Table of contents

The nature of hydration around Li⁺ in two concentrations of LiCl in D₂O has been investigated by the methods of neutron diffraction and isotopic substitution. It is found that the hydration number varies with concentration, and that the angle of tilt between the Li-O axis and the plane of the water molecule, though substantial, is less than that expected if a lone pair orbital of the oxygen atom is directed towards the Li⁺ ion.

At atmospheric pressure N(CH₂CH₂)₃N undergoes a solid state structural transition at 351K. Single crystals of phase II (below 351K) have been grown by slow sublimation in a Lindemann capillary tube. The crystal structures have been determined at two temperatures: T₁=298K and T₂=110K. They confirm the P6₃/m space group of this phase. They also show a marked anisotropy in the molecular rigid-body libration at 298K. This anisotropy becomes smaller at low temperature. An explanation for the transition to a plastic phase is suggested in terms of an increase with temperature of the amplitude of that libration.

The 'compressibility' equation of state for the one-component plasma (and other systems that require a stabilising background) is derived by a diagrammatic approach.

The zero-temperature equations of state of UO₂ and CaF₂ have been computed from semi-relativistic LMTO calculations. The calculated lattice parameters are 1/2% above and 5% below the experimentally determined equilibria for UO₂ and CaF₂ respectively. The computed bulk moduli are 3.0*10¹² and 0.71*10¹² dyn cm^-2 and the band gap of UO₂ is found to be 5.35 eV.

The theory of the radiative tunnel transitions (RTT) of electrons between trapping centres in crystal lattice is applied to the case of hopping conduction (HC) in the strong electric field. This HC occurs by the successive downward spontaneous RTT of electrons (holes) between the localised states near the Fermi level. At each hop the excess energy is emitted as a long-wavelength photon. The numerical estimation of the relative contribution of the HC by RTT is made for the heavily doped compensated germanium.

It is proved that, for the infinite-range spin glass proposed by Sherrington and Kirkpatrick (1972), the logarithmic average of the ground state degeneracy (lng₀((J)))_J is given by the logarithm of the average ln(g₀((J)))_J, so that the zero temperature entropy S₀ is given by S₀/k_b=ln(g₀((J)))_J=0.19923 N from the known value of (g₀((J)))_J.

Compressible Ising systems do not have a second-order phase transition (no fixed points). Using a parquet diagrammatic method, the free energy of the system for non-zero ordering fields is calculated in an approximation that retains the leading fluctuation effects (to order epsilon =4-d). The first-order transition is seen to be fluctuation-induced and order-parameter-limited. The transition parameters are calculated numerically; fairly accurate analytical estimates are presented. The difference with earlier results of Bergmann and Halperin (1976) is pointed out, and application is made to the weakly first-order ferroelectric transition in BaTiO₃.

By means of neutron diffraction on single crystals the gamma and delta modification of NbN_x is studied using samples with approximately the same x=N/Nb approximately=0.85. For the ordered gamma -NbN_0.85 it was possible to refine a tetragonal distorted sodium chloride structure model in spite of the occurrence of twinning. The individual mean square displacements of the N and Nb atoms are compared with those of the disordered cubic delta -NbN_0.84 and the dynamical components from previous inelastic neutron scattering investigations. For the delta -NbN_0.84 single crystal only a small static distortion of the Nb and N sublattices is found. For gamma -NbN_0.85 large static contributions to the mean square displacements of the N atoms occur whereas the sublattice of the Nb atoms is nearly undistorted. The group theoretical relationship between the structures of the gamma and the delta phase of NbN_x is discussed.

Two possibilities of using differential gamma -ray diffractometry to investigate twinned crystals are described. The analysis of the rocking curves traced from a KH₂PO₄ sample in the low-temperature phase allows detection of two deformation processes in its domain structure. Information on the non-linear piezoelectric response of such a ferroelectric crystal is obtained.

Liquid mercury was measured at room temperature by time-of-flight neutron diffractometry on the electron LINAC. The presence of a subsidiary shoulder in the structure factor which was not observed in Vineyard's neutron diffraction study (1954) but which has been cited in recent X-ray diffraction studies is confirmed. Furthermore, a molecular dynamics calculation was made to obtain the radial distribution function, and it was compared with the one derived from the neutron diffraction experiment.

