Table of contents

The influence of local fluctuations on phase transitions to non-uniform states described by Brazovkii's model (1975) is discussed.

The non-linear behaviour of the positive ionic motion in liquid ³He has been studied down to 3 mK. It was found that the influence of temperature and velocity is symmetrical. At velocities comparable to k_BT/p_F the behaviour may be described by the introduction of a reduced temperature T_R where T_R³2/=T³2/+(0.31p_Fv/k_B)³2/.

The thermodynamic properties of two-dimensional semimetals in high transverse magnetic fields are considered. Thermodynamic characteristics are calculated in the Hartree-Fock approximation, when correlation phenomena are negligible. The electron density appears to jump as the magnetic field H changes. It is found that an excitonic phase is formed at the highest occupied Landau level.

Free-exciton absorption measurements in the temperature range 2-20K and corresponding luminescence measurements between 5 and 12K on high-purity germanium are described. Accurate threshold energies have been determined to yield values for the exciton energy gap, the LA and LO momentum-conserving phonon energies and the groundstate splitting of the free exciton.

The phonon transmission spectra of single crystals of Al₂O₃ containing V³⁺ ions have been measured with a superconducting tunnel-junction phonon spectrometer over the range 3-24 cm^-1. In more concentrated samples it was found that the single-ion absorption at 8.3 cm^-1 has three satellite lines and these are interpreted as arising from phonon absorption by V³⁺ pairs. The positions of these lines can be fitted by an isotropic exchange Hamiltonian with J=3.46 and 1.86 cm^-1.

A rigorous treatment that is based on an electrical network theorem and is applicable to regular or irregular networks of resistors is presented. This treatment affords a justification of the effective-medium theory and confirms that the effective conductance of a network whose average degree of nodes is four is the geometrical mean of the distribution of its conductances when this function is log-symmetrical.

A series of measurements of the Hall coefficient, infrared reflectivity, thermoelectric power and electrical resistivity of Ti_1+xS₂ single crystals with various degrees of stoichiometry is described, where, for the first time, each measurement was made on the same crystal (or crystals from the same batch). None of these measurements taken alone can distinguish between the semimetallic or semiconducting models of TiS₂. However, by making all four measurements on each sample, it has been possible to establish correlations between the results for different samples. It was found that the product of the Hall coefficient and the square of the plasma frequency is the same for all samples, a result that is consistent with a semiconductor model, but is inconsistent with a semimetal. Nevertheless the most stoichiometric samples remain metallic with electron concentrations of 2*10²⁰ cm^-3. It was also found that the resistivity data cannot be explained by carrier-carrier or optical phonon scattering. Therefore, both the source of the residual conduction electrons and the scattering mechanism in TiS₂ remain unknown.

The dynamical transport coefficient Gamma for a Heisenberg spin glass with mode-mode coupling and a conserved spin is calculated using the expansion applied to the time dimensionality. The upper critical time dimension d_t^c equals 2 for the spatial dimensionality d>4 and equals d/2 for 2<d<4. To leading order in epsilon =d_t^c-d_t, Gamma is found to exhibit critical 'speeding up'.

Susceptibility and magnetisation curves for amorphous FeF₃ indicate the presence of strong antiferromagnetic exchange coupling which would normally lead to a Neel temperature of the order of 300K in a crystalline lattice. In fact the appearance of remanence and an irreversible susceptibility indicate that spin freezing sets in only below T_f=29K, but there is no sharp phase transition. Mossbauer measurements indicate that the magnetic order is speromagnetic. A low value of the molar Curie constant measured in the range 50-300K (3.54) may be explained by assuming a spread in magnitude of the antiferromagnetic interactions. The results are discussed in terms of magnetic frustration.

High-resolution absorption and luminescence spectra associated with the creation and decay of excitons bound to the neutral phosphorus donor in germanium are reported. The sharp line structure observed is analysed in terms of the Kirczenow shell model, which requires refinement to take account of the interparticle interactions in the excited state of the bound exciton.

An investigation of the dependence on temperature of the extended X-ray absorption fine structure (EXAFS) above the K-edges of Cu and Co in the metals and above the K-edges of Rb and Sr in the compounds RbCl, SrS, SrF₂ and SrCl₂ has been performed. For Cu, Co, RbCl and SrS, the values of the correlated mean square relative displacements of nearest-neighbour atoms derived from EXAFS spectra show a good agreement with those calculated from a Debye model. The experimental data obtained are also compared with available data for mean square displacements of the individual atoms calculated from more-refined lattice vibrational models and with Debye-Waller factors used in X-ray diffraction experiments.

The results of a neutron diffraction study on the short-range order in the TeO₂-Li₂O glassy system are presented. On the basis of the obtained atomic radial distribution function a model for structural recombination in TeO₄ tetrahedra for tellurite glasses is proposed. This model takes into account the influence of the modifier and the free-electron pair of the Te atom in TeO₄ polyhedra. The limits of applicability to this system of the modified structural diffusion model and the model proposed are established.

