Table of contents

Simple probability arguments are used to show that in random packing the average number of discs contacting an origin disc which will ensure the stability of that origin disc is n_s=3.2 when the discs all have the same radius. In binary mixtures of discs n_s varies only a little as a function of concentration, even when the radius ratio is as large as 5:1.

The molecular dynamic simulation results for the average fracture stress sigma _c of a 20*20 Lennard-Jones system has been studied here against the variation of random lattice bond dilution concentration p near the percolation threshold p_c. A reasonable agreement has been obtained, without employing any fitting parameter, to the scaling from sigma _c= square root k(1-p)^-1/2 mod p-p_c mod ^{(nu + t)/2}, obtained employing Griffith's energy balance concept to the 'node-link' superlattice model of percolation clusters.

The problem of using real trajectories in complex time in calculations of the energy levels for the case of the double-well potential is discussed. Reasonable results are obtained for the lowest energy levels when the condition epsilon _n<<V₀ is satisfied. Correspondence to the instanton picture is considered.

The metal-insulator transition, in just metallic and compensated n-type indium phosphide, has been induced by a magnetic field, and some features of the transition predicted by Mott, such as minimum metallic conductivity, have been observed. Corrections to the conductivity due to Coulomb interactions are described and some agreement with scaling theories of the transition is found. On the insulating side of the transition, the conductivity is dominated by hopping mechanisms and its temperature dependence is explained by the opening of a Coulomb gap in the impurity band, due to e-e interactions. Nevertheless the mean results are obtained with the study of the mobility in high magnetic fields down to the lowest temperatures; they show that the agreement with scaling theories seems fortuitous, i.e. the zero temperature conductivity drops discontinuously to zero when the Anderson transition has been achieved.

The 'classical' s-d scattering theory is applied to account for the anomalous temperature dependence of the resistivity in some intermetallic compounds, which possess very narrow peaks in the electronic density of states, due to d or f states. At temperatures where h(cross)/ tau _e-ph approximately=J, where tau _e-ph is the electron-phonon scattering time and J a hybridisation integral, the hybridisation is broken, and at higher temperatures the resistivity follows a linear rho =a+bT law. The temperature-independent part a is due to phonons scattering the d or f states, into which the s electrons (which carry most of the electric current) are scattered by the hybridisation integral J. The bT term is due to phonon scattering of the more itinerant s (or p) states into s states. This term does not saturate because the mean free path of the s electrons is still about 10 interatomic spacings, even at high temperatures. The thermoelectric power has a maximum when h(cross)/ tau _e-ph approximately=J.

The construction of scattering rates in high-field (1973) quantum transport theories is critically discussed in the light of a recent paper by Marsh (1973) and Inkson (1984). The outstanding discrepancy in the literature between the works of Barker (1973) and Thornber (1978), and Herbert and Till (1982) is resolved using time-dependent perturbation theory and a self-consistent Wigner function analysis, which pinpoints the source of the confusion to the lack of a unique definition for a transition rate in high-field quantum transport theories. On the basis of these arguments it is concluded that the analysis of Marsh and Inkson is incorrect. The nature of wavepacket scattering in small devices is also discussed.

The peculiar electrical properties of n-Al_xGa_1-xAs:Si with 0.20<or=x<or=0.45 are caused by the existence of two donors of different thermal activation energy. Besides a shallow hydrogen-atom-like donor, a deep Si donor is present which causes persistent photoconductivity at low temperatures. The persistent photoconductivity in selectively doped heterostructures, which is a result of the deep donor, is explained semi-quantitatively. In addition a transient photoconductivity effect is observed in selectively doped heterostructures at low temperatures after the illumination has been switched off, which does not occur in bulk n-Al_xGa_1-As. The band diagram in real space is calculated for selectively doped heterostructures in terms of the two-donor model. The design parameters for selectively doped heterostructures are discussed on the basis of this calculation and some design rules are proposed.

The authors develop a Monte Carlo position space renormalisation group method to study the scaling properties of bootstrap percolation. In this model sites on a lattice are randomly occupied with probability p and sites with less than m occupied neighbours are culled until a stable configuration remains. Using progressively larger length rescaling factors b, they obtain numerical results on the triangular lattice for the percolation threshold p_c(b), the connectedness length exponent nu (b) and the fractal dimension d_f(b). The large b limit yields numerical values of d_f for m=2 and 3 which are consistent with d_f for ordinary percolation (m=0). Although the small b dependence of nu for m=2 and 3 is qualitatively different from that of ordinary percolation, the large b behaviour of nu suggests that m=2 and m=3 bootstrap percolation on the triangular lattice are in the same universality class as ordinary percolation.

