Volume 60, Issue 6

The singular point analysis of fourth order ordinary differential equations in the non-polynomial class are presented. Some new fourth order ordinary differential equations which pass the Painlevé test as well as the known ones are found. -PACS: 02.30.Hq, 02.30.Ik, 02.30.Gp

The determination of the flow properties of a fluid containing a cylindrical inclusion with its long axis oriented parallel to the vorticity direction is a 2-dimensional problem which is treated as a special case in a calculation of the corresponding D-dimensional problem. The velocity and pressure are obtained from the solution of the equations of hydrodynamics where D-dimensional multipole potential tensors are used. The effective viscosity of a dilute suspension is evaluted via the entropy production, as suggested by Einstein, and via an effective stress tensor. The relative change of the viscosity is proportional to the volume fraction. For D = 2 the proportionality factor Z is found to be 2 and 3 when the inclusion rotates with an angular velocity equal to the vorticity and when the inclusion does not rotate, repectively. The corresponding results for D=3 are the well known number Z = 2.5 and Z = 4.

On the basis of the most recently reported spectroscopic data on vibrational modes in TeCl 4 and structural parameters of TeCl 4 , an estimation of its main force constants complemented with the calculation of mean amplitudes of vibration in a wide temperature range have been performed. Also thermodynamic functions for the ideal gaseous state of the molecule calculated, using the statistical mechanics approach.

SCF-MO calculations of the vibration frequencies and IR absorption intensities, applying the MINDO/3-FORCES method, are reported for the four molecules, mono-, di- (1,2- and 1,3-), and 1,2,3-trimethylene cyclobutane. Normal coordinate analysis of all vibration modes is described for each molecule. The obtained results allow interesting correlations between the frequencies of similar modes as calculated for the different methylene cyclobutanes.

SCF-MO calculations, using the MINDO/3-FORCES method, are reported for the equilibrium geometry, vibration frequencies and IR absorption intensities of 6-radialene, considering the planar and chair form. The chair conformation is found to be more stable. The C=C stretching frequencies of the chair form are found to be higher than those of the planar ones. The =CH 2 bending frequencies of the planar form are higher than those of the chair form. Also the PM3 method was used for the calculation of the vibration frequencies. Its results are compared with those of the MINDO/3- FORCES method.

The conductivity during the complexation reaction between K + or Rb + and 1,3-bis(benzyloxy)- p-tert-butylcalix[4]crown-5 in a CHCl 3 -methanol mixture at 288 - 303 K has been measured. The conductivity data were analyzed using a computer program based on 1 : 1 stoichiometry. The stability constants of the resulting complexes were determined, indicating that K+ is more stable than Rb+ in the solvents used. The ΔH and Δ S values for the complexation processes were determined from the temperature dependence of the complexation constants. Their significance as well as the solvent effect is discussed.

The displacements of Fe 3+ (at the Ta 5+ site) along the [001] direction in KTaO 3 crystal, caused by the electric field, have been studied by calculating the electric-field-induced zero-field splittings from the microscopic mechanisms and the empirical superposition model. It is found that the Fe 3+ displacements obtained by the two methods at the same electric-field strength and temperature are close to each other. These displacements are also close to that estimated from the force-balance equation. It is suggested that the electric-field-induced zero-field splitting can be attributed primarily to the above displacement and the temperature dependence of the electric-field-induced zero-field splitting is mainly due to the change in the dielectric constant of KTaO 3 with temperature.

The EPR parameters (g factors g || , g ⊥ and hyperfine structure constants A || , A ⊥ ) of V 4+ ion in the tetragonal phase of SrTiO 3 crystal were studied by high-order perturbation formulas based on a two-spin-orbit-parameter model, where the contributions from the spin-orbit-coupling-parameter of central 3d n ion and that of ligands are considered. It is found that the oxygen octahedron surrounding the impurity ion V 4+ changes from elongation along the tetragonal axis in the pure crystal to compression and the magnitude of tetragonal distortion of oxygen octahedron (characterized by |ΔR|=|R || −R ⊥ |) inV 4+ center is much greater than the corresponding value in the pure crystal. The cause related to the strong Jahn-Teller effect is discussed.

