Table of contents

The renormalization group approach to critical phenomena is developed for quantum mechanical problems with non-commuting operators. Applying the theory to the spin ¹/₂ Ising model with a transverse field Gamma it is found that the critical exponents are those of the Ising model with Gamma =0 if the transition occurs at T>0. However, for transitions at T=0 the critical behaviour of the d-dimensional transverse system corresponds to that of the (d+1)-dimensional Ising model with Gamma =0, in agreement with series expansion predictions. At T=0 the dynamic, as well as static, critical behaviour is given by mean field theory for d>3.

The electrostatic and the band structure contributions to the total energy in Te and Se are calculated for the A8 structure. Minima of energy at constant volume gives values of the atomic position parameter u close to the experimental ones, while the axial ratio c/a is not well resolved, especially in the case of Se. However, the ratio between the second and the nearest-neighbour distances, which is of relevant physical interest, is determined with a good accuracy. The importance of taking into account the non-locality of the pseudo-potential is also shown.

Reinterpretation of light scattering and conductivity measurements (see abstr. A52767 of 1974) reveals the complexities of precipitation including the existence of precipitation 'imprints' above the temperature of dissolution.

It is argued that long-range fluctuations in potential do not have the effect on eigenstates near the mobility edge suggested by Cohen (see abstr. A47704 of 1970).

A simple treatment of networks containing conductances g_A and g_B gives an exact formula for the conductivity in terms of g_A, g_B, the fraction b of conductances g_B and a quantity lambda . Setting lambda =d^-1 in d dimensions 1 - 2/pi in two dimensions and 0.210 in three dimensions yields effective medium results for the bond, two-dimensional 'non-overlapping' site and three-dimensional 'non-overlapping' site problems respectively. This is shown to be a good approximation for all values of g_B/g_A and b. For the ordinary site problem the lambda values 1 - 2/pi and 0.210 yield good approximations only when b to 0 or g_B=0 and lambda increases by approximately 50% as b to 1 with g_B not=0.

Inelastic neutron scattering studies of the magnetic excitations in the planar Heisenberg random antiferromagnet Rb₂Mn_0.5Ni_0.5F₄ at 7K are reported. Two well-defined bands of excitations are observed. A simple mean crystal model is found to predict accurately the measured dispersion relations using essentially the pure crystal parameters while the zone boundary energy widths are well-accounted for by an Ising cluster mode. Intensities, however, are not properly explained using these simple models.

A discrepancy between transferred hyperfine structure parameters measured by ENDOR (see abstr. A8045 of 1969) and by direct NMR (see abstr. A44334 of 1973) has been resolved by a remeasurement of the ENDOR spectrum. The new values are in excellent agreement with those previously measured.

Dielectric loss measurements on CaF₂:Gd³⁺ show four relaxation absorptions. By correlation with EPR the assignment of a relaxation with activation energy 0.396 eV to a tetragonal site is confirmed. Evidence against assignment of a relaxation with activation energy 0.68 eV to a trigonal site is obtained. Relaxations with activation energy 0.15 eV and 0.076 eV are tentatively assigned to aggregates. Relaxation of the tetragonal Gd³⁺-H₁^- and Gd³⁺-D₁^- sites is shown by EPR to have an activation energy close to the Gd³⁺-F₁^- site but is not observed in the dielectric spectrum.

A microscopical theory is developed which describes the non-steady kinetic phenomena (e.g. conduction and diffusion) for defectons in a crystal. The principal features of the phenomena, the effects of the lattice deformation and the many-level nature of the defecton potential wells are discussed and expressions for the conductivity and diffusion coefficient for free and bound defectons are obtained. The role of the coherent and incoherent underbarrier and overbarrier transitions is explained. The quasiclassical case of non-steady diffusion and Debye-type and resonance type dielectric losses are compared with classical results and the effects of strong external or random internal fields are noted.

Computer simulations of the F-centre accumulation at liquid helium temperatures (LHT) in alkali halides, taking into account the spatial distribution and the tunnelling recombination of the localized F- and H-centres have been undertaken. The presented model easily explains known experimental data at these temperatures, that is: (i) the saturation and possible subsequent decay of the F-centre production rate (ii) the existence of an abnormally high fraction of the aggregate (F₂,H₂,...) centers (in contrast to random distribution), (iii) the formation of large loose aggregates (iv) the existence of F-centre concentrations exceeding 10¹⁹ cm^-3 and (v) the dependence of the production curve on the excitation intensity. A mechanism for loose-aggregates formation is proposed. The applicability of the present model at room temperature is discussed.

Assuming a quasi-lattice model of theoretical expressions for the cross coefficients which appear in the relation for the viscosity of a binary liquid mixture, are derived. The appropriateness of the proposed relations has been tested with success, by calculating the viscosity of several binary mixtures.

For pt.I see abstr. A12890 of 1975. LEED I(V) calculations have been performed for the MgO(100) surface at normal incidence. Various models were tried and the best of these gave good agreement between theory and experiment. On allowing the top layer to relax by +or-3%, this agreement deteriorated, suggesting that the MgO(100) surface is little distorted from a simple termination of the bulk.

An iterative perturbation scheme is constructed for LEED calculations. The subplanes comprising an ideal crystal surface are assigned a definite order and it is shown how to calculate the scattering amplitude to any order in reverse scattering. This method can be used without supplementation by other methods when there are several inequivalent subplanes in a surface layer and has great advantages of speed and low core storage requirements. The scheme is tested by calculations on Ni(111) layer.

