Table of contents

The thermal diffusivity and the electrical resistivity of LaB₆ have been measured at high temperatures from 1300 to 2000 K. An analysis of the data indicates that the Wiedemann-Franz law is not obeyed in this temperature range. The discrepancy arises because of the relatively high lattice thermal conductivity. The observed lattice conductivity is 3.5*10^-2 cal cm^-1 s^-1 K^-1 at 1300 K, which is in good agreement with the calculated value.

Assuming a continuous dependence of the criticality on the energy parameters, it is conjectured that the Ashkin-Teller model has in general two phase transitions. The two critical points coalesce into a single one when the two middle energies in the model are degenerate.

Absorption and magnetic circular dichroism spectra of single- crystal UO₂ show that all the readily observable transitions in the 13000-17000 cm^-1 range involve electronic systems with singlet ground states. The absorption peaks appear to be intrinsic to UO₂, and due to excitons rather than single-ion f to F transitions.

Second-rank tensor order parameters appear for liquid crystals and crystallographic transitions. The simplest model with a disordered high-temperature state has interactions invariant under cubic spin transformations. It is shown that for spin 1 this leads to the 3-state Potts model. It is suggested that this model is therefore relevant to the understanding of phase transitions with such an order parameter. A formalism for series expansions and a new proof of the Kramers-Wannier symmetry on the square lattice are presented. Pade approximants for the series expansions including a procedure explicitly utilizing the symmetry are discussed. The negative interaction 'orthogonal' model analogous to the Ising antiferromagnet is also discussed and shown to have a highly degenerate ground state. On the square lattice this is the degeneracy of Lieb's ice. Relationships to ferroelectric models and the three-colour problem are also discussed.

The critical and tricritical behaviour of an anisotropic compressible Ising model are analysed. The tricritical exponents depend upon the line along which the tricritical point is approached. Various scaling laws from the general scaling theory of tricritical points are examined in the context of the model and some discrepancies are pointed out. As a consequence, some of the general scaling relationships have to be modified.

The evaluation of the time-dependent transverse current correlation function in a dense liquid presents a very difficult many-body problem, but it is shown that by using intuitive physical arguments some progress can be made towards establishing a theory of this correlation function. The latter is presented in terms of a memory function which is itself expressed as a function of the interatomic potential, the radial distribution function and another quantity which describes the relative motion of two atoms in the liquid. The calculation may be carried through for a rigid-sphere fluid, and some physical insight is gained into the effect of the range of the interatomic forces on the time dependence of the memory function. From the results an expression for the shear viscosity of the liquid may be derived. When applied to a rigid-sphere fluid the formula of Longuet-Higgins and Pople is obtained, and it is pointed out that the theory should also be valid for a more realistic interatomic potential.

The dependence of drift velocity on electric field strength in gallium arsenide and indium phosphide is calculated using recent theoretical estimates of the intervalley coupling constants. Screened and unscreened electron-phonon interactions are considered. In gallium arsenide, the results are shown to be in acceptable agreement with experimental data, the agreement being somewhat better if the unscreened interaction is used. In indium phosphide, the theory predicts very strong intervalley scattering and although this leads to a smaller negative differential mobility than in gallium arsenide, a much higher peak to valley ratio is predicted.

Arsenic-antimony alloy single crystals have been grown at the minimum melting point composition (25.5 at%As) where the solidus and liquidus touch on the phase diagram. Measurements have been made between 1.5K and 300K of the twelve components that define the low-field magnetoresistivity tensor and of the orientation dependence of the tensor components rho ₁₁(B₁, B₂, 0), rho ₁₁(B₁, 0, B₃) and rho ₂₁(B₁, 0, B₃). A least-mean-squares fit to the data has been used to obtain the model parameters for a two band, multivalley, ellipsoidal Fermi surface. The alloy model parameters are compared and contrasted with those in arsenic and antimony themselves. Electrons are found to be sited in Fermi surface pockets of tilt -7 degrees and holes in pockets tilted at -34 degrees . The carrier density, somewhat larger than that in antimony, is almost independent of temperature. Carrier mobilities are much smaller than those in the parent elements. The alloy is semimetallic.

