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For a quadratic Thurston map having two distinct critical points and n postcritical points, we count the number of possible dynamical portraits. We associate elastic graph spines to several hyperbolic quadratic Thurston rational functions. These functions have four postcritical points, real coefficients, and invariant real intervals. The elastic graph spines are constructed such that each has embedding energy less than one. These are supporting examples to Dylan Thurston's recent positive characterization of rational maps. Using the same characterization, we prove that with a combinatorial restriction on the branched covering and a cycle condition on the dynamical portrait, a quadratic Thurston map with finite postcritical set of order n is combinatorially equivalent to a rational map. This is a special case of the Bernstein-Levy theorem. [ABSTRACT FROM AUTHOR]

It is a conventional wisdom that the closed-shell structure of a He atom prompts it to occupy the center of a vacancy in metals where the charge density is the lowest. Although it was found accidentally by density functional theory (DFT) calculations that the He sits off-center in a vacancy in vanadium (V), the underlying physics has remained elusive. We have performed systematic DFT study of the positioning of He in a vacancy in 40 elemental crystals, including alkali, alkaline-earth, and transition metals. We find that in addition to V, the off-vacancy-center positioning of He also occurs in Sc , Y, Ti, and Lu. Analyses of electronic structure reveal that d -orbital splitting and density of states (DOS) of the neighboring metal atoms at the Fermi surface play key roles in determining the position of He in a vacancy. Large t 2g - e g splitting and high DOS at the Fermi surface provide the force to drive the He off the center of a vacancy, by compensating the repulsion from the metal atoms to which the He atom is approaching. This discovery adds new knowledge of the behavior of the noble gas atoms in non-uniform electron gas, provides fundamental reference energetics for the development of interatomic potentials, and shed light on understanding the initial stage of He bubble nucleation in materials used in nuclear reactors. [Display omitted] Systematic density-functional-theory study reveals off-center positioning of He in a vacancy in V (left), along with Sc , Ti, Y, and Lu. Charge transfer from t 2g to e g in d-orbital splitting at the Fermi surface of the nearest-neighbor V atom lowers the total energy of system (right). [ABSTRACT FROM AUTHOR]

The realistic InSb nanostructures namely InSb nanoring, InSb nanocube, InSb nanocube-18, InSb nanosheet, InSb nanocage and InSb nanocube-27 are simulated and optimized successfully using B3LYP/LanL2DZ basis set. The stability of InSb nanostructures is studied in terms of binding energy, vibrational studies and calculated energy. The electronic properties of InSb nanostructures are discussed using ionization potential, electron affinity and HOMO–LUMO gap. Point symmetry and dipole moment of InSb nanostructures are reported. Incorporation of impurity atom in InSb nanostructures is studied using embedding energy. The present study provides the information regarding the enhanced electronic properties of InSb nanostructure which finds its potential importance in microelectronics and optoelectronic devices.

The realistic structures such as hexagonal ring, hexagonal sheet, ladder and cube isomers of GaAlAs and InAlAs are designed and optimized using density functional theory. The hexagonal ring structure is found to be more stable from the calculated energy. The dipole moments of GaAlAs and InAlAs nanoclusters are reported and hexagonal ring of GaAlAs and ladder structure of InAlAs nanoclusters are found to have a high dipole moment. The point symmetry of GaAlAs and InAlAs nanoclusters has either C 1 or C s symmetry. The HOMO–LUMO gap provides an insight into the transition of the electron for different isomers of GaAlAs and InAlAs clusters. The electron density depends on the geometry of the cluster. The electronic properties are discussed in terms of ionization potential and electron affinity. The hexagonal sheet isomer has the high value of IP and EA due to its geometry. The cube structured GaAlAs and InAlAs nanoclusters have the highest binding energy. The embedding energy is found to be low for GaAlAs and InAlAs hexagonal sheet isomers. The vibrational studies identify the stable clusters of GaAlAs and InAlAs nanoclusters. The result of the present work will give insight into tailoring and improving the electronic properties of GaAlAs and InAlAs nanoclusters which find their importance in optoelectronic devices. [ABSTRACT FROM AUTHOR]

