Table of contents

It is shown that linear spin wave theory provides for the nearly isotropic antiferromagnet in two and three dimensions an excellent estimate of the zero point spin reduction Delta . The leading corrections to linear spin wave theory for Delta are shown to vanish for vanishing anisotropy alpha like alpha ^1/2 and alpha ln alpha in two and three dimensions respectively.

The technique of electron energy loss has been applied to an investigation of the theoretical predictions of Ashley and Ritchie (1970) on the double plasmon excitation process. Electron energy loss spectra of evaporated silicon and aluminium films have been recorded at an incident electron energy of 60 keV and these spectra have been corrected for plural scattering effects. After this correction, no spectra exhibited a prominent loss in the region 31 to 33 eV, where the double plasmon loss would be expected. It is concluded that for amorphous silicon and polycrystalline aluminium films, the cross section for the double plasmon excitation is less than 0.02 of the cross section for the single plasmon excitation process.

The crystalline potential of a semiconductor is described in the muffin tin potential approximation as a complex lattice of disjoint potential spheres. These consist of atomic potential spheres in the regular lattice sites and hollow spheres, of potential higher than the muffin tin zero, in an interstitial sublattice. The band structure is calculated for carbon in diamond and compared with results of known procedures.

The basic equations of the itinerant oscillator model of liquids proposed by Sears (1965), and modified by Nakahara and Takahashi (1966), and by Damle et al. (1968), are re-examined from the point of view of Newton's third principle and of the second fluctuation-dissipation theorem. This theorem is rederived for any number of coupled harmonic oscillators in the presence of random forces. As a result of this derivation, it is shown that a greater number of parameters must be introduced in the model than generally assumed; this outweighs somewhat its attractive features which were linked to its physical simplicity. However, the present authors have obtained in two cases a good agreement between the values deduced for the various parameters by fitting the computed velocity autocorrelation function with the data of Rahman (1964), and the values estimated for these parameters by Sears from the Lennard-Jones potential.

The itinerant oscillator model of a liquid, which was devised previously by Hill (1963) in a study of dielectric absorption, is considered in more detail. Modified equations of motion are more clearly consistent, but the restricted model analysed predicts much narrower resonances than have so far been found in experiment.

The authors present a theoretical approach to anisotropic relaxation times in dilute substitutional alloys. The analysis is based on the Lippman-Schwinger formalism of scattering theory and introduces band structure information using the multiple-scattering technique of Beeby. The formalism developed leads to an expression for the eigenstates of the alloy system which can, in turn, be used to derive an integral equation for the relaxation time. With certain simplifying assumptions this equation leads to predictions consistent with de Haas van Alphen data.

Recent theoretical predictions of thin film nucleation are reviewed and the relationships between these and critical condensation conditions derived. Experiments of measurements of nucleation density with varying substrate temperature are described and the results compared with theory. Adsorption and surface diffusion energies of silver on silicon oxide have been obtained. Further experiments involving critical condensation are described and the results support the values of surface adsorption energy obtained by the nucleation studies.

Studies have been made of the a.c. electrical conductivity of single crystals of potassium thiocyanate in various states of purity between 446 K and room temperature. For all samples there was a marked change in the conductivity on passing through the 'phase' transition at 414 K. The position of this break was independent of the purity of the specimens. A complete analysis of the curves was not possible due to the existence of pronounced pretransitional and prefusional effects. On the assumption that Schottky disorder predominates in both phases it is deduced that the enthalpy of cation migration is 0.49+or-0.02 eV in the low temperature phase and 0.74+or-0.02 eV in the high temperature phase. The enthalpy of formation of Schottky pairs is less than 3.2 eV in the low temperature phase and about 1.8 eV in the high temperature phase. A second transition has been detected at 444 K.

The classical image potential of electrostatics is generalized to take into account a more realistic dielectric response of metal and semiconductor. The Fermi-Thomas dielectric function is used for the metal while in the semiconductor an interpolation formula is used to approximate the true dielectric function. This interpolation formula leads to an inhomogeneous Fermi-Thomas equation which has, as a particular solution, the classical dielectric case. The image potential near the interface shows rapid variations which are critically dependent upon the relative Fermi-Thomas screening lengths in the two materials but at longer distances the classical image potential is recovered. The physical basis for these results is described in terms of the screening of the test charge by the valence electrons of the semiconductor and the conduction electrons of the metal.

