Table of contents

An exact relationship between the eight vertex (8V) model and the fully frustrated square Ising model (FFSI) is established. On the basis of this it is shown that the T=0 point of the FFSI model corresponds to the F model limit of the 8V model. The critical exponent eta =¹/₄ for the FFSI model is obtained. The corresponding value of eta for the fully frustrated triangular lattice was shown by Stephenson (1964, 1966) to be ¹/₂. Possible reasons for this apparent violation of universality are discussed.

The Harris criterion (1974) is used to argue that the critical exponent alpha is non-positive in the percolation problem if the dimension is greater than one.

The authors have used molecular dynamics simulation to study the central peak recently discovered by quasi-elastic neutron scattering on SrCl₂ in the fast ion conducting state. They find that the peak appears as a component of the simulated partial dynamical structure factors. They find, in agreement with experiment, that this peak is present above the fast ion transition temperature but absent below it. The simulations also reproduce the experimental facts that the intensity of the peak is strongly dependent on wave vector and that its frequency width is almost independent of wavevector.

The dynamical structure factor S(q omega ) and the transverse current correlation function C_t(q omega ) are calculated within a generalised mean-field theory for a two-dimensional classical one-component plasma. The results are compared with recent molecular dynamics simulations, and the general agreement is satisfactory.

Single and double pole dislocation sources are observed to operate in silicon single crystals during in situ straining. This operation is controlled by the lattice friction on segments lying along the (110) directions of the (111) slip plane, and leads to a highly heterogeneous slip.

The optical and the piezoelectric polarons are investigated within the scheme of variational approach based on the unitary transformation and the method of a Lagrange multiplier. The method is found to be valid in both the weak- and the strong-coupling regimes.

Single crystals of the high-temperature variety of In₂Se₃ have been grown by chemical vapour transport reaction with chlorine as the transporting agent. They have been characterised by X-rays, density and magnetic susceptibility measurements. Their electrical transport properties (resistivity and Hall voltage) have been studied in the temperature range 4.2-300K. The results obtained indicate that this compound exhibits a phase transition between 120 and 160K.

The technique of temperature modulation of the AC magnetic susceptibility is used for the first time to examine the critical region above a ferromagnetic-paramagnetic transition. The temperature modulation and low-field susceptibility data indicate a well defined critical exponent behaviour chi = chi ₀ epsilon ^{- gamma} , where epsilon =(T-T_c)/T_c for polycrystalline Gd, and lead to the critical parameters gamma =1.24+or-0.03 and chi ₀=0.001 for 9.9*10^-3<or= epsilon <or=3.7*10^-2.

It is pointed out that recent work on the critical dynamics of the Sherrington-Kirkpatrick (SK) model (1975) contains some important errors, and the correct value Delta _m=1 is derived for the critical index of the uniform magnetisation. It is concluded that the SK model is equivalent to the spherical model with infinite-range random interactions in respect of the critical behaviour.

A system of localised spins s=1 with the bilinear Heisenberg S_f.S_f', biquadratic (S_f.S_f')² and three-atom (S_f.S_g)(S_g.S_f') interactions is considered. Using Anderson's method (1951) sufficient conditions are established for the ferromagnetic state to be the exact ground state.

A review is given of experimental and theoretical work in the last few years which yields information about states in the gap in non-crystalline semiconductors. The discussion is limited to hydrogenated amorphous silicon (a-Si-H) and to the chalcogenides including selenium. Among issues treated are: the evidence for a mobility edge in the conduction and valence bands of a-Si-H; the process of hole transport; the Hall effect and thermopower, and evidence for and against a polaron hypothesis; the deep states, dangling bonds and vacancy-type defects. In chalcogenides, again the polaron hypothesis is discussed, and also the valence-alternation pairs and the nature of the luminescence centres, whether they are VAPS or IVAPS.

The X-ray diffracted intensities of molten CaF₂ and BaCl₂ and the partial structure factors of BaCl₂ are calculated using the mean spherical approximation (MSA) and compared with experiment. A procedure to choose the ionic diameters is also illustrated and results compared with previous work on molten alkali halides.

O₂^- centres can be produced in Ca(OH)₂ by irradiation with 1.5 MeV electrons. The centres have been identified and their properties were studied by means of ESR, ENDOR, optical absorption and Raman measurements. A simple apparatus for the growth of large single crystals of Ca(OH)₂ is described. The results of the measurements of the g tensor can be understood in terms of a model developed for O₂^- in alkali halides. The authors have also measured the hyperfine interaction with the ¹⁷O nuclear spin in a ¹⁷O enriched powder and in a single crystal. The results fit the model. The optical spectra show the characteristic O₂^- absorption at 4.92 eV. From the Raman spectra the vibrational constants were calculated. It was determined from the ENDOR spectra that the O₂^- centre is located at an OH^- site. The interaction of the centre with the neighbouring proton spins can be described in terms of a Hamiltonian with a purely dipolar interaction term and an isotropic hyperfine term. Almost no covalency is expected.

