Table of contents

The authors employ a position-space renormalisation method, using square cells containing up to 365 bonds, to calculate the conduction critical exponent t for the two-dimensional random resistor network problem. Their results are consistent with t being equal to the cluster size critical exponent v.

Using a multiple-scattering X alpha molecular cluster model, the authors studied the electronic structure of GaAs:O_As, including +or-5% symmetric relaxations of the nearest-neighbour atoms. Their results indicate that the oxygen impurity introduces a non-degenerate a₁ energy level in the crystal band gap. Their calculation leads to the conclusion that the oxygen impurity provokes an inward relaxation of the neighbouring atoms, and that Jahn-Teller distortions are not to be expected.

Surface and subsurface mean-square displacements (MSD) are calculated in the classical limit on the dimerised (001)-(2*1) surface of C, Si and Ge crystals. A method of the self-consistent Einstein model is applied to the Appelbaum and Hamann symmetric dimer model. The MSD of surface atoms parallel to the dimer bond is found to be reduced by an order of magnitude in Si and Ge compared to that without reconstruction. Sub-surface MSDs of atoms at pedestal sites are distinct from those at cave sites.

The self-consistent cluster approximation for the Ising model is extended to obtain the wavevector dependence of the fluctuations. When the method is applied to the one-dimensional Ising model the result for the wavevector-dependent susceptibility is the exact result.

The authors present a relativistic generalisation of the Bloch theory of a magnetic electron gas. It is shown that states of uniform magnetisation, as in the non-relativistic theory, do not appear as ground states in the Hartree-Fock approximation including transverse photon contributions. The exchange energy changes sign for certain values of the relativistic parameter ( beta =h(cross)k_F/mc) and magnetisation so that spiral spin arrangements may be favoured.

The Landau-Ginzburg-Wilson (LGW) Hamiltonian associated with n=4 type-II FCC antiferromagnets is discussed. It is shown that the model is expected to exhibit a first-order transition in d=3 dimensions. Recent experimental results on CeS, CeSe and CeTe are discussed.

A computer investigation of the ground state of a Heisenberg spin glass has indicated the existence of localised clusters of spins which may exist in more than one equilibrium configuration. This indicates the presence of two-level systems. Estimates of the size of a cluster and the energy associated with change in orientation are given.

The authors report the observation of surface Brillouin spectra from seven layered transition metal dichalcogenide metals and semimetals. Spectra of all materials clearly exhibit narrow peaks corresponding to thermally excited surface Rayleigh waves which scatter light via the recently proposed surface ripple mechanism. Materials of lower opacity exhibit additional spectral features attributable to scattering from bulk transverse and longitudinal phonons via the elasto-optic mechanism. Peak frequencies, intensities and scattering selection rules are compared with theoretical predictions.

Two prominent surface states have been observed in angular resolved photoemission measurements on reconstructed (2*4) and (4*2) GaAs (100) surfaces, which were grown in situ by molecular beam epitaxy. Changes brought about by adsorption of H₂ and O₂, and also by annealing, indicate the presence on each type of surface of both an As-associated and a Ga-associated surface state. It is also shown that the symmetry of the repeated surface Brillouin zone of the As-stable (2*4) reconstructed surface is observed for the As-associated surface state.

The elastic behaviour of the scheelite-structure, laser host crystal LiHF₄, determined from ultrasonic measurements of the seven adiabatic elastic stiffness moduli C_ijkl between 4.2 and 293K, is expressed in terms of the acoustic symmetry which occurs in such TII Laue crystals. To establish the sense of the Z axis with respect to the interatomic arrangement and the setting angle ( phi _s=+29 degrees ) of the fluorine ion tetrahedron, the positions of the fluorine atoms have been determined by X-ray methods. The signs of C₁₆ and S₁₆ and the sense of rotation in the XY plane about the Z axis of the acoustic symmetry axes are established. The kappa and gamma axes of the acoustic symmetry are used together with the +Z axis as a basis for a set of transformed elastic stiffness constants C'_ijkl. The elastic behaviour is directly compared and contrasted with the oxide scheelites CaWO₄, CaMoO₄, SrMoO₄ and PbMoO₄.