Hexagonal nickel sulphide shows a metal to semiconductor first order phase transition at a temperature T_N which depends on sulphur content. Thermoelectric power, conductivity, Hall and magnetic susceptibility measurements have been made on five single crystals of compositions ranging from NiS-NiS_1.02 in the temperature range 82-300 K. The results suggest that below T_N the Ni 3d states are essentially localized or form a narrow band. The predominant mechanism of conduction is by holes in a wide band. The discontinuity in conductivity at T_N is most likely due primarily to a change in mobility. Impurity band conduction occurs at low temperatures. The susceptibility curves have a markedly different shape from that normally expected for an antiferromagnet. This results from the first order character of the phase transition at T_N.

The authors present some numerical results for the one dimensional Ising model with inverse-square long range interaction obtained by the use of the scaling technique developed in connection with the Kondo problem. Certain new remarks on the Kondo problem are also included.

The dynamic properties of a Heisenberg spin cluster are examined in terms of time and temperature dependent spin-spin correlation functions and their wavevector dependent frequency transforms evaluated exactly in the cluster models. In particular, the Wigner-Eckart theorem is invoked to obtain these spin correlations in closed algebraic form for all spin values and for all temperatures above the transition temperature. The results are compared with the theories of Windsor (1967) and of Blume and Hubbard (1970) and with the experimental data on RbMnF₃.

In a system of magnetically ordered localized electronic spins hyperfine interactions with the corresponding, essentially paramagnetic, nuclear spins lead to coupled spin wave modes. An investigation is presented of the secular relaxation of those coupled modes which have a nuclear-like character. By means of Green function methods a procedure is developed for estimating the line broadening. This procedure is a generalization of the Suhl-Nakamura theory applicable also to situations where an effective relaxation Hamiltonian procedure is inappropriate, such as is the case for the strongly coupled modes predicted to exist in incommensurate arrays. Explicit investigation is made of the lowest meaningful order.

Examination of the edge and exciton luminescence emitted by cadmium telluride before and after monoenergetic electron irradiation (in the 100-400 keV range) coupled with previous results of work on heat treatments in cadmium vapour and tellurium vapour has shown the necessity for considering the existence of not only singly charged defect states but also doubly charged defect states in this material. This permits the explanation, in the case of cadmium telluride, of the weakness or nonexistence of phonon replicas and also the great sensitivity to electron damage shown by certain of the exciton lines. The 1.587 eV emission is attributed to an exciton bound to a neutral double acceptor centre believed to involve the cadmium vacancy. Transition of an electron from the conduction band to the ground state of the same neutral acceptor produces the 1.572 eV emission.

The variation with temperature in the range 20 K to 40 K, of the hyperfine splitting and linewidth of the electron paramagnetic resonance spectrum in n-type silicon has been measured. A theory has been developed which successfully accounts for the temperature dependence of the hyperfine splitting. It was not possible to make a close comparison between the theory and the measured linewidth principally because of the large uncertainties in the spin-orbit splitting and level widths of the excited states of the donor impurity centres.

ENDOR measurements on the nuclei of the first, second and third nearest sets of fluorine ions to Cr³⁺ and Cr⁺ in KMgF₃ are reported. The main results concern the second nearest, whose hyperfine tensors are found in both cases to show significant departures from the values expected on a purely dipolar basis. The axial third nearest fluorines for Cr⁺ also show small departures from the predicted dipolar interaction, but those for Cr³⁺ do not. For Cr³⁺ a term in the spin Hamiltonian cubic in the electronic spin and linear in the first nearest fluorine nuclear spin was detected. ⁵³Cr ENDOR was observed for Cr³⁺, and the hyperfine constant determined to be (17.887+or-0.005)*10^-4 cm^-1.

For pt.I see ibid., vol.4, 681 (1971). Observed departures from a purely dipolar value for the second nearest fluorine interaction for Cr³⁺ and Cr⁺ in KMgF₃ are discussed in terms of an overlap model. The nondipolar contribution is assumed to be caused by overlap with unpaired spin in the orbits of the intervening first nearest fluorine. To give agreement with experiment, displacements of the first nearest fluorines must be allowed. In the case of Cr³⁺ the displacements are inwards, whilst for Cr⁺ they are outwards. The conclusion is consistent with the charge states of the two ions, which are at divalent sites of the lattice.