Table of contents

A model assuming a non-continuous structure of glasses is established to interpret the inelastic neutron scattering and Raman scattering. The 'boson' peak in Raman scattering is related to the vibrational density of states 'excess'. These two related features are a result of vibrations localized in the blobs that compose the glass. Size distributions of the blobs are deduced from neutron and Raman scatterings.

The authors have studied the elastic stability of an arbitrary equilibrium state of a homogeneous solid when Lagrangian parameters are used. They first introduce the notion of subrepresentation (SR) and then they show how the passage from one SR to another can be easily described by a 'passage matrix'. The equation determining the 'strain spinodal' is then obtained in terms of this passage matrix and it is demonstrated that an inflection point on the free-energy surface in Lagrangian parameter spaces does not necessarily correspond to an elastic instability of the solid. These results are finally applied to the localized soft-mode theory, showing the existence of an important harmonic contribution to the strain renormalization of the second-order elastic constants, which has been entirely neglected by Clapp (1973) and subsequent workers. For some alloys, the numerical values prove that this harmonic contribution tends to stabilize the lattice but not enough to compensate the anharmonic effects, and therefore Clapp's model is still likely to be valid.

The resonance theory of incommensurate (IC) phases in insulators studied by Heine and McConnell (1984) is reviewed and applied to ammonium hydrogen oxalate hemihydrate, in which and IC phase is stabilized above 3 kbar between the room-temperature paraelastic phase and the low-temperature ferroelastic phase. It is suggested that this IC phase is due to a structural resonance between the ferroelastic ordering mode and an incipient ferroelectric ordering mode. A simple pressure dependence of the latter reproduces the topology of the p-T phase diagram and the pressure dependence of the IC wavevector at T_IC. Specific predictions concerning dielectric behaviour and diffuse scattering round satellite positions under pressure are made.

A theoretical study of the Si(110)-1*1, Si(100)-2*1, Si(111)-2*1 and Si(113)-1*1 surfaces is presented. The authors use both the semi-empirical tight-binding bond model and the classical potential of Stillinger and Weber to describe interatomic forces. Energy minimization calculations are carried out in order to deduce the stable atomic configurations. The authors show that the semi-empirical tight-binding approach can produce results in reasonable agreement with other experimental and theoretical work and they demonstrate that charge transfer is not an important factor governing the stability of these surfaces. In a comparative study, involving not only static energy minimization but also Monte Carlo simulated annealing, the authors show why the classical potential does not perform well in describing surface atomic structure.

A method for calculating stress/strain distributions in structures containing one or more strained layers is presented. The theory, which is based on that presented by Treacy et al. (1985) is applied to the mesa laser structure containing either a single 3.5 nm strained layer or four evenly spaced 3.5 nm strained layers of In_0.7Ga_0.3As grown on InGaAsP (lattice matched to InP). The theory includes the anisotropy of elastic constants in full. Cases of structures containing four strained layers are examined where the separation between the centre of the layers is 7.0 nm, 10.0 nm and 16.5 nm. The maximum shear strain in the case of the single layer is found to occur at the layer/barrier interface, close to the edge of the sample. This is, therefore, the region where dislocations are likely to nucleate. The shear strain is about 1.3% for the mesa structure which has a mismatch of 0.009. The presence of four closely spaced strained layers does not significantly affect the magnitude of the shear strain in the region of its maximum. Both the in-plane and perpendicular components of the strain, epsilon _yy and epsilon _xx respectively, show relaxation at the edge of the structure with the largest relaxation occurring close to, but not at, the edge.

The effects of temperature gradients and boundary conditions at the surface of a system separating into two phases via spinodal decomposition are studied numerically in one and two dimensions. For suitable cooling rates and thermal noise strengths, an off-critical system cooled from an external surface is found to separate by the formation of alternate layers of the two phases near the surface, a very different structure to that formed in the bulk. A similar pattern is found to be generated by a boundary condition associated with a surface free energy. An approximate solution is derived for the evolution of the boundary pattern in this case, allowing an estimate to be made of how far the pattern will propagate into the bulk.