Inelastic neutron scattering has been used to measure the phonon dispersion relation along (001), (110) and (111) directions of a single crystal of Na₂S at 50K. A simple shell model has been successfully fitted to the data. Dynamic quantities such as density of states, Debye temperature, displacement-displacement correlation functions and mean square ionic displacement are computed from the model and compared with CaF₂. Finally some remarks on the ionic conductivity of antifluorites are given.

It is shown how laser irradiation affects the geometric and electronic properties of dangling bond sites in Si and Ge. Due to strong electron-phonon coupling, a variation of the relative populations of their fundamental and excited electronic states induces changes in the geometric configurations of dangling bond sites. The processes involved are different for isolated dangling bonds, monovacancy, dislocations and crystal surface.

The quasiparticle spectrum of a model semiconductor is studied using the GW approach for the self-energy, i.e. including dynamic screened exchange and the Coulomb hole. Besides the well known electron gas features such as an overall shift of energies and the existence of plasmaron satellites, the main result is the appearance of off-diagonal terms in the spectral function and occupation number when represented in the monoelectronic wavefunctions basis. Special attention is devoted to the dependence of the band gap on different approximations for the self-energy. The authors analyse the many-body contributions to the density matrix by comparing the natural orbitals with the one-electron eigenstates.

The fractions of impurity ions which are in nearest-neighbour pair clusters, in triplet clusters, or not in any cluster are calculated by a new route from available radial distribution functions for impurities and vacancies in AgCl+CdCl₂ at 250 degrees C. The results are compared with a mass action calculation using equations for all nearest-neighbour clusters of four or fewer defects. In both calculations the fraction of pairs decreases at impurity concentrations in the range 1-5%, where triplets, quartets and larger clusters begin to form in appreciable concentrations. Neither set of calculations provides a simple insight into the ionic conductivity measurements of Ebert and Teltow (1955), although it seems probable that the larger clusters are not as effective in reducing the conductivity as the pair clusters.

A formal expression by Stark-ladder representation was developed to explain the non-linear transport properties of wide-band-gap semiconductors, where interband transitions can be neglected. The momentum and energy relaxation time were shown to be functions of the electric field. The momentum conservation law in the electron-phonon interaction held only for the component perpendicular to the electric field, and the component along the field was not conserved. The energy conservation law was also modified by the electric field. The momentum transfer along the electric field shifted the energy conservation and the sharpness of the law was determined by the strength of the field. The hopping conduction at the high-field quantum limit was shown to be proportional to the strength of the scattering. The temperature dependence of the mobility at the hopping region was thus contrary to that of the low-field band conduction.

The authors propose an analysis based on the second logarithmic derivative of the current in order to discriminate between the two typical recombination mechanisms (1st and 2nd order). It is shown that this method is feasible and leads to an unambiguous answer. The experimental case of Si:GaAs material is presented; six major peaks at 30, 60, 90, 140, 175 and 200K are analysed, all referring to first-order kinetics, thus indicating that the active recombination process is controlled by a high density of recombination centres. The exact determination of the recombination type allows a confident and precise determination of the typical parameters of the corresponding traps. It is found that the attempt-to-escape frequency is in the range 10⁷ s^-1 for the first group of traps (30, 60, 90K) whereas the others (140, 175, 200K) lie in the range 10¹¹ s^-1.

A discussion is given of the critical curves (transition temperature T_c versus concentration) of diluted 'low dimensional' magnets (layer magnets, and chain magnets). A model based on real-space renormalisation-group calculations and certain exact considerations is constructed for the Ising case, and analysed. Resulting critical curves are given for various exchange ratios for various types of layer and chain ferro- and antiferromagnet. For the case of an Ising layer magnet, as the magnetic concentration is reduced towards the two-dimensional percolation concentration, KT_c falls until it becomes comparable with the weak exchange between layers. This weak exchange raises the effective dimensionality to three so that the critical curve flattens off and heads towards the smaller limiting concentration for the three-dimensional system. For a quasi-one-dimensional (chain) Ising magnet, KT_c is only non-zero by virtue of the interchain coupling. Dilution causes KT_c to fall very rapidly to values smaller by a factor roughly equal to the ratio of interchain to intrachain couplings, and eventually to vanish at the percolation concentration for the higher dimensionality corresponding to coupled chains.

