Table of contents

The site percolation on a lattice is formulated as a Potts model with many-body interactions. Quantities of interest in the site percolation are expressed in terms of the Potts partition function in the same way as in the Kasteleyn-Fortuin formulation of the bond percolation.

A new numerical method for the calculation of the DC conductivity of disordered systems is developed. Preliminary results are presented for a two-dimensional square lattice with site disorder.

A transport equation is derived for a generalised distribution function. To lowest order in the electron-phonon interaction, it reduces to the semiclassical Boltzmann equation at small frequencies. The temperature dependence of the Van Hove singularities and of the DC dielectric constant are calculated.

LEED and work function measurements of Cs and O₂ on the basal plane of NbSe₂ in the 200-300K range have been made. Caesium on NbSe₂ does not form any ordered structure in this temperature range. The work function of clean NbSe₂ is estimated to be 4.60+or-0.05 eV. The sticking coefficient and maximum density of Cs on NbSe₂ increases drastically with decreasing temperature. Although NbSe₂ is inert to O₂, the presence of Cs on the surface causes a drastic increase in oxygen adsorption, which in turn increases further the amount of Cs that can be deposited on the surface. The coadsorption of Cs and O lowers the work function of the surface to 1 eV.

A simple method is proposed for studying heterojunctions. First, it is shown that a dipole barrier is induced when the charge neutrality points of both semiconductors do not coincide. The interface is analysed including the effects of this dipole and the many-electron interaction. Good agreement is found with available information.

Using the n-replica method a translationally invariant spin Hamiltonian is obtained which, in the n=0 limit, describes a dilute Ising model with random site occupation. A mean-field approximation gives identical results for the random site and bond Ising models.

An easy plane magnetic chain in a magnetic field is equivalent to a Sine-Gordon system. At low temperatures and moderate fields the dynamical behaviour of this system can be discussed in terms of magnons and solitons. Solitons are responsible for a zero frequency peak in the longitudinal part of the dynamic structure factor. They are thus observable in neutron scattering experiments.

Signs of the second degree crystal field parameters of the systems BaCl₂:Gd³⁺ and BaCl₂:Eu²⁺ are reported. With the new results it is possible to assess the relative merits of the superposition and the electrostatic model for the impurity systems under consideration and also for the systems PbCl₂:Gd³⁺, PbCl₂:Eu²⁺ and PbBr₂:Eu²⁺. Implications of the new data for the applicability of the above mentioned models are discussed.

The spin echo responses to resonant 90 degrees - tau - beta _phi degrees RF pulse sequences in solids containing rotating spin-¹/₂ triads (the methyl protons in hexamethylbenzene) are shown to be predicted by a model of two dipolar coupled quasiparticles of spin ³/₂. The observed behaviour is more complex than for an isolated spin-³/₂ particle subject to quadrupole interactions as claimed by earlier workers.

The spectrum was interpreted in terms of Allen's theory (1969), referring to transitions from localised 3d-shells to the conduction band. The ionisation energy and the optical matrix element of electric dipole transitions were determined. Manganese is found to create a deep donor level which is located at about 0.60 eV above the top of the valence band. The observed photoionisation spectrum was compared with the photoconductivity spectrum in the same region.

Arguments are presented in favour of interpreting the M_4.5VV Auger spectrum of Ag as a quasi-atomic M_4,5N_4,5N_4,5 spectrum perturbed by crystal environment in contrast to the analysis by Burkstrand and Tibbetts based on self convolution of band state densities (see Phys. Rev. B. vol.15, p.5481 (1977).

Photoemission-into-electrolyte yields have been measured on a copper single-crystal cylinder with polarized light at normal incidence. Both above and below the direct transition threshold, very similar polarisation dependent crystallographic anisotropies are observed. Intraband transitions within the lower conduction band due to a surface-field effect are tentatively suggested as an explanation for these novel results.

The phonon frequency distribution of KCN was measured in the cubic room-temperature, and the two monoclinic low-temperature, phases by coherent inelastic neutron scattering. At 5K the spectrum splits into three parts which reflect the acoustic, the librational and the optical modes. At higher temperatures these structures are washed out indicating strong anharmonic effects. The results are compared to model calculations of the cubic phase.

Based on the Green function method adapted to polymers and using three different force fields for the polyethylene skeleton, extensive calculations were made on the characteristic vibrational features of conformational defects in deuteropolyethylene for the frequency range 40-456 cm^-1. The results presented show that almost no specific conformational information can be obtained from the defect-induced modes below the torsional cut-off nu ₉(max); however, resonances above nu ₉(max) may be used to advantage for spectroscopic investigations of the morphology of polyethylene.

