Table of contents

The charge densities in ReO₃ were investigated by the X-ray structural analysis. The anisotropic charge distributions were found around a Re atom, which is attributable to the pi bond formed by Re 5d (t_2g) and O 2p electrons. The calculated difference electron density map by the DV-X alpha cluster method supports qualitatively the present observation. The measured thermal vibrations of oxygen atoms were highly anisotropic. The M-mode oxygen displacements will be readily enhanced by the existence of high pressures.

The low-temperature tunnel splittings of reorienting NH₄⁺ ions in tetrahedral surroundings have been measured in (NH₄)₂PtCl₆ and (NH₄)₂ReCl₆ with neutron inelastic backscattering and in (NH₄)₂TeCl₆ with nuclear magnetic resonance and field cycling. The tunnel splittings in these and other ammonium hexachlorides depend exponentially on the lattice dimensions.

Different approximations made by M. Hasegawa and M. Watabe (1982) on the surface tension of liquid metals are analysed. The present authors conclude that the good agreement found between the theoretical and experimental values of the surface tension is fortuitous. Better approximations for obtaining the electron-ion interaction are needed.

The influence of the correlation of local Jahn-Teller deformations upon the magnetic and magnetoelastic properties of TmPO₄-type virtual elastics is examined. This correlation leads to the appearance of contrary flexure points for the field dependence of the magnetic moment and changes the field and temperature behaviour of static magnetostriction. The results obtained are general for crystals, where operators of Zeeman interaction and Jahn-Teller molecular field commute.

The specific heat capacity of malononitrile has been measured in the vicinity of the low-temperature re-entrant phase transition, and the results are shown to be in good agreement with the predictions of a model for re-entrant phase transitions proposed by the authors.

In a recent note P. Hawaii and J. Tilley (ibid., vol.15, p.4075, 1982) raised criticisms against a single continuum theory of liquid helium II proposed a few years ago. It is shown that most of these criticisms are not founded. An analysis of Hawaii and Tilley's work is also carried out.

It is argued that an extended wavefunction at the mobility edge, which occupies an infinitesimal fraction of the volume in a disordered system, should have a self-similar, filamentary structure with a scale invariance.

The scattering of long-wavelength phonons due to the spatial variation of elastic moduli that is produced by the inhomogeneous elastic strain and rotation fields of static crystal defects is calculated in terms of the second- and third-order elastic constants of the undeformed crystal. The present theory is distinguished from those of previous authors by its ability to deal with rotation angles that are not necessarily small, such as those associated with large-angle grain boundaries or macroscopically bent or twisted crystals. For small rotations the classical equations of motion and the second-quantised Hamiltonian obtained by previous authors are rederived and the modifications appropriate to large rotations are discussed. Approximate, but simple, expressions for scattering cross sections, etc., are obtained; these facilitate subsequent calculations of transport coefficients and lead to estimates of lattice thermal resistivities in dislocated crystals that are in good agreement with experiment. Previous theoretical studies of the strain-field scattering problem are reviewed.

A three-terminal, capacitance dilatometer has been constructed and used to measure the linear thermal expansion over the temperature range 3-9K of gamma -irradiated Al₂O₃:Cr relative to 'pure' Al₂O₃. A positive Schottky-like peak has been observed in the expansivity curve at about 3.9K and its presence is attributed to the concentration of Cr²⁺ (produced by gamma -irradiation) in the specimen. The peak is shown to be removed by UV bleaching of the sample at 365 nm.

A theory of acoustic and optic polarons and exciton-polarons in one dimension (1D) is presented. Polydiacetylene crystals are the model 1D electronic systems for which empirical values of the exciton-phonon interaction exists. Binding energies and effective masses of exciton-polarons are thus deduced. For polarons the theory is compared with other model calculations.

The hierarchy of the travelling cluster approximations (TCA) is used to study the spectrum of two-dimensional disordered electronic systems. Working within the single-band model of a two-dimensional disordered binary alloy on a square lattice with nearest-neighbour hopping, the authors analyse ( mod G₀₀(E₀+i eta ) mod ²) as eta to 0⁺ within any finite-diameter TCA. They study the behaviour of ( mod G₀₀(E₀+i eta ) mod ²) as the TCA cluster size goes to infinity for small eta and conclude that for the exact case when all diagrams are summed, there is an absence of extended states in two-dimensional disordered systems, independent of the degree of disorder. In addition they discuss the plausibility that all states can be rigorously shown to be localised by this method. Finally, they present a one-parameter scaling theory for ( mod G₀₀(E₀+i eta ) mod ²) in analogy with the conductance scaling theory of Abrahams et al. (1979) which predicts pure point localised states in one and two dimensions and a mobility edge in three dimensions.

