Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

Sol-Gel Processing of PbZrO3 Thin Films

PbZrO₃ (PZ) thin films have been prepared by 2-methoxyethanol route from lead oxide or lead acetate and zirconium n-butoxide. The use of lead oxide as lead source and the seeding layer of TiO₂ on Pt/TiO₂/SiO₂/Si substrate facilitate the formation of the perovskite phase.     

A Study of Amorphous Precursors for PbZrO3-PbTiO3 Based Ceramic Materials

Amorphous precursors for PbZrO₃ and PbTiO₃ ceramics were prepared from lead acetate and the transition metaln-propoxide inn-propanol orn-butoxide inn-butanol and hydrolysed with an excess of water. According to GLC and TGA/EGA analyses, the type of alkoxide group influences distinctly the structure of heterometallic precursors, i.e., oxo or acetate bridging, and the amounts of hydroxyl and organic groups bound to the metal network. The local environments of metal atoms in the amorphous precursors were also studied by EXAFS. The analysis reveals that in Pb−Zr precursors alkoxide groups modify the coordination spheres of the zirconium atoms. Conversely, local environments of both lead and titanium atoms within the analysed range of 3.4 A depend weakly on the type of alkoxide used.     

Chemical solution-deposited PbZr 0.53 Ti 0.47 O3 on La 0.5 Sr 0.5 Co O3. SIMS investigation of the effect of different precursor additives on the layer structure

Chemical solution-deposited thin films of PbZr(0.53)Ti(0.47)O(3)/La(0.5)Sr(0.5)CoO(3) on Pt/TiO(2)/SiO(2)/Si substrates have been investigated by dynamic SIMS. The PbZr(0.53)Ti(0.47)O(3) (PZT) is intended to serve as a ferroelectric layer for microelectronic or microelectromechanical applications; conducting La(0.5)Sr(0.5)CoO(3) (LSCO) is a buffer layer intended to eliminate fatigue effects which usually occur at the Pt/PZT interface. Depth profiles of the main components were obtained and revealed that significant diffusion occurred during the deposition and crystallisation processes. Two types of sample, with different thickness of PZT and different types of poly(vinyl alcohol) (PVA) added to the LSCO precursor, were investigated.     

Charge location and fragmentation under electron impact. IV—the behaviour under electron impact of some N-methyl,N′-R-1,2,4-phosphadiazetidine-3-ones and related compounds

The ionization potentials of a series of N-methyl,N′-R-1,2,4-phosphadiazetidine-3-ones and related compounds have been determined. The nature of the highest occupied orbital of the molecules and the use of empirical rules to rationalize the variations in the ionization potentials are discussed. The changes in the fragmentation patterns are related to the different low ionization potential site(s) in each molecule. The occurrence of various rearrangement ions are discussed on a similar basis.     

Detecting proximities between quadrupolar nuclei by double-quantum NMR

A robust, easy to optimize, and efficient homonuclear correlation NMR experiment for half-integer quadrupolar nuclei in solids is described and has been experimentally tested on anhydrous Na2HPO4-(23Na, S= 3/2 nucleus) and as-synthesized AlPO4-14 (27Al, S= 5/2 nucleus), an aluminophosphate molecular sieve.     

Vierring-synthesen durch [3 + 1]-cycloaddition . Synthese von 3-imino-azetidinen aus azomethin-yliden und isonitrilen

Azomethine ylide 3 , generated by thermolysis of 3,4-diphenyl-Δ¹-1,2,3-triazoline-5,5-dimethyldicarboxylate 1 , can be trapped by isonitriles to give 3-imino-1,4-diphenylazetidine-2,2-dimethyldicarboxylates 5 . The IR, ¹H-NMR, ¹³C-NMR and mass spectral data of the new compounds are discussed.     

Reactive scattering of sodium clusters with molecular oxygen

The first reactive differential scattering study for atomic clusters is reported. Oxidation of Na _x (x8) with O₂ is investigated in a crossed beam apparatus. Sodium oxide (Na _n O,n4) and sodium dioxide (Na _n O₂,n6) are produced with a total reactive cross section from 50 to 80 Ų, depending on the cluster size. The excess energies for these reactions are estimated by an SCF type ab initio calculation and range from 0.5 to 5 eV. The large cross section may then be understood quantitatively in terms of a harpooning mechanism as a first step in the reaction path. Angular distributions have been determined for the most abundant products, showing strong forward scattering. Two different schemes are discussed for the reaction: while the dioxides Na _n O₂ may be formed by an evaporative cooling process from a highly excited collision complex, formation of Na _n O appears to originate from a direct process. In both cases the experimental data suggest that most of the exothermicity remains in the reaction products.