The equations of motion for longitudinal and transverse waves in a non-linear, dispersive three-dimensional elastic continuum and the conditions under which these waves retain their initial longitudinal or transverse character are obtained. The equations of motion have the one-dimensional continuum form and hence the standing wave results described previously may be applied to the three-dimensional continuum. The example of the rare-gas solids is discussed. The analysis is based on a 6-12 interatomic potential and a FCC lattice. It is found that for the three symmetry directions 100, 110, 111 only the three longitudinal waves and one of the 110 transverse waves can retain their initial character and the standing-wave effects would be masked by acoustic damping above 1K in argon.

The phonon frequencies of gallium phosphide were measured along the Delta -, Sigma -, Lambda - and Z-lines and a valence-force-field overlap shell model, which reproduces the considerable dispersion observed along the Z line, is used to explain them.

Computer simulations of the melting of alkali halides have been carried out using the method of molecular dynamics with force evaluation by the particle-particle/particle-mesh (P³M) technique. The simulated systems were cubic microcrystals of 512 ions, and all the features characterising physical melting were observed in these small systems. Melting was initiated at the surface of the crystal. The ionic pair potential had a simple power-law repulsion and the parameters of the simulation, namely the mass and radius ratios of the ions and the power of the repulsion, were varied in a series of simulations. The melting temperature, expressed in terms of the cohesive energy of the crystal, showed a systematic dependence on the radius ratio and it also varied with the hardness of the repulsion. Comparison with experiment suggests that a simple potential with a fixed value of the power of the repulsion is not able to reproduce the experimental melting temperatures and latent heats. The hardness of the repulsion has an important effect on melting temperatures.

Applying Landau's thermodynamical group theory (1937), the permitted symmetries of soft modes and the permitted symmetries of the low-temperature phase of crystals with the space group D_2d³ undergoing structural phase transitions are determined. It is found that crystals of symmetry D_2d³, as the result of a structural phase transition, can either undergo changes in symmetry within the tetragonal system (D_2d to D_2d,S₄) or change their symmetry from tetragonal to rhombic (D_2d to D₂,C_2v) or from tetragonal to monoclinic (D_2d to C₂,C_s). Ferrodistorsive transitions are possible in which the volume of the unit cell remains unchanged, and antiferrodistorsive transitions in which the unit cell doubles in size. The calculations do not take into account phenomena occurring in the critical region but deal only with the static properties of the crystals.

Microemulsions are investigated for a wide range of concentrations and temperatures. After a direct observation of the samples, light scattering and viscosity measurements are performed. Structural transitions are clearly indicated. In addition, a homogeneity gap is found, in which the sample separates into two phases. Each of these consists of a micro-emulsion but they have different structures.

Theoretical and experimental studies have been conducted of the transmission of phonons in sapphire and their reflection at a crystal-vacuum interface. The effects of crystal anisotropy on the reflection process are discussed in detail. The heat-pulse technique has been used to obtain high-resolution time-of-flight spectra as a function of the angle of incidence in accurately known crystallographic directions. The agreement with predictions from numerical calculations is excellent. The relevance of these observations to studies of the anomalous transmission of energy through a crystal-liquid helium interface is also discussed.

The band structures of the layer compounds SnS₂, SnSe₂, CdI₂ and PbI₂ are calculated by the tight-binding method. They are in closer agreement with experimental results and previous pseudopotential calculations than previous tight-binding results have been. A universal band structure for the family is found by use of approximate algebraic band energies. For the 16-electron crystals a Gamma ₂^- to L₁⁺ indirect gap and a main optical transition due to anion p-cation p orbitals is found, whilst for PbI₂ the gap is direct at A.

The band structures and densities of states for a number of non-transition-metal compounds with the rutile structure are calculated using a tight-binding method with scaled two-centre interactions. For SnO₂, the valence band maximum state is calculated to have Gamma ₃⁺ symmetry in agreement with experimental results, and the calculated valence-band density of states is in fair agreement with photoemission. The simplicity of the LCAO approach is utilised to give algebraic expressions for the energy and nature of each band and used to discuss bonding and ionicity. The importance of the long-pair oxygen orbitals in forming the upper valence bands of SnO₂ is stressed. TeO₂ is discussed as an example of a class of compounds in which the two cation s electrons remain bound, giving rise to a cationic gap. The calculated joint density of states can be used to account for the experimentally observed optical dispersion.

