Table of contents

An approximate expression for the 'RPA-like' response of a non-uniform electron distribution has been obtained. The result incorporates the non-uniform character of the distribution via the structure factor of the system.

Lattice trapping is an unexpected result obtained in a number of atomistic treatments of crack propagation. Molecular dynamic simulation was used in the present investigation to study crack behaviour. Using a large two-dimensional sample of about 11000 atoms and a relatively long-range Lennard-Jones potential, lattice trapping is found to be a negligible effect. Sample size effects and the non-linearity of the modulus were studied and found not to affect the lattice trapping result. Negligible lattice trapping seems to be a consequence of the range of the potential; long-range continuous potentials produce negligible lattice trapping.

Examines the conductivity of two-dimensional weakly disordered systems. It is shown that in a two-dimensional system there is a divergence as 1/q in the probability for an electron to diffuse from a state K to a state K+q, and that this is the origin of the logarithmic term. The method enables the authors to examine the nature of the 'localisation' which occurs. The wavefunctions fall off as 1/r and at zero temperature and for an infinite specimen cannot be normalised. At finite temperatures inelastic collisions give a cut-off at a finite distance, which decreases with increasing T, but overlapping states near the Fermi energy are separated by energies small compared with kT, so conduction is essentially metallic. The logarithmic term depends on the normalisation factor.

A simple method is developed for obtaining results from the interaction theory proposed by Altshuler and Aronov (1979). This method yields the logarithmic singularities in the density of states and the conductivity of disordered 2D metals, in agreement with the results of those authors. It produces also the T^-1/2 behaviour for a disordered long wire. The correlation between the interaction theory, the localisation theory and experiment is discussed. In particular, it is pointed out that, at zero temperature and for materials for which the inverse screening length is much less than the Fermi wavevector K_F, both theories yield the same conductivity. Both effects are probably present in inversion layers.

The influence of Schottky barrier formation of exposing clean indium phosphide surfaces to hydrogen sulphide atmospheres prior to the deposition of gold and silver contacts has been investigated. The exposure time may be used to control the barrier height, and appropriate models are considered.

Hydrostatic pressure up to 4.6 kbar reduces the propagation vector zeta of the incommensurate magnetic phase in NiBr₂ and Ni_0.92Zn_0.08Br₂ and lowers the temperature T_IC of the commensurate-incommensurate transition. The reduction in each quantity is approximately linear: for T_IC about 10% per kilobar and for zeta about 6% per kilobar. The transition is first order and increasing pressure widens the coexistence range between the two phases.

A dynamical Jahn-Teller model for Cr²⁺ and Cr³⁺ in GaAs is proposed in order to account for existing and new experimental data. In contrast to previous models, based on a static Jahn-Teller displacement, the tetragonal nature of the EPR spectrum is shown to arise from sites having particular values for the random strain. It is also shown that the data indicate the existence of at least two classes of chromium. In one class, chromium replaces gallium substitutionally and has T_d symmetry, while in the second class chromium is at a site having trigonal symmetry.

A study of the possible phase symmetries derived from a prototype phase with space group P6₃/mmc (D_6h⁴) has been performed. Only those phases that can be explained as the result of the onset of an order parameter transforming according to one irreducible representation of the prototype space group are considered. The different space groups for the possible distorted phases have been investigated. All the irreducible representations which belong to symmetry points in the hexagonal Brillouin zone are analysed. The Landau and Lifshitz criteria have been considered to determine those transitions which should necessarily be first order. For every representation the authors have calculated the subspace in the representation space along which the displacement of the order parameter must take place to describe the different permitted symmetries for the distorted phase. Every considered irreducible representation D(k, j) and every relevant subgroup G of P6₃/mmc, of the number of times that the identity representation is contained in the representation subduced in G by D(k,j). This information together with the chain subduction criterion permits a complete investigation of the symmetry in the representation space.

In alkali halides doped with bivalent cations the impurity-vacancy dipoles aggregate by a third-order reaction. Comparison of the activation energy of this reaction with the activation energy of the saturation diffusion coefficient gives the binding energy of a loosely bound dimer which is a precursor to the trimer. In a previously reported case (NaCl:Pb²⁺), where the guest ion is appreciably larger (20%) than the host, a binding energy of the dimer of 0.13 eV was found. In contrast, in the case reported here (NaCl:Ca²⁺), where the guest and the host are nearly equal in size, the binding energy of the dimer is not more than 0.02 eV.

