Features of sputtering of nitrides and their components

The sputtering behaviour of hexagonal or wurtzite polycrystal nitrides of boron, aluminium, and gallium was explored employing methods of molecular dynamics. The sputtering yield Y of nitrides and the average energy ē ₁ of emitted particles were studied as dependent on the mass m ₁ of bombarding He, Li, B, N, Ne, Al, Ar, Ni, Ga, Kr, and Xe ions with the initial energy E ₀ between 200 and 10,000 eV. Y(m ₁) and ē ₁(m ₁) were researched upon for preferential sputtering of nitride components at low E ₀. It was revealed that the ratio between the sputtering yield of the light component and that of the heavy one depends on ion energy and mass. At E ₀=200 eV and m ₁=40, the ratio for BN, AlN, and GaN amounts to 1.2, 2.2, and 2.4, respectively. For nitride components, an anomalous dependence of sputtering on ion mass was found, its maximum occurring at a certain ratio m ₂/m ₁, where m ₂ is the averagè mass of two nitride components.     

Solution-grown single crystals of random terpolymer liquid crystal polymers: Chain folding,morphology, and effect of annealing

Thin (100–150 Å thick) single crystals of large lateral dimensions have been grown from dilute solution in xylene of random terpolymer, thermotropic, liquid crystal polymers containing approximately equimolar amounts of C₆ or C₇ flexible segments, oxybenzoate, and dioxyphenyl. With both polymers having molecular lengths of 800 Å or longer, electron diffraction patterns indicate chain folding. The crystal structure, hexagonal, is less perfect than found previously for thin films of the C₇ (and C₅) polymer crystallized from the nematic state by slow cooling (orthorhombic). Annealing of the crystals below the crystal-liquid crystal transition results in merging of overgrowths and rough crystal edges into the main crystal and a surface roughening, followed, at longer times and/or higher temperatures, by lamella thickening. Annealing in the nematic state results in the development of rosettes of lamellae. Implications of the results for crystallization mechanisms and morphology of the nematic state are discussed.     

Theoretical study of the reaction of H2 with a Cu2Pt2 cluster

The study of the interaction of a pyramidal tetramer of Cu₂Pt₂ with the H₂ is reported here through ab initio multiconfigurational self-consistent field (MC-SCF) calculations, plus extensive multireference configuration interaction (MR-CI), variational and perturbative calculations. The lowest three electronic states X ¹A′, a ³A′ and a ¹A′ of the bare cluster were considered in order to study this interaction. For the H₂ C_s approaching a Pt vertex, results show that the Cu₂Pt₂ pyramid cluster in its X ¹A′ and a ¹A′ states can spontaneously capture and dissociate the H₂. For the H₂ C_s approaching a Cu vertex, where H₂ is located in the C_s reflecting plane, the Cu₂Pt₂ cluster in its X ¹A′ electronic state shows capture of the hydrogen molecule after surmounting an energy barrier; moreover, in this approach the Cu₂Pt₂ cluster in its a ¹A′ electronic state shows spontaneous capture of the hydrogen molecule. For the H₂ approaching a Cu vertex, where the C_s reflecting plane bisects the H₂ molecule, the Cu₂Pt₂ cluster in its three lowest-lying states is able to capture the hydrogen molecule after surmounting a small barrier. The Cu₂Pt₂+H₂ C_s face-on interactions show a lower H₂ activation than that which was obtained in the equivalent Pt₄+H₂ interactions.     

Elliptic equations,principal eigenvalue and dependence on the domain

We consider a general second order uniformly elliptic differential operator L and also the set θ of all open sets (not necessarily smooth) in the unit ball of ?ⁿ. We define a metric d in this space (up to an equivalence relation ～) that makes the space (θ/ ～,d) a complete metric space. We show that the principal eigenvalue and eigenfunction of L are continuous with the metric d. Similar results are obtained for the solutions of the equation Lv = ?.     

The row–column multiplication of high dimensional rhotrices

This paper presents the row–column multiplication of rhotrices that are of high dimension. This is an extension of the same multiplication carried out on rhotrices of dimension three, considered to be the base rhotrices.     

Conversion of a rhotrix to a ‘coupled matrix’

In this note, a method of converting a rhotrix to a special form of matrix termed a ‘coupled matrix’ is proposed. The special matrix can be used to solve various problems involving n?×?n and (n?–?1)?×?(n?–?1) matrices simultaneously.     

A New Stable Bubble Element for Incompressible Fluid Flow Based on a Mixed Petrov–Galerkin Finite Element Formulation

A new mixed Petrov–Galerkin formulation employing the MINI element with a non-confirming bubble function for an incompressible media governed by the Stokes equations, which is equivalent to the stabilized finite element by P ¹-P ¹ approximation, is proposed. The new formulation possesses better stability properties than the conventional Bubnov–Galerkin formulation employing the MINI element. In this aspect, the stabilizing effect of this formulation is evaluated by a stabilizing parameter determined by both shapes of the trial and the weighting bubble functions.     

Organocatalysts Derived from Unnatural α‐Amino Acids: Scope and Applications

The organocatalytic properties of unnatural α‐amino acids are reviewed. Post‐translational derivatives of natural α‐amino acids include 4‐hydroxy‐l ‐proline and 4‐amino‐l ‐proline scaffolds, and also proline homologues. The activity of synthetic unnatural α‐amino acid‐based organocatalysts, such as β‐alkyl alanines, alanine‐based phosphines, and tert‐leucine derivatives, are reviewed herein. The organocatalytic properties of unnatural monocyclic, bicyclic, and tricyclic proline derivatives are also reviewed. Several families of these organocatalysts permit the efficient and stereoselective synthesis of complex natural products. Most of the reviewed organocatalysts accelerate the reported reactions through covalent interactions that raise the HOMO (enamine intermediates) or lower the LUMO (iminium intermediates).     

Efficient potential well escape for bi-stable Duffing oscillators

The problem of escape from a potential well of bi-stable oscillators has attracted attention given the diversity of physical and engineering systems described by this mathematical model. Most previous studies have considered quasi-static dynamics leading to escape. In devising efficient escape strategies for structures, transient conditions have not yet received adequate consideration. In this study, the intra-well nonlinear resonant dynamics of bi-stable systems are studied and exploited, yielding a time-efficient strategy for triggering minimal amplitude escape by employing transient perturbations. The response characteristics of both, the symmetric and asymmetric double-well Duffing oscillators are explored analytically to identify the stable solution branches for any given forcing configuration. Based on the basins of attraction of the stable attractors, a novel actuation methodology employing controlled perturbations in the phase of the forcing for driving the system into a series of high-amplitude limit cycle oscillations and eventual escape to the desired stable solution is proposed. Additionally, accelerated settling to the desired configuration is achieved by implementing state feedback techniques. The proposed algorithm serves as a potential tool for implementing fast shape adaptation in bi-stable structural systems.