Table of contents

The effect of nearest-neighbour central force constant changes near vacancies and interstitials in crystals with fluorite structure is investigated by ATA. It is found that they cannot account for the experimentally observed difference in the temperature dependence of the elastic constants c₁₁ (large decrease near the transition temperature to the state with good ionic conductivity) and c₁₂ and c₄₄ (no measurable decrease). Including Coulomb force constant changes to lowest order in perturbation theory, suggests that they may be responsible for the different behaviour.

An error is pointed out in the discussion by Laplaze J. Phys. C, vol.10, p.3499 (1977) dealing with the results of one of the author's lattice dynamical models and Laplaze's results are briefly compared with those based on their model.

A value of the minimum metallic conductivity of order 10³ Omega ^-1 cm^-1 is observed for many transition metal compounds which show a metal-insulator phase transition. When the conductivity at the transition is above this value, the resistance shows the normal metallic behaviour increasing with increasing temperature. When it is below this value, the resistance is activated, as for a semiconductor. In a single valence compound (e.g. V₂O₃, VO₂) a change of conductivity from one form to the other is, due to structural disorder. Compounds with mixed valence (V₄O₇, V₃O₅, etc.) always have an activated conductivity. An hypothesis is offered that this behaviour is connected with electron localisation, due both to the structural disorder and to electron correlation.

In-plane resistivity measurements, both parallel and perpendicular to the Mo chain direction have been performed on single crystals of beta -MoTe₂ between approximately 10K and 295K. The data suggest the existence of a first-order phase transition near 250K.

The 410 cm^-1 line of the IETS spectrum of phenol has been examined at approximately 70 mK. Its lineshape with normal and superconducting electrodes is explained when a natural linewidth of 1.504 meV (12.13 cm^-1) is assumed. The results demonstrate the possibility of using IETS for the study of monolayers at a resolution better than 0.1 meV.

The Monte Carlo method has been used to study the behaviour of Ising model spin glasses. Both the double delta function and Gaussian distributions of interaction strengths have been considered. No evidence for cusp-like behaviour is obtained, but the susceptibilities appear to diverge at low temperature.

ENDOR measurements have been made on the linear bond structure Fe³⁺-F^--Cd²⁺ in crystals of CsCdF₃:Fe³⁺. The observed hyperfine interactions with the ¹⁹F, ¹¹¹Cd and ¹¹³Cd nuclei indicate that the sigma -bonding orbitals on the F^- ion are not symmetrical but have larger lobes pointing towards the Fe³⁺ ion than towards the Cd²⁺ ion. It is suggested that a substitutional trivalent ion in a divalent host lattice site causes hybridisation of the ligand sigma -bonding orbitals by the admixture of excited states for example 3s in the present case. A similar proposal for some rare-earth ions has been made independently by Baker and Christidis (1977).

The effective-medium approximation of Landauer and Kirkpatrick (1973) is extended for bond-percolation conductivity by taking into account clusters of increasing size. In the three-bonds approximation exact results for the critical probabilities of the matching 2D triangular and honeycomb lattices are obtained.

Inelastic neutron scattering has been used to measure the phonon energy dispersion relation along the (001), (110) and (111) directions of a single crystal of lead fluoride, PbF₂, at 10K. Shell model parameters have been successfully fitted to the data, and those giving the best fit have been used to calculate the density of phonon states and values for the elastic constants and the Debye temperature. The results are compared with data obtained by other methods.

Effects of the electron-phonon matrix element (EPME) on phonon anomalies in transition metal compounds due to d-band effects are analysed in detail by using a simple model proposed by Gale and Pettifor (1977). Susceptibilities with and without the EPME and an energy change associated with a second derivative of hopping integrals, Delta E₂, are calculated by using Haydock et al.'s (1972, 1975) recursion method. It is pointed out that the EPME is very important in producing phonon anomalies and an energy change Delta E₂ can enhance them. A discussion from a local bond point of view is also given to elucidate the basic role of the EPME. This argument suggests that the positions of phonon anomalies may be rather insensitive to the choice of parameters.