Two-dimensional and three-dimensional band structures of the GaSe family of crystals have been calculated by the tight-binding method. The author's calculations fit the photoemission bandwidths well, particularly for the anion p_x,y bands and, for GaSe, find similar band orderings and dispersions to those of M Schluter (1973). The tight-binding interactions are evaluated by scaling and the improved valence p bandwidths are attributed to a better ratio of p_sigma :p_pi for the Ga-Se bond. The band gaps are underestimated slightly but a valence maximum at Gamma and conduction minima at Gamma and M are found, in agreement with experiment. The pressure coefficients of the minimum gaps are re-interpreted in the light of the author's calculations. Tight-binding representations of the valence charge densities give polarities of: GaSe, 0.67; GaS, 0.72; GaTe, 0.60; and InSe, 0.70.

A slightly corrected version of the 'boson representation' of fermions in the Luttinger model (that avoids the alpha to 0 limit) is used to obtain explicitly the lowest-order interactions between charge- and spin-density waves in the generalised model that includes backscattering. This is in contrast to the decoupling of these degrees of freedom reported by Luther and Emery. Instead, the results obtained by these authors are identified as applying to a model with long-range coupling between spin densities at different points.

In order to investigate the interplay of randomness and electron correlation in the Anderson-localised states, a general theoretical model which treats the electron-electron interaction between these states is presented. In constructing the model Hamiltonian, the behaviour of localised states with envelope functions is explicitly taken into account. The spin susceptibility and electronic specific heat as well as the density of states are calculated for this model. It is shown that the intrastate correlation gives rise to the occurrence of singly occupied states below the Fermi energy E_F and that this results in a Curie-type susceptibility at low temperatures. As a consequence of the variation in the correlation energy from state to state, the density of doubly occupied states becomes large near E_F. It is also shown that the interactions between different localised states give rise to a kinetic exchange interaction between singly occupied states.

The criteria for localisation in a model that is suitable for non-interacting electrons in an impurity band is investigated. It is shown that the critical density of impurities n_c is given by n_ca_H¹3/=f(W) where a_H is a measure of the range of the overlap integral between impurities, and W the diagonal disorder. The apparent discrepancy in the results of Debney and Economou and Antonio (1977) is shown to be model dependent. It is shown that an increase in W leads to an increase in n_c as expected from the results of Fritzsche (1979). The case of nearest-neighbour off-diagonal disorder is one dimension is also treated.

Ridley's theory (1978) of the multiphonon capture rate at defect centres in semiconductors is compared with the low-temperature experimental results of Henry and Lang (1977) for the B centre in GaAs more critically than hitherto. It is found that the Huang-Rhys factor S=3.0 gives a good fit to both the magnitude and the temperature dependence of the capture cross-section at low temperatures. This is in contrast to Ridley's result of S=1 that only accounts for the temperature variation, albeit for a wider temperature range; the magnitude of the cross-section with S=1 is underestimated by some eight orders of magnitude. In this paper S is determined from an experimental capture cross-section at the lowest possible temperature. This gives a reliable value of S because the capture cross-section varies approximately as S^p, where p is the depth of the level in units of the zone-centre optical phonon energy and is equal to 20 for the B centre in GaAs. It is pointed out that a value of S so derived could be used not only as a means of identifying a deep level but also could be used to help analyse other experiments on the same centre involving electron-phonon coupling, e.g. measurement of photoionisation spectra.

The deep-level transient spectroscopy technique is now well established for the characterisation of deep traps in semiconductors. Gross errors may appear in the trap activation energy and capture cross section, however, when non-exponential capacitance transients are present. This paper describes the mechanism which gives rise to this effect and an example of its observation in experimental data. An analysis of the transient shape is found to be necessary if such errors are to be avoided.

Two-photon absorption measurements on InSb, obtained with a single mode hybrid CO₂ laser, have been analysed, taking into account the fact that the laser is Gaussian in space and the effect of free-hole absorption on the temporal profile. The dependence on wavelength of the two-photon coefficient at room temperature (K₂=8 cm(MW)^-1 for 10.6 mu m and K₂=14 cm(MW)^-1 for 9.6 mu m pumping) agrees well with a new calculation including the effect of non-parabolic bands. A similar measurement on Hg_0.78Cd_0.22Te (K₂=14.0 cm(MW)^-1 for 10.6 mu m pumping) is consistent with this.

