Table of contents

The singular matrix representations of point groups recently discussed by Killingbeck (1972) are special cases of a wider class of representations discussed previously in the literature. It is pointed out that a singular representation can always be reduced by a similarity transformation to the direct sum of a nonsingular representation and a 'null representation'.

It is shown that the distance of exponential localization of a normal mode in a disordered one-dimensional system can be identified with the mean free path for backward scattering, provided that the disorder is weak, so that the mean free path is long.

A resolvent perturbation analysis of the Kubo-Luttinger response formulae is used to predict weak phase shifted minima in the damped magnetophonon structure of the longitudinal thermal EMF in semiconductors.

The time correlation function for homodyne detection of light scattered by a sample of poly(methylmethacrylate) for a range of temperatures below the glass temperature has been observed for polarized scattered light and is approximately a double exponential decay. The shorter correlation time corresponds moderately well with the known correlation frequency for side- chain molecular reorientational motion. It is considered that this new method will be valuable in the investigation of motional processes in polymers.

The dispersion interaction between two atoms in the presence of a plane continuum dielectric substrate is calculated using Lifshitz theory. If the atoms are in a plane parallel to the substrate, the effect of the latter is to renormalize the Hamaker constant. This renormalization affects the two dimensional van der Waals gas critical temperature used in adsorption calculations. It is strongly dependent on the distance of the adsorbate molecules from the surface.

A variational determination of the angular dependence of a ground state product of single particle Bijl-Dingle-Jastrow wavefunctions for a strongly coupled boson fluid in the vicinity of the liquid-vapour transition zone is calculated. The first and second unassociated Legendre harmonics are retained in the angular description, and their amplitudes determined across the density transition. Expressions for the surface energy and surface tension are obtained which, in addition to the classical terms, contain a kinetic contribution which takes account of the zero point motions.

The temperature dependence of the electron mobility in the Gamma _1c band has been calculated for temperatures at, and above, room temperature and compared with experimental results. The relaxation time approximation has been applied with the following scattering mechanisms: interband and intraband polar optical, acoustic, charge-centre and space-charge. It is concluded that charge-centre scattering is dominant in the low temperature region and that some space-charge scattering may be present also. In addition, measurements of the Hall coefficient and resistivity as a function of hydrostatic pressures up to a maximum of 12 kbar have been made at room temperature and analysed on a two-band model taking into account the pressure dependence of the Gamma _1c electron mobility. The analysis of the results of the pressure dependence is in good agreement with the analysis of the temperature dependence of the Gamma _1c electron mobility.

The emission current from a reverse-biased p-n junction in SiC is known to be proportional to the surface component of the junction current, which in turn appears to be related to the junction voltage by a power law. It is suggested that the surface current crosses the p-n junction not in surface microplasmas in the SiC but along paths in a thin surface film of silicon oxide heavily doped with carbon atoms from the SiC lattice. It is postulated that, during the thermal activation required to develop emission, changes occur in the structure of the oxide film which facilitate the ionization of the carbon inclusions to give a high donor density in the region of the reverse bias field. These ideas are shown to give a selfconsistent picture of the conduction and emission processes occurring in SiC cathodes and explanations of several observed phenomena are given.

The incorporation of realistic boundary conditions in solving for the electrical and thermal properties of a Joule heated semiconducting thin film mounted on a substrate is shown to result in current-controlled negative differential resistance. Calculations of the current density-electric field characteristic for representative values of the film and substrate parameters demonstrate the importance of the thermal properties of the substrate, and correlate well with the experimental and theoretical results of others.

A method of decoupling Wannier functions is described which shows that a simple relationship exists between open-shell band energies at symmetry points and the crystal-field and superexchange energies for any crystalline system. This method is far easier to use in interpolating dispersion curves, and makes fewer and more explicit physical assumptions, than the conventional Slater-Koster tight-binding parametrization technique. We illustrate its application by deriving the crystal field splitting in ReO₃.

The point-multipole model, together with the Sawatzky model for overlap effects, has been used to calculate the electric field gradient tensors at the two nonequivalent ferric sites in Ca₂Fe₂O₅. Good agreement with Mossbauer results has been obtained if alpha _D and alpha _Q, which have been considered as variable parameters, are <0.4 A³ and approximately 0.1 A⁵ respectively. The effects of quadrupole moments due to the thermal vibrations of the oxygen ions have been found to negligible.

Experimental evidence, based on data by Kushida (1969) is given that the linewidth-lifetime relation is not generally applicable. Calculations on a crystal field model confirm that elastic ion-lattice interactions are responsible for the observed effect.

