Microstructural assessment of InN-on-GaN films grown by plasma-assisted MBE

The structural properties of InN thin films, grown by rf plasma-assisted molecular beam epitaxy on Ga-face GaN/Al₂O₃(0001) substrates, were investigated by means of conventional and high resolution electron microscopy. Our observations showed that a uniform InN film of total thickness up to 1 μm could be readily grown on GaN without any indication of columnar growth. A clear epitaxial orientation relationship of , was determined. The quality of the InN film was rather good, having threading dislocations as the dominant structural defect with a density in the range of 10⁹–10¹⁰ cm⁻². The crystal lattice parameters of wurtzite InN were estimated by electron diffraction analysis to be a=0.354 nm and c=0.569 nm, using Al₂O₃ as the reference crystal. Heteroepitaxial growth of InN on GaN was accomplished by the introduction of a network of three regularly spaced misfit dislocation arrays at the atomically flat interface plane. The experimentally measured distance of misfit dislocations was 2.72 nm. This is in good agreement with the theoretical value derived from the in-plane lattice mismatch of InN and GaN, which indicated that nearly full relaxation of the interfacial strain between the two crystal lattices was achieved.     

Evidence of formation of H2CN by a concerted reaction

We have investigated the possibility of formation of H₂CN by the concerted reaction H₂ + CN → H₂CN at energy regimes of over 60 kcal/mol relative to the global minimum. We have concluded that this concerted reaction is possible in principle provided that H₂ is vibrationally excited.     

Matrix Kadomtsev–Petviashvili Equation: Tropical Limit,Yang–Baxter and Pentagon Maps

In the tropical limit of matrix KP-II solitons, their support at a fixed time is a planar graph with “polarizations” attached to its linear parts. We explore a subclass of soliton solutions whose tropical limit graph has the form of a rooted and generically binary tree and also solutions whose limit graph comprises two relatively inverted such rooted tree graphs. The distribution of polarizations over the lines constituting the graph is fully determined by a parameter-dependent binary operation and a Yang–Baxter map (generally nonlinear), which becomes linear in the vector KP case and is hence given by an R-matrix. The parameter dependence of the binary operation leads to a solution of the pentagon equation, which has a certain relation to the Rogers dilogarithm via a solution of the hexagon equation, the next member in the family of polygon equations. A generalization of the R-matrix obtained in the vector KP case also solves a pentagon equation. A corresponding local version of the latter then leads to a new solution of the hexagon equation.     

Noncommutative Geometry and Integrable Models

A construction of conservation laws for -models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing theordinary calculus of differential forms with other differentialcalculi and introducing an analogue of the Hodge operator on thelatter. The general method is illustrated with several examples.     

Predissociation lifetime of the 1σ g 2 2σ g diabatic state of He 2 + : a one-channel approach

Summary This work is concerned with the application of a one-channel model to obtaining predissociation lifetimes and transition rates in a system of crossing diabatic states. The calculation focuses on the first shape resonance of the 1 _g ² 2 _g diabatic state of He ₂ ⁺ , which is relatively stable with respect to tunneling. This resonance predissociates as a result of the 1 _g ² 2 _g state being crossed by the 1 _g 1 _u ² dissociative diabatic state near the resonance level. We have estimated its predissociation lifetime to be of the order of 10^–11 s.     

From nonassociativity to solutions of the KP hierarchy

A recently observed relation between ‘weakly nonassociative’ algebras $\mathbb{A}$ (for which the associator ( $\mathbb{A},\mathbb{A}^2 ,\mathbb{A}$ ) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus $\mathbb{A}$ ′ of { $\mathbb{A}$ ) is recalled. For any such algebra there is a nonassociative hierarchy of ODEs, the solutions of which determine solutions of the KP hierarchy. In a special case, and with matrix algebra $\mathbb{A}$ ′, this becomes a matrix Riccati hierarchy which is easily solved. The matrix solution then leads to solutions of the scalar KP hierarchy. We discuss some classes of solutions obtained in this way.     

A band dispersion mechanism for Pt alloy compositional tuning of linear bound CO stretching frequencies

The C-O stretching frequency (nu(CO)) of atop CO/Pt in PtRu alloys is compositionally tuned in proportion to the Pt mole percent. The application of a Blyholder-Bagus type mechanism (i.e., increased back-donation from the metal d-band to the hybridized 2pi CO molecular orbitals (MOs)) to compositional tuning has been paradoxical because (1) a Pt-C bond contraction, expected with increased back-donation as the Pt mole percent is reduced, is not observed (i.e., calculated Pt-C bond is either elongated or insensitive to alloying and the binding energies of CO/Pt decrease with alloying) and (2) the lowering d-band center and increased d-band vacancies upon alloying (suggesting less back-donation to the higher energy metal hybridized 2pi CO MOs) must be reconciled with the alloy-induced red shift of the nu(CO). A library of spin-optimized Pt and Pt alloy clusters was the basis of density functional theory (DFT) calculations of CO binding energies, nu(CO) values, shifts, and broadening of 5sigma/2pi CO MO upon hybridization with the alloy orbitals and a DFT derived Mulliken electron population analysis. The DFT results, combined with FEFF8 local density of states (LDOS) calculations, validate a 5sigma donation-2pi back-donation mechanism, reconciling the direction of alloy compositional tuning with the lowering of the d-band center and increased vacancies. Although the d-band center decreases in energy with alloying, an asymmetric increase in the dispersion of the d-band is accompanied by an upshift of the metal cluster HOMO level. Concomitantly, the hybridization and renormalization of the CO 5sigma/2pi states results in a broadening of the 5sigma/2pi manifold with additional lower energy states closer to the upshifted (with respect to the pure Pt cluster) HOMO of the alloy cluster. The dispersion toward higher energies of the alloy d-density of states results in more 5sigma/2pi CO filled states (i.e., enhanced 2pi-back-donation). Finally, Mulliken and FEFF8 electron population analysis shows that the increase of the average d-band vacancies upon alloying and additional 2pi back-donation are not mutually exclusive. The d-electron density of the CO-adsorbed Pt atom increases with alloying while the average d-electron density throughout the cluster is reduced. The localized electron density is manifested as an electrostatic wall effect, preventing the Pt-C bond contractions expected with increased back-donation to the 2pi CO MOs.     

Algebraic identities associated with KP and AKNS hierarchies

Explicit KP and AKNS hierarchy equations can be constructed from a certain set of algebraic identities involving a quasi-shuffle product. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Moral coherence,moral worth and explanations of moral motivation

Moral internalism and moral externalism compete over the best explanation of the link between judgment and relevant motivation but, it is argued, they differ at best only verbally. The internalist rational-conceptual nature of the link’ as accounted by M. Smith in The Moral Problem is contrasted to the externalist, also rational, link that requires in addition support from the agent’s psychological-dispositional profile; the internalist link, however, is found to depend crucially on a, similarly to the externalist, psychologically ‘loaded’ profile. It is also argued that the differentiation of the two competing explanations is insufficient partly because they both fail to consider crucial quantitative parameters of the judgment-motivation link. Such parameters become very important particularly in the light of Smith’s claim that this link is grounded on the observable “striking fact” where changes in the set of one’s moral beliefs systematically bring about changes in one’s moral behavior. Examples of algorithms measuring moral coherence and moral worth are provided to serve as evidence for what it comes down to, vis-à-vis the alleged fact, only a verbal dispute between the two camps. Finally, the ‘misfiring’ of these explanations is understood in connection to the irreducibility of concepts such as ‘moral worth’, and/or, ‘moral sensitivity’.