Table of contents

Low-energy electron angular spectra have been measured on numerous cleavage surfaces of natural MoS₂ but good angular results have been achieved from very few surfaces. It is very difficult to cleave the crystal well enough to obtain this kind of measurement.

The theory of Hodges and Stott (1972) on the heats of formation within the density functional formalism is extended to include explicitly the change in Wigner-Seitz boundary conditions on the formation of the alloy. The derivation given here leads directly to a surface term in addition to the charge transfer term and the two taken together are shown to be simply the change in the sum of the one-electron band energies.

The electronic properties of pure polyacetylene have been studied on the basis of the one-dimensional tight-binding LCAO-SCF-MO calculations. It is deduced that the sudden occurrence of high electrical conductivity in polyacetylenes doped with electron donors or acceptors is essentially brought about by the transfer of an electron from the highest occupied band ( pi ) or to the lowest unoccupied band ( pi *) of the parent polyacetylene.

The anomaly observed in the dynamical structure factor S(k, omega ), of various metallic systems is explained by considering processes in which a plasmon decays into an electron-hole pair plus a plasmon in addition to the usual RPA single-pair final state. The splitting in the spectrum is shown to result from the existence of two poles in S(kz) for Imz<0 and k<2k_F. The observed structure in S(k, omega ) is reproduced almost exactly.

The splittings, by the electron-vibration interaction, of the vibronic levels associated with a threefold-degenerate odd-parity vibration and a threefold-degenerate electronic state are calculated. The splittings of the n=1 vibronic states are calculated in isolation and then the effect of interaction with the n=3 and n=5 vibronic states is considered. It is shown that for the CaO:Ni²⁺ system the interaction with the n=3 vibronic levels is significant whereas the effect of the n=5 vibronic levels can be neglected. An excellent account of the ¹T_2g vibronic splittings is then obtained.

The Sjolander-Stott integral equation for the static structure factor has been solved by iteration to first order which takes into account non-linear effects. An expression for the correlation function to order 1/(r₀ lambda _D)² is obtained in contrast to the linear response term for electrons disturbed by an impurity of large mass lambda _D is the Debye wavelength and r₀ is the closest distance of approach of the electrons to the impurity.

The effective-medium theory for the random-site model of a percolating honeycomb lattice is formulated. The value of the critical site concentration obtained, x_c=0.707, is compared with the series value x_c=0.70+or-0.01 and the Monte Carlo value x_c=0.688+or-0.015.

A position-space renormalisation group calculation based on the Migdal approximation is presented for a randomly diluted Heisenberg magnet. A crossover from percolative to thermal critical behaviour was found at low temperatures and the associated crossover exponent has been calculated. To investigate the behaviour at higher temperatures, an approximate recursion formula was used for the spin system. The calculated variation in the reduced Curie temperature with the concentration of impurities is in fairly good agreement with series-expansion results.

The dielectric susceptibility of a solid electrolyte of the Hollandite class is found to be virtually independent of temperature in the range 5.2-77K and shows the 'universal' type of frequency dependence chi ( omega ) varies as omega ^n-1 in the frequency range 10^-3-10⁵ Hz. The exponent n is close to unity at the higher frequencies but has a much smaller value, giving rise to a strongly dispersive law, at lower frequencies. The interpretation given invokes many-body processes which are generally responsible for the universal dielectric behaviour.

Experimental evidence is given for two opposing effects of the voltage amplitude on the dielectric loss of solids resulting, respectively, from the injection of electronic charges and the removal of ionic charges. In each case, the condition corresponding to the least density of charge carriers approximates to the 'universal' form of dielectric response of the 'matrix' itself, while the presence of charge carriers gives rise to its own characteristic contribution.

The optical absorption spectra of small (Pt(dapn)₂)(Pt(dapn)₂Br₂)(ClO₄)₄ particles where dapn is 1,2-diaminopropane, exhibit size effects analogous to those of small gold particles. Suspension in carbon tetrachloride or deposits on quartz are red and violet in colour and the absorption spectra show maxima at 510 and 580 nm when the particles are, respectively, 150 and 900 AA in diameter. This material is suitable for the study of the optical properties of very small particles.

The irreducible PUA representations of the Shubnikov point groups are tabulated using the procedure of generalised induction and the decomposition theory of factor systems.

The room-temperature kinetics of colouring in NaCl:Mn²⁺ has been investigated as a function of concentration and aggregation state of manganese. The colouring rates for quenched and as-grown samples are similar at very low dose, but the colouring curves differ markedly at higher dose, the colouring being higher for as-grown samples. The initial F-colouring increases with Mn concentration up to approximately 90 ppm where it roughly saturates. The thermal stability of F centres is greater in as-grown than in quenched samples in accordance with the shift of the thermoluminescence glow peaks to higher temperatures. A prominent band at 220 nm is formed under irradiation in proportion to the concentration of cation vacancies existing prior to irradiation. The kinetics of growth under irradiation and the thermal annealing behaviour of various Mn centres has also been investigated. No linear correlation has been found between the concentration of F-centres created and Mn²⁺ vacancy dipoles destroyed during irradiation.

