Table of contents

In a combined electromagnetic and acoustic experiment it has been shown that the low-energy excitations observed in glasses at low temperatures couple simultaneously to elastic waves and to an RF electric field.

A real-space renormalization group is developed which renormalizes probabilities directly in the percolation problem. An exact transformation is given in one dimension, and a cluster approach is presented for other lattices. The results are in excellent agreement with series calculations for the critical percolation concentration p_c (both site and bond), and in good agreement for the correlation length exponent nu _p. Additionally, in one dimension, a field-like variable is included and the remaining exponents are calculated.

It is suggested that a transition from three-dimensional to two-dimensional transport in the impurity band of n-type GaAs occurs when the thickness of the conducting layer becomes sufficiently small. Depleting electrons from the two-dimensional impurity band results in an Anderson transition. The minimum metallic conductance of the system was found to be in reasonable agreement with theory.

The equations which are currently used to calculate intervalley mixing for shallow impurity states in semiconductors are examined critically. It is shown that terms which have been neglected so far can be responsible for effects of the same order of magnitude as the ones considered. Evidence is given for this by means of qualitative and numerical arguments in the case of donor impurities in silicon.

It is suggested that more direct information on the degree of covalency of the Gamma ₅* orbital doublet, in D_4h complexes formed by d⁹ ions, could be obtained by measuring the splitting produced by the spin-orbit coupling in this state if the Jahn-Teller coupling is quenched. The influence of the near Kramers doublets on this splitting, in Cu²⁺:CdCl₂ and Cu²⁺:K₂PdCl₄, is analysed, showing that they give rise to negative corrections of only -95 cm^-1 and -20 cm^-1 respectively. The role played by the Gamma ₁* level is emphasized.

The Jahn-Teller induced orthorhombic distortion in DyVO₄ has been determined as a function of temperature and magnetic field up to 13 T by measurement of splitting of E_g phonon modes of the tetragonal phase. The results are not well predicted by molecular field theory, reinforcing the conclusion from other experiments that short-range interactions are dominant in DyVO₄.

Exchange interactions of chromium pairs in acid rhodo chromium chloride have been studied by means of neutron inelastic scattering. The observed ground-state splittings are excellently described by a Heisenberg Hamiltonian. The exchange parameter is found to be temperature dependent. The observed intensities are in reasonable agreement with values calculated from the wavefunctions of the coupled chromium pair.

The magneto-optical properties of X-ray induced fluorescence of CsF have been investigated at 1.6K. Magnetic circular dichroism was observed in a fluorescence band at 266 nm and this band is assigned to emission from the lowest triplet state of the self-trapped exciton. The EPR of the triplet state was measured using optical detection techniques and it is concluded that the self-trapped exciton is a neutral complex of the type (F-Cs-F)⁰ aligned along (100).

ENDOR measurements have been made on the linear bond structure Cr³⁺-F^--Cd²⁺ in crystals of CsCdF₃:Cr³⁺. The observed hyperfine interactions with the ¹⁹F, ¹¹¹Cd and ¹¹³Cd nuclei indicate that the unpaired spin fractions in 2p_sigma and 2p_pi orbitals on the F^- ion are f_sigma =-0.1% and f_pi =4.3%. The value of f_sigma , about which there has been some uncertainty in the literature, is considerably smaller than recent estimates.

A calculation is reported which strongly suggests that the 118.5K phase transition in PrAlO₃ is due to coupling between an acoustic phonon and temperature dependent optic modes. Results of other calculations have indicated that the temperature dependence is caused by changing populations of the Pr³⁺ electronic energy levels. The nature of the structural changes at 118.5 is discussed.

For temperatures slightly less than T₀, the antiferroelectric phase transition temperature, the wavevector dependence of transverse acoustic phonons in BaMnF₄ is anomalously dispersive. This dramatic variation of sound velocity with wavevector can be explained by the presence of a 'phason' branch in the noncommensurate phase below T₀.

The L₃-MM Auger spectrum of Zn has been studied. An interpretation of the splittings observed is proposed. It is based on the calculation of the two-hole coupling energies in the final states of the Auger transition and on that of the Auger transition rates.

The pronounced asymmetric broadening in the core level photoemission spectra of chemisorbed atoms is explained in terms of intra- and extra-atomic relaxation and a qualitative comparison is made with similar effect due to the dynamic screening processes.

Detailed intensity-energy LEED spectra from the clean surface (2*1) structures of Si (100) surfaces are presented from three independent and previously unpublished experimental studies at three different laboratories. An extensive range of data is presented and some detailed comparisons of the different data are presented. These comparisons show clearly both the reliable and unreliable aspects of experimental LEED data. The data presented provide an extensive basis for proper interpretations of the structure of this surface.