Two semiempirical crystal orbital schemes are outlined for the calculation of the properties of perfect and defective solids. Both use periodic boundary conditions with a large unit cell (LUC) to map special points of the Brillouin zone onto the point k=0. One method involves the complete neglect of differential overlap (LUC-CNDO), the other uses intermediate neglect of differential overlap (LUC-INDO). The determination of parameter sets for the elements is discussed.

For pt.I see ibid., vol.12, p.2487 (1979). Some properties of diamond and silicon crystals have been calculated using a large unit cell-complete neglect of differential overlap (LUC-CNDO) crystal orbital approach. The dependence of the predictions on the parameter set chosen, on the size and shape of the large unit cell and on the cut-off distance for atomic interactions has been investigated. The results obtained for the perfect solid with a near-optimum parameter set are, in general, in good agreement with experimental values.

For pt.II see ibid., vol.12, p.2497 (1979). A large unit cell-complete neglect of differential overlap (LUC-CNDO) method has been used to predict some properties of lithium fluoride and potassium chloride crystals. A 16 atom cell and a parameter set chosen to match the properties of the relevant diatomic molecules form a basis for the calculation. The results are compared with predictions from a 27 atom cluster model, with previous band-structure calculations and with experiment. It is concluded that the approach has great potential for the study of ionic solids with and without defects.

A coherent potential approximation is developed for a distribution of transfer integrals (off-diagonal disorder) in a single band on a dilute close-packed lattice with first and second neighbour interactions. The moments of the density of states are evaluated and compared to exact results up to order six. It is suggested that this model provides a reasonable approximation to the structurally disordered material with the same distribution of transfer integrals arising via the pair distribution function. Results are computed for distributions based on experimental observation in liquid Fe and on those computed by the Percus-Yevick method for a liquid of hard spheres.

A basis of s, p and orbitals on Pd and s and p orbitals on Si sites is used to calculate the electronic density of states per unit cell of the Pd₃Si crystal and formula unit densities of states for different regions of two network models of the amorphous Pd₈₀Si₂₀ system. In contrast to the results of previous calculations which involved simpler model Hamiltonians for the system, it has been found that the differences in the electronic structure which reflect the local topological environment are rather modest and are certainly less prominent than those obtained in the study of three- and fourfold-coordinated amorphous semiconductors. The results compare favourably with available photoemission data and it is suggested that the s valence features of silicon may be a sensitive probe of topology in the Pd₈₀Si₂₀ system. The local density of states at the silicon site is spread over a wide range of energies and contributes significantly to the Fermi level density of states, thus providing a clue to the strength and transport properties of these amorphous alloys.

Semiempirical molecular orbital calculations have been carried out on some of the common substitutional species in diamond-nitrogen, boron, silicon, oxygen, and the nitrogen pair. The results show that this model reproduces many of the electronic and vibrational properties of these defects extremely well. In particular, the single nitrogen atom has a relaxation of 5% elongation of one of the C-N bonds, with a Jahn-Teller energy of 1.64 eV. The boron substitutional has an acceptor energy of 0.36 eV with a prominent phonon at 159 meV, in excellent agreement with experimental values.

Uniaxial stress measurements are reported on two commonly occurring radiation damage centres in diamond. Their zero-phonon lines, at 17380 and 23530 cm^-1; are shown to be electric-dipole transitions between E (ground) and A₁, or A₂, (excited) states at trigonal centres (C₃, C_3v of D_3d). Other non-degenerate states are found approximately 100 cm^-1 above the ground level. The data are consistent with dynamic Jahn-Teller distortions occurring in the ground states of the centres. On bringing together information on all the known degenerate electronic states at trigonal centres in diamond, two simple generalisations emerge for the occurrence of Jahn-Teller effects at these centres.

The broken strand model is introduced and used to calculate the dielectric constant and the electrical conductivity of one-dimensional conductors. In particular, the large positive value of the dielectric constant observed at microwave frequencies is accounted for quantitatively. It is pointed out that the existence of a large positive dielectric constant is completely consistent with the one-electron picture that has been given recently for these one-dimensional conductors.

Spin pairing at structural defects is shown to be energetically favourable in pnictide amorphous semiconductors under certain conditions of sp³ hybridisation. The presence of the resulting charged diamagnetic centres can explain very many electronic properties of these materials. Trends to be expected in the series P, As and Sb are discussed and it is concluded that negative effective correlation effects should be most marked in a-P and least marked in a-Sb.

Amorphous As and As₂Se₃ were illuminated by light of a wavelength known to excite photoluminescence efficiently, and the effect of this on the AC conductivity was investigated. It was found that the photo-induced change in AC conductivity is small, of the order of 1%. Attempts are made to reconcile this result with existing models for AC conductivity in amorphous semiconductors and, in particular, chalcogenide glasses.

