Growth mechanism of icosahedral and other five-fold symmetric diamond crystals

Five-fold symmetric diamond crystals（FSDCs） were synthesized by hot filament chemical vapour deposition（HFCVD） methods. Their surface morphologies and defects were characterised by scanning electron microscopy（SEM）. From the perspective of nucleation-growth, a growth mechanism for icosahedral and other five-fold symmetric diamond crystals was discussed. Computer modelling was also carried out. The results show that the dodecahedrane（C20H20） molecule is proposed as a nucleus for the growth of icosahedral diamond crystals（IDCs）, wherein the 20 {111} surface planes develop orthogonal to the direction of the original 20 C—H bonds by sequential H abstraction and CH3 addition reactions. IDC can be pictured as an assembly of isosceles tetrahedra, with each tetrahedron contributing a {111} plane to the surface of the IDC and the remainder of the tetrahedral surfaces forming twin planes with neighbouring tetrahedra. The small mismatch（1.44°） between the {111} surface dihedral angle of a perfect icosahedron and that of a twinned icosahedron reveals itself via twin planes in the IDC grain. The modelling suggests how the relief of strain induced by this distortion could lead to the formation of defects such as concave pentagonal cavities at vertices and grooves along the grain edges that accord well with those observed experimentally. Similar arguments based on growth from the hexacyclo pentadecane（C15H20） nucleus can also account for the observed formation of star and rod shaped FSDCs, and some of their more obvious morphological defects.

Effect of cooling rates on clustering towards icosahedra in rapidly solidified Cu_(56)Zr_(44) alloy

The rapid solidification processes of liquid Cu56Zr44 alloys at different cooling rates （γ） were simulated by a molecular dynamics （MD） method. In order to assess the influence of cooling rate on the clustering tendency and degree towards icosahedrons, a ten-indices＇ cluster-type index method was suggested to characterize the local atomic structures in the super-cooled liquid and the rapidly solidified solid. And their clustering and ordering degrees as well as the packing density of ieosahedral clusters were also evaluated by an icosahedral clustering degree （fI）, the chemical order parameter （ηαβ） and densification coefficients （D0, DI and DIS）, respectively. Results show that the main local atomic configurations in Cu56Zr44 alloy system are Z12 clusters centered by Cu, and most of which are （12 0 12 0 0 0 0 0 0 0） standard icosahedra and （12 0 8 0 0 0 2 2 0 0） as well as （12 2 8 2 0 0 0 0 0 0） defective icosahedra. Below glass transition temperature （Tg）, these icosahedral clusters will be coalesced to various icosahedral medium-range orders （IMROs） by IS linkages, namely, icosahedral bond, and their number N, size n, order parameter ηαβ as well as spatial distributions vary with y. As the cooling rate exceeds the critical value （γc） at which a glassy transition can take place, a lower cooling rate, e.g., γ1=10^1K/ns, is demonstrated to be favorable to uplift the number of icosahedra and enlarge the size of IMROs compared with the higher cooling rates, e.g., γ5=10^5 K/ns, and their packing density and clustering degree towards icosahedra in the rapidly solidified solid can also benefit from the slow cooling process.

Golden Quartic Polynomial and Moebius-Ball Electron

A symmetrical quartic polynomial, named golden one, can be connected to coefficients of the icosahedron equation as well as to the gyromagnetic correction of the electron and to number 137. This number is not a mystic one, but is connected with the inverse of Sommerfeld’s fine-structure constant and this way again connected with the electron. From number-theoretical realities, including the reciprocity relation of the golden ratio as effective pre-calculator of nature’s creativeness, a proposed closeness to the icosahedron may point towards the structure of the electron, thought off as a single-strand compacted helically self-confined charged elemantary particle of less spherical but assumed blunted icosahedral shape generated from a high energy double-helix photon. We constructed a chiral Moebius “ball” from a 13 times 180˚twisted double helix strand, where the turning points of 12 generated slings were arranged towards the vertices of a regular icosahedron, belonging to the non-centrosymmetric rotation group I532. Mathematically put, we convert the helical motion of an energy quantum into a stationary motion on a Moebius stripe structure. The radius of the ball is about the Compton radius. This chiral closed circuit Moebius ball motion profile can be tentatively thought off as the dominant quantum vortex structure of the electron, and the model may be named CEWMB (Charged Electromagnetic Wave Moebius Ball). Also the gyromagnetic factor of the electron (ge = 2.002319) can be traced back to this special structure. However, nature’s energy infinity principle would suggest a superposition with additional less dominant (secondary) structures, governed also by the golden mean. A suggestion about the possible structure of delocalized hole carriers in the superconducting state is given.