A cumulant expansion is used to calculate the transition temperature of Ising models with random-bond defects. For a concentration, x, of missing interactions in the simple-square Ising model the author finds -T_c^-1 dT_c/dx mod _x=0=1.329 compared with the mean-field value of one. If the interactions are independent random variable with a width delta J/J identical to epsilon , the result is -T_c^-1 dT_c/d epsilon ² mod _{epsilon =0}=0.312 compared with the mean-field results of zero. An approximation yields the specific heat in the critical regime as C approximately C₀/(1+x gamma ²C₀), where gamma is a constant and C₀ is the unperturbed specific heat at a renormalized temperature. Thus, the specific heat divergence is broadened over a temperature interval Delta T, with Delta T/T_c approximately x⁽¹ alpha )/, where alpha is the critical exponent for the specific heat, and a maximum value of order x^-1 is attained. Heuristic arguments show that this smoothing effect occurs if alpha >0.

The coherent potential approximation (CPA) has been generalized to describe spin waves in a dilute Heisenberg ferromagnet at T=0. The full T matrix of an isolated vacancy in an effective medium is evaluated and the self-energy is obtained selfconsistently. In order to project out the spurious degrees of freedom associated with the fictitious spins on the vacancy sites, a class of pseudopotentials are constructed. The response functions G(k, omega ) and density of states rho ( omega ) for two such pseudopotentials are evaluated in detail. The had core pseudopotential is found to yield the best CPA approximation although it fails near the critical percolation concentration of magnetic sites, as do all the effective medium theories in the face of large fluctuations. The spin-wave stiffness D is calculated and the magnetization and specific heat near T=0. The random phase approximation is used to find T_c, the transition temperature.

An approximation method for determining the response function of a system given the first few frequency moments is presented. The response is assumed to be well represented by poles in the second unphysical sheet of the complex cut frequency plane. Technically, such a description is achieved by first introducing a nonlinear transformation of the frequency to map both first and second sheets on to a single plane of a new variable. The moment series in the new variable is then represented by a Pade approximant. The technique is illustrated by application to a model of a diluted ferromagnet for which the first ten frequency moments of the zero- temperature response have been calculated for arbitrary wavevector and arbitrary concentration of nonmagnetic impurities. Aspects of the diluted ferromagnet that cannot be adequately treated in an effective-medium approach are discussed.

Some temperature-dependent properties of two-dimensional magnetic hamiltonians with uniaxial anisotropy are studied on the basis of the selfconsistently renormalized (SCR) spin-wave approximation. Due to the importance of anisotropy in two- dimensional systems, particular attention is paid to the kinematical consistency of the theory by considering multiple scattering due to anisotropy. In particular the properties of FeCl₂, a layer ferromagnet with large single-ion and exchange anisotropy, and K₂NiF₄, a layer antiferromagnet with small anisotropy have been studied. In both cases good agreement with experiments is found for temperature renormalization of small k spin-wave energies. Improved results with respect to spin-wave theory are obtained for the order parameter. The large k dependence in the temperature renormalization of spin-wave energies is predicted for antiferromagnets with medium and small anisotropy.

The extended Huckel LCAO method is used in a calculation of one- electron energy bands and wavefunctions of a two-dimensional layer of graphite. After adjustment of the calculated sigma - pi overlap to that obtained by Painter and Ellis (1970) in an ab initio calculation good agreement is obtained with experiment for the polarized carbon X-ray emission of graphite. It is shown that, in the experiments performed so far, complete polarization was not achieved. An estimate of the valence band as observed in X-ray photoelectron spectroscopy is also presented.

Measurements of the Faraday rotation and ellipticity at a microwave frequency of 33 GHz in samples of p-type tellurium are reported. Two different geometries are investigated. The transverse mobility, relaxation time and transport effective mass are determined with the magnetic induction B parallel to the trigonal c axis. The anisotropy of these parameters is deduced from data obtained with B perpendicular to c. Furthermore, the dependence of the rotation and ellipticity on sample thickness and on the lattice temperature was studied experimentally between 77K and 180K. From these results the temperature dependences of the mobility, the relaxation time, and of the effective mass and their anisotropy are derived. Possible explanations for the strong increase of the transport effective mass with temperature concerning the peculiarities of the valence-band structure of tellurium are discussed.