Using some simple geometries composed solely of interconnecting 'diamonds', the authors study the competition between long-range magnetic order and quantum fluctuations. Since a four-atom 'diamond' is formed from two-edge sharing triangles, a 'diamond' is topologically frustrated, and hence magnetic order is energetically less favourable than usual. The classical limit yields a ferrimagnetic state with equally large ferromagnetic and antiferromagnetic moments. Symptomatic of the topological problems, there are some zero energy 'spin wave' modes in the classical limit. For low-spin systems these low energy modes become excited in the ground state, which has none of the properties predicted by the classical solution. For spin 1/2, the ground state has only short-range correlations, a broken translational symmetry, and a gap to localised spin-1/2 excitations, which also have a topological quantum number.

The authors solve the Hubbard model for the case of two particles on an arbitrary Bravais lattice exactly. Although the ground state is almost always a spin singlet, agreeing with the work of Kanamori (1963), for topologically frustrated lattices with positive hopping matrix elements, the authors find that the ground state is a spin triplet. This topological effect is shown to be rather weak, and does not always survive the jump to finite densities in the thermodynamic limit, where Pauli exclusion strongly stabilises a low spin state. For the two-dimensional triangular lattice and the three-dimensional face-centred cubic lattice, the competition is fiercer and it is not clear whether the ferromagnetism survives.

The modulating-function (MF) waveform analysis method has been generalized and applied to investigate the deep levels in semiconductors. The advantages of the MF method over other available methods-the method of moments, Fourier transform and least-squares-have been discussed and re-emphasized. As examples, the isothermal capacitance transients measured for GaAs (Si implanted) and Si (Au doped) have been analysed. The results for activation energy, capture cross section and density distribution are in general agreement with the experimental and calculated results published earlier.

Calculations are reported for a hole associated with a lithium impurity in NiO. The method is based on Hartree-Fock molecular clusters embedded in a classical shell-model lattice, with consistent treatment of distortion and polarization. It is shown that the hole is trapped in oxygen 2p states rather than in nickel 3d states, in agreement with experimental X-ray absorption spectroscopy results. In the static lattice approximation the hole localizes on a single oxygen nearest neighbour of the lithium ion, rather than in an O_h-symmetric distribution among all such neighbours.

Second-order reduction factors for spin-orbit coupling in the strongly coupled T₁(X)t₂-Jahn-Teller system are calculated using the symmetry-adapted excited states derived previously by projection operator methods. The results obtained are found to be much closer to the numerical results of O'Brien than those found previously by the authors when a much simpler form for the excited states was found. It is also found that the inclusion of anisotropy in a simplified form improves the results in the strong coupling limit.

From the analysis of electron paramagnetic resonance (EPR) spectra and the electrical characteristics of as-grown, long-period 'annealed' at room temperature and laser annealed PbTe:Mn single crystals with Mn content N_MN approximately=2-7*10¹⁸ cm^-3 the authors infer that Mn²⁺ ions in as-grown crystals are incorporated partly interstitially and partly in the metal sublattice sites. In crystals with N_Mn>or approximately=2*10¹⁹ cm^-3 Mn ions tend to form clusters. In such cases manganese behaves as an amphoteric impurity, as a small amount of Mn ions in the metal sublattice points cannot compensate for the large number of Pb vacancies (N_Pb approximately 5*10¹⁹ cm^-3) that act as acceptors. When creating the conditions that promote migration of Mn ions into PbTe metal sublattice points (long-period 'annealing' at T=300 K, IR laser annealing) which is tested by hyperfine structure and superhyperfine structure of EPR spectra, the Mn²⁺ ions act as pseudodonors, compensating for two holes from each lead vacancy. The electron concentration in such a case is attributed to Te vacancies, which are donors. The spin-Hamiltonian constants were determined at T=20 K for as-grown, long-period 'annealed' and laser annealed PbTe:Mn crystals.

For a 2DEG in a Si MOSFET the important scattering mechanisms at low temperatures are remote impurity, background impurity and interface roughness scattering. The authors perform a detailed calculation of the energy dependence of each scattering mechanism in the extreme quantum limit with a view to explaining the observed electron concentration dependence of the thermopower. For N_s less than 8*10¹⁵ m^-2, scattering by remote impurities dominates. A change of sign of the diffusion thermopower is predicted at low T and high N_s, due to the dominance of scattering by background impurities and interface roughness. The total thermopower is calculated by including the phonon drag contribution, the result being in satisfactory agreement with experimental data.

