Table of contents

The long-time behaviour of classical diffusion of a particle in a randomly interrupted medium is studied. The probability of finding a particle at position x=0 in d-dimensional space if initially it was at x=0 is shown to decay exponentially as P(t)-P(t= infinity ) approximately exp(-ct^d(d+2)/) below the percolation threshold due to localisation.

The phonon lifetime due to the phonon-assisted Auger recombination in electron-hole droplets is calculated and from that the attenuation coefficient is deduced. Numerical estimates are made for electron-hole droplets in Ge. The lifetime of the phonon is estimated to be of the order of 10^-3s and the attenuation coefficient of the order of 10^-4 cm^-1.

It is demonstrated that the variational wavefunctions of shallow acceptors obtained by the procedure closely related to that of Baldereschi and Lipari reconcile the properties of the formerly known acceptor wavefunctions: the variational functions, possessing a Bohr radius of 40 AA, and the asymptotic wavefunctions, possessing a Bohr radius of 80 AA. The wavefunctions that are discussed have an exponential decay constant equal to the former value at small distances from the impurity and equal to the latter one at sufficiently large separations. The structure of the wavefunctions leaves the former model of the piezoresistance effect in the hop conduction in Ge, which involves the variational wavefunctions of the Schechter-Kohn type, fully operational.

An effective-medium approximation is proposed for thermal phase transitions. For quenched bond disorder in the Potts model, the exact critical line is obtained when s=1; for s=2 (Ising), some exact results in the dilute limit and the correct behaviour for T_c(p) near p_c are recovered. The critical concentrations are in good agreement with the known values, in both two and three dimensions. For s>4 (first-order transition) the phase diagram shows a two-phase region.

The neutron first-order difference method has been applied to a 4.49 molal aqueous solution of CaCl₂. Isotopic changes were made in both the Ca²⁺ ion and the Cl^- ion so that a complete picture of ionic hydration could be obtained. Both ions coordinate water in a non-dipolar configuration with ion-oxygen distances close to those predicted by gas-phase quantum molecular calculations. The measured hydration numbers for cations and anions (5.5+or-0.3 and 5.8+or-0.3 respectively) imply substantial sharing of water molecules between the ions.

It is shown that to lowest order in an expansion in the ratio of potential energy to incident kinetic energy, the classical motion of a particle in a periodic potential is governed by the so-called string potential. Corrections to orbits calculated using such a potential are explicitly obtained in terms of these orbits.

The electronic structure of the transition metal dichalcogenide layer compounds is studied using hybridised orbitals appropriate to the transition metal atom coordination. Non-bonding orbitals on the transition metal atoms give the conduction electron bands which are responsible for the charge-density-wave phase transitions in the VB compounds, and the band structure of 1T- and 2H-TaS₂ is found using tight binding. The phase transitions are studied by a tight-binding calculation of the conduction electron contribution to the dynamical matrix, Phi ^el. In 1T-TaS₂ there is a Kohn anomaly in Phi ^el close to the displacement wavevector of the incommensurate phase, sufficiently large to make the ideal structure unstable. The ideal 2H structure is also unstable, though there is only a weak Kohn anomaly. As Phi ^el is fairly temperature independent, the stability of the high-temperature phase must be due to phonon entropy, and this is studied using a mean-field theory of anharmonic effects. The low-temperature commensurate phases are stabilised by chemical bonding effects.

Several new ideas are presented for the interpretation of the Compton profiles of tetrahedrally bonded semiconductors. It is shown that the zero values of the Fourier transformed Comtpon profile (FTCP) can be predicted analytically by a modified free-electron model with no free parameters. A simple LCAO model demonstrates the critical influence of the orthogonality of the ansatz functions. It is concluded that the zero values of the FTCP are mainly a property of the Bravais lattice and the number of occupied bands.

The binding energies of the lowest excited S and P states of the Wannier exciton and Wannier-exciton-ionised-donor complex in crystalline CdS are calculated using the best effective electron-hole interaction potentials available. For the exciton, reasonably good quantitative agreement with experiment is achieved. For the complex, some states of S symmetry are found which do not have any counterpart in the experimental results. Possible reasons for the discrepancy are pointed out. The binding energies of the P states of the complex are calculated for the first time, and a corresponding experimental investigation is suggested.

Z₂ centres are produced in KCl:Sr by various methods and their optically excited triplet state is investigated by means of ESR measurements. In general the ESR spectra are very complicated and contain a large number of lines. Analysis is only made possible by varying the impurity and F-centre concentrations and by variation of the optical excitation conditions. Five different types of triplet centres are found and interpreted as Z₂ centres. Three types have triplet lifetimes of about 20 ms and absorptions in the usual Z₂ absorption region >or=1.8 eV. The two others possess triplet lifetimes of 100 ms and 1.6 s, not previously reported. They exhibit additional absorptions at low energies (<or=1.5 eV). All the types of Z₂ centres have large fine-structure parameters ( mod D mod >0.3 cm^-1) and none of them show simple axial symmetry. At very low temperatures (1.6K) a remarkable optical electron-spin polarisation can be detected. It is used for the determination of the absolute sign of the axial fine structure parameter of two Z₂ centre types.