For pt.I see ibid., vol.6, p.3047 (1973). A numerical study is made on the phonons in cellular disordered systems with off-diagonal as well as diagonal randomness, and moreover with configurational short-range order between the neighbouring particles. The study is carried out on the basis of the cluster theory previously presented by the author because it has the following merits compared with many theories based on the CAP: (i) Exact solutions are obtained in the limiting cases where the short-range correlation forces the system to be an aggregation of ordered systems. (ii) Correlations of higher order (the short-range order and the cluster effects) can well be taken into account, and (iii) various conditionally averaged quantities can easily be calculated, even for systems with off-diagonal randomness. It is concluded that for the system with strong short-range order the off-diagonal randomness can be taken into account particularly well.

The phase transition in octafluoronaphthalene has been investigated by Raman scattering and neutron powder diffraction. The weight of the experimental evidence points to a unit cell doubling in the a direction, but with no change in space group symmetry. Lattice dynamics calculations support this evidence and indicate that the mechanism of the phase transition may well be the instability of a zone boundary acoustic mode of librational character. The structure of the low-temperature phase has been refined and the Raman spectra of the upper and lower phases are reported.

The diffusion coefficients for carrier-free ⁵⁴Mn in pure NaCl and KCl single crystals and ⁸⁵Sr in pure KCl single crystals were measured in the intrinsic conductivity region as functions of temperature. Results for Sr and Mn in KCl were unexceptional compared with results for other ions in the alkali halides but results for Mn in NaCl were characterized by unexpectedly large diffusion coefficients, a low activation energy (0.62 eV) region above 830K, and a region of larger activation energy below this temperature. These results were difficult to rationalize by the usual vacancy-diffusion model.

A free-energy functional which describes two possible phase transitions in superfluid ³He is investigated with renormalization group techniques. The phase transitions are found not to be controlled by stable fixed points, at least within an in expansion. 1/n calculations suggest that in this instance the transitions are first order. An 'improved' one-loop calculation of the free energy is given to illustrate the difficulties of calculating the free energy in a systematic manner in the absence of control by stable fixed points.

A number of workers have estimated surface tensions of solids from measurements of the differences in the lattice parameters of bulk crystals and microcrystals. The data are then analysed by an expression valid only for spherical, isotropic microcrystals. The author discusses problems arising from the fact that real microcrystals are generally faceted. A general expression is given for the change in volume of a microcrystal for an arbitrarily anisotropic surface tension and arbitrary crystal habit; common special cases are also given. The discussion of the relation between the volume change and the change in X-ray lattice parameter includes the effects of the dispersions in crystalline sizes and shapes, and the possible non-uniformity in internal strain produced. It is concluded that any errors will be small.

The solution of Poisson's equation is an essential step in the formulation of self-consistent calculations. An efficient method of solution is presented for a system of arbitrary geometry. The charge density and potential within a cell of arbitrary shape are expanded in spherical harmonic series. A truncation function is introduced which converts integration over a sphere to integration over the cell. Tables of this function for common cell shapes are presented. The properties of the spherical harmonic series are investigated for the Green function which appears in the integration. Its convergence is much slower than has previously been assumed. An optimum approximate treatment is proposed.

A theory of broken-symmetry and ground states, originally introduced to describe the electronic properties of n-type inversion layers in silicon, is applied to germanium and gallium phosphide systems where the conduction band minima possess different symmetries.

The band structures of the group III-VI monochalcogenides GaSe and InSe have been calculated using a semi-empirical tight-binding method in a two-dimensional approximation. Many of the discrepancies between experimental work and previous calculations for GaSe have been resolved. The results for InSe appear for the first time.

The electronic band structure of vacuum cleaved single-crystal indium selenide has been investigated by X-ray and ultraviolet photoelectron spectroscopy. The valence band consists of three well separated groups, one derived from the Se 4s levels, and two derived from p-like wavefunctions. The band structure and valence band density of states has been calculated using a tight-binding single-layer approximation and all the major features in the experimental spectra are well accounted for. The spin-orbit splitting and electron loss structure associated with the In 4d core level is also reported.

The theory of the coherent pairing of excitons in the presence of a resonant electromagnetic field is generalized to describe the biexciton spectra of molecular crystals, which contain several molecules (atoms) in the unit cell. The excitation spectrum for crystals like anthracene having two molecules per unit cell is discussed in detail. It is found that, at high exciton densities and under resonance of near-resonance conditions and at temperatures below some value T_c, the formation of four biexciton states is feasible provided that the dielectric gaps induced by the electromagnetic field are less than those of the corresponding biexciton states. Expressions for the absorption coefficient describing optical transitions to the biexciton states are derived.

Anderson localization is studied by the analysis of the time dependence of a randomly specified wavefunction. It is shown that the average inverse participation ratio may be efficiently calculated in this way and results are given for lattices of one to four dimensions. Various refinements and generalizations are indicated.

A calculation of the electronic structure of the charged zinc vacancy in ZnSe using a cluster model is reported. The additional charge introduced onto the vacancy is simulated in the cluster using covalent and ionic models for this defect. A highly localized singlet state emerges from the valence band which is accounted for by realizing that zinc selenide is of mixed covalent and ionic character.

