Table of contents

It is shown that variational hard-core models result in universal high-density equations of state, for one and three-dimensional systems. The one-dimensional energy functional is given asymptotically by a fluid Madelung constant and a correction term quadratic in the free volume. The three-dimensional functional, based on the Percus-Yevick hard-sphere pair correlation function, is given asymptotically by a Madelung constant and a correction term, cubic in the free volume.

Two approaches to the parameterisation of LCAO cluster calculations for the solid state are compared with reference to the band structures of diamond and graphite. It is suggested that CNDO parameters have to be greatly modified relative to the free atom values to fit solid state properties largely because of the need to compensate for overlap effects inherently neglected in the method. In contrast, a modified self-consistent extended Huckel method incorporating the Lowdin transformation is capable of comparable results with parameters more readily capable of physical interpretation.

For an arbitrary dimensionality, an elastic scattering is described by matrices whose composition law is linear with respect to each of the scatterers. A residual resistance provided by the scattering, is related to the free energy of a certain ID nearest-neighbour Hamiltonian. For a sufficiently long wire the resistance increases exponentially with the wire length.

Electrical resistivity study of the organic charge transfer complexes tetramethyl benzidine-TCNQ and tetramethyl p-phenylene diamine TCNQ has been carried out up to pressure 80 kbar. Using the structural aspect, a conduction mechanism under pressure is suggested.

Optical absorption band measurements of Au⁺ substitutional impurity in KCl were obtained at room temperature. A molecular cluster model interpretation using the electronic structure calculated by the multiple scattering-X_alpha method is in fairly good agreement with the experimental results.

The M_4,5N_4,5N_4,5 Auger transitions of Pd in Mg₇₅Pd₂₅ are shown to have the narrow spectral features and overall profile characteristic of the M_4,5N_4,5N_4,5 spectra of pure Ag. The Auger spectra of Al₈₀Pd₂₀ and pure Pd are broader, and the extent of the broadening correlates with an increase in the Pd (4d) bandwidth and with the density of states at the Fermi energy. It is suggested that the differences in the Auger profile in Mg₇₅Pd₂₅, Al₈₀Pd₂₀ and Pd are due to the influence of the (4d) band on the (4d²) two-hole final states.

It is shown that the PdM_4,5N_4,5N_4,5 Auger spectra of AgPd alloys do not approach an atomic spectral profile as the Pd concentration is reduced. This is contrary to the behaviour of Pd and Ag Auger spectra observed from alloys of these metals with Al and Mg, and is also contrary to the predictions of a previously successful theoretical model. It is suggested that the difference between the Pd Auger spectra of AgPd alloys and of Pd alloyed with Mg and Al could result from the participation of Ag (4d) states in Auger emission from Pd.

A fast-ion conductor might be constructed from a stable regular lattice of large atoms in which holes can be partially filled by small ions without destroying the original structure. For example, large halide ions form a suitable basis, and a hexagonal close packed array of such ions can be stabilised by a six-coordinated ion such as U⁶⁺. In UCl₆, the chlorines are in almost perfect close packing with the small uranium atoms occupying only one sixth of the available octahedral holes. Some of these remaining holes can be filled with a monovalent cation such as Na⁺ without changing the structure; the uranium valence then changes from 6⁺ to 4⁺. These Na⁺ ions should then become available for ion transport, especially since the UCl₆ octahedra are expected to rotate at higher temperature, thus dynamically unblocking the channels between empty octahedral holes. It is shown that the room temperature structure of Na₂UBr₆ conforms to these principles, which might explain the 652 and 663K phase transitions at which the conductivity of the solid state exceeds that of the liquid state.

Calculations of the defect energies and geometries of small impurity ions (Li⁺, Na⁺ and F^-) substituted in the alkali halides are presented. The calculations are based on a recent set of interionic potentials. In host crystals with the rocksalt structure, previously found trends in the occurrence of off-centre displacements are confirmed. Large off-centre displacements are also predicted for Li⁺ and Na⁺ substituted in CsCl, CsBr and CsI. In many cases it is found that, if the impurity is held at a lattice site, the defect energy is substantially lowered by even-parity distortions of the surrounding host. A recalculation of the binding energy of a V_k centre to an off-centre Na⁺ impurity in CsI is also presented.

The ionic conductivity of pure KCl samples irradiated at room temperature with X- and gamma rays in a wide dose range has been studied. Some measurements in pure NaCl samples are also presented. The thermal annealing of the radiation induced effect on the ionic conductivity shows rather conclusively that this effect is not related to the radiation induced F-centres and their corresponding interstitial halogen atoms. The thermal recovery of the free-cation-vacancy concentration in irradiated KCl samples exhibits two recovery steps at 350 and 510-520 degrees C respectively. The latter step moves to 590 degrees C in heavily irradiated samples. Similar recovery steps have been found in quenched samples. The formation by irradiation of dislocations and divacancy clusters which act as dipole traps is considered.

The generalised Falicov-Ramirez-Kimball model is analysed by means of the Caron-Pratt approximation. The authors introduce an order parameter Delta related to the fluctuations in the number of electrons per atom: the insulating phase is characterised by Delta =0 while a non-vanishing Delta corresponds to the metallic phase. They obtain second- and first-order parametric phase transitions, the latter having two jumps in the mean number of conduction electrons. Mixed-valence states appear in both phases in accordance with experimental results.