An expression is found for the integral of the density of states, rho (r, E), over an arbitrary volume in terms of the Green's function of the medium, its energy and spatial derivatives, evaluated on the surface of the volume. It is also possible, within the rigid muffin-tin approximation, to express the phonon energies in terms of similar functions.

The problem of Anderson localisation of an electron for q0 is used to calculate the frequency dependent dielectric in terms of results of quantum scattering theory. Thus, localisation is characterised as follows: (i) the localised state belongs to the pure point spectrum of the Hamiltonian operator; (ii) the inverse participation ratio E(EG)=E_g Sigma _i=1³(h(cross)²k_i²/2m_i*). At room temperatures states belong to the continuous spectrum of the Hamiltonian operator; and (iv) when there is no pure point spectrum, the inverse participation ratio is zero. A weighted inverse participation ratio, which is constructed only from generalised eigenfunctions associated with a subset of the spectrum, is formulated. A rigorous localisation criterion can then be defined, and the concepts of the localisation edge and the Anderson transition are made precise.

The general formula for the dielectric function epsilon ( omega ,q) for q to 0 is used to calculate the frequency dependent dielectric function of the semimetal Bi. Both the electrons at the L-points and the holes at the T-point are described by two-band models for which k.p theory gives the dispersion relation E(E+E_G)=E_g Sigma _i=1³(h(cross)²k_i²/2m_i*). At room temperatures the calculation shows that the unknown temperature dependence of m₂* cannot deviate much from the T-dependence of m₁* and m₃* found by Vecchi and Dresselhaus (1974). Further it turns out that the difference between the values of epsilon _{perpendicular to} and epsilon /sub ///( perpendicular to and // to the trigonal axis) can be explained by the contribution of the holes. Finally, the calculation can be used for doped Bi. The results for the change in epsilon by doping agree with measurements on Sb-doped Bi.

Precise measurements have been made of the specific heats of the antiferromagnetic solid solutions pMnO-qCoO and of the pure oxides MnO and CoO in the temperature range 20 to 700K. From these measurements, the Neel temperatures have been deduced and, through the application of the BPW effective field model, the exchange integrals have been estimated: in spite of the change which occurs in the lattice parameter, these integrals appear to remain effectively constant over the range of compositions. A hybrid method based on a combination of the corresponding states method with the effective phonon spectrum has been found to give consistent results when the lattice contribution is separated for MnO and CoO. There is good agreement between the experimental and theoretical entropy for most of the range of compositions. However, there appears to be some anomalous behaviour for the magnetic energy where there is small substitution of one oxide in the other.

Molecular cluster predictions for electronic structures of cubic, tetragonal and orthorhombic NbO₆^7- clusters, obtained within the self-consistent-field X alpha framework, are related to the electronic and optical properties of KNbO₃ crystals in the cubic, tetragonal and orthorhombic phases. Distortions in electronic state levels and electronic populations induced by atomic displacements from the cubic perovskite positions are examined. Ground state electronic distributions are used to determine the inequivalent populations of oxygen ligands inside the valence band, pictured by local densities of states of O 2p-type. X alpha -cluster ionic charges allow the theoretical determination of the spontaneous polarisation, P_s in ferroelectric phases, and comparison with experimental data shows a rather correct estimation of P_s from cluster computations. The band gap anisotropy and the band edge polarisation potentials are obtained using transition-state calculations. A rough estimation of the anisotropy of the imaginary part of the dielectric constant is obtained from the energies of dipolar-allowed transitions. X alpha results are discussed according to different choices of atomic sphere radii.

Polarised Raman spectra of chloro- and bromo-sodalite (Na₄Al₃(SiO₄)₃Br)₂ single crystals have been recorded, and 28 of the predicted 32 Raman-active phonon modes observed. A full group-theoretical analysis of the zone-centre phonons is given. The internal modes are assigned using as a basis the normal mode frequencies of the XO₄ complex (X=Si or Al). A 'super-lattice' approximation has enabled qualitative predictions to be made about the intensities of the Raman Raman and infrared modes, leading to a consistent model for the interpretation of the Raman spectrum of the infrared spectrum of Henderson and Taylor (1977-8).

Studies the inelastic scattering of fast electrons by spherical metallic particles or by solids containing spherical cavities. The energy losses are due to the excitation of bulk or surface plasmons. The interaction Hamiltonian between the electron and the plasma oscillations is established and an expression for the loss probability, both for surface and bulk modes, is given. For the latter, the 'Begrenzungseffekt' is taken into account. As a numerical application, the scattering of 50 keV electrons by Al surfaces is treated and compared with experimental results.