Measurements of F- and M-centre colour curves in NaCl during irradiation at temperatures between 15 and 95 degrees C and at dose rates of the order of 10⁴ rad h^-1 indicate quite clearly two distinct processes for M-centre production. One, the statistical process, leads to an M varies as F² relation at both low and high doses. The other, an F-centre thermal diffusion process, produces a deviation in this relationship and furthermore is responsible for the maximum observed in F-centre colour curves at high temperatures. These two processes, together with an interstitial trapping model, provide a comprehensive picture for the first-stage colouring process in NaCl, over the range of temperatures and dose rates used here.

A discrete basis set has been used in conjunction with many-body perturbation theory to calculate correlation contributions to the Sternheimer quadrupolar antiscreening parameter gamma _infinity in the Pr³⁺. A very large contribution, omitted in previous work, is shown to arise from the use of Hartree-Fock potentials in generating the basis states. The remaining correlation contributions have been calculated to lowest order and are shown to be relatively small.

A many-body theory for the phase transition to a metallic condensed state of electron-hole drops in elemental semiconductors like Ge and Si and compounds like GaAs is presented. Calculations have been done with the realistic many-valley band structure including the effects of anisotropy. As the transition was expected to be of the first-order Mott type, the Hartree-Fock approximation has been used to truncate the Green function equations. Results are presented for both 0K and for finite temperatures. The computed values of the critical temperature T_c for these materials have been found to give good agreement with experimental results.

The model one-dimensional electron gas, defined by a particular ultraviolet cut-off procedure, is shown to decompose into two parts, a Tomonaga-Luttinger model and a model equivalent to the two-dimensional Coulomb gas. For a particular value of one of its coupling constants, this latter model is shown to be equivalent to a model of free fermions. These results, familiar features of the boson representation of the one-dimensional electron gas, are here derived entirely within the context of fermions. The cut-off procedure used differs from those normally considered in the literature. The significance of these differences is discussed.

An approximation scheme is derived for the dynamical conductivity of a non-interacting fermion gas moving at zero temperature in a three-dimensional random potential, which exhibits a non-linear feedback of the fermion density fluctuation spectrum to the frequency-dependent current relaxation rate. The approximation equations describe an insulator-conductor phase transition caused by strong memory effects and important non-localities in the equations for the current relaxation. Close to the transition point the dynamical conductivity obeys a scaling law with a scaling function which is a solution of an algebraic equation. The main features of the conductivity in the transition regime are a divergence of the insulator polarisability and a continuous decrease of the conductor DC mobility towards a zero at the transition point, a critical slowing down of the current spectrum, a semiconductor-like excitation threshold of the insulator and a strong non-Drudian frequency of the dynamical conductivity.

It is shown that in the framework of a generalised Ginzburg-Landau scheme based on the microscopic model of chains of 1D Fermi gases interacting via a Coulomb-type interaction it is possible to account for the observed critical behaviour near the 53K phase transition of TTF-TCNQ. The pseudogap is also calculated and its effect on the electronic density of states is found to disappear above the critical region.

The model for spin-state transitions described by Bari and Sivardiere (1972) is static and can be solved exactly even when the dynamics of the lattice are included; the dynamic model does not, however, show any phase transition. A coupling between the octahedra, on the other hand, leads to a phase transition in the dynamical two-sublattice displacement model. A coupling of the spin states to the cube of the sublattice displacement leads to a first-order phase transition. The most reasonable model appears to be a two-phonon model in which an ion-cage mode mixes the spin states, while a breathing mode couples to the spin states without mixing. This model explains the non-zero population of high-spin states at low temperatures, temperature-dependent variations in the inverse susceptibility and the spin-state population ratio, as well as the structural phase transitions accompanying spin-state transitions found in some systems.

The coherent potential approximation has been applied to the bond diluted Ising model in a transverse field. Green function techniques decoupled in a generalised RPA have been used. The static and dynamic properties of this system have been studied at T=O and it is concluded that the form of the CPA equations inhibits the appearance of a second-order phase transition, if the divergence of the static susceptibility is the only criterion locating the transition. A discussion of this problem and its relation to other models is also included.

A position space renormalisation group procedure is developed for the compressible Ising model. The procedure is essentially a generalisation of the cell variable approach of Niemeijer and Van Leeuwen (1974) in that vibrational cell variables are introduced in addition to spin cell variables. The procedure is applied to the two-dimensional triangular lattice, the shearless square lattice. In both cases the rigid Ising fixed point is stable to spin-lattice coupling as long as the latter is small. Beyond a critical strength of the spin-lattice coupling, the system develops instability leading to, presumably, a first-order transition. For the shearless square lattice the conclusion is at variance with the exact result of Baker and Essam (1971), so the approximation is regarded as unreliable for larger values of the spin-lattice coupling (1971).