Studies of the temperature dependence of the X-ray powder diffraction and single-crystal Raman spectra of Hg₂Cl₂ are reported for temperatures from 300K to below the phase transition at approximately 180K. From the X-ray data it is established that the crystal class changes from tetragonal in the high-temperature phase to monoclinic in the low-temperature phase. The Raman spectra at low temperatures are explained by a primitive monoclinic cell of doubled content and the space group identified as C_2h². The temperature dependence of the Raman spectrum of a 'soft' acoustic branch is observed above the phase transition and used to suggest a mechanism for the transition.

For trigonal selenium the coefficients of thermal expansion, alpha /sub ///, parallel to the chains, and alpha _{perpendicular to} , perpendicular to the chains, have been calculated from dilatometric measurements in the temperature range 10K to 300K. By means of values of the specific heat c_p(T) and the adiabatic elastic constants C_ik(T) from literature the Gruneisen functions gamma _in and gamma /sub /// have been computed in the quasiharmonic approximation. For vitreous selenium the coefficient of thermal expansion has been measured in the same temperature range. The Gruneisen function has been calculated from data of specific heat and the adiabatic bulk modulus K_s evaluated from ultrasound measurements. For comparing the thermomechanical behaviour of vitreous and trigonal selenium, respectively, the temperature dependent Gruneisen functions are discussed by means of a linear chain model.

Reports measurements of the electrical conductivity and ¹⁹F nuclear magnetic resonance (NMR) relaxation times T₁, T₂, T_{1 rho} and T_1D in BaF₂ single crystals over a temperature range 300K-1200K. The dominant process responsible for the ¹⁹F spin relaxation is self-diffusion. The magnitude and temperature dependence of the relaxation times are satisfactorily interpreted using the Wolf theory. Absolute values of diffusion coefficients calculated from NMR relaxation data assuming a vacancy diffusion process are in excellent agreement (within 15%) with those calculated from ionic conductivity data using the Nernst-Einstein relation. From the temperature dependence studies, the diffusion parameters were determined. The formation enthalpy for a Frenkel pair was found to be 1.91 eV and migration enthalpies for free F^- vacancies and F^- interstitialcies were found to be 0.57 and 0.76 eV respectively.

The mobility of positive ions in liquid ³He is calculated using a modification of the theory of Josephson and Lekner (1969). The mobility is predicted to increase linearly with ln(T₀/T) for temperatures between 2 and 50 mK. This is in accord with the experimental results. There is no discontinuity in the mobility according to the theory. It is suggested that the rapid drop in the mobility at 70 mK is caused by ⁴He atoms condensing on to the surface of the ion, resulting in an increase in the radius of the ion.

A method for calculating energy levels and wavefunctions of bound states associated with deep impurity centres in semiconductors is presented. The impurity system is replaced by a crystal, whose unit cell consists of the impurity surrounded by a large number of host crystal atoms. The impurity bands for this crystal, represented by a real potential, are calculated by expanding in orthogonalised Bloch waves. To find the discrete level and the corresponding isolated impurity wavefunctions, a tight-binding extrapolation scheme has been developed. As a first application, the method is applied to substitutional neutral zinc in silicon, using 54 atoms per unit cell. The total impurity bandwidth is found to be quite large, 1.5 eV, arising from a discrete level at about 0.2 eV above the top of the valence band. The many-band nature and probability distribution of the impurity of Bloch states are explored, showing moderate localisation in both real and reciprocal space.

The positronium-surface interaction has been studied experimentally and theoretically. The angular correlation of photons from annihilation of positronium on the internal surfaces of porous Vycor glasses has been measured as a function of pore size in the range 2.2-14.0 nm. When the pores were filled with oxygen the angular distribution showed an intense narrow peak, arising from parapositronium annihilation in the pores, superimposed upon a broad distribution. The width of the narrow peak was approximately independent of pore diameter suggesting localisation of the positronium in a surface state. The possible states of positronium in a spherical cavity have been studied theoretically as a function of the strength of the surface potential. The positronium-glass interaction that best fits the data was found to be attractive and strong enough to localise the positronium atom near the surface of the pores. The theory gives a good description of the data with strongly attractive surface well, e.g. approximately 1 eV deep and 0.4 nm wide. The likely origin of the attraction is the strong van der Waals interaction of the highly polarisable positronium atoms.

A theory is developed for the decay of surface charge due to a time-dependent bulk conduction process. Assuming that the time dependence of the conductivity of the insulator is proportional to f(t), specific cases of f(t), e.g., t^-0.5 are solved analytically while the more general t^-n dependence is solved numerically. The charge decay plots produced show the rapid initial decay followed by a quasi steady level observed by several experimenters. It is suggested that a combination of voltage step-response and charge-decay measurements is necessary to confirm whether the charge-decay process involves injection of the surface charge into the bulk of the insulator.

Theoretical values of weak-field Hall mobility and Hall ratio of electrons in InP at 77K and 300K are presented for different impurity concentrations and compensation ratios. Calculations were done by an iterative method taking into account all the complexities of the band structure and the electron scattering mechanisms and using the most recent values of the physical constants. Calculated values are in close agreement with the recent experimental results.