Beyond a Quartic Polynomial Modeling of the DNA Double-Helix Genetic Code

By combination of finite number theory and quantum information, the complete quantum information in the DNA genetic code has been made likely by Planat et al. (2020). In the present contribution a varied quartic polynomial contrasting the polynomial used by Planat et al. is proposed that considered apart from the golden mean also the fifth power of this dominant number of nature to adapt the code information. The suggested polynomial is denoted as g(x) = x4 - x3 - (4 - ϕ2 )x2 + (4 – ϕ2)x + 1, where is the golden mean. Its roots are changed to more golden mean based ones in comparison to the Planat polynomial. The new coefficients 4 – ϕ2 instead of 4 would implement the fifth power of the golden mean indirectly applying . As an outlook, it should be emphesized that the connection between genetic code and resonance code of the DNA may lead us to a full understanding of how nature stores and processes compacted information and what indeed is consciousness linking everything with each other suggestedly mediated by all-pervasive dark constituents of matter respectively energy. The number-theoretical approach to DNA coding leads to the question about the helical structure of the electron.

A STUDY OF NEW RHODIUM COMPLEX WITH CARBORANE LIGAND

The complex [closo-3,3-（PPh3）2-3-H-3,1,2-RhC2B9H11]has a rich derivative chemistrythat is currently under active investigation.The resultant compound shows an increasing stabilitythat is often associated with metallocarboranes.This paper deals with the novel and the produc-tion area of carborane complexes of transition metals.The paper indicates that some reactions can easily proceed and the resulting compound hassome new properties and uses.K[18-crown-6][closo-3-Ph3P-3-CH2Ph-3-Br-3,1,2-RhC2B9H11]can be synthesized by the reaction of K[18-crown-6][（Ph3P）2RhC2B9H11]withbromo-toluene under the condition of dry benzene.IR and 1H,11B,31p nuclear magnetic reso-nance and elemental analysis comfirm the structure for this species with one carborane groupbonded to the central metal.

The Stability of Icosahedral Cluster and the Range of Interaction Potential

The relation between the stability of icosahedral clusters and the range of interaction potential is discussed.We found that the stability of icosahedral clusters nay decrease with decreasing range of interaction potential.A simple formula about the critical number of icosahedral clusters and the range of interaction potential(M^(1/3)_(c)=A_(1)+A_(2)r^(2)_(eff))was proposed.The calculation of the stability of icosahedral fullerence molecular clusters shows that our idea is right.

Mathematical Approach to the Platonic Solid Structure of MS2 Particles

Bacteriophage MS2 is a viral particle whose symmetrical capsid consists of 180 copies of asymmetrical coat proteins with triangulation number T = 3. The mathematical theorems in this study show that the phage particles in three-dimension (3D) might be an icosahedron, a dodecahedron, or a pentakis dodecahedron. A particle with 180 coat protein subunits and T = 3 requires some geometrical adaptations to form a stable regular polyhedron, such as an icosahedron or a dodecahedron. However, with mathematical reasons electron micrographs of the phage MS2 show that 180 coat proteins are packed in an icosahedron. The mathematical analysis of electron micrographs in this study may be a useful tool for surveying the platonic solid structure of a phage or virus particle before performing 3D reconstruction.

Geometric architecture of viruses

In the current SARS-CoV-2 disease(COVID-19)pandemic,the structural understanding of new emerging viruses in relation to developing effective treatment and interventions are very necessary.Viruses present remarkable differences in geometric shapes,sizes,molecular compositions and organizations.A detailed structural knowledge of a virion is essential for understanding the mechanisms of capsid assembly/disassembly,antigenicity,cell-receptor interaction,and designing therapeutic strategies.X-ray crystallography,cryoelectron microscopy and molecular simulations have elucidated atomic-level structure of several viruses.In view of this,a recently determined crystal structure of SARS-CoV-2 nucleocapsid has revealed its architecture and self-assembly very similar to that of the SARS-CoV-1 and the Middle-East respiratory syndrome virus(MERS-CoV).In structure determination,capsid symmetry is an important factor greatly contributing to its stability and balance between the packaged genome and envelope.Since the capsid protein subunits are asymmetrical,the maximum number of inter-subunit interactions can be established only when they are arranged symmetrically.Therefore,a stable capsid must be in a perfect symmetry and lowest possible free-energy.Isometric virions are spherical but geometrically icosahedrons as compared to complex virions that are both isometric and helical.Enveloped icosahedral or helical viruses are very common in animals but rare in plants and bacteria.Icosahedral capsids are defined by triangulation number(T=1,3,4,13,etc.),i.e.,the identical equilateral-triangles formed of subunits.Biologically significant defective capsids with or without nucleic acids are common in enveloped alpha-,flavi-and hepadnaviruses.The self-assembling,stable and non-infectious virus-like particles have been widely exploited as vaccine candidates and therapeutic molecules delivery vehicles.