Superlattice spots observed by X-ray and electron diffraction in the tetragonal, metallic, quasi-one-dimensional compounds NbTe₄ and TaTe₄ are interpreted in terms of charge-density waves. It is shown that three slightly different types of columns occur in the crystals. In NbTe₄ at room temperature two types of chains have incommensurate distortions with wavevectors q₁=(0, 0, 0.311c*) and q₂=(0.5a*, 0.5b*, 0.344c*): the third type has a very weak distortion with q₃=(0.5a*, 0, ¹/₃c*). The wavevectors for TaTe₄ are as above except that the component along the metal chain is exactly ¹/₃c* in each case. The vectors q₁ and q₂ are independent of temperature but can be varied by substitution of Ta for Nb. These are structurally the simplest inorganic crystal structures in which CDW have been observed and are the only reported crystals in which three CDW coexist.

Conducting properties of two-dimensional two-phase materials are considered. The locally generated Joule heat is invariant under an interchange of the conductivity values without altering the phase boundaries, but with a rotation by 90 degrees of the external electric field E_a and a simple rescaling of E_a. Under the same transformation, current lines become equipotential lines. Numerical calculations, illustrating these features, are performed for a generalised chequer-board geometry with conductivity ratios 50 and 7. In particular, it is studied how the spatial fluctuations in the electric field decrease as one phase is diluted.

The current distribution is investigated for a two-phase material with chequer-board geometry and a low conductivity ratio sigma ₂/ sigma ₁ ( identical to s²). The current density at small distances r from the corners where the phases meet varies as r^-1+s, in the limit of small s. The current lines from circle arcs in the poorly conducting phase and straight lines in the well conducting phase. For small s, the Joule heat is concentrated to the phase boundaries. As a consequence, the effective conductivity of alternatively packed cubes is 2 ( sigma ₁ sigma ₂)¹2/.

A simple intuitive model is used to derive the effective nuclear many-body Hamiltonian for a Van Vleck enhanced (singlet ground state) system, in preference to the use of high-order perturbation theory. It is shown that in the case of either pure dipole-dipole or exchange interactions, the Hamiltonian reduces to a formally simple expression. However, for mixed dipole-dipole and exchange forces, the situation is much more complex. Some remarks are also made concerning the Hamiltonians used by Bleaney et al. (1982) in connection with the nuclear antiferromagnet HoVO₄, and Kubota and coworkers (1980) in their analysis of the properties of the nuclear ferromagnet PrNi₅.

From linear birefringence measurements the authors have deduced the temperature dependence of the magnetic energy, related to the short-range order, in the quasi-1D Ising S=¹/₂ diluted antiferromagnet CsCo_1-xMg_xCl₃. Considering the limits of the exact theoretical model to interpret the temperature dependence of the magnetic energy of the pure CsCoCl₃ crystal, the experimental data for diluted samples (x=0.08 and x=0.114) agrees with calculations. NMR was used to study the long-range order. As expected for quasi-1D Ising systems the Neel temperature is highly sensitive to the dilution and varies linearly with it: (1/T_N(x=0))/(dT_N(x)/dx)=-10.35.

The nature of the local minima of the 'planar' spin glass Hamiltonian at zero temperature in two and three dimensions is investigated by means of computer simulation. The authors find that the eigenvalue density rho ( lambda ) of the Hessian varies as lambda ^1/2 for small lambda in three dimensions but that only approximately 40% of this can be accounted for by a spin-wave argument. In two dimensions all the eigenvectors appear to be localised but in three dimensions there appears to be a sharp transition from extended to localised states at a critical value of lambda . The addition of a uniform magnetic field or uniaxial or cubic anisotropy also produces in three dimensions localised states at small values of lambda , together with a large reduction in rho ( lambda ) as lambda to 0. The authors deduce that the 'hole' picture of the dynamics (based on the assumption that the system stays in the vicinity of a particular local minimum for macroscopic periods) is not likely to be an accurate description at long times.

The first two non-trivial terms in the virial expansion for the specific heat, magnetic susceptibility and non-linear susceptibility for an RKKY spin glass are evaluated. Use of an interaction, lattice structure and spin appropriate to CuMn gives good agreements with the high-temperature data. In the region of the spin-glass temperature scaling violations are significant for the susceptibilities, but not for the specific heat.

An analysis of the ratio of the intensities of the first-order TO and LO Raman lines in GaAs as a function of wavelength and with a particular emphasis on misorientation effects is presented in view of its use as a quantitative signature of the crystal perfection. It is demonstrated that this ratio depends strongly on even small angular misorientations. Moreover, the basic mechanisms responsible for building up the intensities of the transverse and longitudinal modes are evaluated at three photon energies located between the E₀ and E₁ electronic gaps of GaAs, leading to a determination of the electronic part in the electrooptic Raman tensor.

Various forms for the ion density profiles of Cs and Na have been tested in the density functional formalism. The large oscillations expected for Coulombic systems are largely suppressed by the pseudopotential. While oscillatory profiles give some improvement in surface tension, the values obtained are still about twice the experimental ones. It is concluded that the treatment of the pseudopotential or the gradient expansion of the functional is responsible for the unsatisfactory results obtained.