The authors study the well known kink in the Arrhenius plots of the DC conductivity of undoped hydrogenated silicon. The widespread transport model above a mobility edge is assumed and the possible explanations for the kink are reviewed. A careful analysis shows that only thermal-equilibrium processes can account for the author's present experimental data. Furthermore, they show that the kink temperature is the temperature at which the sample becomes frozen in a non-equilibrium configuration.

The spin-lattice relaxation of the protons in the compound was investigated at nu _L=13.5 MHz and 270 MHz for 4.2 K<or=T<or=100 K. The field corresponding to nu _L=13.5 MHz, B₀=0.31 T, is below the upper critical field and allows NMR measurements right in the superconducting state. Two kinds of samples were prepared: coarse grain crystals and finely powdered crystallites. In the finely powdered samples the proton relaxation at nu _L=13.5 MHz follows an exponential-square-root law. This law is traced back to proton relaxation caused by localized paramagnetic centres. At nu _L=270 MHz the relaxation follows a superposition of an exponential and an exponential-square-root law. The temperature dependence of the exponential contribution obeys the Korringa relation. This contribution is ascribed to conduction electrons. In coarse grain crystals the proton relaxation is exponential at nu _L=270 MHz for T>10 K and becomes non-exponential for T<10 K. At nu _L=13.5 MHz the transition from exponential to noticeably non-exponential relaxation occurs already at T approximately=25 K. The cause for the non-exponential proton relaxation in the coarse grains is finite penetration of the RF-field (skin-effect) into the electrically conducting crystals. Powdering the crystals suppresses the skin-effect; this procedure, however, generates relaxation sinks in the form of localized paramagnetic centres. There is reason to believe that the skin-effect in coarse grains and generation of relaxation sinks by a powdering procedure complicate proton relaxation studies as well in other organic superconductors.

A novel solution to the problem of incorporating a strong axial crystal field interaction into the RPA model of a Heisenberg ferromagnet is presented and discussed. The method is based on technique widely used in the interpretation of nuclear quadrupole resonance (NQR) experiments, where the Hamiltonian is first transformed into the interaction picture and terms which oscillate rapidly in time are subsequently dropped. It is shown that when this method is applied to an S=1 Heisenberg ferromagnet with an axially symmetric quadrupole interaction, unique solutions can be obtained for the ensemble averages (S_zⁿ). The results are compared with those of earlier workers and it is shown that (i) in the limit T to 0 K and D to 0 the usual spin wave result is obtained, (ii) both excitation branches exhibit dispersion at finite temperatures, and (iii) a unique solution can be obtained for the Curie temperature T_c in the presence of crystal fields, in contrast to previous work.

The Callen and Shtrikman result, which demonstrates an exact correspondence between the higher order moments (s_zⁿ) of the Heisenberg ferromagnet calculated using either the RPA or an effective single-particle density matrix is generalized to include a strong axial crystal field interaction. In particular, it is shown that a two parameter analogue for the Callen and Shtrikman result can be obtained for the S=1 easy-axis ferromagnet using the transformed Hamiltonian/random phase approximation (TH/RPA).

A novel solution to the problem of incorporating crystal field interactions into the RPA model of an Heisenberg ferromagnet, known as the transformed Hamiltonian/random phase approximation (TH/RPA), is applied to an easy axis S=3/2 Heisenberg ferromagnet, subject to an axially symmetric quadrupole interaction. It is demonstrated that unique solutions can be obtained for the ensemble averages. In addition, it is shown that (i) in the limit T to 0 K and D to O the usual spin-wave result is obtained, (ii) three excitation branches are present, which exhibit dispersion at finite temperatures, (iii) a unique solution can be obtained for the Curie temperature T_c in the presence of crystal fields, in contrast to earlier work, and (iv) a two-parameter analogue of the Callen and Shtrikman single-particle generating function can be constructed which exactly mimics the TH/RPA ensemble averages.