The Parisi replica symmetry breaking scheme is considered for spin glass models without reflection symmetry (e.g. Potts glass, uniaxial quadrupolar glass). It is shown that the retention of all the quartic terms in the free energy functional allows one to demonstrate the invalidity of naive applications of Parisi's scheme to such models.

The non-analytic behaviour of the dielectric function plays an essential role in the calculation of the screening density induced by an external point charge. It is shown that the logarithmic singularity of the slope of the static local field correction near to k=2k_F leads to an amplitude modification in the Friedel oscillation.

KL_2,3-L²_2,3V satellite Auger transitions have been observed from Al. The kinetic energies of the multiplet structure of these transitions are in good agreement with excited-atom Delta SCF Hartree-Fock calculations. It is not possible to reproduce the spectral profile by associating the lineshape of the K-L_2,3V transition with each component of the multiplet structure and weighting the intensities of components according to their statistical weights.

Measurements of specific heat capacity and thermal conductivity have been carried out on unextruded and extruded samples of semicrystalline polyethylene, in the temperature range below 2K. It was found that the specific heat capacity has the form c=aT+bT³ and that the magnetic does not change on extrusion. The thermal conductivity has an approximately linear temperature dependence over a significant range of temperature, and this range of temperature is different for the unextruded and extruded samples. The departure of the thermal conductivity from the T^1.9-dependence, which is observed in truly amorphous materials, means that the two-level tunnelling theory does not account, even qualitatively, for the experimental observations.

The thermal conductivity of a semicrystalline material is explained by assuming that the long-wavelength phonons, which are dominant at very low temperatures, are scattered by localised tunnelling states, while the phonons dominant at higher temperatures are scattered by the structure of the semicrystalline polymer. The authors use the structure scattering theory developed by Morgan and Smith (1974), which introduces the correlation lengths a_s and a_c, which are related to the dimensions of the structural units present within the amorphous and crystalline regions of the polymer respectively. The conductivity curves obtained for samples of both isotropic and extruded polyethylene have been explained in this manner. The effects of structure scattering and tunnelling state scattering on the thermal conductivity of amorphous and semicrystalline materials are discussed.

The transfer matrix approach for the calculation of layer Green functions with a tight-binding Hamiltonian is extended to the case of a nonorthogonal basis. The problem can be rewritten in terms of an energy- and overlap-dependent pseudopotential. An application is made to the calculation of the spectral and total densities of states for the (100) and (100) faces of tungsten. Comparisons with calculations without overlap indicates that overlap effects do not play an important role except at the point Gamma of the (100) surface, where changes in the energy positions and the intensities of the peaks are found.

The large polaron in a magnetic field is treated within the Fock approximation. In order to investigate the nature of the phase transitions that can occur in the internal structure of the polaron, model spectra of various symmetries are used to calculate the ground-state energy. These models involve an electron in a magnetic field (external or internal in origin) and harmonically bound to a fixed point (isotropically or anisotropically). A variational procedure is used to determine, within a specific model, the symmetry that gives the lowest energy for given parameters. The authors find that phase transitions occur that are functions of the magnetic field or of electron-phonon coupling constants. For some models, these transitions are similar to those found by Peeters and Devreese (1981, 1982), using a Feynman integral formalism for a large electron-phonon coupling: strong lattice polarisation for a small magnetic field and small polarisation for large external fields. Furthermore, they also find transitions for smaller electron-phonon coupling, using models involving the presence of an internal magnetic field. This makes the observation of these transitions more susceptible to experimental verification.

The conductivity of noninteracting electrons in a two dimensional disordered system is calculated to two-loop order by employing diagrammatic Green function methods. From perturbation theory the authors have found that a second-order next-leading logarithmic term is present only in the limit of l/L to 0 and finite omega , where l, L and omega are respectively the mean-free path, length of the sample and the frequency associated with the external field. This result is in agreement with the self-consistent theory of Vollhardt and Wolfle, (1982). This approach can also be used to study the case in a strong magnetic field if the contribution from the diffusion mode in the particle-particle channel is completely suppressed. In this situation the results reduce to those of Hikami and Efetov and predict that the system is localised. The application of the results in a weak magnetic field will also be discussed.

The magnetoconductivity and Hall conductivity of a two-dimensional disordered non-interacting electron system are studied in an arbitrarily strong magnetic field up to the two-loop order. These two-loop diagrams have been assumed to come entirely from the diffusion propagators in the particle-hole channel. The set of conductivity diagrams the authors have calculated are equivalent to those considered by Hikami (1981). They found that there is no second-order leading logarithmic term in the magnetoconductance. If these diagrams are evaluated in the 2- epsilon ( epsilon to 0⁺) dimension there exists a second-order next leading logarithmic term. This result shows that the scaling function beta (g), up to the order 1/g², is a universal function of the conductance g and independent of the magnetic field. They also found that, although each of the two-loop diagrams contributes to the Hall conductivity, their sum, however, is equal to zero.

