Table of contents

It is shown how the notions of group generator, class sum and isomorphism permit an intuitive geometrical approach to the theory of the permutation groups S₃ and S₄. This approach enables some defects of the traditional Young diagram method to be analysed and bypassed.

It is shown that a theory developed by Kaplan and Gray (ibid., vol.9, p.L483 (1976)) for elementary excitations in disordered systems with short-range order does not agree with the exact numerical calculations for a one-dimensional binary A-B alloy; in particular it fails to predict the fine structure in the electronic density of states.

New lines have been detected in the absorption spectrum of P doped Si associated with the creation of bound excitons in an excited state. The positions and strengths of these lines are in agreement with corresponding features recently identified in the luminescence spectrum. These results support the shell model for bound exciton and multiple bound exciton complexes.

The equation for the binding energy of donor impurity states in multi-valley semiconductors, with full inclusion of the Umklapp contributions to intervalley potential matrix elements and of the mass anisotropy is solved variationally for a point-charge impurity pseudopotential. The results are in very good agreement with experiment for Si:P, and Ge:As. The crucial role of Umklapp intervalley scattering contributions to the binding of the ground state is discussed.

The magnetophonon effect is observed in thin films of high-purity p-type PbTe and in a bulk sample of p-type Pb_0.8Sn_0.2Te with very low carrier concentration. The fundamental fields of the series of peaks and the frequencies of the phonons involved are found to be independent of the carrier concentration (which ranged from 1.1*10²² m^-3 to 1.5*10²⁴ m^-3). The phonon frequency estimated from the fundamental field and the cyclotron mass in the PbTe is 115+or-10 cm^-1 even though the coupled plasmon-phonon-cyclotron frequency observed in magneto-optical experiments with the same samples was in excess of 150 cm^-1 and increased rapidly with carrier concentration.

A configuration interaction calculation for Gd³⁺ is presented, showing that the lowest order perturbation contributions to the spin correlated crystal field are a similar order of magnitude to those recently postulated by Judd (Phys. Rev. Lett., vol.39, no.4, p.242 (1977)) on phenomenological grounds.

Measurements on V³⁺ in Al₂O₃ using the frequency crossing technique show that it is capable of providing values of g_{perpendicular to} to an accuracy comparable with that of more conventional techniques.

Expressions for the spectral functions of number and charge density fluctuations are obtained for a binary fluid using Mori's memory function approach. Numerical calculations are done for liquid rubidium bromide and the results are compared with molecular dynamics and neutron inelastic scattering data. It is found that the theory reproduces very well the density fluctuation spectrum without any adjustable parameter. In the case of charge fluctuations, the theory predicts optic-mode peak at small wavenumbers. The peak positions are also in good agreement with molecular dynamics results. At large wavenumbers the agreement is again semiquantitative.

For pt.I see ibid., vol.10, p.4181 (1977). The expressions for the partial dynamical structure factors obtained in pt.I have been used to calculate numerically the number-number, concentration-concentration and number-concentration fluctuations in liquid Na-K alloy at 373K. It is found that the variation of absolute intensity at zero-energy transfer and full width at half maximum for the number and concentration fluctuations is correlated with the corresponding static structure factors. The intensity of concentration fluctuation spectra attains its maximum value when the concentration of Na atoms becomes equal to that of K atoms.

Radiation damage in KCl can be produced by the decay of a self-trapped exciton into an F centre and an H centre. The authors present calculations of the energies of the states involved for various stages in the evolution of the damage. These lead to important conclusions about the very rapid damage process, and support strongly Itoh and Saidoh's suggestion (1973) that damage proceeds through an excited hole state. The results also help in understanding the prompt decay of F and H pairs at low temperatures, the thermal annihilation of F and H centres, the effects of optical excitation of the self-trapped exciton, and some of the trends within the alkali halides. The calculations use a self-consistent semi-empirical molecular-orbital method. A large cluster of ions is used (either 42 or 57 ions) plus long-range Madelung terms. The ion positions were obtained from separate lattice-relaxation calculations with the HADES code. The choice of CNDO parameters and the adequacy of the method were checked by a number of separate predictions.