Abstract: The realistic InSb nanostructures namely InSb nanoring, InSb nanocube, InSb nanocube-18, InSb nanosheet, InSb nanocage and InSb nanocube-27 are simulated and optimized successfully using B3LYP/LanL2DZ basis set. The stability of InSb nanostructures is studied in terms of binding energy, vibrational studies and calculated energy. The electronic properties of InSb nanostructures are discussed using ionization potential, electron affinity and HOMO–LUMO gap. Point symmetry and dipole moment of InSb nanostructures are reported. Incorporation of impurity atom in InSb nanostructures is studied using embedding energy. The present study provides the information regarding the enhanced electronic properties of InSb nanostructure which finds its potential importance in microelectronics and optoelectronic devices. [Copyright &y& Elsevier]

The realistic ZrN nanostructures namely ZrN nanocube-4, nanocube-6, nanocube-8, nanosheet-12 and buckycage-10 are constructed and optimized using density functional theory utilizing B3LYP/LanL2DZ basis set. ZrN nanostructures stability is studied using calculated energy, binding energy and vibrational studies. The dipole moment and point symmetry are discussed. The electronic properties of ZrN nanostructures are invoked with HOMO-LUMO gap, ionization potential and electron affinity. The embedding energy gives the insight to incorporate the foreign atom in the nanostructure. The stability and electronic properties of nanostructures leads to tailor new materials of ZrN with enhanced properties. [ABSTRACT FROM AUTHOR]

The present study reports the geometry, electronic structure, growth behavior and stability of neutral and ionized nickel encapsulated germanium clusters containing 1-20 germanium atoms within the framework of a linear combination of atomic orbital density functional theory (DFT) under a spin polarized generalized gradient approximation. In the growth pattern, Ni-capped Ge and Ni-encapsulated Ge clusters appear mostly as theoretical ground state at a particular size. To explain the relative stability of the ground state clusters, variation of different parameters, such as average binding energy per atom (BE), embedding energy (EE) and fragmentation energy (FE) of the clusters, were studied together with the size of the cluster. To explain the chemical stability of the clusters, different parameters, e.g., energy gap between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO gap), ionization energy (IP), electron affinity (EA), chemical potential (μ), chemical hardness (η), and polarizability etc. were calculated and are discussed. Finally, natural bond orbital (NBO) analysis was applied to understand the electron counting rule applied in the most stable GeNi cluster. The importance of the calculated results in the design of Ge-based superatoms is discussed. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

The present study reports the geometries, electronic structures, growth behavior, and stabilities of neutral and ionized copper-doped germanium clusters containing 1-20 Ge atoms within the framework of linear combination of atomic orbitals density functional theory (DFT) under the spin-polarized generalized gradient approximation. It was found that Cu-capped Ge (or Cu-substituted Ge) and Cu-encapsulated Ge clusters mostly occur in the ground state at a particular cluster size ( n). In order to explain the relative stabilities of the ground-state clusters, parameters such as the average binding energy per atom (BE), the embedding energy (EE), and the fragmentation energy (FE) of the clusters were calculated, and the resulting values are discussed. To explain the chemical stabilities of the clusters, parameters such as the energy gap between the highest occupied and the lowest unoccupied molecular orbitals (the HOMO-LUMO gap), the ionization energy (IP), the electron affinity (EA), the chemical potential ( μ), the chemical hardness ( η), and the polarizability were calculated, and the resulting values are also discussed. Natural atomic orbital (NAO) and natural bond orbital (NBO) analyses were also used to determine the electron-counting rule that should be applied to the most stable GeCu cluster. Finally, the relevance of the calculated results to the design of Ge-based superatoms is discussed. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