A semiclassical random walk hopping model is proposed in order to explain the anomalous magnetoresistance in amorphous germanium and silicon in the hopping regime. A general expression is derived for the magnetoresistance. The magnetoresistance is deduced to be the result of the modification of the spin-flip relaxation time by the external magnetic field. Explicit formulae are derived within the variable range hopping theory of Mott and the spin relaxation model described previously by the present authors. The model can then account for the variety of experimental observations in these materials.

In the Dyson-Maleev boson formulation it is shown that the kinematical interaction, as a statistical phenomenon, can be investigated by evaluation of the partition function. An expression is derived for the thermal expectation value of magnon occupation numbers in which the kinematical interaction is incorporated. By means of this correct magnon distribution function, the correct magnon renormalisation can be selfconsistently determined, which now is also valid in the high-temperature regime. It constitutes an appreciable extension beyond earlier magnon results. In order to compare the results with experimental data, the two-magnon Raman cross-section is evaluated by means of the improved magnon renormalisation and magnon distribution function. This is done for the two-dimensional antiferromagnet K₂MnF₄ and excellent agreement with experimental results is found.

A theory is presented for one-magnon light scattering by reflection from the surface of a semi-infinite Heisenberg antiferromagnet at low temperatures T<<T_N. The calculations involve deriving expressions for the transverse spin-spin Green functions for the semi-infinite medium, and these results are then employed to obtain the light scattering cross-section. The theory includes an evaluation of the scattering contribution from surface spin-waves, as well as from the bulk spin-waves.

Calculations are presented for the lineshapes associated with light scattering by spin-waves in absorptive (semi-opaque) magnetic materials at low temperatures. Scattering at normal incidence to the surface is considered, and it is predicted that the lineshapes are asymmetric and that there is an 'opacity broadening' contribution to their width. Both ferromagnetic and antiferromagnetic materials are considered, although it is shown that the effects may be considerably larger in antiferromagnets with small anisotropy. The theory is applied to obtain numerical results for the antiferromagnets RbMnF₃ and MnF₂.

The spin-lattice relaxation of the ²³Na nuclear spin system in monocrystalline sodium nitrate has been studied at room temperature by CW double resonance experiments. The main technique consists of severely saturating one component of the quadrupole-split spectrum and measuring the change in amplitude of the other components. In this way, the electric quadrupole and magnetic dipole contributions to the nuclear spin-lattice relaxation have been determined separately. Measurements were made on two different crystals set at various orientations relative to the large external magnetic field. The orientation dependence of the ratio of the electric quadrupole relaxation rates W₂/W₁ is in excellent agreement with theory, if W₁ and W₂ are assumed to be characterised by the same quadrupole relaxation tensor. This, in turn, indicates that the relaxation is caused by a Raman-type interaction with the lattice phonons.

ENDOR measurements were done on ¹⁵⁵Gd³⁺ and ¹⁵⁷Ge³⁺ in CaO, using the natural distribution of Gd isotopes. For H//(100) the following parameters were measured. Some ENDOR complications related to the presence of more than one isotope are discussed. The main objective of the experiments is to investigate the isotropic electric quadrupole interaction term. Comparison with earlier experiments show that B is not very sensitive to the host crystals. This result permits the test of a recent theoretical value of B obtained for free Gd³⁺ with aid of relativistic linked cluster many-body perturbation theory. Satisfactory agreement between theory and experiment is found.

Mossbauer spectra of K₂FeF₅ obtained in a magnetic field applied parallel to the antiferromagnetic axis show that in a field of 3.7T the spins reorientate (flop) to become perpendicular to the applied field. The experimental value of the spin-flop field yields an approximate value of 1.4*10^-3 for the ratio B_A/B_E of the anisotropy field to the exchange field. The applied field spectra also show a dependence of the hyperfine field on the applied field. This behaviour together with the anomalously low value of the saturation hyperfine field (41.0+or-0.5 T) and the temperature dependence of the hyperfine field are discussed in terms of the spin reduction, which results from a spin-wave treatment of an antiferromagnet. Calculations show that this spin reduction is enhanced in a one dimensional system. Comparison of the calculated and experimental values leads to an estimate of around 10^-3 for the ratio J'/J of the interchain to the intrachain exchange constants, which shows that K₂FeF₅ provides a good approximation to a one dimensional magnetic system.

Absorption measurements at room temperature and 90K on single crystals of Cd₃P₂ are given. Free carrier absorption can be interpreted in the simple classical model while the interband absorption is interpreted in the Kane band model using exact solutions of the secular equation and without neglecting the free electron term. The best fit of the theory to experimental points is found for E_g(300K)=0.53 eV, E_g(90K)=0.56 eV, P=6.7*10^-10 eVm, Delta =0.1 eV and m_v1=0.5 m₀. Some results of thermomagnetic transport properties are discussed in the same model.