Single Covalent Bonding Structure in Fullerenes, Carbon Nanotubes and Closed Nanotubes

The present paper deals with carbon in highly organized solids like graphene and its three-dimensional derivatives: fullerenes, carbon nanotubes and capped carbon nanotubes. It proposes an alternative to the typical bonding pattern exposed in literature. This novel bonding pattern involves alternating positively and negatively charged carbon atoms around hexagonal rings, then a few uncharged and partially bonded atoms close to the pentagon rings. The article focuses on fullerenes inscribed into a regular icosahedron, then addressing the most common fullerenes like C60. Carbon atoms are found to have predominantly three single bonds and less often two separated single bonds. The same pattern explains equally well carbon nanotubes and closed-tip nanotubes, of which C70 is a special case.

DEDUCTION OF QUASILATTICE WITH FIVE-FOLD SYMMETRY AND PARTICLE FRACTAL STRUCTURE MODEL

In the structure of quasicrystal, the coordination icosahedron has long ordering but no translation ordering. The author dealt with the building principle ofquasicrystal and thought that two principles played a certain role in the quasicrystal structure, i.e. the icosahedron principle and the golden mean principle. We obtained the most simple.structure model of quasicrystals, and could explain all details of the high-resolution electron microscopic image of the A1-Mn quasicrystal based on the two principles. The author’s model has the characteristic of fractal structure, therefore, we call it the particle fractal structure madeh The author has made a systematic deduction of quasicrystal point group, forms, possible type of quasicrystal lattice.

TWO NEW FORMULAS FOR TRIANGULATION NUMBER T

The present paper reports two [new formulas for calculating triangulation number T.They are T =L^2/l^2 and T = 1.45r^2/l^2, where L is the distance between pentons, l the distancebetween any two adjacent capsomeres, r the radius of viral nucleocapsid. The formulas havebeen verified and applied. It is worth noticing that the triangulation number, viral size anddistance between capsomeres are fully connected by the formula r/(Tl)^(1/2) = 0. 83, and the capsidparameters of all icosahedral viruses are unified in one constant, 0.83.

Solvent-dependent evolution of cyclic penta-twinned rhodium icosahedral nanocrystals and their enhanced catalytic properties

Cyclic penta-twinned noble metal nanocrystals exhibit promising properties due to their unique geometric and electronic structures. However, the controlled synthesis of cyclic penta-twinned nanostructures, especially of noble metals with a high cohesive energy （e.g., Rh）, is very difficult, and the corresponding growth mechanism is not fully understood. Herein, we report a facile one-pot hydrothermal approach for the synthesis of cyclic penta-twinned Rh icosahedral nanocrystals. It was found that apart from regulating the surface free energy by changing the concentration or category of the capping agents, the solvent might influence the adsorption ability of the surfactant on the Rh crystal surface, which results in a change in the surface free energy and thus allows the formation of Rh cyclic penta-twinned nanostructures. In addition, due to their unique electronic and geometric structures, the Rh icosahedral nanocrystals exhibit superior catalytic activity and stability for the electrooxidation of ethanol as compared to single-crystal Rh tetrahedral nanocrystals and commercial Rh black.

H-Implanted Pd Icosahedra for Oxygen Reduction Catalysis: From Calculation to Practice

Although palladium(Pd)has gradually emerged as the most likely candidate to replace platinum(Pt)in the oxygen reduction reaction(ORR),the specific electronic structure of conventional Pd results in too strong Pd–O binding strength and unsatisfactory ORR performance.Herein,guided by density functional theory,we have explored a strategy to expand lattice spacing by implanting hydrogen(H)atoms in Pd nanocrystals(NCs),which realizes decreased electron density to boost ORR.