Approximate wavefunctions and energies of the ground state of the shallow acceptor in Ge were obtained by solving the effective mass equation possessing terms proportional to the deformation tensor components. The variational approach was used involving trial wavefunctions similar to those of D Schechter, but possessing transformation properties required by the symmetry of the uniaxially deformed crystal. Results were obtained for the stresses X in the (100) directions, varying from -600 MPa to +600 MPa. At X to 0, where the energies of the impurity and the band states are expressible through the deformation potential constants (respectively b' and b), it is found that the value of b'/b is 0.55 and for sufficiently large X, b'/b to 1, in agreement with experiments. The calculated energies were further used for finding the solutions of the effective mass equation for large distances from the impurity nucleus. The solutions have two components with different spatial extent and anisotropies, and they are traceable to the light and heavy hole bands of Ge. Their behaviour with stress explains some of the observed features of the hopping piezoresistance in p-type Ge.

A real-space rescaling method is applied to the mixed, spin-¹/₂, Ising ferromagnet. Both bond and site disorder are considered where, respectively, bonds J_A, J_B or sites A, B occur with probabilities p, 1-p. For the bond-disordered case, critical curves are obtained for the square lattice for a range of alpha identical to J_B/J_A. Slopes at p=0,1 are in very good agreement with exact results previously obtained and T_c(p-¹/₂) agrees to within a few per cent with an exact result obtained by Fisch. For the more realistic site-disordered problem only the case where bond strengths are related by tanh J_AAtanh J_BB=tanh² J_AB is considered. Critical curves are plotted for various alpha for the square and triangular lattices. The results agree well with exact limiting slopes available for the square lattice. Thermal, percolation and crossover exponents are also calculated for both the site- and bond-disordered cases.

The theory of the inelastic scattering of light by semiconductors with the emission of one phonon in the final state is developed. The formalism takes into account scattering from both single-particle states and collective modes. Analysis of the problem entails the calculation of the three-particle correlation function. The equation for this quantity is derived and solved in an approximation consistent with the Hartree-Fock and random phase approximation. The theory is applied to one-dimensional polyene chains. The non-interacting resonant scattering amplitude is shown to possess a Van Hove-like structure which is washed out when interactions are taken into account. In fact, the scattering is dominated by collective or excitonic modes.

The polarised Raman spectra of CdI₂(Fe²⁺):2, 3, 5 and 10 at% have been measured over the range 0 to 700 cm^-1. Spectral features due to first-order scattering from phonons and Fe²⁺ electronic excitations have been analysed and assigned to symmetry species. All expected transitions are identified and the results are in excellent agreement with ligand-field theory. Resonance enhancement of the electronic spectrum is observed as the wavelength of the Ar* ion laser excitation approaches the metal-ligand charge transfer absorption near 4500 AA.

Low-temperature optical absorption on the zero-phonon lines and stress-induced linear dichroism on the broads bands for V³⁺, Cr³⁺ and Co³⁺ ions in corundum showed that the uniaxial stress induces a local deformation in the site of the doping ion different from the deformation for the whole crystal. Detailed examination of this local deformation is carried out and shows the importance of an odd deformation. Diagrams are proposed describing the local deformations epsilon _xz* and epsilon _xx* when stresses sigma _xx and sigma _xz respectively are applied.

Stress-induced linear dichroism measurements have been carried out at low temperature on the broad band of the optical transitions ³A₂(³T₁) to ³T₂ of V³⁺- alpha -Al₂O₃ and ⁴A₂ to ⁴T₂ of Cr³⁺- alpha -Al₂O₃. The results are analysed together with the stress experiments on the zero-phonon lines in order to deduce which modes are responsible for the Jahn-Teller effect. It is shown that the active mode is a doubly degenerate E mode mixing of E trigonal and E tetragonal modes originating from the cubic T_2g and E_g modes respectively. The coupling to the E trigonal mode is shown to be stronger. Qualitative analysis of the Jahn-Teller effect in the fundamental ³T₁ level is also given.

Single crystals were grown by the method of chemical vapour transport at 1150 degrees C. The fundamental spectroscopic properties are determined from absorption, photoluminescence and excitation spectra as well as lifetime measurements. Strong luminescence of the Nd³⁺ transitions ⁴F_3/2 to ⁴I_{9/2,11/2,13/2} has been observed in the three materials when pumping Nd³⁺ directly. Luminescent lifetimes are 45 mu s in the alpha -phase, 60 mu s in the beta -phase and 65 mu s in the delta -phase. Non-radiative energy transfer of the band excitation into the 4f shell has been established in beta -La₂S₃, and delta -Y₂S₃ at 300K. The direct and indirect bandgaps are 1.65 (0.94) eV, 2.58 (1.38) eV, and 2.53 (1.63) eV for alpha -, beta -, and delta -type, respectively.