A continuum model is presented for the evaluation in real space of lattice sums of phase-modulated retarded multipole interactions in finite crystals. The validity of the model is first established by showing that it produces the same results for the retarded dipole-dipole interaction as the Ewald and the planewise methods of summation, both for crystals of different shape and for a number of different lattice structures. The model is then used to evaluate lattice sums of phase-modulated retarded higher multipole interactions in crystals, up to and including the octopole-octopole interaction.

The author studies the radiation damping of polaritons in finite molecular crystals for dipole, quadrupole, and octopole transitions. She calculates both the average work done by the molecules against the damping forces, and the average power emitted by the crystal, and demonstrate that these are equal, as required for energy balance. For crystal slabs of uniform thickness, the author finds that the polariton having k_p approximately= omega _p'/c corresponds to a super-radiant state of the crystal, having a lifetime shorter than the free-molecule lifetime by a factor proportional to the number density of the molecules, the square of the wavelength, and the thickness of the crystal.

A resonant strain modulation technique has been used to measure the shifts of the optical transitions within the shielded 4f shell of lanthanide ions. The experimental technique and its limitations are described. The accuracy of the method was evaluated by measurements on crystals, CaF₂:Sm²⁺ and SrF₂:Sm²⁺, for which static shifts with strain have been reported. The shifts of vibronic sidebands for these materials were investigated. Experimental data for Er³⁺ and Pr³⁺ ions in CaF₂ and SrF₂ lattices are presented.

Second-order orbit lattice parameters are deduced from strain shifts of Pr³⁺, Er³⁺, Sm²⁺ ions substituted in fluorite lattices to be typically 10³ cm^-1. The radial power dependence of the second-order crystal field was found using the superposition model to be 35 for CaF₂:Pr³⁺, 70 for SrF₂:Pr³⁺. This is compared with the value of 3 expected from a point charge model. Strain-induced angular and radial changes of the ligand field surrounding the impurity ion are determined from the energy level shifts and from bulk elastic compliances.

An evolution operator appropriate for studying the behaviour of Bloch electrons in the presence of both an electric field and an optical field simultaneously, is developed. This evolution operator is seen to be capable of providing a unified approach for understanding various features related to Wannier-Stark ladders. By applying this evolution operator, the authors have investigated (i) the nature of the energy spectrum of Bloch electrons in the presence of an electric field alone and (ii) the absorption of electromagnetic radiation by Bloch electrons in the presence of an electric field. The principal results obtained are the following: (a) Wannier-Stark ladders would exist even in the presence of Zener tunnelling provided it is retained only up to first order. The effect of Zener tunnelling higher than the first order is to produce a broadening of the discrete Stark levels; numerical analysis relevant to this aspect is carried out with respect to a one-dimensional GaAs crystal. (b) A formula is derived for the coefficient of absorption of electromagnetic radiation by Bloch electrons in the presence of an electric field, by taking into account the k dependence of the momentum matrix element and using a nearly-free-electron model.

The Shubnikov-de Haas oscillations are observed in the magnetoresistance of mercury manganese selenide. The measurements are performed on samples which contain different amounts of manganese. The free-electron concentration in the samples is changed by annealing in either a mercury or a selenide atmosphere. The oscillations are recorded at magnetic fields up to 30 T in both perpendicular and longitudinal configurations. The galvanomagnetic measurements are complemented by magnetisation measurements. Owing to the wide range of free-carrier concentrations and magnetic field, it is possible to assign unambiguously the observed oscillations to computed Landau levels and to determine band parameters.

The contribution of collective magnetoplasma excitation to the free-carrier absorption in polar, narrow-gap semiconductors is investigated. High-frequency conductivity in the presence of a weak magnetic field is calculated. In contrast to all previous theories the non-spherical, non-parabolic and multivalley conduction band structure is taken into account. The the oretical results are adopted for lead chalcogenides and compared with the experimental data for lead selenide and with recent theories in which band structure effects are neglected.

Renormalisation-group methods are applied in 6- epsilon dimensions in an attempt to determine the critical behaviour at the phase boundary between paramagnetic and spin glass phases in a finite magnetic field (i.e. at the de Almeida-Thouless instability). No stable fixed points, accessible from the domain of physical initial Hamiltonians, are found. Possible interpretations of this result are discussed.

Recently obtained high-temperature series expansions of the susceptibilities of the Heisenberg model ferrimagnet RbNiF₃ are analysed. The possible exchange constants, corresponding to the experimental critical temperature are evaluated. The high-temperature behaviour of the susceptibility is compared with available experimental data.

The author calculates lower bounds for the ground state energy of the linear antiferromagnetic Heisenberg chain with nearest- and next-nearest-neighbour interactions. From these lower bounds new upper bounds are derived. Several approximations of the ground state energy given in the literature are compared with these upper and lower bounds. It is found that the best approximation is given by extrapolation from finite cyclic chains. This extrapolation, however, is restricted to certain values of the relative strength of the interactions. Here he extrapolates the ground state energy from finite open chains where no such restriction occurs.

Lithium ammonium sulphate (LAS) undergoes a phase transition at T_C1=459.5K from a paraelectric phase (phase I) to a ferroelectric phase (phase II) and again at T_C2=283K to a polar ferroelastic phase (phase III). Proton spin lattice relaxation time measured at 10 MHz in powdered LAS in the temperature range 480 to 77K shows discontinuous changes at the two transitions.