A model for the interaction of two oxygen molecules is presented. It accounts for the antiferromagnetism of solid oxygen as well as for the optical properties of the condensed phases. The latter include: (a) the two-molecule double transitions; (b) the enhancement of the single-molecule absorption lines; (c) vibronic aspects of the double transitions. The model also describes a mechanism for exciton transfer which produces an exciton dispersion bandwidth comparable with magnon bandwidths.

Experiments have been performed to measure the scattering function of RbMnF₃ at 1.17 T_N. In parallel with the experiments a computer simulation has been carried out by solving numerically the motion of spin vectors with the nearest- neighbour Heisenberg exchange interactions appropriate to RbMnF₃. Most features of the observed scattering are in good absolute agreement with the predictions of the simulation. These include the appearance of triple-peaked energy spectra near the zone boundary regions of the antiferromagnetic zone, the short-range order at this temperature being sufficient to sustain a quasi-collective type of motion. In addition, critical speeding-up, the increase in the spin diffusion constant near the nuclear reciprocal lattice point, is observed.

This describes an examination of the behaviour of ferromagnetic anisotropy and magnetostriction when the anisotropy is strong.

Nuclear magnetic resonance measurements on single crystals of the 5d transition-metal-ion salts K₂IrCl₆ and K₂ReCl₆ are reported. Transitions between the mod +or-¹/₂) ³⁵Cl nuclear spin energy states (and a linear combination of them) have been studied and the paramagnetic shifts due to the transferred hyperfine interaction measured. The parallel and perpendicular components of the magnetic transferred hyperfine shift tensor are calculated, and the signs of the hyperfine parameters unambiguously determined. A subsequent discussion of the unpaired spin distribution in the (ReCl₆)^2- ion suggests that the amount of pi bonding in the Re-Cl bonds is approximately 8% which is essentially the same amount present in the Ir-Cl bonds in the (IrCl₆)^2- ion. The contributions to the isotropic portion of the hyperfine interaction due to s electron transfer and core polarization effects are discussed.

This paper deals with phase-matched second harmonic generation in ferroelectric, biaxial NaNO₂ at 1.065 mu m fundamental wavelength. The second harmonic intensity was measured as a function of phase-matching directions. Experimental results can be adequately described by electromagnetic theory in the parametric approximation. Information is obtained about relative values and signs of the five nonvanishing components of the nonlinear susceptibility.

Normal incidence reflectivity spectra using polarized light have been measured with E perpendicular to c as well as E//c for the layer type crystals of transition metal dichalcogenides WS₂, WSe₂, alpha -MoTe₂, NbS₂ and NbSe₂ at 78 K and 300 K. Reflectivity peaks observed in the spectra of two polarizations are derived from transitions of quite different symmetry and these have been broadly identified using the band structure of single layer MoS₂ as the model. A discussion is given for the free carrier reflection in relation to the effective mass anisotropy in NbSe₂, as well as for the possible existence of two-dimensional excitons.

The Raman spectrum of the ferroelectric 5PbO.3GeO₂ has been recorded at various temperatures. A 'soft' phonon mode associated with the phase transition, which interacts with other modes, was observed and the spectra are analysed in terms of a response function for coupled modes. The variation of the frequency and width of the ferroelectric mode with temperature does not agree completely with conventional theory.

The Raman spectrum of copper formate tetrahydrate Cu(COOH)₂.4H₂O, has been determined in the range 3500 to 79 cm^-1 from 90 to 250 K. Several lines are found to disappear rather abruptly as the antiferroelectric transition temperature 235.5 K is crossed. By comparison with the spectrum of the deuterate, Cu(COOH)₂.4D₂O, at 90 K, some of these lines are identified as translatory and rotatory water modes. This agrees with crystallographic and other evidence that ordering of the water molecules occurs at the phase transition. Although most internal modes do not change significantly from 90 to 250 K, the symmetric stretching mode of water at 3092 cm^-1 broadens slightly and decreases appreciably in peak intensity.

The multiphonon absorption spectra of MgO and CaO single crystals have been recorded, and analysed in terms of the infrared active sum modes of lattice vibrations. A critical point analysis was carried out using the dispersion curves obtained from previous neutron scattering studies and the 'breathing shell' model, and it produced similar mode combination patterns for both substances. The two main peaks I and II (846.5 cm^-1 and 981 cm^-1 for MgO; 628 cm^-1 and 738 cm^-1 for CaO) in the two- phonon region are interpreted as the sum modes W'₂+W"₃ at W and Sigma ₁LO+ Sigma ₃TO near X respectively, in both crystals. Three- phonon bands were observed for both MgO and CaO and a four- phonon band in MgO, all at wavenumbers in agreement with theoretical predictions.

The two-photon absorption coefficient of indium antimonide at 10.6 mu m and room temperature has been deduced from transmission measurements using a mode-locked and a Q-switched CO₂ laser. The value obtained, namely (16+or-5) cm MW^-1, is in adequate agreement with theory.