Measurements of the photocurrent and the Hall current in electron-irradiated type IIb diamond have been made at 290 and 4.2K. The free carriers were stimulated by an argon-ion laser. Measurements were carried out with magnetic field up to 4 T. At low light intensities the Hall mobilities for positive holes excited by light of wavelength 514.5 nm (2.410 eV) and 488.0 nm (2.541 eV) were found to be 0.137 T^-1 at 290K and 0.59 T^-1 at 4.2K. Similar experiments were carried out with a dye laser. Over the range 432 nm (2.87 eV) to 428 nm (2.90 eV) the majority photocarriers are positive holes. It is concluded that optical excitation of the GR defect using resonance radiation at 430.4 nm (GR2, 2.881 eV) and 429.4 nm (GR3, 2.88 eV) corresponds to excitation of a positive hole at the neutral vacant atomic site in diamond.

The spin -¹/₂ Ising Hamiltonian with a single non-magnetic impurity is analysed. An exact expression in terms of perfect lattice correlation functions is found for the average value of the spin on a site neighbouring the impurity. The latter quantity is a measure of the importance of probe disturbance effects in hyperfine field measurements of critical exponents. It is shown for the case of a simple cubic lattice that the hyperfine probe does not disturb the measurement of the critical exponent beta if the temperature is in the presently experimentally accessible range close to the critical temperature. It is also found that mean-field theories overestimate the importance of probe disturbance effects.

The bond-diluted classical Heisenberg ferromagnet is treated by a position space renormalisation group method valid when the valid behaviour is at low temperatures. The method is outlined and used to obtain exact (one-dimensional) and approximate (two- and three-dimensional) results for the critical behaviour of the correlation length near the percolation limit. The procedure agrees in the pure limit with exact results of Polyakov and Migdal for the two-dimensional case. At general concentrations an exact correspondence with related treatments of random resistor networks is exhibited. This implies that the percolation-to-thermal crossover exponents of the Ising and Heisenberg systems are the same. The generalisations required for a proper comparison with neutron scattering experiments are briefly discussed.

The effect of a small anisotropy of dipolar origin on the behaviour of the one-dimensional Heisenberg ferromagnet is studied. A crossover from isotropic Heisenberg (order-parameter dimensionality n=3) to Ising (n=1) behaviour is found.

Geometric models of the percolating cluster as introduced by de Gennes (1976) are used to discuss dispersion and excitation spectra in dilute Heisenberg ferro- and antiferromagnets. New scaling relations for the spin-wave stiffness and conductivity exponents are derived and differences from those given by de Gennes interpreted geometrically. Consideration of dispersion in the antiferromagnet leads to an alternative derivation of a scaling relation for the perpendicular susceptibility exponent.

The electric field gradients (EFG) V_zz and V_xx-V_yy at the nucleus of ¹⁵⁷Gd³⁺ have been determined, using ENDOR, for CaF₂:Gd³⁺M⁺(M⁺=Li,K⁺) and SrCl₂:Gd³⁺Na⁺. The results are compared with the electronic zero-field splitting parameters of Gd³⁺, B₂⁰ and B₂² for the same sites. A simple relation between the EFG and B₂⁰ and B₂², which is expected because the host crystals are ionic, is not found. The EFG at the nucleus of Na⁺ in SrCl₂:Gd³⁺Na⁺ have also been determined, along with the magnetic dipole hyperfine interaction between this nucleus and Gd³⁺. The strength of the latter interaction reveals that the Gd³⁺-Na⁺ distance is at least 0.1 AA larger than the corresponding Sr²⁺-Sr²⁺ distance.

The absorption, magnetic circular and linear dichroism (MCD and MLD) spectra, between 5000 and 16000 cm^-1, corresponding to the ²E_g to ²T_2g optical transition are reported. The data for a sharp magnetic dipole line assigned to the ² Gamma _1g to ² Gamma _4g transition in the D_2h site symmetry group are analysed by taking into account the spin-orbit coupling and the Jahn-Teller effect. The in-plane magnetic field dependence of its absorption and MLD are shown to be due to the Jahn-Teller effect giving rise to an alternate disposition of the fluorine octahedra surrounding the copper ions. It also induces a reduction of the MCD as found experimentally. The authors' assignment of the other sharp vibronic lines appearing in the spectra is also given starting from their magneto-optical data.

Photoelectron spectroscopy studies have been conducted for UHV-cleaved single crystals of MoS₂ and alpha -MoTe₂. Angle-integrated studies have been conducted for a range of incident photon energies. For the variation of peak intensities with increasing photon energy the contributions from d-like and p-like bands have been separated. These variations can, to a first approximation, be understood in terms of the energy dependence of photoionisation cross sections from tightly bound initial states to plane wave final states. Angle-resolved photoemission studies were conducted at one value of the photon energy (21.2 eV). The observed angular variations of spectral intensities are discussed in terms of the symmetry of the initial state wave functions and possible multiple scattering effects. Two-dimensional band structures have been determined from the data, but in these materials agreement with calculated structures is not as good as for layered solids composed of lighter atoms.