Table of contents

An Ising model is defined on a simple quadratic lattice which has the usual nearest neighbour pair potential terms (-J₂ sigma _k sigma _l) and also triplet potential terms (-J₃ sigma _k sigma _j sigma _l) coupling the spins over the elementary triangular mesh cycles formed by connecting half of the next nearest neighbour sites, such that when J₂=0 the model reduces to a triangular lattice with only the triplet potentials present. It is shown that the well known self dual property for the case J₂ not=0, J₃=0 also holds for the case J₂=0, J₃ not=0, thereby yielding the likely result that the transition point for both of these cases is given by exp(-2J_2,3/kT)= square root 2-1.

Calculations of the activation energy for xenon diffusion in caesium iodide show that the gas does not diffuse as an interstitial but migrates in association with mobile vacancy pairs. Results obtained assuming this mechanism agree well with measured activation energies and explain the observation that the activation energies for gas release are very similar for Ar, Kr and Xe diffusion in several different materials.

The susceptibility, neutron diffraction spectra and specific heat have been measured in cobaltous oxide- and ferric oxide-phosphorus pentoxide glasses. Both glasses showed antiferromagnetic interactions but the cobalt glass showed no evidence of an antiferromagnetic transition.

The authors examine the theory of the effective long range interaction between two closed shell atoms in a dense liquid. An approximate theory is developed in which the effective van der Waals constant A_eff, relative to that in free space, say A, is expressed in terms of the three-atom correlation function g₃ in the liquid. Results are worked out using a Kirkwood form for g₃. It appears from their work that the main dependence is on the fluid density.

A method due to Nutkins and Ledbetter is used to calculate the Debye temperature of alkali halides. For these crystals, the weighting coefficients for the three principal cubic directions are found to differ from those for metals. Applicability of the method for obtaining (³ Sigma _i=1 v^-n) is also examined. The weighting coefficients for the (110) and (111) directions are found to depend on n.

Averaged LEED spectra can be fitted with good accuracy by a curve of kinematic form. However, theoretical arguments show that a true kinematic average is impossible. The paradox is resolved by a new theory which shows that averages have a quasi-kinematic form with parameters different from those of the true kinematic theory. Some of the new parameters can be simply related to old ones, but others involve complicated corrections. Finally second order averaging schemes are proposed whereby more information can be extracted from experiments.

It is shown that the Mott expression for the electron-phonon interaction is more rigorous than is apparent in its original derivation. An alternative expression, due originally to Wilson and corrected recently by Mitra, is shown to be already contained in the Mott result.

It is shown that in problems involving electron states in finite crystals it is necessary to consider the solutions at band edges more carefully than is usually done. A new form is given for the non-Floquet type solution at a band edge in a one dimensional crystal; it is the derivative in k space of a Floquet solution. Examples of this solution are given for the free-electron model, the Kronig-Penney delta well model, and the tight binding model.

It is shown that there is a QSE solution of the simple model exactly at a band edge if and only if the one Floquet solution at that band edge vanishes at the surface. This condition is applied to the free electron model, the nearly free electron model, the Kronig-Penney delta well model, and the tight binding model. The solutions near a band edge are also studied, and found to have simple approximate forms, namely u₀(x) cos pi nx/L or u₀(x) sin pi nx/L according as there is or is not a solution exactly at the band edge. The importance of the solutions at and near the band edges for spectroscopic studies of the QSE is pointed out.

The electron-electron screened interaction near the metal-semiconductor junction is calculated analytically by the introduction of model bulk dielectric functions which contain all of the essential energy and wavelength dependent features of the real dielectric functions of the metal and semiconductor. The poles of the interaction give the dispersion relations for the surface plasmon excitations at the junction and these are studied for various parameters of the two bulk media. It is shown that there are two possible plasmon modes characteristic of bimetal and metal-classical dielectric interfaces. Also, the role of surface plasmons in Schottky barriers is discussed.

The coherent potential approximation has been extended to provide a theory of the magnetic excitations in substitutionally disordered quasi-binary antiferromagnetic alloys. It is shown how the self consistent equations for a two sublattice antiferromagnet may be reduced to a scalar form with the aid of the single site approximation and time reversal symmetry. The theory is applied to the Mn_1-cCo_cF₂ and KMn_1-cCo_cF₃ systems and numerical results obtained for comparison with recent neutron scattering experiments. The theory correctly predicts the two-peaked spectral function observed experimentally at each wavevector, and gives a good description of the dispersion relations of the two bands, and of the widths, relative intensities and lineshapes of the excitations.

A spin hamiltonian formalism is used to develop the theory of spin-lattice relaxation by the direct process in a system S=¹/₂, I=¹/₂ with hyperfine coupling in cubic symmetry. It is shown that when J is a good quantum number the probabilities for the direct ( mod Delta m mod =1, Delta M=0) as well as the 'skew' ( mod Delta (m+M) mod =0,2) transitions can be expressed for all orientations of the magnetic field as a function of three parameters. A new experimental method is devised for measuring the 'skew' transition probabilities, effective only when high fields and low temperatures are used. The results of such measurements are presented for Tm²⁺ ions in CaF₂ and SrF₂.

The theory of two-photon absorption with provision for exciton effects is built on the basis of general principles without using any model of electronic states of the crystal. Electron-phonon interaction is neglected. The splitting of exciton levels into levels of transverse and longitudinal excitons is taken into account. The polarization dependence of two-photon absorption coefficient of allowed two-photon dipole transitions from the ground state of crystal for all 32 crystallographic classes is calculated. The results obtained are compared with the experimental data available.

(For pt. I see abstr. A16442 of 1972.) It is verified, using a Green function formulation of lineshape theory, that dynamic lattice splittings of degenerate electronic levels cannot occur.

The cathodoluminescence emission spectrum of Yb³⁺ in cadmium sulphide at 10 K has been studied before and after irradiation with electrons capable of producing atomic displacements. The spectrum has been assigned to emission from Yb³⁺ on a weakly distorted tetrahedral site such as it would be if the Yb³⁺ were replacing a cadmium ion. Multiplets with the main groups of lines are believed to result from the influence of sulphur ions, possibly at nearby interstitial sites. Electron radiation damage above the threshold energy for sulphur displacement, and with the sample at a temperature ( approximately 320 K) at which the defects are sufficiently mobile, causes a redistribution of sulphur amongst the interstitial sites which changes the relative intensities of the rare earth emission lines.