Table of contents

The diffuse scattering of silver-chalcogenide-type fast-ion conductors is examined. It is shown that in an actual crystal the correlation of cation-anion pairs produces the most prominent diffuse scattering. The contribution from anion-anion pairs is small unless the amplitude of the anion thermal vibration is very large. The results support previous analyses of the diffuse haloes for alpha -Ag₂S and alpha -AgI by Tsuchiya and co-workers (1978-79).

On the basis of a geometrical interpretation of the direct correlation function of a hard-core fluid the authors propose a general expression for it that is consistent with the known results for hard rods, hard discs and hard spheres and that is considerably simple than Leutheusser's recent proposal (see J.Chem. Phys., vol.84, p.1050, 1986).

A thin film of superfluid ³He-A film containing a polar domain wall has a normal current flowing in it even at zero temperature. The authors calculate this current from the Gorkov-Nambu equations in a way similar to that of Volovik (1985) for bulk ³He-A. An earlier calculation by the authors working to first order in gradients yielded a singular normal current (proportional to a delta function). In the present work the authors show that the singular nature is an artefact of the gradient expansion. An additional length scale in the problem smooths out the delta singularity. They show that the current obtained has its origins in a zeroth Landau level.

Approximate expressions for the Coulomb U and exchange-correlation E_xc energies in LDF theory for molecules and atomic clusters are discussed. Evaluating U using a constrained fit to the charge density leads to terms in the potential, derived from U, not discussed by previous workers. A method is described of evaluating E_xc which is fast and requires only a fit to the charge density. Results of self-consistent pseudopotential calculations are given for the molecules C₂ and H₂O.

The authors develop a theoretical description of the trapping of electrons by voids in a tight-binding solid. A new microscopic model is introduced in which the internal pore surfaces are parametrised by dimensionless ratios R and eta . Critical values R_c and eta _c of these ratios exist at which the fraction f of bound states at the pores vanishes. For a small pore embedded in a finite solid, numerical results for the bound state energies and their degree of localisation are presented. For larger pores in an infinite solid analytic results are obtained. On the basis of these results, the authors examine the possibility that field-dependent losses found experimentally in RF sputtered semiconductors are due to the trapping of electrons by voids and suggest that the field effect arises through transitions between bound pore states and nearby localised states.

A Green function technique is used to study the spin-dependent phonon Raman scattering in EuS. The temperature and magnetic field dependences obtained for the line-width and line intensity below and above T_c are in very good agreement with the experimental data.

A theoretical approach is presented intending to unify tunnel model and structural defect concepts existing in the theory of amorphous solids. Origins of double-well potentials (DWP) are discussed and two types of DWPs-soft and rigid-are emphasised. Soft DWPS are mainly responsible for low-temperature properties whereas rigid DWPs determine the properties of glasses at higher temperatures. Tunnelling in rigid DWPs is largely influenced by the barrier fluctuative preparation, the multi-phonon processes are of importance at higher temperatures. The DWP relaxation time up to room temperature is analysed. The sound attenuation due to the relaxation and multi-phonon mechanisms is calculated and their relative contributions are compared. The role of these processes in the thermal conductivity and temperature plateau formation is discussed.

A Monte Carlo technique based on the Metropolis approach has been employed to simulate the energy and structure-related properties of systems containing Si and O atoms. The method uses a semi-empirical potential function comprising two- and three-body interactions. The potential does not utilise any covalency or ionicity concept nor does it categorise the interactions between particles into short or long range. The only many-body term considered to be significant is that due to the long-range triple-dipole interaction. Calculated results for energetics and structural properties of four different allotropic forms of SiO₂ (for crystalline bulk) agree well with experimental data within acceptable limits. In addition, simulations were performed to estimate the properties for the (001) surface of low-cristobalite. The importance of three-body interactions on the structural stability of SiO₂ phases is also discussed.