The present study reports the geometry, electronic structure and properties of neutral and anionic transition metal (TM = Ti, Zr and Hf)) doped germanium clusters containing 1 to 20 germanium atoms within the framework of linear combination of atomic orbitals density functional theory under spin polarized generalized gradient approximation. Different parameters, like, binding energy (BE), embedding energy (EE), energy gap between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO), ionization energy (IP), electron affinity (EA), chemical potential etc. of the energetically stable clusters (ground state cluster) in each size are calculated. From the variation of these parameters with the size of the clusters the most stable cluster within the range of calculation is identified. It is found that the clusters having 20 valence electrons turn out to be relatively more stable in both the neutral and the anionic series. The sharp drop in IP as the valence electron count increases from 20 to 21 in neutral cluster is in agreement with predictions of shell models. To study the vibrational nature of the clusters, IR and Raman spectrum of some selected TM@Ge (n = 15,16,17) clusters are also calculated and compared. In the end, relevance of calculated results to the design of Ge-based super-atoms is discussed. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

The potential energy in materials is well approximated by pair functional which is composed of pair potentials and embedding energy. During calculating material potential energy, the orientational component and the volumetric component are derived respectively from pair potentials and embedding energy. The sum of energy of all these two kinds of components is the material potential. No matter how microstructures change, damage or fracture, at the most level, they are all the changing and breaking atomic bonds. As an abstract of atomic bonds, these components change their stiffness during damaging. Material constitutive equations have been formulated by means of assembling all components’ response functions. This material model is called the component assembling model. Theoretical analysis and numerical computing indicate that the proposed model has the capacity of reproducing some results satisfactorily, with the advantages of great conceptual simplicity, physical explicitness, and intrinsic induced anisotropy, etc. [ABSTRACT FROM AUTHOR]

Abstract: Potential energy can be approximated by “pair-functional” potentials which is composed of pair potentials and embedding energy. Pair potentials are grouped according to discrete directions of atomic bonds such that each group is represented by an orientational component. Meanwhile, another kind of component, the volumetric one is derived from embedding energy. Damage and fracture are the changing and breaking of atomic bonds at the most fundamental level and have been reflected by the changing of these components’ properties. Therefore, material is treated as a component assembly, and its constitutive equations are formed by means of assembling these two kinds of components’ response functions. This material model is referred to as the component assembling model. Theoretical analysis and numerical computing indicate that the proposed model has the capacity of reproducing some results satisfactorily, with the advantages of physical explicitness and intrinsic induced anisotropy, etc. [Copyright &y& Elsevier]

This paper describes a dry coating process in which fine ceramic guest particles are mechanically compounded with soft metal host particles by embedding the guest particles on the surface of host particles using a high-speed elliptical-rotor-type powder mixer (HEM). The optimum rotor speed and processing time were determined on the basis of allowable deformation of host particles in a single compression by the rotor and the mechanical energy required for embedding all the guest particles, respectively. From measurements of the size distribution and morphology of composite particles, we confirmed that the composite particles were prepared according to powder design regardless of the physical properties of the guest particles. In order to investigate the hardness of composite particles, composite particles were deformed using HEM and the deformation was measured with an image analyzer. The coefficient representing hardness was determined from the deformation and magnitude of mechanical energy applied to the composite particles. It was proportional to the total volume of guest particles and inversely proportional to the distance between guest particles on the surface of host particles. The hardness of metal particles in which fine particles were embedded could be evaluated similar to that of particle-dispersion-strengthened materials. [Copyright &y& Elsevier]

This paper describes the method for determining the optimum operating conditions of equipment on dry coating processes based on the energy requirement for immobilizing the fine materials on the surface of coarser particles. In the model system consisting of the spherical copper particles (host particles) and the submicron-sized fine alumina particles (guest particles), the guests are immobilized by embedding onto the surface of the host with a high-speed elliptical-rotor-type powder mixer (HEM) to which Zirconia beads are added. The embedding process is approximated by the intruding process of the diamond indenter at the measurement of Vickers hardness of copper plate, and the energy required for embedding is estimated. We have found that both the allowable deformation of copper particles in a single compression by the rotor and the depth of embedding of alumina particles are important parameters in the determination of operating conditions (the rotor speed and the operation time). When the allowable deformation is set to be approximately 0.5% (corresponding to the strain in the intermediate region between the elastic and plastic ones of copper particle), the shape and size distribution of copper particles can be maintained throughout the coating process. Furthermore, the surface condition of coated particles can be controlled quantitatively by the depth of embedding. [Copyright &y& Elsevier]