Bombardment of KCl by electrons with energies in the range of 2-10 keV results in the creation of F-centres to a depth 100-1000 nm. Such centres are identified by a characteristic absorption band centred at a wavelength of 556 nm. The time- and energy-dependence of F-centre absorption have been studied in the past, with some lack of concordance among the results obtained by different observers. Absorption measurements have generally been made in transmission, a matter of some difficulty in weakly absorbing layers of small thickness. It is shown that provided suitable precautions are taken, ellipsometry may be used to obtain consistent, reproducible results. It is established that within close limits. F-centre layers of practically uniform density are produced. The thickness/energy relation obtained in these experiments is found to agree closely with theoretical estimates.

Starting with the 'family tree' which shows the group-subgroup relations between the various structural phases of perovskite-type layer materials with organic ions, the symmetry types of the lattice vibrations and, for some selected cases, the symmetry coordinates are derived by standard group theoretical methods. Special emphasis is given to the possibility of soft or condensating modes in the phase transitions involved and to the applicability of the Landau theory of phase transitions.

It is shown that the stress tensor can be symmetrised by a proper redefinition of the (linear) momentum density, even if an intrinsic angular momentum is present. The difference between 'intrinsic' and 'external' angular momentum turns out to be a matter of definition. There is no independent hydrodynamic variable due to the angular momentum conservation law. Some expressions for the (linear) momentum density are discussed and the use of the symbol C_ij for different quantities by various authors is clarified. The tensor C_ij contains two independent parameters by Galilean invariance. Angular monentum conservation including the dipole-dipole interaction is discussed. The orbit wave spectrum shows a quadratic k dependence in the hydrodynamic region and different results are obtained only outside that region or by the use of non-hydrodynamic variables. In two appendices the mode spectrum (with unclamped normal fluid) is discussed and Graham's free energy is explicitly written down.

The band structure of CdI₂ has been calculated using a modified semi-empirical tight-binding method and the results obtained have been compared with both angularly averaged and angularly resolved photoemission spectra. The theoretically computed density of states distribution is in excellent agreement with angularly averaged results and all the main features observed experimentally are reproduced in the theory. Angularly resolved spectra have been used to draw up energy band dispersion curves directly and agreement with calculated bands in both the Gamma M and Gamma K directions of the Brillouin zone is good.

After a discussion of the resonance modes (long-wavelength magnons) the authors find the dispersion relation of the polariton modes formed by coupling of these modes to the electro-magnetic field. For relatively low fields, near the critical field for the transition to the anti-ferromagnetic phase, the dispersion curves are similar in appearance to those found in that phase, and it is shown that one can use an expansion method to get an explicit approximate form of the dispersion relation. Near the critical field for the transition to the paramagnetic phase, the curves resemble those for a ferromagnet, and it is shown that the dispersion relations in the spin-flop and paramagnetic phases are identical at the critical field. Detailed discussions of the dispersion curves are given for propagation along the uniaxis and along the two principal directions at right angles to it. The authors indicate how the cross section for inelastic light scattering would be calculated, but no details are given.

The Anderson model of localisation has been extended to a two-band model of the Thorpe-Weaire type by studying the convergence of the resolvent operator series. Taking values of parameters reasonable for a-germanium and position of the mobility edge is plotted as a function of the disorder parameter w. It lies at a value about 0.2 eV inside the conduction or valence band edge for w=0.5 eV. The results are significantly different from those which would be obtained by treating the bands as separate.

A theory of electron states due to transition metal impurities in semiconductors which includes the real symmetry of the crystal has been developed. The resonance potential, which describes the scattering of valence electrons by excitation of the atomic shell and has the symmetry of the crystal point group, results in the splitting of impurity d-levels and does not affect shallow s-levels. The proposed scheme unites the resonance model of deep levels with conventional ligand field theory which is usually used to explain the optical spectra of wide-gap semiconductors. The possibility of virtual Friedel states in the valence or conduction band and their influence on shallow hydrogen-like impurity levels is also considered.

For pt.I see ibid., vol.10, p.1239 (1977). The method of Weaire and Williams is applied to the problem of Anderson localisation in two and three dimensions with careful attention to the time extrapolations involved and analysis of the dependence of results on the size of the samples used. In two dimensions, the conclusions are fully in accordance with previous numerical results. In three dimensions a much lower value of critical disorder is obtained than that tentatively advanced by Thouless (1974), resolving an apparent discrepancy between analytic theory and numerical calculations in this case.

