Icosahedral Polyhedra Research Articles

Central Density and Low-Mode Perturbation Control of Inertial Confinement Fusion Dynamic-Shell Targets

The dynamic-shell target is a new class of design for inertial confinement fusion (ICF). These targets address some of the target fabrication challenges prevalent in current ICF targets and take advantage of advances in manufacturing technologies. This study first examines how the dynamic-shell design can be used to control the density of the central region and therefore convergence ratio, thus expanding the design space for ICF. Additionally, the concern of low-mode perturbation growth is considered. A new class of high-performing beam configurations, based on icosahedral polyhedra and charged-particle simulations is proposed. These configurations achieve low levels of irradiation nonuniformity through selection of beam shapes that suppress the dominant symmetrical mode.

Evaluation of glass forming ability of Zr–Nb alloy systems through liquid fragility and Voronoi cluster analysis

In the present study, a molecular dynamics (MD) simulation-based investigation has been carried out for Zr-Nb binary system to analyze structural evolution during the glass formation along with its underlying physics for identifying suitable composition having better glass forming ability (GFA). The analysis is performed through the determination of liquid fragility, coordination numbers, and Voronoi cluster analysis. Results from Angell’s plot have shown that Zr50Nb50 specimen is a strong liquid and has the highest glass forming ability. It is revealed from Voronoi cluster analysis, that Zr50Nb50 metallic glass has a higher population fraction of icosahedral cluster, which also confirms its better glass forming ability. Apart from 〈0 0 12 0〉 icosahedral polyhedra, some Zr-centered clusters like 〈0 1 10 2〉, 〈0 2 8 5〉 and 〈0 2 8 4〉 are also found to be the key factors with respect to slowing down the dynamics of the system during liquid to glass transition. In addition, a pathway for Zr50Nb50 metallic glass formation is presented to show different stages of structural transformation from liquid to glass state.

Cooling rate dependence and local structure in aluminum monatomic metallic glass

The local atomic structure in aluminium monatomic metallic glass is studied using molecular dynamics simulations combined with the embedded atom method (EAM). We have used a variety of analytical methods to characterise the atomic configurations of our system: the Pair Distribution Function (PDF), the Common Neighbour Analysis (CNA) and the Voronoi Tessellation Analysis. CNA was used to investigate the order change from liquid to amorphous phases, recognising that the amount of icosahedral clusters increases with the decrease of temperature. The Voronoi analysis revealed that the icosahedral-like polyhedral are the predominant ones. It has been observed that the PDF function shows a splitting in the second peak, which cannot be attributed to the only ideal icosahedral polyhedron 〈0, 0, 12, 0〉, but also to the formation of other Voronoi polyhedra 〈0, 1, 10, 2〉 . Further, the PDFs were then integrated giving the cumulative coordination number in order to compute the fractal dimension (df).

Molecular dynamics study of atomic-level structure in monatomic metallic glass

Molecular dynamics simulations have been performed to study the vitrification process and the local atomic structures in Ni monatomic metallic glasses (MG). The interatomic interactions are described by embedded atom method (EAM) potentials. Short-range order (SRO) and medium range order (MRO) in nickel monatomic MG is studied using several structural techniques such as the Radial distribution function (RDF); the Common neighbor analysis method (CNA) and the Voronoi tessellation. As a result, we found that the atomic packing in metallic glasses can be described globally as a superposition of the spherical-periodic order (SPO) and the local translational symmetry (LTS). From CNA method, we found that the majority of icosahedral clusters in Ni monatomic MG are connected together by vertex-sharing (VS), edge-sharing (ES), face-sharing (FS) and intercross-sharing (IS) rather than isolated clusters. These typical cluster connections constitute to the partial RDF of icosahedral atoms except the edge sharing which is hidden between the second and the third subpeaks of RDF. Furthermore, the visualization technologies are applied to follow the formation of clusters during rapid quenching. It is found that the clusters ⟨0,1,10,2⟩ and ⟨0,2,8,4⟩ are more dominant than the full icosahedral polyhedron ⟨0,0,12,0⟩ in our monatomic system. Furthermore, the splitting of the second peak in RDF curve in Ni glass is not only caused by the icosahedral clusters, but also by the Voronoi polyhedrons ⟨0,1,10,2⟩ and ⟨0,2,8,4⟩.

New perspectives on polyhedral molecules and their crystal structures

AbstractRelevant families of ideal polyhedra (Platonic, Archimedean, prisms, Johnson, and Fullerenes) are briefly summarized, and an overview of polyhedral alkanes and alkenes, existing or hypothetical, is presented. The assignment of a polyhedral shape to a specific compound with the help of continuous shape measures and derived tools is also briefly discussed, and application of shape analysis to cyclic molecules such as cyclobutane, cyclohexane, and cyclooctatetraene is presented to illustrate the usefulness of ideal polyhedra in the stereochemical description of non‐polyhedral molecules. Finally, the presence of latent octahedral symmetry in icosahedral polyhedra is used to design new molecules with nested shells of the two supposedly incompatible symmetries, and to explain the cubic crystal structures of icosahedral molecules such as dodecahedrane and Buckminsterfullerene. Copyright © 2010 John Wiley & Sons, Ltd.