The magnetic properties of intermediate valence systems described by the periodic Anderson model are studied within a mean-field approximation for a wide range of localized 4f-level occupation n_f. It is found that the linear susceptibility chi ₀ shows divergence at two critical temperatures T_c1 and T_c2, indicating instability in magnetic ordering. Ferromagnetic order exists for T_c1<or=T<or=T_c2, indicating a re-entrant behaviour. For another range of n_f, the system exhibits spin-glass-like magnetic response with almost divergent non-linear susceptibility as the external magnetic field goes to zero, at a temperature T₀ where the linear susceptibility has a cusp-like behaviour. As n_f is scanned, it is found that T_c1 and T_c2 merge for a particular value of 4f-level position. This temperature T_g (=T_c1=T_c2) is found to increase with the increase in hybridization between the localized and band states. It is observed that the linear response for T>or=T₀ can be represented by a scaling relation.

Elastic neutron scattering experiments were performed on single crystals of the solid solution RbFe_(1-x)Mg_xCl₃ (x=0.02, 0.03 and 0.05) to study the influence of diamagnetic dilution on the magnetic ordering processes of the induced-moment, pseudo-one-dimensional ferromagnet RbFeCl₃. All the samples appeared to have finite-range magnetic correlations with order vectors similar to those of the commensurate, C, and the two incommensurate magnetic phases, IC₁ and IC₂, of pure RbFeCl₃. The x=0.02 and 0.03 samples showed transitions from the paramagnetic to the IC₁ phase at the same temperature of 2.55 K, then transitions to the IC₂ and C phases at temperatures that decreased sharply with x. The x=0.05 sample also showed a transition to the IC₁ phase at 2.55 K, but no further transitions down to the lowest experimental temperature of 1.38 K. All samples showed an additional elastic diffuse magnetic scattering component centered at the commensurate magnetic ordering vector (¹/₃¹/₃ O)_N. This diffuse component became broader and weaker as x increased from 0.02 to 0.05 and as the sample was warmed, but persisted until about 10 K.

Expressions in the form of operators that enable one to calculate the intensity of allowed ( Delta M=1, Delta m=0) and 'forbidden' ( Delta M=1, delta m=+or-1) hyperfine EPR lines have been derived (M and m denote, respectively, the electron and nuclear magnetic quantum numbers). The spin Hamiltonian considered consists of the electron Zeeman, zero-field and hyperfine terms. The axis of quantization for the nuclear spin is assumed to be along the direction of the effective magnetic field at the nucleus. The various spin Hamiltonian 'tensors' are considered to be anisotropic, having non-coincident principal axes. These operators depend only on the components of the spin operators S and I along their respective axes of quantization. To calculate the intensity, it is sufficient to determine the square of the matrix elements of these operators between the zero-order states that take part in resonance. The present results are compared with those published previously. The angular variation in the intensity calculated using the present expressions compares favourably with experimental values.

The Raman spectra of Li₂SO₄.H₂O under small DC electric fields (20, 30, 40 and 50 V) have been obtained in order to study the conduction mechanism and group vibrations for this compound. New bands have been observed at 1680 and 773 cm^-1 owing to the formation of H₃O⁺ during electrolysis. With an increase in voltage and time the stretching bands of water broaden and finally coalesce into a single band. A slight reduction in the intensity of the bending mode of water (1605 cm^-1) is also noticed. These are due to the polarizability changes induced by the proton movement along the O-H . . . O bond, reorientation of the bonds and subsequent distortion of the lattice.

Directional Compton profiles have been measured along the (100), (110), (111), (112) and (221) crystallographic axes in GaAs using 412 keV and 59.54 keV gamma -radiation from ¹⁹⁸Au and ²⁴¹Am radioisotope sources, respectively. The results have been compared with the prediction of a pseudopotential calculation both in momentum space and in position space. The pseudopotential approach predicts the anisotropy of the valence electron distribution and is consistent with an increase in the ionic bond character compared with Ge. On the other hand, the total electron distributions are not well described due to the omission of core orthogonalisation terms.

A pseudopotential technique has been applied to calculate lifetimes for positron annihilation in copper defected with bubbles of the noble gases Ne, Ar, Kr and Xe at various gas densities. The positron in each case was found to be in a surface state of the metal on the interior surface of the bubble, the wavefunction deviating slightly from a perfect surface state according to the strength of the attractive polarization potential from the gas atoms in the bubble. This effect was particularly noticeable in the case of xenon where the surface annihilation rate was reduced to about 40% of the perfect surface state.