The relationship between the zero-field splitting parameter D and the C₃ crystalline potential components for ⁶S ions is established with the use of the high-order perturbation method. It is found that the effect of the spin-spin interaction within the d⁵ configuration is comparable with the mechanism suggested by Orbach et al. (1962). By using the d-orbital theory proposed by Zhao et al. (1982, 1983, 1984) the optical levels and the zero-field splitting of Mn(I):Ca₅(PO₄)₃F are calculated. The results agree well with the values measured experimentally.

The Anderson model of a magnetic impurity in a metal is considered in the limit U to infinity excluding multiple occupancy of the f level. The fourteenfold degeneracy of the configuration 4f¹ is lifted by the spin-orbit coupling and the ground-state properties, e.g. the valence, occupation of the j=⁵/₂ and ⁷/₂ multiplets and the magnetic susceptibility, are discussed as functions of the spin-orbit splitting. It is concluded that for Ce ions the excited multiplet j=⁷/₂ is important in the mixed-valence regime, but not in the Kondo limit.

The physical background of the method of temperature-modulated steady-state space-charge-limited currents is described. It is a self-consistent spectroscopic method applicable to the determination of both arbitrary energy distributions of bulk electron-localised states and charge carrier mobility. It is based on the measurement of the current-voltage characteristics together with the current activation energy-voltage dependence in the space charge regime, i.e. the current and its change due to the modulation of temperature are measured at a given applied voltage. The applicability of the method is illustrated by means of computer-simulated characteristics, calculated for various typical distributions of traps.

The electronic structure of a disordered two-dimensional system in strong magnetic fields is studied for a sample consisting of two rings with a junction connecting them. The gauge transformation study reveals interference effects for the complex wavefunction specific to multiply connected systems, in which the electronic structure is a doubly periodic function of the magnetic fluxes penetrating the openings in the system, as in the Josephson effect in a similar geometry. The relevance to the quantised Hall effect is discussed.

It is populated that Bruggeman's symmetric and asymmetric effective-media theories describe the two extreme behaviours of metal-insulator mixtures. A single equation which interpolates between these two extremes, in two and three dimensions, is proposed. It involves a single parameter, probably a fractal dimension, which is determined by the composition at which the metal-insulator transition occurs. Excellent agreement is found with experimental and computer simulation data.

2D spin-1 Ising models with nearest-neighbour and crystal-field interactions exhibit tricritical behaviour. A new method that applies to a wide class of random systems is used to study the influence of site and bond dilution on this behaviour. The authors have calculated temperature-crystal-field-concentration phase diagrams and determined, in particular, the influence of dilution on the zero-temperature critical field and on the tricritical temperature. The results are in agreement with those obtained recently for bond dilution by a real-space renormalisation-group technique. The method appears more tractable.

The effects of spin fluctuations on the magnetic excitations in the slightly under-critical ground-state system Cs₃Cr₂Br₉, which were recently studied by neutron scattering, are investigated by using correlation theory to extend the RPA by one order. The theory renormalises the single-triplet separation from the RPA value of 1.03 meV at 1.6K to the more reasonable value of 0.58 meV. The temperature dependence of the excitations is calculated self-consistently and compared with experiment. From the calculated density of states the lineshapes of the magnetic excitations are calculated and compared with the experimental lineshapes obtained from neutron scattering. The agreement is very good.

The authors solve exactly the large-n limit of the n-vector model with a quenched random field, allowing for the possibilities of both long-range correlations in the random field and long-range exchange interactions. It should be emphasised that, although the ideal Bose gas is frequently assumed identical to the large-n limit of the n-vector model, their identity has only been demonstrated for models with full translational symmetry (Gunton and Buckingham 1968, Stanley 1968). Indeed, without such symmetry, there are examples where several kinds of chemical potential must be introduced into the Bose gas in order to preserve the relationship with the n-vector model (Knops 1973, Fishman and Ziman 1982). In fact, the authors find that the two models behave equivalently. In addition, they are able to extend earlier results in the various ways necessary to present a comparison of the large-n limit with recent work (Chang and Abrahams 1984, Kardar et al. 1983) using epsilon -expansions about the lower and upper critical dimension some discrepancies emerge.

The authors construct the replica mean-field theory of a set of m-dimensional uniaxial quadrupoles interacting via quenched random exchange with non-zero mean. Replica-symmetric theory yields a transition which is continuous for m<m_c approximately=4.6 but discontinuous m>m_c. For m>2 replica-symmetry breaking effects are much stronger than for conventional systems. Using the replica-symmetry breaking scheme of Parisi (1979), a solution is obtained but it appears to be unphysical for m>¹/₂(1+ square root 33) approximately=3.4. At sufficiently low temperatures, and for m>2, mean-field theory predicts that 'ferromagnetic' order is inevitable in the presence of disorder, regardless of the mean exchange.

