energy absorption for the second-order octet. Analytical solutions of the effective elasticity modulus for the first- and second-order octet lattices are compared to validate the simulations. The findings of this paper and the provided understanding will aid future works in lattice design optimization for energy absorption.

In this paper, we develop a Kinetic Monte Carlo (KMC) based model to simulate the atomistic growth behavior of metallic nanoparticle in the solution of its ions and understand the growth pattern. KMC is used as it can model the growth of nanoparticle to the timescale comparable with that actual experiments. Energy minimas where metal atom can adsorb or surface diffuse have been found using Shrake–Rupley algorithm and conjugate gradient energy minimization algorithm. The rate of adsorption, desorption, and surface diffusion was artificially accelerated, and decelerated to observe different shapes. We demonstrate the model by a case study on growth of gold nanoparticles and find that shapes like the truncated octahedron, cuboctahedron, truncated cube, cube, rhombic dodecahedron, and sphere are seen to form by the model during the growth of NP. This KMC model provides a simplistic understanding of the mechanism and progression of shapes that may be seen during the growth of nanoparticle; these in turn may provide clues to synthesize NP of specific shapes.

Understanding the structure of bimetallic clusters is increasingly important due to their emerging practical applications. Herein we investigate the structure of 38-atom CuPd clusters using a genetic algorithm with cluster energies described by the semi-empirical Gupta potential. Selected clusters are then refined with density functional theory. Three different parameterisations of the Gupta potential are used and their performance assessed to understand what features of bulk and surfaces are necessary to capture for accurate description of small clusters. Three general regions of motif stability exist; for the Pd majority clusters (Pd38 to Cu4Pd34) the truncated octahedron is most stable, while for clusters of intermediate compositions (Cu5Pd33 to Cu25Pd13) a “pancake” icosahedron is most stable, and for the Cu majority clusters (Cu26Pd12 to Cu38) again the truncated octahedron is most stable. CuPd clusters tend to segregate to a Cu-core, Pd-shell structure if possible, and at higher Cu compositions, the Pd segregates to the faces of the cluster. Using multiple parameterisations of the Gupta potential ensures the full variety of possible structures is found, and improves the search for the most stable CuPd clusters.

Palladium nanoparticles (Pd NPs) of different shapes and sizes have been synthesized by reducing potassium tetrachloropalladinate(II) by l-ascorbic acid (AA) in an aqueous solution phase in the presence of an amphiphilic nonionic surfactant poly ethylene glycol (PEG) via a sonochemical method. Materials have been characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), energy dispersive X-ray soectrscopy (EDX), Fourier transform infrared (FTIR), surface-enhanced Raman spectroscopy (SERS), particle distribution, and zeta potential studies. Truncated octahedron/fivefold twinned pentagonal rods are formed at room temperature (RT) (25 °C) while hexagonal/trigonal plates are formed at 65 °C. XRD results show evolution of anisotropically grown, phase-pure, and well crystalline face-centered cubic Pd NPs at both temperatures. FTIR and SERS studies revealed adsorption of ascorbic acid (AA) and PEG at NP’s surface. Particle’s size distribution graph indicates formation of particles having wide size distribution while the zeta potential particle surface is negatively charged and stable. The truncated octahedron/fivefold twinned pentagonal rod-shaped Pd NPs, formed at RT, while thermally stable and kinetically controlled hexagonal/trigonal plate-like Pd NPs, evolved at higher temperature 65 °C. The obtained Pd NPs have a high surface area and narrow pore size distribution. To predict protein reactivity of the Pd cluster, docking has been done with DNA and lung cancer-effective proteins. The cytotoxicity of the Pd NPs has been screened on human lung cancer cells A-549 at 37 °C. The biological adaptability exhibited by Pd NPs has opened a pathway in biochemical applications.

