Table of contents

It is shown that tetragonal spectra arising from distorted sites in cubic crystals do not necessarily originate at sites having tetragonal distortions.

The number of solutions of the equations of Thouless et al. (1977) is obtained as a function of temperature. The density of solutions with a given free energy is calculated for free energies greater than a (temperature-dependent) critical value.

Single-crystal X-ray diffraction data were collected and interpreted for the plastic phase of 2-adamantanone at 293K. The unit cell is face-centred cubic with a=9.524(4) AA, space group Fm3m. Assuming a rigid molecular skeleton, two types of orientational disorder were investigated: isotropic rotation of the molecules about their mass centre and hindered reorientations between equally weighted orientations. For the second model, which was the better one, the authors find an agreement observed and calculated structure factors (residual reliability factor R_w=12.5%) for a molecular packing in which the C=O bond is aligned along one of the six fourfold axes of the crystal.

The authors have studied the approach towards classical behaviour of a dynamical system which exhibits strong quantum effects at low temperature. By combining nuclear magnetic relaxation and inelastic neutron scattering data, the rate of thermally activated methyl-group reorientation is measured from 10 to 65K for the 4-methyl group of MDBP (4-methyl-2,6-ditertiarybutylphenol). At low temperatures reorientation occurs by thermally assisted quantum tunnelling processes. The reorientation rate converges towards the predictions of classical theory with increasing temperature, but still deviates significantly at 65K. It appears that the classical theory may be used without important errors only at temperatures for which kT exceeds the methyl torsion splitting. In this high-temperature range a simple classical calculation of the reorientation rate is within a factor of 2 or 3 of the measured value.

The Jahn-Teller Mn³⁺ ions in Al₂O₃ have been studied by phonon spectroscopy using superconducting tunnel junctions (80 to 700 GHz) and by thermal conductivity measurements (50 mK-150K). In both cases, uniaxial stress has been used as an external parameter and the effect of the orientation of the stress has been investigated in the phonon spectroscopy experiment. The results are compared with the other data available on this system. From the analysis of the results from both techniques, a coupling constant V_Eb=40000+or-16000 cm^-1 is determined.

A theoretical analysis of experimental data obtained recently by Raman and tunnel-junction phonon spectroscopy experiments on the Mn³⁺:Al₂O₃ system is presented. The Jahn-Teller model is re-examined and extended to include the effects of uniaxial stress. The model is shown to give a satisfactory explanation of all the experimental data available on this system and from the computed fit it is concluded that the ion-lattice coupling constant V_Eb=44500+or-12500 cm^-1. The results obtained for Mn³⁺ are then compared with the values for the parameters deduced previously for the isoelectronic Cr²⁺ ion in the same host. Mn³⁺ appears to experience a much smaller trigonal field than Cr²⁺ and the implications of this result in relation to other experiments are discussed in detail.

The virial theorem of an arbitrarily inhomogeneous electron gas together with the minimum condition for the ground state is formulated and, as a special case, a finite electron gas with constant background density up to the boundary is considered. In this case the Budd-Vannimenus condition is rederived and generalised. For the homogeneous electron gas the known virial theorem and the minimum condition are reproduced. Conditions are given for the additional terms describing the full response of an electron gas to an impurity (positive point charge with additional neutralising electrons). For comparison, the virial theorem for molecules and solids with fixed or mobile nuclei and within a finite for infinite volume are considered.

The rate of generation of a free electron and a trapped hole due to the Coulomb interaction between charge carriers of two Frenkel excitons (one free and one trapped) is derived for molecular crystals by time dependent perturbation theory. Electron-lattice and spin-orbit interactions are neglected. The theory is finally applied to benzophenone single crystals where a transition rate approximately 10⁹ cm^-3 s^-1 is obtained.

The mean spherical model is solved for two-component plasmas-fully ionised systems of two species of ions in a uniform neutralising background of electrons. The ion-ion potential is the sum of a bare Coulomb part and a hard-core part. The authors obtain the direct correlation functions C_ij(r) as polynomials in r and give the general solution (ions with different hard cores) up to a set of algebraic equations in the polynomial coefficients: these equations are then solved explicitly for the case of equal hard cores. For the particular case of a hydrogen-helium mixture the excess energy, the excess energy of mixing and the excess energy in a 'one-fluid model' for the two-component plasma are given for several values of coupling parameter and helium concentration: the comparison with Monte Carlo and hypernetted chain equation results is quite satisfactory in spite of the equal radii approximation. Some structure factors are also plotted for an H⁺-He²⁺ mixture.

A self-consistent procedure for interpolating defect parameters from perfect lattice tight-binding Slater-Koster parameters is applied to a 17 atom silicon cluster. Deep-level states associated with the neutral lattice vacancy, and charged states of some deep donors in silicon, are studied where meaningful quantitative results are established for both energy levels and particularly the associated lattice relaxation. The model is finally applied to study the amphoteric Au centre, where it is concluded from structural bonding considerations that a lattice reconstruction about the centre is responsible for the acceptor behaviour of the defect. It is then suggested that donor behaviour is associated with a deep level relating to an s orbital of the chemical defect itself.