For pt.I, see ibid., vol.12, p.79 (1979). A recent investigation of the Ising spin glass using the n to O replica method is generalised to m-vector spins. As for Ising spins (m=1), the order-parameter correlation functions contain, within mean-field theory, massless modes which become unstable at first order in perturbation theory about the mean-field solution. An alternative formulation of perturbation theory restores stability, giving massless modes once more, but yields an expansion for the order parameter which breaks down for dimensionalities d<or=4 due to infrared divergences. A dimensionality of four is therefore interpreted as the lower critical dimensionality of the theory, as for the Ising spin glass.

In a previous paper the dynamical properties of the S=₂/¹ Heisenberg ferromagnet were discussed using an extension of the RPA. This theory is extended to theS=₂/¹ Heisenberg antiferromagnet. The method consists of representing the effect of temperature by a fixed array of up and down spins. The spin-wave excitations are calculated in this disordered array using the coherent potential approximation for a system of potentials due to the appropriate distribution of bonds. A relation between the number of reversed spins and temperature is derived from self-consistency and the transition temperature T_N is found to be the same as the RPA result. The method gives a reasonable approximation overall to the spin-wave response at T<or=T_N, although it is not correct in the low-T limit.

Discusses the equilibrium configurations and the phase transitions of a semi-classical model system consisting of two equal magnetic moments coupled by isotropic, anisotropic and antisymmetric exchange, with uniaxial anisotropy terms up to fourth order, in the presence of a transverse magnetic field. No restriction is imposed on the values of the interaction parameters. Magnetic configurations of the 'conical' type appear for non-negligible values of the antisymmetric exchange and of the fourth-order anisotropy term, and are found to be stable over a wide range of values of the physical parameters and the external field. The results of the theoretical model are applied to the interpretation of the neutron scattering data and the transverse magnetisation measurements on some diamagnetically substituted hexaferrites of the Y and Z types.

Magnetisation and neutron studies have been performed on single crystals of UTe and USb_0.8Te_0.2. The magnetisation measurements demonstrate that the magnetic moments are confined to the (111) direction, and that derivations from this direction, even in fields up to 90 kOe, are negligible at low temperatures. The saturated magnetic moments are 1.91+or-0.05 mu _B in UTe and 2.58+or-0.05 mu _B in USb_0.8Te_0.2. Polarised-neutron experiments on the same single crystals give values for the 5f ordered moments of 2.25+or-0.05 mu _B and 2.64+or-0.05 mu _B, respectively. The discrepancies of -0.34 mu _B in UTe and -0.06 mu _B in USb_0.8Te_0.2 are attributed to the polarisation of the 6d-7s conduction electrons.

The EPR spectra of axial VO²⁺ ion impurities in Na₂Zn(SO₄)_2.4H₂O single crystals have been observed at X-band. The VO²⁺ enters the Zn²⁺ site and the V-O axis is found to have three possible orientations with populations in the ratio 14:6:1. A correlation between the Zn-O distances and the populations of the different V-O orientations is observed. The spin-Hamiltonian parameters at 305K have been calculated for all the three VO²⁺ centres.

For pt.I, see ibid., vol.10, p.4599 (1977). One-quantum scattering of Mossbauer radiation is considered, taking into account the dispersion of the real and imaginary parts of the frequency of the critical fluctuation in a condensed medium. Scattering in the soft optic and damped acoustic modes are studied in detail. The importance of many-particle scattering is also discussed.

The decay of the charging current in bis(catena-poly(methylarsenic), (CH₃As)_x, a quasi-one-dimensional long chain polymer, due to step and ramp voltages confirms that its dielectric behaviour is anomalous for frequencies below 1 Hz. After the DC conduction is removed, the dielectric loss factor epsilon " varies as f^-0.5 for 2*10^-4<f<10^-1 Hz at both T=295 and 392K. This implies a static dielectric constant in excess of 100. The effect is examined in terms of Jonscher's 'universal' dielectric response and the hopping mode of carrier transport present in the material at these low frequencies.

The optical transmittance of thin PdO films has been measured in the range 0.5-5.4 eV. From these data the optical constants have been determined by Kramers-Kronig analysis. A small band gap (0.8 eV) and a high dielectric constant (8.0) have been found.

The resonance fluorescence of a crystalline solid consisting of two-level atoms is studied. The method of Heitler and Ma (1949) is used to solve the equations. From the calculated result, it is found that the probability of emission of photons is discrete in angular and in wavelength distributions. The emission line in the incident direction is identical in shape with the absorption line. While there is no actual trapping of radiation, the effect of photon-trapping manifests itself in both the emission and the absorption spectra.