LEED, Auger, and electron-loss spectra are reported for a UHV-cleaved NiO (100) surface. Data are given for the clean surface and a surface contaminated mostly with about half a monolayer of chlorine. Large systematic intensity variations are found between different LEED beams, and the possibility of anisotropic electron mean free paths is suggested. The loss spectra are interpreted as containing features due to charge transfer excitons.

A close analogy is traced between LEED and emission processes resulting in a generalization of LEED calculations to encompass the emission case. The theory describes all multiple scattering corrections to angular dependence of emission by making use of RFS perturbation theory and is expected to be of use for interpretation of Auger and XPS experiments, especially those using synchrotron radiation.

A theory of the difference in photoemission from a solid with and without a chemisorbed atom is presented. The final electron state is taken as a plane wave, damped to simulate the finite mean free path. The matrix of the spectral density function is obtained from the Hartree-Fock theory of chemisorption developed by Grimley and Pisani (see abstr. A72634 of 1974). The difference photoemission has been investigated for hydrogen on (100) simple cubium and on lithium and shows the expected four lobed intensity variation characteristic of the C_4v symmetry of the adsorption site. For hydrogen on lithium, the angular dependence is slight since most photoelectrons come from a well localized site below the bottom of the conduction band. The possibility of determining the adsorbate density of states from photoemission measurements is considered.

Using the perturbation expansion for the one-electron Green function a new selfconsistent method for the determination of parameters f_lambda , denoting the lattice distortions around an excess electron is introduced. It is shown that f_lambda depends mainly on the quotient between the polaron group velocity and the phonon phase velocity, and on the damping Gamma of the polaron states. From polaron eigenstates and their Gamma , the one-electron spectrum is calculated for the adiabatic and the nonadiabatic case. Abrupt temperature-dependent changes in the spectrum are not observed.

The way a zero-phonon line splits under uniaxial stress can give useful data on the symmetry properties of optical centres in crystals. This note shows that the splitting pattern may be considerably altered if the crystal is incorrectly oriented by as little as a few degrees. It is shown that conflicting experimental results for the GRI band in diamond can be plausibly reconciled through misorientation effects.

The ground-state energy and wavefunction associated with the two-electron impurity state in GaP:O, and the optical cross section involving this state and the conduction bands are presented. The unusual shape of the cross section and the position of the impurity state in the forbidden gap are explained in terms of the multi-band nature of the impurity wavefunction and the effect of lattice relaxation. Both the conduction- and valence-band contributions to the formation of the state are shown to be of importance.

A study of self-energy corrections to the RPA dielectric function shows the possibility of a new X-ray scattering process (XCPS) in which both a plasmon and an electron-hole pair are created simultaneously. Appropriate energy-momentum conservation equations are formulated and solved. The differential scattering cross section for XCPS is obtained in a simple way and numerical calculations are presented for the case of CrK_{beta 1} radiation incident on beryllium. The XCPS lineshape is asymmetric and consists of two components arising from the RPA dielectric function and the plasmon singularity of the self-energy function. The total intensity under XCPS is about 10 per cent of that under the pure plasmon scattered spectrum.

It is shown that the critical bond number in randomly bonded systems runs from B_c=2 for z=2 to B_c=1.84 for z= infinity (z=maximum number of bonds per site), and the large discrepancy between these results and those of the treeing model is discussed.

It is shown that classical formulae which describe acoustoelectric amplification can give the values of the coupling coefficient the dielectric relaxation frequency and the trapping parameters if one can measure the change of phase velocity as a function of the accelerating electric field. A method based on measurement of the phase velocity in the pulsed mode is proposed, which allows the direct determination of these various parameters. Experiments are performed on photoconducting CdS operating in the Rayleigh mode. The dielectric relaxation frequency omega _c is not proportional to the semiconductor conductivity. The trapping time tau varies linearly from 10^-9 s to 5*10^-9 s with the conductivity in the range explored.

An analysis of the time decay of the surface charge on an insulator resting on an earthed plate is made in terms of the internal field and the spatial distribution of volume charge. It is shown that Davies' analysis (see abstr. A29860 of 1967), is valid for terms shorter than a charge transit time and full solutions are obtained for the zero external field (Kelvin) case. The analysis is based on a transformation of the field equation governing charge transport into an equivalent heat transport formalism and it is shown that this transformation may have general applicability in surface and volume charge problems.

The effects of elastic anisotropy on calculations of the direct process spin-lattice relaxation time for ions in cubic lattices are derived analytically. The results are shown to be in good agreement with numerical solutions for particular examples of cubic crystals.

A general formalism is developed to calculate free energies of inhomogeneous spatially dispersive media in terms of bulk dielectric properties. To illustrate the application, two semi-infinite half spaces separated by a vacuum are considered. All previously known results for surface energies and interaction energies for dielectrics and electrolytes derived using continuum theories emerge as special cases. The result for the interaction free energy of two like media across a vacuum reduces to a form which is identical to that obtained by Lushnikov and Malov (see abstr. A82652 of 1974) using diagrammatic methods. In addition it is demonstrated that, subject to certain reasonable assumptions about the dielectric permittivity, it is equivalent to the results obtained using the method of surface modes.