The phonon dispersion relations in FeBr₂ have been measured by inelastic neutron scattering and fitted to a static-displaced shell model. The results of the calculations emphasise the importance of static polarisation in this hexagonal layered material, but fail to shed light on the origin of the hexagonal-rhombohedral polytypes which exist in the Fe(Cl_xBr_1-x)₂ system.

The two-phonon critical scattering occurring near a structural phase transition is studied within the framework of a time-dependent Landau-Ginzburg model. It is established that the width of the critical low-frequency scattering appearing in the two-phonon spectrum (accessible to light-scattering experiments) and the width of the critical scattering in the one-phonon spectrum (accessible to neutron-scattering experiments) form a universal ratio, which is calculated to second order in epsilon =4-d. Implications for scattering experiments on structural phase transitions are discussed.

It is well known that the properties of scaling and universality exhibited by the polymer system have a very natural description in terms of the critical behaviour of an analogous magnetic system. This analogy is used to derive renormalisation-group equations directly for the polymer system. Solving these renormalisation-group equations a compact parametric description is obtained of the crossover from the Wilson-Fisher to gaussian fixed point displayed by the mean square size of a polymer (R²) and the second A₂ and third A₃ virial coefficients correct to O( epsilon ²) in d=4- epsilon spatial dimensions.

Using molecular dynamics techniques, properties of the supercooled amorphous state have been studied for the soft-core model. By examining the temperature dependence of the pair distribution function, velocity autocorrelation function and self-diffusion constant for each quenched system, a glass transition is predicted separating supercooled liquid from a rigid amorphous solid. Below the glass transition temperature the structures are less temperature dependent than above the temperature. It is noted that no significant change on the temperature dependence, has been observed in the previous results of thermodynamic properties. The obtained pair distribution functions in the glassy state are successfully compared with those of some metallic glasses.

Coupling of the soft mode to a thermal diffusion mode is investigated near the structural phase transition on the basis of the Mori formalism (1965) applied to the tunnelling model. These modes couple linearly in the ordered phase through the order parameter, which produces a narrow central peak in the structure factor. It is also shown that the ratio of integrated intensities of the central peak to the soft mode in the ordered phase satisfies the generalised Landau-Placzek relation. These modes in the disordered phase do not couple linearly, so the mode-mode coupling theory is used in order to study the non-linear coupling which produces a logarithmic singularity in the response function to given an extremely narrow central peak. The numerical value of the coupling constant is estimated from experimental values and is shown to be sufficiently large, at least in the ordered phase, to observe the central peak due to the thermal diffusion mode. When the soft mode is one-dimensionally anisotropic, a pole-like singularity is found in place of the logarithmic one.

When orthogonalising the localised basis functions in crystals with Lowdin's symmetrical method (1956), the inverse of the metric matrix plays a crucial role. A practical method of inverting the general metric matrices of crystals is evaluated. The procedure is based on the cluster method, introduced for spherically symmetric states by Lundqvist and Froman (1950), and it exploits completely the rotational symmetry of the crystal. The general equations for solving the elements of the inverse metric matrix are derived, and explicit coefficients are given for s and p states. Calculations have been performed for some alkali halides and magnesium oxide, and numerical results for sodium fluoride are given and considered in some detail. The series expansion approximation for the inverse metric matrix elements is found to be reasonable for alkali halides but not at all suitable for magnesium oxide. However, 'exact' values for inverse metric matrix elements should be used in all accurate theoretical calculations.

An approximate contraction is defined which enables the perturbation series for the intermediate valence model to be summed to all orders. Two forms of Coulomb correlation, U, are considered and in both cases it is demonstrated that the Fermi level at absolute zero cannot lie in the gap of the pseudo-particle energy spectrum. A general expression is derived for the ground state energy. Finally, the validity of the method is examined when the number of lattice sites, N, tends to infinity.

A numerical Monte Carlo technique is used to calculate the density of states and the conductivity of model binary alloys. The strength of the method is its ability to accurately account for local atomic configurations while avoiding explicit many-atom-cluster calculations. Another important feature of the method is its ability to describe Anderson localisation. Results for densities of states and conductivities are presented for various model systems and compared with the corresponding results of an effective-medium theory. A new result of the theory is the occurrence of multiple mobility edges separating regions of Anderson localised states inside the minority band.