Dynamical spin correlation functions in (q, omega )-space are calculated numerically for linear quantum-mechanical Heisenberg systems containing up to ten spins with s=¹/₂ and s=1. The authors consider ferro- and antiferromagnets including single-site and exchange anisotropies. They compare their results with various other theoretical treatments and draw conclusions for the dynamics of infinite chains. In the case of the s=1 planar Heisenberg ferromagnet direct comparison is made with inelastic neutron scattering cross sections of CsNiF₃. The theoretical and experimental results are in good agreement.

A coherent potential approximation (CPA) ansatz for a Heisenberg ferromagnet which possesses both nearest and next-nearest neighbour exchange interactions, is given. Spatial randomness caused by introduction of non-magnetic impurities, i.e. magnetic site dilution, is treated in the approximation where the bonds are taken to be independent. The occurrence of exchange bond fluctuations between pairs of magnetic atoms, is also considered. Numerical results are given for the coherent exchange integrals, spin-wave stiffness and the Curie temperature (which is derived within a random phase type of approximation) for a variety of situations.

A high-temperature power series for the second moment of the relaxation-shape function including second neighbour interactions is calculated to order (J/k_BT)⁵. The second neighbour specific heat series is inferred from this calculation. For first neighbours only it is shown how this second moment can be obtained from the specific heat series.

Analytic expressions for the low-order frequency moments omega ⁿ (n=0,2,4,6) of the spin correlation function for a dilute isotropic Heisenberg paramagnet at infinite temperature are obtained for arbitrary spin and arbitrary range of the magnetic interactions. A check on the accuracy of the expressions is provided by computer results for a number of simple lattices restricted to nearest-neighbour magnetic interactions.

The low-frequency, long-wavelength properties of a paramagnet in d dimensions are studied within the framework of a non-linear Langevin equation. The frequency and wave-vector dependent transport coefficient Gamma (k, omega ) has a singular part which varies as omega ^d/2 at k=0 so its time Fourier transform decays as t^-(1+d2)/, in contrast to the assumptions of linearised hydrodynamics according to which Gamma (k,t) decays rapidly in a microscopic time. Both reversible and irreversible processes give contributions to this effect but with opposite signs. The latter contribution is non vanishing as k to 0 only because we include a drift term in the Langevin equation which depends explicitly on the energy density. The consequences of this generalisation of the usual Langevin equation are investigated in detail in a perturbation expansion.

For pt.II see Physica, vol.86-88B, p.1391 (1977). The authors have studied the localised modes which exist in the neighbourhood of an isolated cluster of overlayer spins on an otherwise homogeneous (001) surface of a Heisenberg ferromagnet. They have found a rich variety of such modes and comment upon their possible effects upon magnetocatalytic rates and thermodynamic properties.

A theory of the macroscopic van der Waals force in conducting media is formulated with a conductivity tensor which may be nonlocal and anisotropic. The local van der Waals force density is evaluated from fluctuating electrodynamics. It is shown that Lifshitz' (1955) prescription of including the conductivity in an effective dielectric constant gives the correct result for the total van der Waals force between bodies, but that an additional force density affecting the distribution of charge exists which is not obtained in this way. A general theory is presented in which the dielectric constant and magnetic permeability may be anisotropic and nonlocal as well. A comparison is made with the free energy resulting from the theories of Casimir (1948) and Dzyaloshinskii et al. (1961).

A theory is presented of the temperature dependence of one-magnon light scattering in ferrimagnets. The Hamiltonian describing the interaction of light with the magnetic system is taken as linear in the spin operators. Light scattering results are obtained for two-sublattice ferrimagnetic systems with nearest neighbour inter- and intra-sublattice exchange, and are shown to reduce in the appropriate limits to the ferro- and antiferromagnet. Results are also obtained for two-sublattice magnetic systems with extended range exchange in a mixed Heisenberg and Ising representations of order. Formal results are given for one-magnon light scattering from a multi-sublattice magnetic system.

