Table of contents

The mean spherical model for a binary fluid of charged hard spheres with arbitrary radii has been solved numerically. The results are used to illustrate several aspects of the dependence of the structure of an ionic liquid on the relative sizes of the ionic components.

Infrared reflectivity measurements at room temperature and 77K are reported for all three principal polarisations. The hitherto missing B_1u phonon is shown to have a frequency of 315 cm^-1. A new order of pairing with the known Raman active modes is suggested and the resulting splitting factors and force constant ratios calculated. The work suggests that GeS is even less anisotropic than has been thought up to the present.

The problem of an electron moving in a random potential in four dimensions is examined. It is argued that the apparent simplicity of the white-noise potential is due to an improper limiting process. It is demonstrated that localised states occur when finite ranged potential fluctuations are considered, and that they do not disappear as the range of the fluctuations gets shorter. The Ioffe-Regel criterion for localisation is examined, and the coherent potential approximation is used to estimate the deviation of the density of states from a linear dependence on energy.

Surface-state energies have been calculated for the copper (111) face in the energy region close to the Fermi level, using a parametrised form of surface potential. By fitting the calculated results to photoemission data, the author obtains a surface barrier which has the correct scattering properties for the valence electrons.

A theoretical value for the intermolecular contribution to the second moment of the NMR absorption lineshape of cyclohexane has been calculated, based on a recent determination of the crystal structure in the lower solid phase. The result agrees very well with the original estimate made by Andrew and Eades (1953) using indirect methods. This agreement supports the use of these indirect methods for the estimation of the intermolecular second moments in other substances whose crystal structures have not been found.

A narrow c-axis transmission band at 136 cm^-1 has been observed in single crystals of KH₂PO₄ at 300K. The results give the minimum value of epsilon _c^" as 1.05+or-0.15 in this important spectral region.

A random Ising magnet with ferro- and antiferromagnetic interactions J_A and J_B, is treated by the method of a modified cumulant expansion regarding the effective field and its square as random variables. Phase boundaries between the glass-like phase (GLP) and the ferro- and the antiferromagnetic phases, are determined. It is shown that the susceptibility and the specific heat have cusps at the transition temperature T_G between the glass-like phase and paramagnetic phase.

Some results of a systematic study of the entropies and structure factors of fourteen liquid simple metals are presented. The ab initio model potentials of Shaw (1968) and the dielectric function of Vashista and Singwi (1972) have been used to construct effective pairwise interatomic potentials for these liquid metals. These pairwise potentials have then been employed in both the Weeks-Chandler-Anderson (WCA) and the variational thermodynamic perturbation theories to determine appropriate effective hard-sphere diameters. The authors examine in detail the short-range repulsive part of the pairwise potential in several liquid metals and show, within the WCA theory, how the softness of this influences the form of the liquid structure factor. The calculation is briefly discussed of the compressibility from the long-wavelength limit of the structure factor.

Brillouin scattering from bulk samples of the liquid crystal 4'-n-octyl-4-cyanobiphenyl has been measured in the smectic and isotropic phases. The hypersound velocity (V) and attenuation were found to vary smoothly with temperature (T) with no marked changes on approaching the smectic-nematic, isotropic-nematic transitions; scattering from a shear mode was not observed. The value of C₁₁ is found to be (3.07+or-0.27)*10⁹N m^-2 at 25 degrees C, and (2.50+or-0.23)*10⁹N m^-2 at 50 degrees C and Delta V/ Delta T is approximately 8.1 m s^-1 degrees C^-1 in both phases. These measurements are discussed and compared with observations for other materials.

Describes the first application of a method, which is implicit in the writings of Maradudin, Montroll, Weiss and Iptatova (1971), of calculating the non-configurational entropy change s_d associated with the formation of point defects in ionic crystals. The equivalence of this method and the formulation of Mahanty and Sachdev (1970) is demonstrated, and it is then applied to the calculation of the entropy changes associated with the substitution of an Na⁺, Rb⁺ or Ag⁺ for a K⁺ ion in KCl. The calculation requires a knowledge of the Green functions for the perfect crystal and these are evaluated using eigenvectors calculated from shell-model parameters that fit the neutron scattering data for KCl. The calculation of s_d includes effects due to the change in mass and to force-constant changes, and the latter are calculated using the best available two-body potentials for the alkali halides.