The Scher-Lax model (1973) describing AC conductivity in terms of a continuous-time random walk on a lattice is generalised to cases where the hopping in the random system is governed by transition rates which do not decay exponentially in time and which thus correspond to a non-Markoffian process. This requires a proper treatment of the waiting-time distribution for the first observed hop of a carrier on the lattice. The waiting-time distributions for both the first observed hop and for time intervals between consecutive hops are defined in terms of configuration averages of the random walk on the random medium. The treatment includes explicitly the effect of an important disorder-induced space-time correlation, which is found to be entirely responsible for the frequency dependence of the conductivity, sigma ( omega ). The closed-form expression for sigma ( omega ) may account for the observed frequency dependence in disordered systems.

The magnetoconcentration effect, its main subeffects and applications are studied with regard to semiconductor doping for the various parameters: electric and magnetic fields; bulk and surface recombination rates, etc. In comparison with the well known intrinsic case, important consequences are associated with the effect in slightly p-doped semiconductors. It is shown that during the magnetoconcentration effect, doping is responsible for anomalous negative or positive magnetoresistance as well as for the Hall voltage increase, reduction or even inversion. The effect is generally a maximum in p-doped semiconductors; the optimum doping depends on the ratio of the electron and hole mobilities and on the magnetic induction. The experimental data on n- and p-type germanium with resistivity from 10^-2 to 0.7 Omega are in good agreement with the computed results.

Exact expressions for the free energy are derived for some regular 2D Ising models with frustrated squares. The existence of the phase transition depends on the mutual disposition of the frustrated squares. The conditions for the appearance of the phase transition in such systems are discussed. It is shown that the calculation of the partition function of the random 2D Ising model is reduced to the calculation of the determinant.

A generalisation of the drone-fermion representation is presented for spin values S satisfying (2S+1)=2", where n is any integer greater than or equal to unity. The case of n=1 is the usual drone-fermion representation for S=¹/₂, whilst the next two cases of n=2 and n=3 lead to representations for systems with S=³/₂, and S=⁷/₂ respectively. The generalisation has a number of advantages for the field-theoretical treatment of magnetic systems with these spin values, and this is illustrated by some perturbation calculations applied to Heisenberg ferromagnets.

Measurements of ODMR in the excited states of Cr³⁺ ions in cubic and tetragonal sites in MgO have been used to elucidate the nature of the vibronic sidebands. A comparison of the experimental spectra for zero-phonon line and vibronic sideband with the theoretically calculated selection rules shows that interaction with T_2u odd-parity modes of vibration is the dominant interaction giving rise to the vibronic sidebands.

Optical absorption and magnetic circular dichroism (MCD) spectra of KCl:Ga⁺ in the region of the A and B bands have been measured over the temperature range 4.5-210K. Moments of the lineshape of the resolved A and B bands have been determined up to the fourth moment for absorption and up to the third moment for MCD. The lineshape of both the absorption and MCD spectra in the A and B region have been calculated theoretically using a model that includes spin-orbit coupling and the dynamical Jahn-Teller coupling to modes of A_1g, E_g, and T_2g symmetry. Because of difficulties connected with the determination of the first and third MCD moments for the A band, the coupling constants could not be determined completely from the experimental data. Calculated absorption spectra are in quite reasonable agreement with experiment over a range of temperatures. The lineshape of the MCD spectrum agrees less well with experiment and this emphasises the greater sensitivity of the MCD spectrum to fine details of the theoretical model employed.

The absorption spectrum of 70K X-irradiated SrF₂:Mn is measured. It shows two main bands at 325 and 425 nm. From several option bleaching and thermal annealing experiments it is found that the 325 nm band is due to V_k-centres and the 425 nm band to Mn⁺ ions in a Sr²⁺ substitutional position. The X-ray excited emission and the TL of 70K X-irradiated samples are also measured. An emission band found at 500 nm is associated with the ⁴T_1g(⁴G) to ⁶A_1g(⁶S) transition of Mn²⁺ ions. The decay of the 500 nm emission under X-ray excitation is studied as a function of temperature. The lifetime of the ⁴T_1g(⁶G) level is obtained as well as the different contributions to the decay probability. The results are in agreement with those of Mn in CaF₂ and CdF₂.

Presents a study of the influence of correlations on the electronic optical excitations of transition metal surfaces. A Hubbard model in the band limit is solved by a second-order perturbation method previously developed for bulk metals. Excitation spectra of Mo(100) and Ni(100), (110) and (111) are shown to differ strongly from their respective one-electron local densities of states. This explains some features of experimental UV photoemission spectra of Mo.