Table of contents

Wavevector dependences of the transverse phonon energy widths, determined by neutron scattering, in monocrystalline lead provide evidence for a transition from a zero-sound, collision-free mode of high-frequency phonon propagation to a first-sound, collision-dominated regime at about 500 to 550 K. Hence the propagation of phonons having wavelengths on the scale of the interatomic spacing is heavily damped, similarly to that in the liquid state, prior to melting.

⁵⁷Fe Mossbauer spectra of a sample of YBa₂(Cu_0.95Fe_0.05)₃O_{7- delta} for which T_c approximately=57 K show that long-range magnetic order is established below about 12 K. A model in which the Fe and Cu ions are aligned with the crystallographic c-axis provides satisfactory agreement with the observed relaxation spectra. This result is discussed with reference to current theoretical models of high-T_c superconductivity which invoke magnetic coupling mechanism.

The application of the superposition approximation for the three-particle distribution function in a liquid, within the context of the Born-Green equation, is re-examined. It is shown how to correct this approximation for configurations in which one particle is well separated from the other two, and then demonstrated explicitly for the dipole-induced dipole pair potential that this correction is consistent with the known asymptotic expression for the radial distribution function. A modified form of the Born-Green equation is proposed which contains this improved description of triplet correlations.

Electron paramagnetic resonance of trivalent terbium ions is reported in a glass based on zirconium fluoride at liquid helium temperatures and at frequencies in the range 9 to 30 GHz. The results are interpreted as arising from a nonKramers doublet ground state with g/sub ///=17.3+or-0.5, A/sub ///=0.209+or-0.001 cm^-1 and with a zero-field-splitting parameter delta taking a continuous range of values from zero to at least 1.0 cm^-1. A simple theoretical model is developed that satisfactorily reconstructs the essential features of the observed resonance spectra. It is concluded that terbium ions act as network formers. They occupy a relatively well defined type of site, similar to those found in crystalline hosts, with a dominant crystal-field term of axial symmetry but with a continuous range of small site-to-site variations.

The order-disorder transition of the Ag atoms in the intercalation compound AG_xTiS₂ has been investigated using differential scanning calorimetry. Measurements have been carried out for Ag concentrations in the range 0<x<0.45. The Ag_xTiS₂ samples were prepared by thermally intercalating TiS₂ powders which were characterised using X-ray fluorescence and X-ray diffraction techniques. Results obtained for the critical temperature were in good agreement with previous measurements and no measurable hysteresis was detected. The variation of the specific heat near T_c was measured and the results were compared with the predictions of a two-dimensional theoretical model.

A defect model for (111) off-centre substitutional impurities in alkali halide crystals is developed. The model includes changes in the force constant between the impurity and its nearest neighbours in addition to mass changes. The model is applied to calculate the local density of states of (111) off-centre Ag⁺ in RbI which is expected to give peaks at the possible resonant mode frequencies.

The authors present a tight-binding model of cohesion and interatomic forces which exploits the variational principle of density functional theory. The binding energy of a solid is expressed as a sum of four terms, each of which has a clear physical meaning. The first two terms are the covalent bond and promotion energies, which are found by solving the electronic Hamiltonian to obtain the density matrix. The remaining two terms describe changes in the total electrostatic and exchange-correlation energies on forming the solid from isolated atoms. The variational principle allows these two terms to be expressed as functionals of a superposition of frozen atomic charge densities. The authors show that they may then be approximated by a sum of pair potentials. The importance of self-consistency in tight-binding models is discussed with particular attention to the evaluation of the bulk modulus and certain interatomic force constants by frozen-phonon calculations. It is shown that serious errors may arise in non-self-consistent models due to the violation of charge conservation and the neglect of variations in the potential caused by charge flow. The authors advocate local charge neutrality as the simplest approximation to self-consistency which overcomes these problems. This assumption leads to a remarkably simple expression for the force on an atom due to its neighbours, which is both physically transparent and computationally efficient. These concepts are illustrated for three-dimensional solids by calculations of covalent bond energies in BCC, FCC and HCP transition metals using a canonical d-band model. Model one-dimensional calculations are also presented which illustrate the computation of covalent bond energies and interatomic forces at surfaces and interfaces, and the importance of local charge neutrality in the model.

