Table of contents

A detailed investigation of what will happen when more than one exciton is present in the initial stage of a metal-insulator transition is presented. It is found that under some approximations a 'vacuum polarization' term causes the excitons to attract each other, which suggests a first order transition to a condensed phase of finite exciton density, which could be of molecular, metallic or van der Waal's type.

Dislocation theory is used to define long range order for two dimensional solids. An ordered state exists at low temperatures, and the rigidity modulus is nonzero at the transition temperature. Similar arguments show that the superfluid density is nonzero at the transition temperature of a two dimensional superfluid.

The longitudinal and transverse conductivities in K₂Pt(CN)₄Br_0.30.3(H₂O) are shown to be limited by carrier transitions between the Pt chains. Simple theoretical considerations concerning the temperature dependence of the transition rate are presented.

The Ashkin-Teller model and the eight-vertex model are related by a duality relation.

The effects of the pseudotetragonal symmetry on the nonlinear optical properties of beta -Gd₂(MoO₄)₃ and beta -Tb₂(MoO₄)₃ are discussed. The empirical nonlinear optical polarizability of the Mo-O bond is found to be large, indicating that other molybdates with more favourable geometric arrangements may have large second harmonic generation coefficients.

Acoustic paramagnetic resonance measurements have been made on a ruby crystal doped with iron and silicon. The presence of Fe²⁺ ions is confirmed but no other fast relaxing ions were found. The results are discussed particularly in relation to previous measurements of T₁ of the Cr³⁺ ions in ruby.

The authors investigate the scattering properties of small clusters of atoms using the multiple scattering formalism developed by Lloyd (1967). The transition and reaction matrices for different ensembles of scatterers are evaluated and used to calculate the density of electron eigenstates and the angular scattering cross sections. The dependence of the convergence of the angular momentum expansions for these quantities on the orientation, geometry and size of the cluster is examined. The calculations have been made for clusters of carbon atoms arranged in the geometry of the diamond lattice. It is found that it is more expedient to determine the density of states from an expression derived by Lloyd than to employ the cluster scattering matrices. An initial insight is obtained into the scattering properties of the tetrahedrally bonded elemental semiconductors and correlation with the known existence of an absolute energy gap in the corresponding crystalline and amorphous solids is discussed. Definite evidence is given for the 'channelling' of electrons along the bonds at energies well above the muffin tin zero.

Crystallographic studies of La₂O₃ and the oxides isostructural with it have failed to decide between noncentrosymmetric space group D₃²(P321) and the centrosymmetric space group D_3d³(P3m1) for their structure. The infrared and Raman spectra of La₂O₃ and Nd₂O₃ have been obtained and the absence of coincidences between the spectra unequivocally favours the centrosymmetric space group. The vibrational spectra have been analysed using the Wilson FG matrix method and force constants for metal-oxygen and oxygen-oxygen interactions derived, assuming a quadratic central force field.

The dependence of the resistance and ionic thermal currents (ITC) and CdF₂ crystals on the NaF and YF₃ content, temperature, applied voltage and other factors has been investigated. It is shown that the current passing through the crystals is due to the transport of anion vacancies and fluorine interstitials, which under favourable conditions associate with the monovalent sodium and the trivalent yttrium impurity respectively. It is further shown that the observed ITC signals are due to the accumulation of charge carriers (space charge) and defect-impurity complexes at the electrodes. The energies of formation of the defect-impurity complexes and the activation energy of motion of the defects are obtained from both kinds of measurements independently and good agreement is found between the respective values. The energies of formation of the intrinsic defect pairs are also obtained from the conductivity measurements.

Measurements of the electric field dependence of the phonon scattering in vitreous silica indicate that the energy levels of the localized modes generally presumed to contribute to phonon scattering at low temperatures are independent of electric field to a high degree. The thermal conductivity of soda lime glass doped with Fe²⁺ ions in octahedral sites was found to be independent of magnetic field to a comparable degree. This provides a lower limit to the distortion at the Fe²⁺ site.

The authors discuss the nature of deformation of the electron charge cloud of an ion implied in the deformable shell model and considers an application of the model to the case of LiF crystals. It is found that the properties of the crystal are fairly well reproduced by the present model and certain discrepancies noted by earlier authors are removed. The results of other theoretical investigations are also included for comparison.

The authors report a theoretical analysis of the density of localized states in a fluid. The basic mathematical technique employed is the conversion of partially summed, infinite order, perturbation theory to integral equation representation. Two integral equation approximations to the renormalized perturbation series for the one electron two site Green function of an offdiagonal disordered system are developed. These treat the radial disorder in a realistic although not exact, fashion. The integral equations themselves have a structure analogous to that of the successful Percus-Yevick and Hypernetted Chain approximate theories of the pair distribution function of a simple liquid. Numerical calculations which delineate the properties of the integral equations developed are also reported. The numerical calculations show the existence of localized states below a critical energy and are consistent with the predictions from much simpler lattice models of disordered systems.