Photovoltaic spectra of pure and doped (Cu, Cd, Sb) samples of GaSe were measured at temperatures between 1.5 and 300K. The spectra are composed of a large background modulated by a fine structure whose excitonic origin is established. The presence of this fine structure in the vicinity of the indirect transition reveals the existence of an indirect exciton in GaSe. The effect of the excitonic coupling on the photovoltaic spectra is strongly dependent on the purity of the sample: it produces dips in pure crystals and peaks in doped ones. The corresponding recombination mechanisms of electrons and holes are examined and a model is proposed, which is consistent with earlier luminescence data.

It is shown by experiment that a conjugated polymer chain can be a high-mobility pure one-dimensional semiconductor. Experiments are described on DC photoconduction and on pulse photoconduction and total charge transfer in response to a 2 mu s laser pulse in a large single crystal of a conjugated polymer: the bis(p-toluene sulphonate) ester of 2.4-hexadiyne-1.6 diol-(PDATS). The spectral dependence of the efficiency of creating free carriers is determined absolutely and shown to be linear in electric field characteristic of a one-dimensional system. The carriers are shown to travel a constant distance of order 1 mm in less than 1 mu s, independent of field, before trapping, at what is probably a chain end. Subsequent trap release takes several seconds. The carrier mobility is greater than 10^-2 m² s^-1 V^-1.

Two improvements to a previous calculation of the transition temperature for the three-dimensional Ising ferromagnet with combined two- and four-spin interaction are presented. The first improvement follows from the complete implementation of a refined product average decomposition (PAD) method which distinguishes between nearest-neighbour and non-nearest-neighbour pairs. The second improvement comes from a comparison of the value for the ordinary two-spin interaction average of order four calculated using the PAD method, with its more accurate value calculated using a critical correlation-function approximation method. The comparison with the available values of the transition temperature for the FCC lattice obtained from low-temperature expansions shows that the errors are below 0.1% at alpha = infinity ( alpha =J₄/J₂), below 5.8% for alpha <or=2, and below 2.4% for alpha <or=1. At alpha =0 the errors are less than 0.3%. For intermediate values of alpha (4<or= alpha <or=8, for example) the errors are about 11%.

Both single-site (SCP) and multicomponent (MCP) theories are developed to investigate the problem of spin waves in diluted ferro- and antiferromagnets. The SCP theory gives a good description of the effect of a given spin on its neighbours, whereas the MCP theory treats well the effect of neighbour composition on the Ising levels of the given spin. The SCP theory conserves moments of the spectral weight function up to and including the third moment, whereas the MCP theory is only correct up to the second moment. Results for the two approaches are compared with data obtained by computer simulation. For ferromagnetic systems the two theories give rather similar results, but the SCP theory is slightly preferable. For antiferromagnetic systems, however, there are striking differences between the two theories and the MCP theory is clearly superior.

A quantitative theory is presented for the frequency dependence of the ultrasonic attenuation in the nearly one-dimensional antiferromagnet which has small, but not negligible, interchain couplings. At temperatures well above the Neel temperature T_N, the ultrasonic attenuation alpha is described by a scaling function, alpha = omega ³G( omega t₀), where t₀ indicates the characteristic time after which the three-dimensional diffusion takes over. The theory is compared with the frequency dependence of the ultrasonic attenuation in CsNiCl₃ (a one-dimensional Heisenberg antiferromagnet) and the effect of the interchain coupling on the one-dimensional spin dynamics is discussed.

The effect of stress on the magnetoelectric polarisability is represented by a fourth-rank axial magnetic tensor called the piezomagnetoelectric effect. The non-zero independent components of the piezomagnetoelectric effect have been determined for each of the 90 magnetic crystal classes using a computer.

