Table of contents

This paper describes the reasonable molecular configuration and inter-molecular packing of the poly(di-n-hexyl-silane) crystal. The crystal lattice is determined using a wide-angle X-ray diffraction method for the powdered specimen. The experimental diffraction pattern is compared with the theoretical one, in order to clarify the atom positions in the unit cell. The obtained unit cell contains the two polymer chains having an all-trans silicon backbone. The hexyl substituents are found to be asymmetrical conformations because of the steric hindrance. The orientation of the prepared thin film is also discussed on the basis of the obtained crystal structure.

We studied the problem of the bound state in a slightly bent two-dimensional quantum wire with the confining potential being an arbitrary function. The problem is mapped to a particle Hamiltonian with a slowly varying centre of the confining potential. For the class of even analytic potentials we proved that an arbitrary small bend will always produce a resonant state, but a true bound state will be absent. The energy of the resonant state is calculated to the lowest order in perturbation theory, for the case of the harmonic oscillator confining potential.

Starting from the Emery model, which is assumed to describe the copper-oxygen planes, and including direct oxygen hopping matrix elements, t_pp, we have been able to derive the effective t-J Hamiltonian for the copper orbitals using the linked cluster expansion method up to fourth order in t_pd, the hybridization matrix element. The spin-dependent part of the effective Hamiltonian is composed of two contributions: the superexchange interaction, and another one of RKKY type. The effective parameters (t and J) depend on doping, delta . This Hamiltonian can be used to study the magnetic properties of the high-T, materials versus delta .

I consider vortical structures in superfluid helium in the form of knots and links. Then I give some basic notions and facts from knot theory, necessary to understand the rest of the paper. I consider framed knotted vortices and identify these frames with some excitations. The statistics of these excitations is actually fermionic.

The time and spatial correlations of the equilibrium fluctuations in isotropic incompressible fluids are studied. The reasoning is based on the example of Brownian motion using the memory function formalism and the hydrodynamic expression of the Langevin force as an integral of the stress tensor fluctuations over the solid particle surface. Relations thus obtained allow the determination of some correlation characteristics of the stress tensor fluctuations and the Langevin force, which depend on both dissipative and thermodynamic parameters. These results are in a good agreement with the known experimental data from ellipsometric studies of spatial correlations of thermal fluctuation capillary waves on gas-simple liquid interfaces.

The experimental observation of the sudden collapse of a two-dimensional colloidal crystal at a water-air interface is reported and explained here for the first time. A thin film of an aqueous suspension of polystyrene particles of 0.53 mu m diameter is confined between a smooth glass plate and an air bubble. A single layer of a 2D colloidal crystal is observed in this thin film using an optical reflection microscope equipped with a video camera and an image processor. On gradual draining of water from this thin film, particles forming a 2D colloidal crystal suddenly emerge to the water-air interface. At the interface they flocculate to form a compact 2D sheet of particles in which the particles touch each other, forming hexagonal and square 2D structures. This phenomenon is explained on the basis of the interfacial surface energies and the interparticle interaction potential at the water-air interface.

Reverse Monte Carlo (RMC) simulation was applied for modelling the atomic level structure of the Ni₆₅B₃₅ amorphous metallic alloy. Three experimental total structure factors from isotopic substitution neutron diffraction measurements were used as input data. Using the particle configurations that were provided by the RMC calculations, neighbour distribution functions and cosine distribution of bond angles were evaluated. Local symmetries were found to be well defined around Ni atoms. B atoms are distributed more randomly. Using constraints on the B-B coordination number it is shown that the presence of boron pairs or the formation of boron chains are possibilities. None of these implications changed the local structure considerably, although we could not fully impose the constraints, because the level of RMC fit would have deteriorated.

Evidence of a temperature-induced, cyclable transition in the structure of point-defect complexes in AgCl crystals is reported. The effect is attributed to an entropy-driven change in the equilibrium structure of defect configurations, analogous to a phase transition in bulk solids. Such a transition is likely to occur in a system where the entropy term is a significant part of the defect Gibbs free energy, and where the energies of different defect configurations are very close. A crude thermodynamic analysis provides an estimate of the energy and entropy changes associated with the transition.

The quasifermion approximation based on the weakening of conditions imposed on the density matrix of a many-electron system is considered in the present paper. In this approximation, a rather simple construction for the density matrix and for the energy can be obtained. The application of this approximation to a variety of materials science problems is shown to be in good agreement with experimental results.

We study here the acoustic properties of a layered medium with randomly distributed layer thicknesses. The propagation of transverse elastic waves with polarization in the direction parallel to the laminations is investigated. The bulk modes and the transmission coefficients in a finite sample are calculated by the use of the transfer-matrix method. It is found that the density of states of these modes is drastically affected by the extent of disorder of such a system. Owing to the randomness, most of the waves are localized in the direction perpendicular to the laminations, but there still exist some waves with special frequencies which are completely extended. In some special cases we can analytically determine the frequencies of these extended waves. On the basis of this calculation a possible application of such structures is suggested.

