Table of contents

Arguments are presented why the concept of 'naive' universality may not be valid in the entire parameter space of the two-dimensional Ising model with first- and second-neighbour interaction.

Two-ion-polarizable shell-model interionic potentials for NaCl are derived from solid-state data including ionic radii. Radial distribution functions for the melt are obtained from these potentials by a molecular dynamics simulation and the results are compared with recently reported measurements. Significant improvements over previous calculations based on rigid-ion potentials are found.

The use of a variational n-parameter trial function is compared with a variational one-parameter trial function in the calculation of the lattice conductivity. The use of the former is shown to improve a lower-bound result for the conductivity arising from the use of the latter.

The effects of the random local magnetic fields on the phase transition are studied within the Landau phenomenological theory.

The change in size and magnetic moment of the ions Mn²⁺ and Fe²⁺ associated with the low-spin-high-spin transformation is shown to follow the atomic magnetovolume relation found previously to hold for d-group metals and alloys. The Ni²⁺ ion in hexagonal NiS also obeys this relation during its first-order magnetic-non-magnetic transition, showing that the magnetovolume effect is due to intra-atomic interactions, independent of whether the magnetic ordering is associated with localized or itinerant electrons.

The two-photon excitation spectra of CaF₂(Eu²⁺) and SrF₂(Eu²⁺) have been studied at 300K and at 4.2K in the region between 24100 cm^-1 and 28000 cm^-1. The observed spectra consist of broad bands due to 4f⁷ to 4f⁶ 5d transitions coupled with odd-parity phonons, and two groups of sharp lines due to pure 4f⁷ to 4f⁷ transitions.

The Clebsch-Gordan coefficients (available separately) have been tabulated for single-group co-representations of distinct non-isomorphic magnetic point groups. A short discussion of the algebraic method is also given.

The temperature variation of the specific volume of the nematic liquid crystal (p-ethoxybenzylidene)-p-n butylaniline (EBBA) has been recorded both in isotropic and nematic phases. The nematic-isotropic phase transition is concluded to be a first-order phase transition from the specific volume studies. Pre-transitional variations are found to occur only on the nematic side of the transition and can be explained in best manner on the basis of Maier-Saupe theory (1958). Values of A and S_k are 17.9*10^-9 erg cm⁶ and 0.450 respectively. Adiabatic compressibility ( beta _ad), Rao number (R_n) and van der Waals constant (b) have also been calculated from measurements of the ultrasonic velocity beta _ad and R_n also show pre-transitional phenomena.

The variation of ultrasonic velocity and absorption with temperature has been studied in the nematic liquid crystal HBT. Anomalous increase in absorption and abrupt decrease in sound velocity are observed in the vicinity of nematic-isotropic phase transition.

Phonon dispersion curves were measured by inelastic neutron scattering in the a*-c* reciprocal lattice plane at 85K. The lowest transverse dispersion surface was investigated throughout the Brillouin zone. This dispersion surface shows that the phonon frequencies are considerably higher than the one-dimensional magnons, at least in the region where the magnons were studied in detail earlier. The pronounced anisotropy in the dispersion is analysed qualitatively using a model which consists of stiff rods embedded in a soft material.

The thermal conductivity of MnF₂ and Al₂O₃ has been measured over the temperature range 1.2K to 140K. In each case the conductivity was measured along the direction of highest symmetry and perpendicular to it. The conductivity anisotropy of Al₂O₃ can be explained quantitatively by phonon Umklapp anisotropic scattering mechanisms which are determined by the trigonal Brillouin zone. Excellent agreement is obtained with Simons' theory (1960) which does not take account of phonon dispersion relations. In the case of MnF₂ and MgF₂ which have a similar rutile crystal structure, the Umklapp anisotropy is not predicted accurately by the theory. It is suggested that strong phonon dispersion is responsible for the poor agreement and in particular that there is evidence to show that optical phonons are contributing significantly to the thermal conduction in the direction of the tetragonal c axis.

In order to gain insight into the critical dynamics of structural transitions, which are usually described by a Hamiltonian of linearly coupled anharmonic oscillators, the dynamic behaviour of a few coupled quartic oscillators is investigated. For single-well potentials and weak coupling, the displacement spectral function chi shows a single peak due to phonon vibrations. For double wells and single wells with strong coupling, chi has an additional resonance at low frequencies due to particles jumping from one well to the other. The relation between these results and other treatments of structural transitions is discussed.

Simplified model calculations are presented for the steric properties of the transition metal ions in various crystalline geometries on stepped surfaces. Results derived from these calculations are consistent with available experimental data of catalytic properties of Pt and Au stepped surfaces.

A model Hamiltonian, in which correlation may be treated exactly, is used to discuss the stability of neutral clusters composed of three and four monovalent atoms. Electron repulsion is shown to have a relevant effect on the relative stabilities of four-atom aggregates of different geometries. In particular, it is found that the more stable structure of a neutral four-atom cluster depends upon the ratio between the repulsion energy of a pair of electrons sharing the same atomic orbital and the hopping integral between nearest neighbours. A transition point in the zero-temperature ground state occurs for one of the four-atom structures at a given value of this ratio.