The HCN^- molecular ion was produced in single crystals of KCN: 10^-2 OH^- irradiated by UV light at 77K. The spin-Hamiltonian parameters were measured at 60K and the temperature dependence of the spectrum was investigated between 60 and 170K. This temperature dependance is explained by the rapid motion of the molecule with the increasing temperature and the elastic interaction of the molecule with the surrounding ions. Using the similarity between the paramagnetic HCN^- molecule and the CN^- ions of the host lattice a qualitative picture of the local phenomena occurring in the ferroelastic phase of KCN could be made and the energy of the elastic interaction between CN^- ions was estimated to be of the order of 7 meV.

For pt.II see ibid., vol.11, p.3323 (1978). This paper concludes a series of studies of non-local electrostatics based on a model constitutive relation. In the two previous papers (Kornyshev et al. and Vorotyntsev), the general formalism was given, together with applications to planar and spherical boundaries. Here the formalism is applied to cylindrical interfaces. From the results, the roles of the spatial dispersion of the dielectric permittivities of the media in contact and of the curvature of the boundary (cylinder radius) can be elucidated.

New methods are described for calculating the dielectric constant epsilon _e or the conductivity sigma _e of a two-phase composite and these are applied to a simple cubic array of identical spherical inclusions embedded in a homogeneous host. A spectral representation is derived for epsilon _e, and numerical results are presented for the poles and the residues. Analytical and numerical methods are used to discuss the conductivity threshold of the cubic array, which occurs when the host is an insulator and the conducting spheres begin to touch each other. It is argued that sigma _e as a function of sigma ₁/ sigma ₂ has an essential singularity at the conductivity threshold.

Renormalisation theory can be used to calculate the statistical properties of systems with arbitrary finite size. This method is demonstrated with the order parameter is and specific heat for epitaxial ordering. The system is renormalised until the unit length is of the order of the total length of the original system. Then, the renormalised partition function is directly evaluated with an appropriate distribution of boundary conditions. Resulting curves of the rounded transition are compared with experimental data. Underlying the finite-size calculation, Migdal-Kadanoff-type recursion relations for q-state Potts models are adjusted by varying q to yield the expected specific-heat exponent in the infinite-system limit. Additionally, it is noted that, with no adjustment, these recursion relations are self-consistently correct for q to infinity on the triangular lattice, and give the first-order transition at the exact temperature and with probably the exact latent heat.

When there is a dipole moment in the repeat unit perpendicular to the surface in an ionic crystal, lattice sums in the electrostatic energy diverge and the calculated surface energy is infinite. The cause of this divergence is demonstrated and the surfaces of any ionic or partly ionic material are classified into three types. Type 1 is neutral with equal numbers of anions and cations on each plane and type 2 is charged but there is no dipole moment perpendicular to the surface because of the symmetrical stacking sequence. Both these surfaces should have modest surface energies and may be stable with only limited relaxations of the ions in the surface region. The type 3 surface is charged and has a dipole moment in the repeat unit perpendicular to the surface. This surface can only be stabilised by substantial reconstruction. These conclusions are important for the analysis of the surface structure of ionic crystals.

The two-component structure predicted by Barton in the resonant coupling of molecules to surface plasmons is further investigated. The elastic scattering of light resonant with a molecular excitation near the surface plasmon frequency is considered and the spectral behaviour of the scattered intensity is investigated. The jellium model is adopted for the metal-plus-field system taking account of relativistic dispersion but ignoring hydrodynamic pressure effects. For different sets of the system parameters the existence of the double peaks is clearly demonstrated and the positions of the peaks relative to the surface plasmon frequency, their widths and the division of the total weight between them is discussed.

AC conductivity of evaporated silicon-monoxide films sandwiched between gold electrodes has been investigated in the frequency range 0.1 to 10⁵ Hz and in the temperature range 173 to 415K For most of the specimens studied it is shown that, for high frequencies, the AC conductivity is proportional to omega ⁿ, omega being the circular frequency and n a temperature-dependent quantity; the value of n decreases linearly from 0.82 to 0.48 when the temperature increases from 173 to 415K. It is emphasised that these experimental results cannot be analysed in terms of a quantum hopping conduction mechanism proposed by Pollak and Geballe, but they seem in agreement with a theory derived by Pike. In this theory, the hopping of electrons between two localised sites over the separating barrier is considered; the height of the barrier is lowered by the overlapping of the Coulomb-like potentials. The activation energy of the localised states deduced from the Pike model agrees with the value of the DC activation energy.