Rigorous numerical calculations on the non-radiative multi-phonon transition probability based on the adiabatic approximation (AA) and the static approximation (SA) have been accomplished in a model of two electronic levels coupled to one-phonon mode. The numerical results indicate that both the diagonal non-adiabatic operator and the mixture and split of the potential sheets have a significant effect on the adiabatic vibrational states near or above the classical cross point and on the transition rates between these states. For strong electron-phonon coupling, the calculated transition rates based on AA are more reliable; on the other hand, for weak coupling the difference between transition rates near or beyond the crossing region based on different approximations can be beyond an order of magnitude. When the transition occurs far below the crossing point, both approximations give the same results. The relationship among the transition matrix element and the vibration level shift, the Huang-Rhys factor, the separation of the electronic levels and the electron-phonon coupling are analysed and discussed.

As an extension of the Ising model for calculations on order-disorder phenomena in alloys, normal modes giving rise to a vibrational entropy contribution, were allowed. Calculations were performed on a (hypothetical) AB alloy crystallising in the simple cubic (NaCl) structure, where an exact analytical expression for the vibrational entropy exists. As a first step the problem was handled using the Bragg-Williams approximation. Arguments are given for why the introduction of the vibrational entropy should have a drastic influence on quantities of interest, such as the degree of order at a certain temperature, the order-disorder temperature and the specific heat. It is argued that for 'exact' solutions and realistic structures, computer simulation studies are necessary.

Effects of lattice fluctuations on the charge-density-wave transition are studied for a three-dimensional system of the basis of a two-band model. Using the thermal Green function method the authors calculate the polarisation function for phonons and the self-energy for electrons in the mode-mode coupling approximation. The renormalised phonon frequency and the lattice fluctuation are obtained self-consistently as functions of temperature. The coherence length is given in a concrete form. Taking lattice fluctuations into account, the electron density of states, spin susceptibility and electrical resistivity are calculated and compared with their anomalous temperature dependences observed in 1T-TiSe₂.

Two Peierls instabilities with different critical temperatures and nearly equal wave vectors are considered in the limit of weak bilinear coupling. This coupling is important close to the first transition, when the unstable phonon induces the ordering at the same wave vector in the other phonon branch. The low-temperature transition is of the sine-Gordon type. It occurs when the second branch develops its own instability, and, through the appearance of 'discommensurations', the tendency to have its own periodicity. These results are compared with the experimental situation in ortho-TaS₃ and blue bronzes.

An effective non-local Lagrangian for phase and amplitude fluctuations of a one-dimensional charge-density wave is derived from the microscopic Frohlich Hamiltonian. The range of the forces is found to be of the order of the (amplitude) coherence length xi . This Lagrangian is used to study numerically the impurity-induced lattice relaxation. Strong distortions both in the phase and in the amplitude are produced around an impurity. A microscopic approach for calculating the lattice response to impurities yields similar results. In addition is shows that an impurity potential can produce localised electronic states within the (Peierls) gap which depend both on the potential strength and on the phase of the charge-density wave at the impurity site.

The authors present results of ESR measurements on the linear chain compound dimethylmorpholinium-TCNQ₂ in its triclinic modification. They offer a new interpretation of the phase transition at 1.65K. They argue that to understand the resonance behaviour one has to assume a spatial modulation of the dimerisation order parameter.

It is demonstrated that the infrared spectrum of a typical organic linear chain conductor can be understood as follows. The near infrared shows typical plasmon behaviour, and it appears that the plasma frequency is related to the crystal structure and one-electron parameters as in ordinary metals. Thus band structure parameters can be derived and the infrared oscillator strength for the corresponding non-interacting electron gas can be predicted. In all cases the actual measured oscillator strength is significantly smaller. The information contained in this deviation can be quantified by means of a sum rule, which relates oscillators strength and electron kinetic energy. The latter is a measure of the Coulomb driven electron localisation.

In this paper it is argued that the generality of the Meyer-Neldel rule compels one to adopt a phenomenological approach if a universally valid model is aimed at. It is shown that there exists only one possible phenomenological model. This model is based on an exponential probability distribution of energy barriers. The model predicts a power-law frequency dependence of the AC conductivity with the exponent s given by s=1-T/T₀ where T₀ is the characteristic temperature of the Meyer-Neldel rule. It is conjectured that the exponential energy barrier distribution derives from a 'glass transition' at T₀. The generalisation of the model to account for the compensation effect in other contexts is briefly discussed, using the case of heterogeneous catalysis as an example.