The tetragonal-to-orthorhombic phase transition in RbAlF₄ at approximately= 290 K has been investigated using X-ray scattering techniques. For temperatures above approximately= 290 K, the wavevector dependence of the critical scattering at the X point was measured and was well described by an anisotropic Lorentzian, with no evidence for a second Lorentzian-squared component as has recently been reported close to the anti-ferrodistortive transition in several perovskites. The critical exponents describing the temperature dependence of the primary and secondary order parameters, inverse correlation length and static susceptibility were determined and found to be consistent with those expected for the isotropic n=2, d=3 model.

The electronic structure of ferromagnetic amorphous alloys Fe_1-xB_x (0.14<or=x<or=0.23) is calculated from first principles using the tight-binding linear muffin-tin orbital method in the atomic spheres approximation for realistic structural models. The concentration dependences of magnetization and average hyperfine parameters at iron nuclei (hyperfine magnetic fields and isomer shifts) are discussed with respect to the main mechanisms of their origin and to the structural characteristics of the atomic models used. The concentration behaviour of the magnetization is explained by means of the charge transfer from boron to iron which amounts to 0.75 electrons per boron atom and which is accompanied by a change in the shape of the density-of-states curves. It is shown that the composition dependence of the isomer shift is controlled by the interatomic charge transfer together with the intra-atomic s-d electron conversion. The behaviour of the hyperfine field can be explained by a core polarization proportional to the local magnetic moment of iron atom and by a valence contribution due to the s-d hybridization. The calculated values agree fairly well with existing experimental data.

The structure of the phonon cloud surrounding the polaron and the ground-state energy is investigated. The proposed variational wavefunction consists of a few squeezed effective phonon modes.

The known three-band model of electrons in the CuO₂ plane of HTSO and the mean-field (MF) theory are used to classify the possible types of pairing and to find the contributions of all local interactions to the linearized MF Hamiltonian on the assumption of frozen lower bands. The on-centre interactions U_d and U_p on Cu d_x2_-y2 and O p orbitals, the Coulomb (Q) and exchange (J) interactions of adjacent p and d orbitals and the terms K_d and K_p describing the correlated hopping are taken into account. The phase diagrams for transitions from normal state to each separate type of pairing (antiferromagnetic or superconducting) and solutions of self-consistent equations for the order parameters are studied numerically for various sets of parameters. The results show that, at certain doping after destruction of antiferromagnetic ordering, superconductivity might be expected at sufficiently large K_d and K_p. This requires the condition in _d- in _p<O for the renormalized energies of the Cu d and O p orbitals, i.e. the preferential occupation of the O site by holes. If K_d approximately=K_p and their values are equal to about the p-d transfer integral t, then only the s type of superconductivity is possible whereas, for K_d=0, K_p=1.5t, only the d type of superconductivity is revealed for the models considered.

A modification is proposed of the Blonder, Tinkham and Klapwijk (BTK) theory for heterogeneous normal metal-superconductor (N-S) point contact. Contact is heterogeneous when the normal state electronic dispersion relations in the left-hand and right-hand electrodes are different (in the original BTK theory dispersion relations in both electrodes are equal). For characterization of the dispersion relation difference the author uses the amplitude of reflection r(E) at the clear interface for electrons incoming from the normal metal electrode with energy E_F+E when the 'superconductive' electrode is in the normal state. He calculates the amplitudes of ordinary and Andreev reflection at the N-S interface for electrons incoming from the normal metal electrode as functions of r(E). This enables him to obtain an expression for differential conductance of the point contact as a function of applied voltage and r(eV). For a suitable function r(eV) the calculated differential conductance decreases with increasing voltage in the low-voltage region (as is observed experimentally for some point contacts between normal metal-high-T_c superconductor) in contrast to the BTK theory which provides only non-decreasing dependences of differential conductance against voltage.

The temperature dependence of the z(yy)x Raman spectrum was studied in (NH₄)₂SO₂ single crystal in the temperature range 300-100 K. The temperature dependence of the NH₄ translational Raman bands in the region of 200 cm^-1 seems to support the hypothesis that the peculiar temperature dependence of the spontaneous polarization in (NH₄)₂SO₄ single crystal may be ascribed to the competing polarization contributions from the NH₄⁺(I) and NH₄⁺(II) dipoles of opposite direction with differing reorientational relaxation temperature dependences, and also the NH₄⁺-SO₄² displacive lattice polarization, which was neglected in the point-charge model.