Table of contents

An expression for the resistivity of a liquid metal is described, which is exactly of the form proposed by Ziman. The advantage over the usual derivation of this formula is that a unique definition of the pseudopotential is possible.

By the use of the vector addition theorem for the decomposition of product spaces, an arbitrary spin space can be expressed in terms of the sums of powers of spin one-half spaces, implying that there is a relationship between the traces in these spaces and thus a generalization of the drone fermion method.

An Ising model, which is defined on a face centred cubic lattice in which nearest neighbour spins are coupled via a special four spin coupling term involving the 4-point simplex subgraphs of the lattice, is shown to have a self dual property of the type originally put forward by Onsager for the conventional square net Ising model problem. Assuming that this model has one and only one critical point, the location of the singularity can be determined exactly.

The optimized model potentials developed by Shaw are used to calculate the effective interaction between ions for seven simple liquid metals. Exchange and correlation corrections are included in the calculations. The ion-ion potentials are used to determine effective hard-sphere diameters, entropies and specific heats at constant volume. The results are compared with experimental data.

Including in a simple approximation the effect of short range correlations between the electrons, the linear coefficient in the dispersion relation of surface plasmons in a classical half-space is calculated as a function of a parameter which represents the radius of the correlation hole. Values of this parameter which are appropriate at metallic densities are determined by requiring that the dispersion relation of bulk plasmons agree with the experimental data. Adopting the criterion leads to the conclusion that short range correlations modify only slightly the dispersion of long-wavelength surface plasmons.

Useful and general relations between the frequencies, the polarization vectors and the elements of the dynamical matrix are developed by means of a technique known as the spectral decomposition of an operator and by investigating the analytical behaviour of the resolvent operator of the dynamical matrix in the complex plane. This new technique is especially useful when one comes to investigate complicated crystal structures where the conventional way of analysing a given system by straightforward inspection fails through being too elaborate. The question of exactly how much experimental information is required to permit the derivation of a unique solution for the dynamical matrix at a given wave vector k is discussed. To illustrate the new method it is applied in detail to the lattice vibrations of gallium metal, which is orthorhombic base centred in structure and has four atoms per primitive unit cell.

The problem of an electron moving in a one dimensional Coulomb potential e²/ mod x mod is of interest in connection with the energy levels of the hydrogen atom in a strong magnetic field. It is shown that the ground state energy of the one dimensional hydrogen atom is profoundly changed if a repulsive core is included in the Coulomb potential. The sensitivity of the ground state energy to this repulsive potential is investigated and it is found that if the core is sufficiently 'hard' the ground state energy is very nearly the first Balmer energy. The results appear to be relevant to the Yafet-Keyes-Adams theory of a hydrogen atom in a strong magnetic field and suggests that this theory may need modification.

A microscopic theory for the tunnelling current through a superconductor-insulator-superconductor junction containing a pair of paramagnetic impurities is developed. A general interaction between the impurity spins is considered and the tunnelling current is calculated by considering both the elastic and inelastic scattering of conduction electrons with the impurity pair. It is found that the single particle tunnelling current exhibits discontinuities as a function of the bias voltage. The positions of discontinuities occur at voltages which depend on the energy gap and the strength of the impurity-impurity interaction.

The AC hopping conductivity is written in terms of the Green matrix of the linearized rate equations. The diagonal elements of the Green matrix are eliminated and the configuration average of the hopping conductivity is then expressed as the fourth moment of a 'diffusion function' of frequency and intersite distance. The behaviour of the diffusion function and the AC conductivity is discussed at high frequencies, intermediate frequencies and low frequencies for both degenerate and nondegenerate statistics. A variational formula is given for the real part of the configuration average of the AC conductivity. It provides a lower bound and has the additional merit that the configuration average may be taken at the outset of the variational calculation.

High temperature expansion techniques are used to study the changes in the critical behaviour of the susceptibility of the Ising ferromagnet arising from the introduction of nonmagnetic impurities.

A low temperature theory, which makes use of pseudo-boson operators is given, of the dispersion, absorption and light scattering by magnons in FCC crystals. Particular attention is paid to NiO, for which in addition, a classical spin vector picture of the resonant modes is given, and on which the effects of a magnetic field are considered.

Measurements of the frequency dependent susceptibility of ruby at liquid helium temperatures show that at certain harmonic fields the thermal equilibrium within the system of the Cr³⁺ single ions (S=³/₂) is established by two steps. At first, two-spin cross-relaxation processes bring three Cr³⁺ levels into equilibrium. The fourth level then thermalizes with the former ones by means of much slower three-spin processes. The susceptibility of the spin system after the first equilibrium step, calculated within the framework of generalized thermodynamics, agrees excellently with the experimental results with regard to both magnitude and to temperature dependence.

A calculation of the impurity induced infrared absorption in GaAs is presented on the basis of a Green function technique. Numerical values for the scalar effective charges of different single defects and their lattice neighbours have been obtained by comparison with the experimental absorption rates. It is shown that the full effective charge tensor has to be employed for the description of double defect absorption bands, although the non-diagonal elements are likely to be small compared with the diagonal elements. Good agreement between theory and experiment is found for the proposed structure of a Te-Li complex.

Reflectivity measurements have been made on single crystal ZnSiP₂ using polarized infrared radiation in the wavelength range 4-250 mu m. The data have been analyzed using classical dispersion theory to obtain mode frequencies, strengths and damping factors. A simple group theoretical analysis has been performed and six of the seven predicted infrared active modes have been observed. The polariton dispersion curves have been calculated and the possible use of ZnSiP₂ in resonant Raman scattering from polaritons for the generation of tunable far infrared radiation is discussed.

Mossbauer scattering experiments have been performed on the following substances in the glassy and supercooled liquid states: n propyl benzene, n butyl benzene, di ethyl phthalate, di n butyl phthalate, di 2 ethyl hexyl phthalate, ethyl cyclohexane, 1, 2 propanediol, and squalane.

Irradiation of zinc selenide with electrons of sufficient energy to displace selenium atoms results in the enhancement of two cathodoluminescence emission bands, occurring at 830 nm and 970 nm. These bands were enhanced by electron damage at 10 K or 77 K but not by damage at room temperature. Correlation, for various electron energies, of the rate of increase of emission with the theoretically evaluated number of selenium displacements per incident electron leads to an accurate value of 236 keV for the threshold electron energy for selenium displacement. Isochronal annealing characteristics have also been determined.