For pt.I see ibid., vol.11, p.563 (1978). The theory of one-magnon light scattering from a two-sublattice ferrimagnetic system is applied to four ferrimagnetic materials: YIG, GdIG, the Li ferrite Fe(Li_0.55Fe_1.45)O₄ and the Li-Cr ferrite Fe(Li_0.5Fe_0.25Cr_1.25)O₄. YIG and Li ferrite have no compensation effects, and GdIG and the Li-Cr ferrite do. The results for the different materials are compared with those in scattering for the ferro- and antiferromagnet in T<or=T_c. The compensation ferrimagnets GdIG and Li-Cr exhibit new features in the compensation region absent in both the ferro- and antiferromagnet.

The Raman spectrum of a solid is formulated using quantum field theory. The photons are assumed to couple via localised electronic states, e.g. paramagnetic impurities. The laser is assumed to be of low power and to have a frequency well away from any electronic resonance. It is shown that the phonon-induced shift and width of each of the lines corresponding to an electronic transition, a first-order phonon line, and a vibronic transition is formally the same whether the transition is studied by absorption or by Raman spectroscopy. Width and shift contributions are given to second order in broadening interactions for the second-order phonon Raman spectrum. These results exhibit complications in some attempts to compare broadening parameters in different experiments. Some consequential adjustments to formulations of the spectrum of resonance fluorescence are suggested.

The pressure dependence of reflection, absorption and resonant Raman spectra of single crystals of toluene sulphonate dicetylene polymer have been measured under hydrostatic conditions to 5 kbars. The peak of the reflection spectrum near 2 eV shifted to lower energies with increasing pressure at a rate of 7.3+or-0.3 meV per kbar. This result is shown to be in qualitative agreement with the prediction of molecular orbital calculations. The temperature and pressure dependence of the resonant Raman spectra are discussed using a simple point mass and anharmonic spring constant model.

Infrared reflectance spectra are reported for oriented single crystals of MAMC and PAMC with the electric vector parallel to the anionic sheets for temperatures from 50 to 295K. Single-crystal Raman spectra were also obtained at similar temperatures. The main features of the spectra, particularly for the ambient temperature phases, are assigned with the aid of a factor group analysis. This phase for MAMC, although orthorhombic, behaves spectroscopically as pseudo-tetragonal, but PAMC is plainly orthorhombic. Modes above 260 cm^-1 are attributed to cation internal modes, including torsions. The phase III (tetragonal) to phase IV (monoclinic) transition is distinguished in the Raman spectra by disappearance of an intense broad features at about 35 cm^-1/.

X-ray absorption edges in solids show extended fine structure up to 30-60 Hartrees (1 or 2 keV) above the edge which is known to be caused by electron scattering from other atoms surrounding the absorbing atom. In addition other structure is sometimes observed, of a slower period, especially nearer to the edge, which are shown to be caused by scattering in the periphery of the absorbing atom. The new structure is closely related to the derivative of the p-phase shift in the case of K-shell excitation, and improved values of the phase shift can be extracted from experiment.

L₃M_2,3M_4,5, L_2,3M_2,3M_2,3 and L₃M₁M_4,5 Auger spectra obtained from solid Cu, Zn and Ge are compared with multiplet structure calculations in which transition rates are evaluated in a jj-intermediate coupling scheme and multiplet splittings are calculated using Slater integrals found from Hartree-Fock treatments of the two-hole final states. It is suggested that Auger vacancy satellite processes contribute to the L₃M_2,3M_4,5 spectra of Cu and Zn. There are discrepancies between calculated and measured splittings in the L₃M_2,3M_2,3 groups of all three elements.