The electromechanical constants and polarisation moments of KTaO₃ have been determined for samples of varying size. The polarisation moments exhibit a large size dependence, and this effect is interpreted in terms of space charge, which is formed by ionisation of traps. Space-charge fields are shown to arise spontaneously and are also induced by external fields. Large external fields have been observed to alter the electro-mechanical response irreversibly. This observation is explained in terms of electron tunnelling between shallow traps and rectification of the metal-dielectric Schottky barrier.

Charging and discharging currents have been measured in sandwich structures as a function of applied voltage, temperature and film thickness with both electrodes aluminium or gold. It is suggested that the general shapes of the I-t curves are largely controlled by the contact characteristics, which at a given temperature are blocking below a critical field E_c and injecting above it. For applied voltages U and film thicknesses L, such that U/L<E_c, there is no injection at time zero, but it may commence at later times if the electrode field rises above E_c due to the drift of a low equilibrium density of free carriers. As the temperature increases, the critical field value decreases and may become insignificant compared with the applied field, leading to injection from time zero.

Gradient invariants which couple the bases for irreducible representations are tabulated for all magnetic crystal point groups. These invariants are necessary for the construction of thermodynamic potentials used in the phenomenological description of incommensurate phase transitions. As an example, the description is given of such a transition in a ferroelectric crystal.

The critical temperature T_c of the random mixture of the ferromagnetic and antiferromagnetic exchange interactions J_A and J_B on both the two-dimensional square lattice and the simple cubic lattice are discussed by using Pade approximations of the high-temperature expansion of the susceptibility. It is suggested that the critical temperature T_c (between the paramagnetic and the ferromagnetic phases) which decreases with p_A, where p_A is the concentration of J_A, disappears at a certain concentration p_A^c1 before it reaches the absolute zero temperature. This fact supports the theory of the glass-like phase and there are triple points where the paramagnetic phase, the ferromagnetic (antiferromagnetic) phase and the glass-like phase join together.

For pt.I see ibid., vol.10, p.2471 (1977). The results on partially aligned groundstates found in pt.I in the two-spin case are extended to the many-spin case by a generalized mean-field theory with a site-dependent axis of quantization. It is found that the corresponding groundstate is partially aligned in regions of the parameter space agreeing qualitatively with the exact two-spin results. For the case of sufficiently symmetrical lattices with isotropic nearest-neighbour interactions, the partially aligned groundstate is degenerate with respect to a one-parameter family of helical spin structures. Such helical states are shown to be unstable in the presence of an infinitesimal external field against conversion to a canted two-sublattice structure.

Results for the zero-temperature spin-wave stiffness, frequency-wavevector response functions and density of states for a randomly diluted, two sub-lattice antiferromagnet on a body-centred cubic lattice are presented for various impurity concentrations. The authors (1972, 73, 75) extend and employ a path type of CPA originally used by Brouers and associates, for studying random electronic systems and later developed by Theumann and Tahir-Kheli (1975) for treating site random ferromagnets. The results are compared with those given by an exact Monte Carlo computer simulation study by Holcomb and Harris (1975). Considering the fact that the authors' is a single-site CPA, the agreement between these results is found to be good. At low impurity concentrations, the authors have evaluated appropriate perturbation theory T-matrices such that all magnetic excitations are removed from non-magnetic sites and find an exact agreement with them. Whenever possible, they have also compared these results with those given by Holcomb's CPA and find the overall quality of the results to be somewhat superior.

For pt.I see ibid., vol.9, p.3819 (1976). The authors discuss the experimental results on the effect of uniaxial stress on the EPR of the Gamma ₈ ground states. Baker and Currell (in pt.I) used the data to calculate eight of the nine unknown parameters of the orbit-lattice Hamiltonian H_OL. Such a large number of parameters can be measured only for the few systems which exhibit EPR in a Gamma ₈ state. Hence, to make quantitative calculations involving H_OL it is imperative to be able to express H_OL in terms of fewer parameters. The data of Baker and Currell have been used to make a rigorous test of two models for reducing the number of independent parameters of H_OL: (1) the generalised electrostatic model of Buisson and Borg (1970) and (2) the superposition model of Newman (1971). These models have also been modified to relax the relationship between H_OL and the static crystal field, and to make allowance for local variations of elastic constants and other local ionic displacements. Within the context of a pure LS coupling approximation for the two ions, neither the simple nor the modified form of either model is adequate to describe H_OL.