Neighbourhood-Perfect Line Graphs

We show that the line graph of any balanced hypergraph is neighbourhood-perfect. This result is a hypergraphic extension of a recent theorem in [GKLM] saying that the line graphs of bipartite graphs are neighbourhood-perfect. The note contains also a graphical extension of the same theorem: the characterization of all graphs with neighbourhood-perfect line graph. The proof relies on a characterization of neighbourhood-perfect graphs among line graphs in terms of forbidden induced subgraphs.     

Substrate and elastic recovery effects in hardness measurement of CVD WC-based coatings

Hard coatings are used in a very broad range of applications, for example in the automotive, tooling and gas industries. The apparently simplest way to compare different coatings is to measure their hardness. However, interpreting such measurements is not a trivial problem for thin coatings (10 μm or less); standard micro-indenters (with a typical minimum applied load of 10gf) usually produce a penetration depth such that the substrate influences the measurements, giving a ‘composite’ hardness value of the coating and the substrate. At the same time there might be a more or less evident recovery of the indentation, because of residual elasticity around the sub-indentation plastic zone or because of residual stresses. One possible solution is the use of a nano-indenter. An alternative method for obtaining ‘true’ Vickers hardness values for the coating is described here, using changes in shape of Knoop micro-indentations to characterize the elastic recovery effects, together with use of a composite model for thin film microhardness. Results of hardness testing on thin WC-based coatings, using nano-indentation, Vickers and Knoop indenters, are compared.     

Interactions of dislocations with disconnections in fcc metallic nanolayered materials

Embedded-atom method potentials and atomistic models of coherent (010) interfaces were used to study slip across interfaces in cube-on-cube oriented Cu/Ni nanolayered materials. (111) disconnections form during slip across Cu–Ni interfaces and become significant barriers to continued deformation. A significant barrier exists for the flat coherent interface owing to the large coherency stresses in the Cu/Ni layers that must be overcome by applied stresses but, once these have been overcome, interface transection occurs readily. A disconnection adds an additional barrier because of a residual dislocation with a Burgers vector magnitude equal to the difference between b _Cu and b _Ni. This barrier depends on the position of the disconnection relative to the glide plane of the transecting glide dislocation and on the disconnection height. Disconnections cause work hardening that prevents shear band formation during deformation and encourages homogeneous shear processes. Disconnection energies are shown to be relatively small and to depend on the disconnection type and size.     

Nucleation of the Al6(Fe,Mn)-to-α-Al–(Fe,Mn)–Si transformation in 3XXX aluminium alloys. I. Roll-bonded diffusion couples

Roll-bonded diffusion couples are used to investigate a transformation of intermetallic particles from Al₆(Fe,?Mn) to α-Al–(Fe,?Mn)–Si that occurs upon homogenization of 3XXX aluminium alloys. By diffusing silicon into an Al–Fe–Mn alloy, the couples permit a progressive increase in the driving force for this 6-to-α transformation, thus allowing study of the nucleation of the transformation. Initially, the aluminium matrix is highly defected from rolling. This microstructure gives frequent (yet stochastic) nucleation of a eutectoid 6-to-α transformation expected from study of direct-chill-cast 3XXX alloys. However, once the matrix has recrystallized, nucleation is restricted to particles that lie on the matrix grain boundaries. The remaining particles, unable to transform eutectoidally, dissolve and supply growth of these α-phase particles, producing marked coarsening.     

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.     

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.