The axially symmetric force-constant model of Elcombe (1966-7) for alpha -quartz is developed to take account of (i) forces between SiO₄ tetrahedra and (ii) rotational invariance. For a non-ionic model without rotational invariance, stiffening the Si-O-Si angles with an Si-Si interaction leads to rather better agreement with experimental phonon frequencies and much better agreement with elastic constants. However, subsequent imposition of the conditions for rotational invariance reduces some of the calculated frequencies, especially that of the lowest acoustic mode at the A-point on the Brillouin zone boundary; this indicates that further weak intertetrahedral forces are required. Ionic (rigid-ion) models are also investigated, but give little improvement. The observed variation with temperature of certain phonon frequencies as the alpha - beta transition is approached can be qualitatively explained by the change in lattice geometry.

NMR techniques have been used to investigate the charge density wave (CDW) state in NbSe₂. Above the transition temperature T₀, the Knight shift and electric field gradient (EFG) tensors have been measured. Broadening of quadrupolar transitions above T₀ has been attributed to fluctuations in the EFG which are a precursor to the formation of CDW's. Below T₀, a Knight shift distribution is observed whose width can be correlated with the amplitude of an incommensurate CDW which shows a temperature dependence characteristic of BCS type order parameter. The width of the distribution extrapolated to T=0 is shown to be proportional to T₀, a fact which supports the hypothesis of a BCS model for the CDW state.

It is shown that the basic exponential dependence of the polaron hopping mobility in a d-dimensional (d=2,3) disordered structure can essentially differ from the Mott law in a certain range of 'intermediate' temperatures due to the polaron effect. The conditions for the realisation of such dependences are analysed.

A method is suggested for computing hopping current density in a strong electric field. It is pointed out that in thin samples in which the energies of localised electron states take on values over a narrow interval the current density is inversely proportional to the square of the intensity of the strong electric field.

Drift velocities in indium phosphide are recalculated using recently revised phonon energies. Theoretical estimates of the phonon energies are used to confirm the new experimental values. The possibility of optimising peak-to-valley ratios by alloying to obtain degenerate X and L valleys is also considered.

The frequency-dependent ionic conductivities of molten AgCl, AgBr and AgI have been measured in the far-infrared (15-300 cm^-1). The results can be satisfactorily described by a simple phenomenological model which is based on the memory-function approach. Qualitative agreement is found between our experiments on molten silver halides and computer experiments on molten alkali halides. In the solid superionic conductor alpha -AgI a pronounced restrahl resonance was found. Remnants of this resonance still exist in the liquid state, but oscillation and diffusion occur on the same timescale. Superionic conductors of the AgI type thus occupy an intermediate position between an ordered ionic solid and an ionic liquid.

Low-density series expansions for the moments mu _n(p), n=0,1,...,4, of the pair connectedness are obtained for the site problem on the triangular and face-centred cubic lattices.

The quantum-classical crossover critical behaviour of the Ising model in a transverse field Gamma is first studied in one dimension where exact results are obtained. The correspondence between the quantum-classical crossover behaviour of this d-dimensional quantum model and the finite-size crossover behaviour of an equivalent (d+1)-dimensional classical model exact for d=1 is extended to higher dimensions. The crossover depends strongly on the relative magnitude of the crossover exponent phi and of the critical line-shift exponent Psi . In particular, if Pi > Psi approaches the critical line along a path of constant transverse field less than the critical field Gamma _c and a low temperature, only classical behaviour is seen, quantum effects do not show up. There is some controversy about the value of Psi . Experiments are suggested to give an answer.

An Ising model in a transverse field with general spin S is considered within RPA Green-function theory in the paramagnetic region. Expressions for the temperature renormalised collective excitation spectrum with a gap decreasing as the exchange interaction increases, the transverse correlation function, and the critical exchange-field ratio for magnetic ordering, are derived. Zero-temperature expansions are given in the limit of weak interaction. Critical values at T=0K are calculated for several values of S and an asymptotical expression for S>>1 is given.