Previously reported experiments provide a precise description of the ³T_1u relaxed excited state of the Au^- centre in KCl. This vibronic model has been extensively used for the interpretation of the fluorescence properties of this system under various perturbations such as magnetic field and uniaxial stress. The high-temperature limit allowed the previously proposed model to be checked by another independent evaluation of the Ham reduction factors. At low temperature, various processes tend to quench the measured polarization ratios. A careful study of these polarization degrees as functions of the applied perturbations and of temperature provided some information about the relaxation processes between the split Jahn-Teller levels.

A simple theoretical model for the trapping kinetics of one type of carrier in photoconductor containing several species of localized level, all of them broadened, is presented. Both steady-state behaviour and transient behaviour are described, and simple expressions for the time constants and amplitudes of the decay terms are obtained. Rose's model (1951) of an exponential distribution of traps plus a set of deep levels, advanced to explain a law of the type n varies as I^v, where n is the carrier density, I the illumination intensity and ¹/₂< nu <1, is explored in detail. A condition for its validity is obtained, and the characteristic transient behaviour predicted by the model is derived.

The effect of electron irradiation on the photoconductivity of natural type Ia diamond is examined with the aid of the split-electrode method for recording the Hall effect. It is found that electron irradiation transforms the photoconductivity of natural type Ia diamond from n-type to p-type. This is due to the introduction of irradiation-induced acceptor centres. This result combined with the previous work on the effect of electron irradiation on p-type semiconducting diamond demonstrates that electron irradiation damage produces both donor and acceptor centres in diamond.

Measurements are reported of the electron drift mobility and the DC electrical conductivity of crystalline arsenic triselenide, the data being obtained for the (010) direction. In the room-temperature regime, the electron drift mobility is in the range 20-80 cm² V^-1 s^-1, and shows little dependence on temperature. However, at lower temperature it becomes thermally activated. The complete data are well described by a model in which free carriers in the conduction band are in thermal equilibrium with a set of trapping centres of depth 0.17 eV and density 10¹⁴-10¹⁵ cm³. In the low-temperature regime, the mobility increases with electric field, suggesting a field-dependent trap release probability.

The ground-state energy E and momentum distribution n_k of the electrons are expanded from the atomic limit for the half-filled Hubbard model. The coefficients of expansion are represented by the spin correlation functions of the spin ¹/₂ Heisenberg model. Using the spin-wave theory, approximate values of coefficients are calculated for the square lattice and the simple cubic lattice. In one dimension, the theory shows a good agreement with the exact solution. An effective spin Hamiltonian for the half-filled Hubbard model with arbitrary hopping integrals is obtained up to the fifth order. It is shown that the fourth term contains four spin interactions.

The authors estimate the cross section for the magnetic octupole scattering of neutrons by rare-earth ions. These scattering events can change the magnetic quantum number of the ions by up to three units. For high momentum transfers and a proper scattering geometry, the cross sections for magnetic octupole mod Delta M mod =2 and 3 transitions are comparable with those for magnetic dipole mod Delta M mod =1 transitions. If a beam of polarized neutrons is used, mod Delta M mod =2 excitations, i.e. quadrupolar waves, can be produced without exciting spin waves mod Delta M mod =1. Examples are quoted where this scattering is expected to be of particular interest.

The magnetic excitations of CsCoCl₃ (T_N=21.3K) have been studied by inelastic neutron scattering. The experimental results confirm that CsCoCl₃ behaves as one-dimensional, anisotropic antiferromagnet with fictitious spin S=¹/₂.

Precise values of the dielectric constant of gadolinium gallium garnet (GGG) single crystals are reported. The dielectric constant has been measured using a substitution method at 1 kHz and room temperature. The effect of impurities, lattice imperfections and lack of stoichiometry on the dielectric constant has been studied. The value of the dielectric constant of a pure GGG crystal along (111) is 12.11+or-0.02. For a GGG crystal containing 1% excess of Gd₂O₃, the dielectric constant is 12.24+or-0.01. Wafers of alpha -Al₂O₃ cut from pure and Cr-doped CVD-grown single crystals and from Czochralski-grown single crystals were also investigated, to investigate the effects of purity and perfection on the dielectric constant.

The Raman spectra of 2H and 4H-SnS₂ and 6Hb-SnSe₂ have been studied at room and liquid nitrogen temperatures. Interpretation of the observed Raman modes is given in terms of the different symmetries of these polytypes and the more important short-range forces involved in determining the energies of the higher-energy phonon modes are identified by the use of a simple force-constant model.

The complete Raman spectra of single-crystal synthetic zircon and thorite are reported for the first time. Results are presented for thorite at 295K and zircon at 295 and 90K. The temperature-dependent study was essential for distinguishing between weak first-order bands and second-order features which can have narrow half-widths. The lattice vibrations in both crystals are notably harmonic. The spectra are analysed in terms of internal and lattice modes of the SiO₄^4- complex with some success. The crystal-field splittings for the internal modes are large. A comparison between the zircon and thorite results enables an assignment to be made of the Raman spectrum of powdered hafnon (HfSiO₄) reported by Nicola and Rutt (1974).