The 'plate domain' structure in an Fe(5% Si) bar crystal with Neel orientation (bar axis (110); side faces (110) and (001)) is scanned by perpendicular transmission with polarised neutrons ( lambda >or=0.4 nm) and subsequent three-dimensional polarisation analysis, using a 80 mu m slit. The domains magnetised parallel to (100) are identified and the 'shadow width' of the 90 degrees domain walls due to the zigzag folding is found to be of the order of 0.1 times the plate width l for l=450, 310, 190 and 137 mu m. The occurrence of a domain structure in which the zigzag amplitude varies over the height being in antiphase in neighbouring 90 degrees walls is demonstrated. A similar scan 8.9 degrees out of perpendicular transmission provides consistency with earlier 'angle-dependent' depolarisation measurements made in the same crystal.

The effect of pressure on the magnetisation of UFe₂ at 4.2K and the effect of pressure on the Curie temperature are compared with interpreted as indications for itinerant ferromagnetism. Moreover, these pressure effects, studied in the series U(Fe_xCo_1-x)₂ show a behaviour that is in qualitative agreement with this model. Magnetisation curves around the Curie temperature are analysed in terms of critical behaviour. The pressure dependence of the parameters so derived is obtained and related to the temperature and pressure dependence of the intrinsic moment. From this analysis it is deduced that, contrary to what is expected in Stoner-Edwards-Wohlfarth theory, the magnetic moments do not completely disappear above the Curie temperature.

The three-lowest-energy absorption bands of the Tl⁰(1) centres of KF, NaCl, KCl, RbCl, RbCl, and KI were identified by the technique of measuring their magnetic circular dichroism tagged by ESR and/or by measuring the excitation spectrum of the near-infrared emission band. The transition energies of the two lowest-energy absorption bands and the emission band as function of the lattice parameter can be explained by the atomic model with the change of the crystal-field splitting. The temperature dependence of the absorption and emission bands could be measured in all of the compounds except for NaCl and KF. Its analysis reveals two different effective phonon frequencies in each electronic state. The low frequency is due predominantly to an atomic Tl motion along the centre axis, while the higher frequency is associated with modes in which mainly the host-lattice ions are moving. A comparison of the frequencies in the ground and excited states suggests that the Tl atom is more relaxed towards the vacancy in the ground state than in the excited state.

The experimental results obtained by laser narrowing of the R line in MgO:Cr³⁺ are reported. Two lines appear by fluorescence narrowing-one in resonance with the excitation line and another that shifts in the opposite direction to the excitation with respect to the maximum of the R line. This behaviour is shown to come from e-type internal strains, which are mainly contractions along the tetragonal axis. A model is given that fits the inhomogeneous shape of the R line and the effect of FLN. In particular it is shown that the e internal strains are induced by Mg²⁺ vacancies, dislocations inducing mainly cubic strains.

The photoluminescence spectra, excitation spectra and radiative decay times of CsBr:In⁺ have been investigated in the temperature range 4.2-300K. Excitation in the A (4.38 eV; 283 nm) absorption band at 4.2K gives rise to two partly overlapping emission bands at 2.42 and 2.75 eV. When excitation occurs in the B (4.68 eV; 265 nm) or C (5.19 eV; 239 nm) absorption bands an additional emission band at 3.25 eV is also observed. The relative intensities of these bands are strongly dependent on the wavelength of the excitation and also on the temperature. All the emission spectra were resolved into an appropriate number of skew-gaussian components. The effective frequency of the lattice vibrations coupled to the relaxed excited states was determined by moments analysis. At 4.2K the radiative decay times for the emission bands each exhibit a slow component ( approximately 10^-4-10^-5 s) and a fast component ( approximately 10^-7-10^-8). The consequences of the two phenomenological models, (i) JT>>SO and (ii) JT<<SO, where JT is the Jahn-Teller interaction and so the spin-orbit coupling, are examined. It is concluded that the latter leads to a consistent interpretation of all the experimental results.

A time-dependent Anderson Hamiltonian coupled to a local boson mode is used to describe screening effects in inelastic metal surface scattering. Assuming, in the spirit of the slowness approximation, that the perturbation by the approaching adsorbate is too slow to excite real plasmons, the boson degrees of freedom are removed to retain an effective purely electronic problem. The results show that, apart from the well known downward shift of the adsorbate level resonance, screening affects the shape of this resonance in a way that depends on the ratio of the two characteristic energies B (width of the substrate conduction band) and omega (plasmon frequency): for omega >>B a polaron-like renormalisation of the width is found, whereas for B>> omega the height of the resonance is reduced. The model is extended to include plasmon dispersion in a time-dependent scaling calculation.