The nature of the ground state of the V centre in ionic oxides is discussed, where two holes are trapped by a cation vacancy. Experiment appears to indicate an S=1 ground state for BeO and Al₂O₃ and possibly ZnO, with S=0 in MgO and CaO. Simple theoretical arguments suggest S=0. It is shown that a weak mixture of (O⁰O^2-) configurations into the dominant (O^-O^-) configuration can explain the observations. Quantitative calculations are given for MgO, and suggest the singlet state is lowest by about 30 cm^-1.

Energy bands in FeS₂ are calculated using the LCAO method. An extension of this band structure to CoS₂, NiS₂ and CuS₂ is presented and these energy bands are compared with the experimental data available.

Compton profiles of polycrystalline titanium and titanium carbide have been measured with 59.54 keV gamma rays. All results are corrected for double Compton scattering. In the case of Ti the experimental result agrees fairly well with the outer electron configuration 3d²4s² where the renormalized free atom model has been used for two 4s electrons. The TiC profile has been compared with a theoretical model where Ti is a donor and with a model where Ti is an acceptor. The experimental result is found to support the model where electrons transfer from titanium to carbon when titanium carbide is formed.

A new EPR determination of the spin-Hamiltonian parameters for Gd³⁺:YAG has been made. A direct comparison of garnet crystal-field and spin-Hamiltonian parameters, as well as the success of the superposition model analysis, enables us to eliminate the possibility of large non-linear (e.g. quadratic) crystal-field contributions to the Gd³⁺ ground-state splitting. Spin-Hamiltonian superposition model parameters are derived and an analysis of the n=2 crystal-field and spin-Hamiltonian parameters suggests that the coordinate angles derived from X-ray data are in error by about 1 degrees .

The dispersion relation of the magnetic excitations of the hexagonal ions in DHCP Pr and the selection rules for the linear coupling to the phonons are determined by general symmetry considerations. The magnetic excitations propagating in the symmetry directions are considered in the cases of an external magnetic field applied along an a and a b direction. The magnetic excitations are approximated by pseudo-boson excitations of the spin sub-space, J=4, M_J=0 and +or-1, and the presence of the ions on the cubic sites is neglected. The selection rules deduced agree with experimental observations. The experimental result for the strength of the exciton-phonon interaction is used in an estimate of the effects of an applied field on the elastic constants of Pr at zero temperature.

The ESR spectra of five Cr³⁺ centres in KMgF₃ and KZnF₃ are reported. All are axially symmetric and can be described by the spin-Hamiltonian H=g/sub /// beta B_zS_z+g_{perpendicular to} beta (B_xS_x+B_yS_y)+D(S_z²-¹/₃S(S+1)) with S=³/₂. In KMgF₃ one finds spectra with D=-0.1528 cm^-1 (trigonal), D=-0.2167 cm^-1 (tetragonal) and D=-2.4 cm^-1 (tetragonal). In KZnF₃, centres are found with D=-0.1613 cm^-1 (trigonal) and D=-0.0522 cm^-1 (tetragonal). The trigonal spectra are ascribed to Cr³⁺ ions associated with K⁺ vacancies. The tetragonal spectra are attributed to Cr³⁺ ions with divalent cation vacancies with O² ions or with other impurities on the tetragonal axis.

The coupled relaxation of the Zeeman magnetization and the rotational polarization have been derived for a polycrystalline sample consisting of methyl protons and other protons, assuming the rapid reorientation of the methyl groups to be the dominant relaxation mechanism. The observed relaxation behaviour is found to depend on the preparation of the spin system, because different initial values of the rotational polarization can be obtained. Moreover the behaviour of the Zeeman relaxation can be altered by an external rotation of the sample, or by a sudden flip of the sample over an angle of 180 degrees , because this influences the coupling between the magnetization and the rotational polarization. The experimental results are verified on a polycrystalline sample of 2,6-dimethylphenol at room temperature.

For pt.II see ibid., vol.8, p.3211 (1975). A general expression, including retardation effects, is derived for the van der Walls free energy of interaction between two spatially dispersive semi-infinite half spaces using the infinite barrier model in which the currents are reflected specularly at the interface. The answer is given in terms of model independent longitudinal and transverse bulk dielectric permittivities which are functions of the wavenumber. Numerical estimates of the effects of spatial dispersion on the interaction energy are given using the hydrodynamic model for the permittivities. It is demonstrated that, for two like metallic half spaces across vacuum, spatial dispersion can cause at least a 20% reduction in the effective Hamaker 'constant' at separations approximately=4k_F^-1 where k_F is the Fermi wavenumber. Some inadequacies in the hydrodynamic model are pointed out.

The dynamical image interaction between a moving charge and a spatially dispersive medium has been evaluated as well as the Van der Waals dispersion energy between a dipole and the same substrate. The spatially dispersive medium is represented by the 'infinite barrier' model with specular reflection of current fluctuations at the interface. Numerical estimates of the effect are computed using a hydrodynamic model for the dielectric permittivity.