The authors have extended earlier numerical investigations of the harmonic collective excitations in the Edwards-Anderson model (1976) of a planar spin glass to one and two dimensions. In two dimensions, as in three, low-frequency excitations propagate modes with a linear dispersion law. They outline a theoretical analysis based on the coherent potential approximation (CPA) which reproduces the spin-wave velocities that were inferred from the numerical work. In one dimension the CPA accounts for the density of states and the dynamic structure factor over the entire zone except possibly at very long wavelengths where a non-linear dispersion law is predicted.

Reports phonon, magnon and high-energy (6800 to 14000 cm^-1) electronic Raman scattering in CsNiF₃. One-magnon scattering is observed with an applied magnetic field which ferromagnetically aligns the spins: both experimental frequency and selection rules for polarised spectra are interpreted. The high-energy electronic spectra involve transitions, within the Ni²⁺ ion (3d)⁸ configuration, from the ³A_2g ground level to the ³T_2g and ³T_1g^a excited states; each transition shows sharp zero-phonon electronic lines in addition to a broad phonon-assisted band. The widths and the peak positions of the sharp lines are related to spin correlation functions which depend upon the temperature and the applied magnetic field, as experimentally observed. The intensities of the polarised spectra are also discussed in terms of spin correlation functions for all the irreducible representations which can be assigned to the excited states.

Phonons in the quasi-one-dimensional compounds ZrS₃, ZrSe₃, ZrTe₃ and HfSe₃ have been investigated by Raman spectroscopy. Most of the structures observed have been assigned to Raman active zone centre phonons. Although twelve such k=0 optical phonons are theoretically predicted, some of them are still missing; particularly, the authors failed to excite most of the B_g modes (which involve atomic motions along the b axis of the crystal) even with different laser frequencies. The more complete A_g spectra are characterised by two sets of three major lines, well separated in frequency except for ZrTe₃. The low-frequency set is attributed to scattering by rigid chain modes while the upper-frequency set is assigned to intrachain modes. The close relationship between analogous spectra from the different compounds suggests the establishment of one-to-one correspondence between the phonons and their wavenumbers by simple scaling relations. The A_g spectra from HfSe₃ exhibit a strong dependence upon laser frequency in the range 1.83-2.73 eV.

The effect of antiferromagnetic ordering on the optical absorption edge in alpha -MnS is studied experimentally and theoretically. The absorption edge (3.33 eV) is conclusively determined from the dispersion of the interference fringe in a thin platelet crystal. The edge shows a blue shift of 0.22 eV on decreasing the temperature from room temperature to 4.2K. The electronic structures of MnS in both paramagnetic and antiferromagnetic phases are calculated by using the self-consistent-charge extended Huckel method in order to clarify the nature of the transition and the mechanism of the edge shift. The observed blue shift can be reasonably explained by a model which attributes the edge to a transition corresponding to the magnetic exciton constructed with a hole in the 3d orbitals and an electron in the 4p orbitals of Mn ions.

The near-infrared photoluminescence spectrum of GaP:Fe consists of four zero-phonon lines. These have been subjected to uniaxial stress and magnetic fields and the results prove conclusively that they are transitions between crystal-field split levels of Fe²⁺ (d⁶) in a tetrahedral environment. Effects of Jahn-Teller coupling on the positions of the energy levels are considered.

The theory of one-quantum inelastic electron scattering from adsorbate vibrations is developed using field theoretical methods. The relevant S-matrix element is expressed in terms of a mixed boson-fermion Green function. This matrix element is shown to involve one-particle amplitudes (LEED wavefunctions), and the functional derivative with respect to an external potential of the electron self-energy for fixed nuclei. If the self-energy is local in time, a simple formula is obtained from which numerical calculations can be made with roughly the same labour as for angle-resolved photoemission. The limitations of the muffin-tin potential for this work, particularly the absence of the long-range dipole potential, are discussed.

Angle-resolved loss spectroscopy methods have been applied to study elementary excitations on molybdenum disulphide basal surfaces with incident electron energy in the range 50 to 250 eV. The lamellar structure of this compound results in inelastic process anisotropy. The authors have found: (i) interband transitions; (ii) a volume plasmon with p perpendicular to c at 8.8 eV; (iii) an excitation p//c at 7 eV, tentatively interpreted as Tosatti 'anisotron'; (iv) a collective excitation which may be a surface plasmon at 18 eV; (v) two volume plasmons (p perpendicular to c and p//c) at 24 eV.