LiNi0.5Mn1.5O4 materials with three different particle shapes, including octahedron composed of {111} surface, truncated octahedron with {111} and {100} surfaces, and chamfered polyhedron with {111}, {100}, and {110} surfaces, have been synthesized via a combined coprecipitation-hydrothermal method followed by three different calcination processes. The materials were characterized by XRD, FT-IR, SEM, EIS, XPS, and galvanostatic charge/discharge tests. All samples have a main disordered structure and similar primary particle size. Electrochemical results show the rate capability degrades in the order of chamfered polyhedron > truncated octahedron > octahedron, while the cycling stability deteriorates in the order of truncated octahedron > octahedron > chamfered polyhedron. It can be concluded that the particle shape, more specifically, surface orientations, exerts great influence on the electrochemical performance of LiNi0.5Mn1.5O4 material. Therefore, appropriate tailoring of surface orientations can simultaneously satisfy power capability and long cycle life. The particle shape design is of significance to LiNi0.5Mn1.5O4 material.

Sensor deployment in a wireless sensor network (WSN) is a challenging task due to the high chance of occurrence of the error in the deployment process, which makes the network inefficient. Particularly in three-dimensional (3D) WSN, the ideal positioning of sensor nodes over the ground with precise coverage and connectivity is a very significant consideration in the deployment of sensors. Various models for 2D sensor deployment have been proposed to date, but in real-world scenarios, the target field (field of interest) is not always 2D flat surface and therefore a 2D deployment model cannot address the issue of deploying sensor nodes on uneven surfaces such as hilly terrains. In this paper, we presented a surface approximation-based sensor deployment using truncated octahedron (SASD-TO) to solve the problems of sensor deployment on an irregular surface. Using the B-Spline, a 3D model of the target surface is approximated and then a Truncated Octahedron is used to estimate the exact coordinates of a sensor node. A very decent coverage area as high as 98% on average, whereas at lowest 2% of the uncovered area and 8% of the superimposed area were observed.

Let M M be a 3 × 3 3\times 3 integer matrix each of whose eigenvalues is greater than 1 1 in modulus and let D ⊂ Z 3 \mathcal {D}\subset \mathbb {Z}^3 be a set with | D | = | det M | |\mathcal {D}|=|\det M| , called a digit set. The set equation M T = T + D MT = T+\mathcal {D} uniquely defines a nonempty compact set T ⊂ R 3 T\subset \mathbb {R}^3 . If T T has positive Lebesgue measure it is called a 3 3 -dimensional self-affine tile. In the present paper we study topological properties of 3 3 -dimensional self-affine tiles with collinear digit set, i.e., with a digit set of the form D = { 0 , v , 2 v , … , ( | det M | − 1 ) v } \mathcal {D}=\{0,v,2v,\ldots , (|\det M|-1)v\} for some v ∈ Z 3 ∖ { 0 } v\in \mathbb {Z}^3\setminus \{0\} . We prove that the boundary of such a tile T T is homeomorphic to a 2 2 -sphere whenever its set of neighbors in a lattice tiling which is induced by T T in a natural way contains 14 14 elements. The combinatorics of this lattice tiling is then the same as the one of the bitruncated cubic honeycomb, a body-centered cubic lattice tiling by truncated octahedra. We give a characterization of 3 3 -dimensional self-affine tiles with collinear digit set having 14 14 neighbors in terms of the coefficients of the characteristic polynomial of M M . In our proofs we use results of R. H. Bing on the topological characterization of spheres.

The synthesis of DNA polyhedra has attracted more interest because of its wide application prospect, but its formation mechanism from mathematical viewpoint remains poorly understood. This paper presents the assembly process and mechanism of DNA truncated tetrahedron, cuboctahedron and truncated octahedron by the means of mathematics and computer program. Firstly, based on the assumption that the total number of all the crossings within each face of a DNA polyhedron must be an even number, potential types for three DNA polyhedra above are calculated by computer programs; Secondly, the projections of the truncated tetrahedron, the cuboctahedron and the truncated octahedron are plotted based on data fetched by the program; Thirdly, the component number, the odd-crossing edge number and even-crossing edge number for the corresponding polyhedral links are computed by analysis of their projections. This study gets some assembly mechanism on the structure of DNA double helix, promoting the comprehending and design efficiency of DNA polyhedra.