The low-temperature behaviour of an Ising spin model for a one-dimensional incommensurate structure (which is equivalent to the discrete Frenkel-Kontorova model in the non-analytical regime) is analytically investigated. Its specific heat exhibits an infinite series of Schottky anomalies at temperatures T_m going to zero. These anomalies correspond to crossover which can be physically associated with a hierarchical melting of the incommensurate chain. In contrast with early work, the authors show that certain types of phase defect (discommensurations) are the essential low-temperature excitations of the system and in addition that they can be hierarchically classified according to the continued-fraction expansion of the commensurability ratio zeta . Their characteristic energies k_BT_m and their weights are explicitly calculated at all orders. They present first a physically simple but empirical approach which allows one to predict and to calculate approximately these anomalies. Next, the validity of this approach is confirmed by a more sophisticated and new method of renormalisation with unequal blocks, which becomes exact as T goes to zero. The authors discuss the application of this theory to experimental measurements of the specific heat in K-hollandite.

The authors present convenient expressions for both the unscreened static electronic Lindhard susceptibility, chi ⁰(q/sub ///,z), and for the screened chi (q/sub ///,z), within both the RPA (random-phase approximation) and the LDF (local density functional) theories. The efficient methods for calculating the bulk chi s presented here are useful because the bulk chi s, in (q/sub ///,z) representation, are the basic ingredients in a very accurate mimic function of the equivalent surface susceptibilities.

The authors discuss the existence of fractional quantised Hall states in other than the lowest (n=0) Landau level. They present the results of numerical studies of systems with up to nine particles in the n=1 Landau level. They find that a fractional quantised Hall state is likely for filling fractions of the n=1 Landau level, nu ₁, with nu ₁^-1=5. At nu ₁^-1=3 they find that the Laughlin trial wavefunctions is not a good candidate ground-state wavefunction. If there is a gap at nu ₁^-1 it is predicted to be small. At nu ₁^-1=⁷/₂ they predict the existence of a fractional quantised Hall state despite the small or non-existent gap at nu ₁^-1=3. They also show that introducing truncated pseudopotential interactions is not always a physical procedure outside of the lowest Landau level.

The authors consider the electronic eigenstates of one of the simplest examples of a disordered system, namely an impurity cluster in an otherwise perfect solid. The charge density appears to have two fractal dimensionalities rather than having, as had been proposed previously, a single one. The authors also propose new criteria for describing the fractal nature of the eigenstates.

1D systems have proved amenable to both numerical and analytical calculation. Previous work has shown how to construct a theory of averaged quantities in a 1D disordered system for the case of diagonal disorder. In this paper the authors extend the theory to include the case of mixed off-diagonal and diagonal disorder. An explicit expression for the inverse localisation length and density of states is evaluated for several types of disorder including mixed and off-diagonal disorder. In addition they obtain the relations for the localisation length: l approximately=E^{- nu} as E to 0 and l approximately=W^-s for pure off-diagonal disorder. Their results are compared with published simulations and are found to be in good agreement.

A model of field-assisted thermal ionisation which takes into consideration the contribution of the internal electric fields is proposed. The results of single-centre theories of the effect are obtained on the basis of the present model as a consequence of averaging over the internal field distributions. Two possible emission cases are examined: one in which the electron emission takes place mainly in the direction of the applied field, and the other in which the emission is spherically distributed. Experimental data from CdF₂ crystals and SiO films are in good agreement with the proposed model and give an evaluation of the internal field comparable with that obtained by other researchers.

The authors present calculations of the specific heat of 1D quantum spin chains for a number of integrable and non-integrable Hamiltonians, in the presence of a magnetic field. For S=1 the Hamiltonian has both bilinear and biquadratic isotropic exchange and includes ferromagnetic and antiferromagnetic versions of the Heisenberg, Takhtajan-Babujian (TB), Lai-Sutherland (LS) (permutation) and biquadratic models. The two methods used are (i) direct numerical diagonalisation for chains of up to nine atoms and (ii) numerical solution of the Bethe ansatz equations for the integrable models (TB and LS). Generalisations of the latter method to S>1 are also given. For the integrable models the two methods give results in good agreement. Various types of behaviour, particularly at low T, are found and these are related to known phase changes at T=0. The results of the first method for the non-integrable Hamiltonians are discussed with reference to the existence of the Haldane gap in the S=1 Heisenberg model and a possible gap in the biquadratic model.

Phonon dispersion data on Ni(100) for the (011) direction are calculated using the matching procedure. The Rayleigh mode is shown to be a surface state over the whole of the two-dimensional Brillouin zone, and a new odd surface state is found. The Van Hove singularities are analysed in detail and a practical definition of surface resonances is given. A new initial condition describing the scattering of an incoming bulk phonon by the surface is introduced. The calculated dispersion curves of surface resonances are compared with other authors' work. Eventually a new interpretation of EELS data is proposed.