A self-consistent Green function theory of the Anderson lattice Hamiltonian is presented. The approximations include spin and charge fluctuations beyond mean field and are similar to previous approximations made for the impurity problem by Theumann (1969). The self-energy integral equations are solved exactly and the static physical properties are obtained for almost the entire strongly mixed valent regime. The temperature dependence of the electronic specific heat, C(T), gamma (T)=C(T)/T, densities of states, Fermi level and valence are discussed for both one and two electrons per atom. The behaviour of gamma (T) is similar to that found experimentally.

A calculation of the temperature and f-level dependence of the static f-electron susceptibility of the periodic Anderson Hamiltonian (PAH) for the cases of one (N_t=1) and two (N_t=2) electrons per atom and in the strongly mixed valent regime is presented. Correlations are included beyond meanfield. Evidence for a tendency towards ferromagnetic order is found for some parameter values in the case N_t=1. For N_t=2, the susceptibility exhibits a peak at finite temperature, a feature typical of many mixed valent compounds, and this peak correlates with the appearance of a pseudo-gap in the f-electron density of states. The theory is correct at high temperature, where the known perturbative results are correctly reproduced.

The author extends to zincblende crystals and compounds with conduction d electrons the calculation of homopolar and heteropolar energy gaps using the plasma frequency formalism already employed for ionic rock-salt crystals. The calculated values of these gaps and the ionicity are in fair agreement with the values reported by earlier workers.

The authors have measured the equipotential distribution in modulation-doped GaAs-AlGaAs heterojunctions while observing the quantum Hall effect (QHE), at T=4.2K and 2.2K. They present equipotential maps at various applied magnetic fields and discuss the changes in the equipotential distribution in quantised Hall plateau regions, where the Fermi level moves between Landau levels and the magnetoresistance, rho _xx, approaches zero. The charge and current distributions within the specimens may be inferred from the equipotential patterns. The authors extend the observations of others on the internal impedance of QHE samples to include the case of interior contacts.

A dynamical theory for the Potts, model, recently introduced by the author, is applied to the two-dimensional, nearest-neighbour system. A decimation procedure is defined and, in the leading order of the approximations involved, the critical dynamical exponent is obtained for different numbers of Potts states.

In this work magnetisation and lattice parameter data obtained for aluminium and gallium substituted lithium ferrite (90% Fe) are presented. Some trends of the diamagnetic impurities distributions for the tetrahedral and octahedral sublattices are derived. The lattice parameter and the saturation magnetisation of the double substituted lithium ferrite are linear functions of the difference in the concentrations of gallium and aluminium.

A perturbation-type theory is presented which deals with the evolution, following an RF pulse. of the longitudinal and transverse ²D nuclear magnetisation of molecular groups undergoing thermally activated, random, hindered reorientations in the solid state. The reorientational mechanisms may be characterised as 'symmetric' or asymmetric' according as the jump probabilities P_ij(t) (that a deuteron will jump from site i to site j in a time t) are described by one time constant or by multiple time constants. The theory covers the computation of either case, for any assumed combination of allowed reorientations, fast or slow, and the circumstances are explored in which it is permissible to restrict the perturbation expansion to second-order terms in the perturbation.

The authors present a new approach for the calculation of multi-photon transition probabilities in solids which incorporates the relevant features both of the quantised electromagnetic field and of the electronic states in the crystal. The formalism yields an expression which allows transition probabilities between any two bands in the solid to be calculated in a systematic manner, involving only the unperturbed and perturbed electronic states expansion coefficients in terms of plane waves and the electromagnetic field parameters. As a simple illustration, the dressed bands approach is applied to a Kronig-Penney model crystal and the results are discussed and compared to previous calculations.

Infrared reflection spectra of the fluoperovskites RbCaF₃, CsCaF₃ and KZnF₃ have been measured in the range 50-4000 cm^-1 at several temperatures. A systematic study of the temperature dependence of the TO and LO frequencies, dampings, and oscillator strengths of the three polar phonon modes is reported. The ionic effective charges have been calculated from the TO-LO splittings. A slight increase of the static dielectric constant upon cooling indicates incipient ferroelectric character.