The surface topography of a grinding wheel is an indispensable prerequisite for the modelling, simulation and optimisation of grinding. In this study, the basic topographic parameters of grains and two new indices are proposed to parametrically evaluate the surface topography of the grinding wheel, and then a three-dimensional model for the surface topography of the grinding wheel is established. The basic topographic parameters are characterised using statistical methods. Based on the concept of the fraction of the grain protrusion area Sr that is optically detected, two new indices, the grain protrusion degree βd and the dispersion degree of the grain protrusion area δs are defined. Although the grain shape is irregular, a truncated octahedron is used to simulate the diamond grain. By continuous adjustment the distribution of the grain protrusion height σ2 and the coordinate value of the bond surface zb, the surface topography model becomes closer to reality, when the two indices βd and δs are similar to that of the actual grinding wheel. Finally, the established three-dimensional model is compared with an actual grinding wheel by the total number of grains per unit area ρgnS and the grain protrusion height hg, and the accuracy of the model is verified.

Morphology evolution of primary Mg2Si in Al-20Mg2Si alloy is investigated by controlling the molar ratios of Ca/Sb. Dendritic primary Mg2Si are formed when the Ca/Sb molar ratios are 1/3 and 1/2; truncated octahedral, jewel-like truncated octahedral and truncated cubic primary Mg2Si are formed when the Ca/Sb molar ratios are 1/1, 2/1 and 3/1, respectively. Skeleton-type growth process of the jewel-like truncated octahedral primary Mg2Si is investigated for the first time. It is found that the adsorption of Ca atoms can affect the whole process of primary Mg2Si crystallization, which restricts the nucleation and controls the growth of the crystal. However, the formation of CaSi2 and CaSb2 can only affect the nucleation of primary Mg2Si, leading to the refinement of the particle size. Brinell hardness of the alloy increases from ∼75 to ∼98 HB when the 3-D morphologies of primary Mg2Si transform from dendrite to truncated octahedron; the hardness decreases to ∼80 HB with the formation of jewel-like truncated octahedral and truncated cubic primary Mg2Si. The study provides a simple method to change the morphology and size of primary Mg2Si, which is important to tailor new light-weight alloy with high strength and toughness.

Crystal facets usually play an important role in the catalytic activity of inorganic single crystals. In this work, two α-Mn2O3 single crystals with an octahedron (exposed with (1 1 1) facet) and a truncated octahedron (exposed with both (1 1 1) and (0 0 1) facets) were successfully prepared by a simple solvent-thermal reaction, and their catalytic activities were evaluated by the selective catalytic reduction (SCR) of NOx with NH3. The results show that the catalytic performance of the α-Mn2O3 single crystal with a truncated octahedron was enhanced in comparison with the α-Mn2O3 single crystal with an octahedron by the exposure of a small fraction of (0 0 1) facets. This can be attributed to the new active sites created by charge redistribution on the surface of the (0 0 1) facets, which provides more adsorption sites, facilitating the further adsorption and reaction of NH3 and NO molecules, and thereby enhancing the catalytic performance. This work should provide new insight into the understanding of crystal-facet-dependent reactivity and important guides for the design and preparation of SCR catalysts with high activity.

資料番号: SA1190171000

Tuning the morphology and structural evolution of metal nanoparticles to expose specific crystal facets in a certain reaction atmosphere is conducive to designing catalysts with a high catalytic activity. Herein, coverage dependent hydrogen adsorption on seven fcc Ru surfaces was investigated using density functional theory (DFT) calculations. The morphology evolution of the fcc Ru nanoparticles under the reactive environment was further illustrated using the multiscale structure reconstruction (MSR) model, which combines the DFT results with the Fowler-Guggenheim (F-G) adsorption isotherm and the Wulff construction. At constant pressure, the shape of a fcc Ru nanoparticle changes from a rhombic dodecahedron to a truncated octahedron with an increase of the temperature. More importantly, the desired Ru morphology, with abundant open facets, was predicted to occur at a high temperature and low pressure. Our results provide an insightful understanding of the reshaping of Ru nanoparticles during real reactions, which is crucial for its rational design for use as a nanocatalyst.