Structural organization of icosahedral coordination polyhedra in a molecular dynamics model of the Ni60Ag40 metallic glass

Features of the formation of a percolation cluster structure composed of interpenetrating and contacting icosahedra during the glass transition in an amorphous Ni60Ag40 alloy have been studied using the molecular-dynamics method and statistical geometric analysis. Data on the morphology of clusters composed entirely of the interpenetrating icosahedra and on the character of their conjugation in the percolation cluster are presented.

Molecules and crystals with both icosahedral and cubic symmetry

Notwithstanding the apparent incompatibility between octahedral and icosahedral symmetries, fragments with the two types of symmetry coexist in many molecules and crystals, as evidenced by continuous shape and symmetry measures. A geometric analysis of Platonic and Archimedean polyhedra and of a variety of molecular and crystal structures strongly suggests that octahedral symmetry is latent in icosahedral polyhedra and vice versa. In this Feature Article, new concepts and structural data from the literature combine to offer a perspective view of complex molecular and extended structures. Its influence on the common cubic packing of icosahedral molecules is discussed for a variety of examples, including water clathrates, dodecahedrane, Buckminsterfullerene, the Pd145 and Mo132 clusters and several intermetallic phases.

Investigation of multicomponent chemical short-range order in NiZr 2

The local atomic configuration of multicomponent chemical short-range order (MCSRO) in NiZr2 has been investigated by means of molecular dynamics simulation (MD) in a wide temperature range. The potential functions for the system based on the embedded atom method are constructed and the parameters are obtained by fitting the structure and properties of NiZr2 crystal. The static structures such as pair distribution functions and the distribution of coordination number have been calculated. The local atomic configurations of the MCSROs in the melt were demonstrated as distorted coordination polyhedron of the compound structure and/or the structure similar to cubooctahedron analogues. It is indicated by the results of MD simulation that above the melting point the atomic packing of long-range order disappears, but the chemical interaction of coordinated atoms still exists, which leads to the formation of various MCSROs with atomic configurations similar to the stable or metastable unit cell of NiZr2 compound. When the system is just melted, many icosahedral polyhedron configurations appear, which decrease as the over-heating temperature increases.

Highly faceted growth shape of microvoids in icosahedral Al-Mn-Pd

Faceted microholes in icosahedral Al-Mn-Pd quasicrystals form by condensation of thermal vacancies, typically during annealing in the temperature range above approximately 700oC. Prolonged annealing at temperatures between 750 and 830oC leads to the growth of large and highly faceted microholes through a classical Ostwald ripening process. The indexing of all facets of such a microhole is presented. The idealized morphology is found to correspond to an icosahedral polyhedron with 302 facets.

The morphology of the polyhedra of a host range-expanded recombinant baculovirus and its parents.

The host range-expanded recombinant baculovirus, RecB-8 was isolated from BmN-4 cells coinfected with Autographa californica and Bombyx mori nuclear polyhedrosis viruses. Its genome was compared with those of its parents by restriction endonuclease digestion and their polyhedra compared in an electron microscope. Interestingly, the polyhedra of RecB-8 were tetrahedral although the polyhedrin gene was the same as that of the BmNPV parent which has icosahedral polyhedra. Thus the morphology of the RecB-8 polyhedra resulted from host cell factors and/or another viral genome in the host cells.

Energetics of Fullerene Clusters

AbstractA new phenomenological model for calculation of formation energy of carbon nano-clusters of definite shape is proposed. The model uses only three energetic parameters: two first, Ec and ω5, being determined from comparison with experimental data, results of computer simulation for various carbon nano clusters, and the last one is dangling bond energy. Eb Energies of formation of carbon clusters shaped as cylinder, sphere, icosahedral polyhedra, capsule, were calculated in frame of unified phenomenological approach, which allows to judge relative energetical stability of these clusters.

Approximate indexing of icosahedral polyhedra with fibonacci numbers

Abstract In general, indexing faces of icosahedral face-forms requires irrational numbers. However, for many practical purposes an approximate indexing based on triplets of integer numbers can be used. Two possible approaches called, respectively, “Fibonacci Matrix Methods” (FMM) and the “Linear Combination Method” (LCM) are described. FMM relies on the use of “auxiliary” matrices Fn, F2 n, F3 n and F4 n which have Fibonacci numbers as their elements. These matrices allow good approximation of the results usually obtained using the standard five-fold rotation matrices which are typical of icosahedral symmetry. LCM is based on the use of a classical crystallographic rule i.e. the so-called “Goldschmidt Complication Law” which is just a particular case of linear combination of triplets of face indices, with integers as coefficients. The occurrence of large integer indices is remarked.