Various effective-field approximation schemes are presented for describing the effects of fluctuations due to random spatial disorder on magnetic spin systems. An S=1/2 Ising model Hamiltonian is used, for which the spins occupy sites on a regular lattice but the exchange bonds are taken to be independent random variables. Both ferromagnetic and spin-glass types of ordering are considered. The results of the various approximation schemes are compared and related to previous work on disordered magnets.

The antiferromagnetic structure of Cu_0.5Ga_0.5Cr₂S₄, a mixed A-site normal spinel has been determined by neutron power diffraction methods. There is no evidence for chemical ordering of the copper and gallium atoms, either from neutron or X-ray powder data. The antiferromagnetic structure is not commensurate with the chemical unit cell and has a propagation vector of magnitude 0.827 nm^-1 at 4.2K. The relationship of the magnetic structure to that of the related compound Cu_0.5In_0.5Cr₂S₄ is discussed with particular reference to their magnetic Patterson radial distribution functions.

U₃P₄ and U₃As₄ are cubic at room temperature and become ferromagnetic below 138K and 198K, respectively. At 4.2K it has been found that both are rhombohedral with angles between cell edges of alpha =89.92 degrees for U₃P₄ and 89.93 degrees for U₃As₄. These are very small distortions from cubic symmetry so that profile analyses of the broadened diffraction peaks are necessary to interpret them. Both single-crystal and powder X-ray diffraction techniques were used to determine the magnitude and sign of the distortion. These observations reinforce the conclusions of Kuznietz and Wedgwood (1972), based on the distortions in ferromagnetic US, USe and UTe, that the uranium ion is highly aspherical.

An integral equation is given for the spin-correlation function G(t), which determines the free-induction decay at high temperatures. This equation is deduced by an equation-of-motion method where the full hierarchy of correlations (s₁^zd₀⁺), (s₁^zs₂^zs₀⁺) etc., is considered. G(t) is calculated for the case of CaF₂ and is compared with the experimental results of Engelsberg and Lowe (1974) who extended the measurements to long times.

An isotropic spectrum with g=1.9776+or-0.0005 and consisting of a main line flanked by six equally intense, equally spaced lines of about 2% of the intensity of the main transition, is observed in calcium oxide crystals irradiated with visible light. This spectrum is attributed to Mg⁺ ions present in both magnesium-doped CaO and in small concentration as an impurity in ostensibly pure crystals; the six satellite lines are believed to be due to the hyperfine interaction of the ²⁵Mg nucleus of natural abundance 10.5% and I=5/2. The hyperfine constant is found to be A=(32.30+or-0.01)*10^-4 cm^-1. On the basis of a simple molecular orbital model involving both the Mg(3s) and O(2p) orbitals the measured g-value is accounted for satisfactorily.

The magnetic circular dichroism spectrum of the R₁ band of the R centre in KCl has been calculated in the frame of Silsbee's model (1965) taking into account the dynamical Jahn-Teller interactions in both the ground and excited states. A satisfactory fit to the experimental magnetic circular dichroism spectrum at 1.8K observed by Binet, Margerie and Thuau (ibid., vol.6, p.2733 (1973)) is obtained by using the existing values of the involved parameters. Good qualitative agreement between theory and experiment is also found for the zeroth and first moments of this spectrum as a function of temperature.

Measurements are reported of the L_2,3M_2,3M_2,3 Auger spectrum from films of solid argon deposited, at various thicknesses, on silver. The spectra show considerable variation with film thickness. Spectra from the thinnest films show much more detailed fine structure than spectra from the thicker films and the energy of the Auger peaks shift to lower values as the thickness increases. The Auger spectra of both very thin and very thick films could be simulated using broadened gas-phase data and this enabled line breadths to be estimated. Spectra from films of intermediate thickness could not be explained on this simple quasi-atomic basis. The shift in energy is interpreted as arising from differences in environmental effects experienced by atoms situated on top of the metal compared with the effects experienced by atoms surrounded by other argon atoms.