Thermodynamic concepts relating to carrier capture and emission processes are reviewed and revised for interactions at deep-level defects where lattice (Jahn-Teller) interactions are important. Criteria for the applicability of concepts like atomic degeneracy ratios, which are used to relating emission and capture rates, are established. Mechanisms for capture of both electrons and holes at the Au defect and some other centres which are similarly bonded are discussed. It is suggested that the mechanism of electron capture at Au, Pt, Pd, Rh and A centre defects is a smooth relaxation process akin to multiphonon tunnelling emission, possibly involving motion of the chemical impurity, and giving an 'energy gap' dependence for the capture cross section on the thermal ionisation energy. Hole capture involves a localisation of the hole on the reconstructed bonds adjacent to the chemical defect prior to recombination with the donor electron.

The authors report on susceptibility and magnetisation measurements of amorphous manganese aluminosilicate and demonstrate that they can be considered as insulating spin glasses with large antiferromagnetic interactions. In particular, the cusp of chi (T) at T_f is easily rounded under weak static magnetic fields. The in-field magnetisation curves for H<5 kOe and the field and time dependence of the remanent magnetisation have a similar behaviour to classical metallic spin glass alloys. The spin freezing temperature T_f depends weakly on the frequency used in susceptibility measurements and this cannot be understood on the basis of the small magnetic particle model.

A scaling description of dilute easy-axis anisotropic magnets near the percolation threshold is derived. The dependence of inverse correlation lengths on temperature, concentration and anisotropy is represented in terms of two-variable scaling functions.

The author treats critical behaviour in dilute anisotropic magnets near the percolation threshold. The inverse correlation lengths and transition temperature are discussed, for comparison with experimental results, by using simple arguments to obtain the main properties of the scaling functions occurring in a representation, derived previously, for such systems. Anisotropy-induced crossover and percolation-thermal crossover are included.

The time evolution of a two-level spin system for thermal equilibrium towards the saturated state (saturation transient) is experimentally investigated in paramagnetic samples of dilute ruby (Cr³⁺:Al₂O₃). The authors show that near an inhomogeneously broadened resonance line the transient response to a step-modulated excitation is characterised by a non-exponential shape of the time-dependent susceptibility chi (t). Moreover they report experimental evidence that the absorption and the dispersion parts of chi (t) follow dissimilar time evolutions during the saturation transient. The experimental results are compared with the transient behaviours expected on the basis of two different models of an inhomogeneous system; the authors find that a spin packet picture is suitable to account for almost all the experimental data.

The power narrowing of the phase curves of the second harmonic (SH) wave radiated by a resonant spin system is experimentally investigated in a dilute DPPH sample. The experimental results are compared with the predictions of two different theories of the SH emission by saturated spin systems. The authors show that, as long as the saturation is achieved by means of narrow pulses of intense radiation, the observed power narrowing of the phase curves is to be ascribed to the spin decoupling effect rather than to the variations of the temperature T_SS of the dipolar energy reservoir.

It is shown how to extend the Hanke-Pick-Sham formulation (1971) of the inversion of the dielectric matrix so that no Brillouin zone integrations are required. This leaves a matrix inversion suitable for the recursion method.

Infrared reflectivity measurements are performed with a scanning interferometer on a single crystal over a wide range of temperature (300-1350K) especially in the cubic paraelectric phase of barium titanate (T_c=395K). The temperature dependence of TO and LO frequencies, dampings and TO oscillator strengths is reported. An overdamped soft mode, which follows a Curie-Weiss law over 800 degrees , is evidenced. A deviation from this law occurs over a hundred degrees above the tetragonal-cubic transition. The discrepancy of the value of dielectric constant obtained from optical mode frequencies and that obtained by direct dielectric measurements is discussed in terms of the possibility of a disorder which would appear progressively on cooling, in the cubic phase, and which complicates the displacive-type mechanism.

A theoretical study of impurity-induced first-order Raman scattering has been reported for zincblende-type crystals using Green function techniques. The perturbation model parameters obtained from the analysis of localised and gap modes have been incorporated to compute the Raman scattering structure for mixed indium pnictides in the low-impurity concentration limit. The calculated results correspond very well with the existing experimental data of Carles et al. (1978).

The order of kinetics of thermoluminescence of the most prominent glow peak of a single crystal of pure LiCl is investigated by the isothermal decay method. The order of kinetics is found to be 1.25+or-0.05.

A detailed low-energy electron diffraction analysis of a clean Fe(110) surface is described. The experimental data base consists of intensity-versus-energy curves (spectra) at 5 directions of incidence with a total of 34 spectra at energies up to 210 eV. A statistical analysis carried out with the reliability factor (r-factor) of Zanazzi and Jona (1977) gave a first interlayer spacing d₁₂=2.04+or-0.04 AA (95% confidence interval, the bulk value is 2.03 AA), and an (energy-independent) inner potential, V₀=11.5+or-0.4 eV, with an overall r-factor of 0.10. The effects of using an approximate procedure to vary V₀, a rigid translation along the energy axis, are compared with exact calculations.

Scaling theory is derived for the ordinary, extraordinary and surface transitions in percolation processes at a surface and 'special plane'. The scaling theory is supplemented by the results of the real space renormalisation group for square and cubic lattices. In addition it is shown that the single cell RSRG is consistent with a crossover exponent phi =1- nu for the special plane problem (for all sizes of cell).