Reactions of the [Ni 6(CO) 12] 2- dianion with stibine and bismuthine reagents: synthesis and stereophysical characterization of the [Ni 10(SbPh) 2(CO) 18] 2- dianion containing a noncentered icosahedral Ni 10Sb 2 core and Ni 2(CO) 4(μ 2-Ph 2SbOSbPh 2) 2 containing a centrosymmetric eight-membered (NiSbOSb) 2 ring

In a further exploration of the types of high-nuclearity, mixed metal-(main-group) clusters accessible from the electron-rich [Ni 6(CO) 12] 2- dianion ( 1), reactions of 1 (a direct descendent of nickel tetracarbonyl) with antimony and bismuth reagents have been carried out. The main product isolated in 50–60% yields from reactions of 1 with either chlorodiphenylstibine, Ph 2SbCl, or dichlorophenylstibine, PhSbCl 2, in THF solutions at room temperature is the [Ni 10(SbPh) 2(CO) 18] 2- dianion ( 2); its identity was unambiguously established from X-ray crystallographic determinations of four different ionic compounds, viz., [NMe 4] + 2 [ 2] 2- · 2THF ( 2a), [NMe 4] + 2 [ 2] 2- · 2Me 2CO ( 2b), [(Ph 3P) 2N] + 2 [ 2] 2- · 2THF ( 2c), and [NMe 3Ph] + 2 [ 2] 2- ( 2d). In each salt, the geometrically similar nickel stibinidene carbonyl dianion possesses a closo 1,12-disubsituted, icosahedral Ni 10Sb 2 core, (i.e., a bi-Sb-capped pentagonal-antiprismatic Ni 10 configuration) of crystallographic C i- 1 site symmetry encapsulated by two antimony-attached phenyl substituents, 10 terminal carbonyl ligands (one per nickel atom), and four doubly bridging and four triply bridging carbonyl ligands. This nickel-antinomy cluster is the third member of the homologous series of [Ni 10(ER) 2(CO) 18] 2- dianions (E = P, R = Me; E = As, R = Me). A comparative geometrical analysis of their icosahedral Ni 10E 2 cores, which are electronically equivalent analogues of the regular 12-boron icosahedral polyhedron of the classic [B 12H 12] 2- dianion, is given. The fact that 2 was the only nickel-stibinidene cluster isolated from a room-temperature reaction with Ph 2SbCl is attributed to the facile cleavage of one of the two Sb-Ph bonds of the Ph 2SbCl under the reaction conditions and to the apparent thermodynamic stability of 2. An X-ray diffraction analysis coupled with laser desorption/Fourier transform mass spectrometry (LD/FTMS) established conclusively the formulation of a side product, obtained in ∼ 5% yield from room-temperature reactions of 1 with chlorodiphenylstibine, as Ni 2(CO) 4(μ 2-Ph 2SbOSbPh 2) 2 ( 3). This molecular dimer is best viewed as a disubstituted Ni(CO) 2L 2 derivative of nickel tetracarbonyl in which two electron-donating Sb III atoms from two bridging Ph 2SbOSbPh 2 ligands have replaced two carbonyl ligands around each tetrahedrally-coordinated, zerovalent nickel atom. The resulting eight-membered cyclo-(NiSbOSb) 2 complex of crystallographic C i- 1 site symmetry possesses a chair-like conformation presumably due to the bulky antimony-attached phenyl substituents. This compound ( 3) is the first example (to our knowledge) of a metal complex formed from bis(diphenylstibine)oxide which itself exists as a molecular compound. The origin of the bridging Ph 2SbOSbPh 2 ligand in 3 can be readily attributed to the partial hydrolysis of the Ph 2SbCl reagent with adventitious water (i.e., “wet” solvent). The reaction of 1 with Ph 2SbCl gave a third nickel-antimony compound, Ni(CO) 3(SbClPh 2); although not isolated from solution, the proposed existence of this monosubstituted derivative of Ni(CO) 4 is based upon its infrared carbonyl frequencies being virtually identical to those previously reported for the analogous Ni(CO) 3(SbClEt 2) and Ni(CO) 3(SbPh 3). Reaction of 1 with ( p-tolyl)BiBr 2 in THF gave no isolatable carbonyl-containing products.

Non-periodic Packings of Icosahedral Polyhedra

A method for deriving packings of icosahedral polyhedra from periodic and non-periodic space grids based on icosahedral symmetry is presented. Corresponding to the three axes of symmetry, three classes of packings exist. For each class, an inter-transforming family of 64 (theoretically) possible packings is suggested. Their details remain to be worked out and examples are illustrated with packings of icosahedra.