Global Integrability of the Derivative of a Quasiconformal Mapping

We establish an essentially sharp growth condition on the quasihyperbolic metric of a domain sufficient for the global higher integrability of the derivative of a quasiconformal mapping.     

Nitrogen vacancies as major point defects in gallium nitride

We present results of ab initio calculations for vacancies and divacancies in GaN. Particular attention is paid to nitrogen vacancies and mixed Ga-N divacancies in negatively charged states, which in n-type GaN are found to be energetically comparable with gallium vacancies. We also demonstrate that the activation energy for self-diffusion over the nitrogen sublattice is lower than over the gallium one for all Fermi-level positions, which implies the nitrogen vacancies are major defects in samples annealed at high temperatures. Possibilities for direct observations of nitrogen vacancies through positron annihilation experiments are discussed.     

Muon states in metals: Recent progress

We report on our results in two interesting questions related to muon spin rotation studies in condensed matter: (i) energetics of muons in metals, including lattice relaxation and zero point motion in self-trapping phenomena, and (ii) systematics of Knight shifts and hyperfine fields.In the former topic, a comprehensive theory is developed which entails the construction of the muon potential energy field in terms of the effective-medium or quasi-atom theory first introduced by Zaremba, Stott, NØrskov and Lang. The muon wave function is then solved by numerical (3-D) relaxation techniques. From this the forces exerted by the muon on the neighbouring lattice atoms are calculated, and the ensuing relaxations are evaluated by lattice Green's function techniques. These in turn modify the potential energy field, and the calculation is iterated to self-consistency. We search for the stable trapping sites in bcc and fcc metals, calculate self-trapping energies, diffusion barriers and excitation energies. Other hydrogenic imputies are also considered, and isotopic effects in e.g. heats of solution are investigated.In the latter topic, the spin-density functional theory is applied, including in the Knight shift calculation both the contact spin density and the diamagnetic shielding. The lattice potential is described in terms of the spherical solid model. A systematic behaviour as a function of the electron density and the host valency is found in good agreement with the experimental results.     

Correlation effects in positron-electron systems: A Quantum Monte-Carlo study

We present Quantum Monte-Carlo results for various positron-electron systems. We discuss the energetics of the bound state of a positronium (Ps) with finite atomic systems: a massive point charge Z, hydrogen (H) and lithium (Li). We also analyze the screening cloud around the positron in the positronium hydride (HPs) and in the homogeneous electron gas in order to determine the positron annihilation rates.     

Electron impact mass spectra of 2-(2-pyridyl)methylene-1,3-dicarbonyl compounds: Unusual abundance of the [M + 1]+ ion and the effect of stereochemistry

Electron impact mass spectra of 2-(2-pyridyl)methylene-1,3-dicarbonyl compounds and related heteroaryl species have been investigated. In 3-(2-pyridyl)methylene-2,4-pentanedione, its 6′-methyl and 6′-methoxycarbonyl derivatives and in E- and Z-ethyl 3-oxo-2-(2-pyridyl)methylenebutanoates the base peak arises from the loss of methyl radical from the molecular ion to produce a 3-oxo-3H-indolizinium ion. A marked difference is observed in the behaviour of the geometric isomers of the keto esters. The diketones and E-keto ester carrying a 2-pyridyl substituent and ketone functionality on the same side of the carbon-carbon double bond exhibit an unusually high [M + 1]⁺/[M]^+˙ ratio (about 2.5) under normal ionization conditions (pressure 10–100 μPa). This abnormality is a function of pressure only and independent of temperature. In the case of the Z-keto ester, the corresponding malonate, 3- and 4-(2-pyridyl)methylene-2,4-pentanediones, and 2-furyl, 2-thienyl and phenyl diketone analogues, the ratio does not differ much from that due to the natural isotope abundance. Results for 1,1,1,5,5,5-hexadeuterio-2-(2-pyridyl)-methylene-2,4-pentanedione (strong M + 2 peak) suggest one mass unit transfer as an intermolecular proton shift from a methyl group to give a 3-hydroxy-3-methyl-3H-indolizinium ion. This real mass spectrometric phenomenon is a unique example of low pressure self-chemical ionization.     

Determination of aluminium in AlCl3 and Al2O3 modified silica catalyst supports

X-ray fluorescence spectrometry (XRF) was applied to determine aluminium in AlCl₃- and Al₂O₃-modified silica catalyst supports that were prepared by gas-solid reactions in an atomic layer epitaxy (ALE) process using aluminium chloride or aluminium chloride and water as adsorbates and silica as support. INAA and AAS were used as reference methods to determine the aluminium content of the supports. The calibration of XRF results was done by plotting the Al/Si intensity ratios against the aluminium content as determined by atomic absorption spectrometry (AAS) and verified by instrumental neutron activation analysis (INAA). Correlation factors for the calibration graphs were 0.984 for AlCl₃/SiO₂ and 0.995 for Al₂O₃/ SiO₂ samples in the aluminium content range 0–2.6 g Al per 100 g of sample. Received: 19 October 1998 / Accepted: 14 December 1998     

Determination of Stoichiometric Dissociation Constants of Benzoic Acid in Aqueous Sodium or Potassium Chloride Solutions at 25°C

Equations were determined for the calculation of the stoichiometric (molality scale) dissociation constant K_m of benzoic acid in dilute aqueous NaCl and KCl solutions at 25°C from the thermodynamic dissociation constant K_a of this acid and from the ionic strength I_m of the solution. The salt alone determines mostly the ionic strength of the solutions considered in this study and the equations for K_m were based on the single-ion activity coefficient equations of the Hückel type. The existing literature data obtained by conductance measurements and by electromotive force (EMF) measurements on Harned cells were first used to revise the thermodynamic value of the dissociation constant of benzoic acid. A value of K_a = (6.326 ± 0.005) × 10^-5 was obtained from the most precise conductivity set [Brockman and Kilpatrick] and this value is supported within their precisions by the less precise conductivity set of Dippy and Williams and by the EMF data set measured by Jones and Parton with quinhydrone electrodes. The new data measured by potentiometric titrations in a glass electrode cell were then used for the estimation of the parameters of the Hückel equations of benzoate ions. The resulting parameters were also tested with the existing literature data measured by cells with and without a liquid junction. The Hückel parameters suggested here are close to those determined previously for anions resulting from aromatic and aliphatic carboxylic acids. By means of the calculation method based on the Hückel equations, K_m can be obtained almost within experimental error at least up to I_m of about 0.5 mol-kg_-1 for benzoic acid in NaCl and KCl solutions.