We present a formalism for the calculation of the scattering of electromagnetic waves by a substitutionally disordered two-dimensional array of spherical particles. The formalism, which constitutes an extension of the coherent-potential approximation scheme to electromagnetic waves is valid for any frequency of the incident wave and for any size and/or concentration of the particles. We demonstrate the applicability of our formalism by applying it to the evaluation of the absorbance of disordered arrays of plasma spheres.

A model for the structure of doped Cu^II oxides is proposed. To perform accurate ab initio Green function calculations, a small cluster is introduced and found to mimic the metallic doped oxides consistently. The results obtained are consistent with the experimental observations. In particular, the calculations predict, in agreement with photoemission experiments, the appearance of two weak bands close to the Fermi level and identify them as non-quasi-particle excitations originating from metal-to-metal resonant electron transfer. Some implications for superconductivity are briefly discussed.

We calculate the effects of weak disorder on a strongly correlated electron system, namely a version of the infinite-U Hubbard model with general charge for which a 1/N expansion can be carried out (N being the orbital degeneracy). The partition function and quasiparticle decay rate are calculated to next leading order in the 1/N expansion by summing all ladder type diffusive corrections in the impurity potential. We find that away from the critical metal-insulator filling these quantities exhibit the power law behaviour expected on the basis of general weak-interacting theories. Very close to the metal-insulator filling, however, the situation changes and new, sublinear power law components are obtained. These new power laws are a result of the diffusion pole crossing over to a q⁴ behaviour, which is in turn a consequence of the 'holon' like propagation of the charge fluctuations in the pure system.

The hyperfine interaction at ⁵⁷Fe nuclei in Bi₂Sr₂Ca_0.3Y_0.7Cu_1.96⁵⁷Fe_0.04O_8.37 was investigated by Mossbauer spectroscopy in the temperature range 4.2-417 K. Magnetic ordering was observed below the Neel temperature of about 412+or-5 K. The temperature dependence of the magnetic hyperfine field at ⁵⁷Fe nuclei could be well described using a highly anisotropic three-dimensional antiferromagnetic model. The intra-planar exchange energy J and the ratio gamma of effective inter-planar to planar hopping strength are determined to be 2728 K and 0.004, respectively, by fitting. The effective magnetic hyperfine field H at 4.2 K is 499 kOe.

The induced magnetization density has been measured at T = 36 K (above the antiferromagnetic ordering temperature of 14 K) in a single crystal of the heavy-fermion material UPd₂Al₃. A magnetic field of 5 T was applied along the easy axis of magnetization. The magnetization density as measured by the polarized-neutron technique is associated totally with the uranium atom; no spin transfer is found on the Pd atoms. The induced moment, as measured by neutrons, is some 12% below that measured by magnetization measurements on the same crystal. This indicates the presence of a significant positive (with respect to the uranium moment) conduction electron polarization. The ratio of the orbital to the spin moment of uranium found experimentally is -2.01(25), compared with the free-ion values of -2.56 (for U³⁺) and -3.29 (for U⁴⁺), and a recent theoretical prediction of-1.35.

A new method for the numerical modelling of the thermal fluctuations in micromagnetic systems is presented. The approach is based on the set of stochastic Langevin equations, which are derived from the energy expression for the system studied. The correlation matrix of the corresponding random forces required to perform numerical simulations is evaluated using the fluctuation-dissipation theorem following a transformation to the normal coordinates. The method is tested for the finite 1D chain of classical magnetic moments. The temperature dependence of the average magnetization deviation Delta M/M(O) exhibits good agreement with analytical theory.

Specimens of (Co_xNi_1-x)_1-yFe_y with 0<or=x<or=1 and y<or=0.01 obtained by electrochemical deposition were tested by X-ray diffraction and Mossbauer spectroscopy. The structural transformation from the face-centred cubic to the hexagonal close-packed structure has been observed in the range 0.685<x<0.795. The dependence of the hyperfine interaction parameters on the changes in atom number in the nearest-neighbour (NN) shell of the ⁵⁷Fe nuclear probe has been determined. Changes in the preferred direction of domain magnetization with the increase in the number of Co atoms in the NN shell have also been observed.

Calculations of the Faraday rotation and ellipticity spectra at photon energies between 0.98 and 3.50 eV (wavelengths between 1260 and 360 nm) resulting from Ce ions in the Ce-substituted yttrium iron garnets based on the quantum theory are presented. The Faraday effect contributed by the Ce ions is caused mainly by the intra-ionic electrical dipole transitions between the 4f and 5d configurations. The crystal field (CF) and the superexchange interaction are two crucial factors in determining the Faraday effect contributed by the Ce sublattice. The energy differences between the lowest and the second CF-split 5d levels and the lowest CF-split 4f level are 1.36 eV and 3.10 eV, respectively. Therefore there are anomalous rotatory dispersions at about 1.36 eV and 3.10 eV. The difference between the transition intensities for the right- and left-handed circularly polarized light between the lowest CF-split 5d level and the ground state is negative. while the corresponding value for the transition between the second CF-split 5d level and the ground state is positive. So the Faraday rotation is positive over the whole photon energy region between 1.36 and 3.10 eV and is negative outside this region. The calculated spectra are in good agreement with experiment.