A crystal field analysis of the energy level structure of Cr 3+ in MgO crystal is performed, using the exchange charge model of the crystal field theory. The crystal field parameters acting on the optical electrons of Cr 3+ are calculated from the crystal structure data; good agreement between the calculated and observed energy levels of Cr 3+ in the title host is demonstrated. The Stokes shift S=5.9 and the energy of the phonons effectively interacting with the impurity center ħω =405 cm −1 are derived from the experimental spectra of absorption and emission. The obtained values of S and ħω were used for the computer modeling of the Cr 3+ 4 T 2g → 4 A 2g emission and 4 A 2g → 4 T 2g absorption bands. From this modeling, the zero-phonon energy for the considered transitions was estimated to be 14,000 cm −1 .

Some physical properties of ferric chloride-dimethyl sulfone (FeCl 3 -DMSO 2 ) melts were investigated. The phase diagram was determined by differential scanning calorimeter and thermogravimetric analyzer. The electric conductivity, measured with computerized direct-current method, increased with increasing temperature and DMSO 2 content. The conductivity was maximal (0.02149 S/cm) at 115 °C for 30 mol% FeCl 3 . The densities of all melts decreased with increasing temperature and DMSO 2 content. The equivalent conductivities were given by Λ = κM mix /ρ, where M mix is the mean equivalent weight of the binary melts. These equivalent conductivities were fitted by the equationΛ =Λ o exp(−E Λ /RT), where the activation energies E Λ were 8.63, 22.94, 25.92 kJ/mol for 30, 40, 50 mol% FeCl 3 , respectively.

NiO-doped sodium metaphosphate glasses (NaPO 3 ) 1−χ (NiO) χ (0.008 ≤ χ ≤ 0.30) show a color shift from yellow to orange-brown with increasing NiO concentration. XANES and EXAFS spectra of these glasses suggest the presence of [Ni II O 6 ] groups as chromophores. EXAFS (Ni K-edge) analysis of the NiO-doped phosphate glasses including an evaluation of higher coordination shells leads to d av (Ni-O) = 2.06(2) Å. Evidence is provided for an increased connectivity of [Ni II O 6 ] chromophores at higher NiO concentration in the glasses. A decrease in the intensity of the main absorption edge with increasing nickel oxide concentration is observed. This systematic decrease is attributed to a change in the bonding characteristics between nickel(II) and the coordinating phosphate groups from mainly ionic to a small but significant contribution of covalent bonding. A similar effect is observed in the electronic absorption spectra of glasses showing a decrease of the Racah parameter B for the Ni 2+ ions.

A method has been developed to obtain quantitative electron diffraction data up to a value of Q = 20 Å −1 of the modulus of the scattering vector. The experiments were performed on a commercially available transmission electron microscope equipped with a so-called omega energy filter. An analytical multiple scattering correction was applied. The electron diffraction results obtained with amorphous germanium were compared with X-ray and neutron diffraction data and showed good agreement. For an amorphous Ni 63 Nb 37 sample it was shown that it is possible to estimate the multiple scattering intensity without exact knowledge of the sample thickness. This technique was applied to derive the structure factor for electron diffraction of two precursor-derived amorphous Si-C-N ceramics (a-Si 24 C 43 N 33 and a-Si 40 C 24 N 36 ). The results are consistent with corresponding X-ray diffraction data and with an existing structural model for such ceramics.

In this study, clathrate of benzoic acid-tetracyanonickel, given by the formula M(benzoic acid) 2 Ni(CN) 4 ・(1,4-dioxane) (M = Ni, Cd and Co), is obtained for the first time through chemical methods. The similarities of the observed spectra indicate that the obtained clathrate of benzoic acidtetracyanonickel is a new example of Hofmann-type clathrates. - PACS numbers: 33.20.Ea, 33.20.Tp