An electron in a random array of dense, weak scatterers is presented as a model which is expected to exhibit the typical features of a disordered system. An average Green function for the electron is defined and derived as a Feynman path integral. In this formulation there is a clear similarity of the problem to that of a nonmarkovian random chain and this is used to further the understanding of the problem. A selfconsistent method of solving the path integral for the average Green function is proposed and then used to elucidate the nature of the localized electronic states of the system. Particular attention is paid to states at the mobility edge and the spatial extent of the wavefunction near the edge is shown to behave as mod E-E_c mod ^-35/.

For pt. I see ibid., vol. 5, 1183 (1972). The general selfconsistent method derived in pt. I is used in a description of the extended states of an electron in a disordered system. The properties of the localized and extended states near the transition energy are compared, and the continuity of the relation between E and k, (E approximately k⁵3/), is shown across the mobility edge.

A direct method for constructing the canonical density matrix C(r, r_o; beta ) for a single site problem using the complete set of normalized scattering solutions of the Schrodinger equation is described. For a spherical potential well the partial wave density matrices, C_i(r, r₀, beta ), bring out several qualitative features. By this construction, it is shown that the information put into the many site problem of a liquid are on the same footing as in other single site approximations, namely, (i) phase shifts, and (ii) the radial distribution function. Since the Laplace transform of C(r, r₀; beta ) is related to the Green function G(r, r₀ -E), the usual Green functions of the conventional scattering theory can be used to compute C for simple systems. Finally, it is shown that the method of Rousseau, Stoddart and March (1970) for calculating the density of electronic levels in liquid metals is a single site approximation and is similar to the quasicrystalline approximation given by Ziman (1966).

It is postulated that low energy vibrational modes could be present at nonideal surfaces. Their effect on the Kapitza resistance is considered. A model structure of two parallel layers of solid and helium has been used. It is shown that the Kapitza conductance is appreciably enhanced even for phonon wavevectors much less than inverse layer thickness. The degree of enhancement over quite a wide range of temperature is approximately (solid density/helium density)¹2/. The pressure dependence is less than in the Khalatnikov theory and the model also offers a possible explanation for the observed dependence on the Debye temperature.

Measurements are reported of the photoelectron energy distributions from atomically clean surfaces of GaS single crystals, produced by photons of photon energy up to 10 eV. Structure in the energy distribution curves is consistent with calculation and is interpreted in terms of direct interband transitions.

Herbert (1969) suggested that the Morin transition temperature of haematite is not given by the temperature at which the acoustic mode magnon energy vanishes but is given by the temperature at which the optic mode energy vanishes. In his expression of the optic mode energy E⁰, the correction term due to the magnon interaction is proportional to the inverse of the free optic mode energy E_f⁰, and therefore E⁰ is large if the E_f⁰ is small. Then, the free spin wave theory may not be used in the analysis of the experimental value on E⁰ even at low temperature. The present authors studied the effect of magnon interaction on the magnon energies of haematite by use of the random phase approximation. According to the theory, the optic mode energy becomes small if the free optic mode energy is small. Thus, the conclusion of the present theory is contrary to that of Herbert. On the other hand, if one uses the conventional random phase approximation adopted by, for example, Oguchi and Honma (1961), the optic mode energy is found to become large when E_f⁰ is small.

The far infrared spectra of the rare earth sesquioxides, cerium dioxide, and nonstoichiometric praseodymium and terbium oxides have been observed over the range 10-250 cm^-1 at liquid helium temperatures. Absorption due to the excitation of phonons and low-lying electronic states of the rare earth ions occur in this region. The long wavelength phonons in the sesquioxides involve motions of the rare earth ions in an effectively rigid oxygen lattice. To a first approximation, the absorptions can be described using the rare earth ion site symmetries. This, together with observations of the line widths and frequencies in mixed crystals, suggests that these phonons and the electronic excitations of the rare earth ions have been observed. In general, the observed electronic energies agree with those obtained by less direct methods; however, in a few cases significant differences were found. The spectra of the other oxides indicate the presence of complex or mixed phases.

The optical absorption spectra of the antiferromagnetic insulator NiCl₂ and NiBr₂ single crystals have been measured between 5*10³ and 33*10³ cm^-1, and from 300 to 4.2 K. The electronic spectrum of Ni²⁺ in these materials has been analysed using the spin-orbit matrices for a (3d)⁸ system and the parameters of the crystal field have been derived. It is found that Dq=692 cm^-1, lambda =:140 cm^-1 and F₄=91 cm^-1 for NiCl₂, and Dq=680 cm^-1, lambda =-390 cm^-1 and F₄=85 cm^-1 for NiBr₂. A detailed discussion of all the bands of the spectra and comments on the interesting structures of vibronic and magnonic origin of the ³T_1g^(a) band are given. The absorption peaks located around 16.6*10³ cm^-1 in NiBr₂ are not easily interpreted but their puzzling origin is discussed.

Crucible grown and high purity floating zone silicon specimens have been irradiated at room temperature with gamma rays. High resolution cathodoluminescence spectra of the vibronic bands with zero phonon lines at 0.717, 0.724, 0.790, 0.795, 0.898 and 0.969 eV are given. The widths and energies of these lines, and the intensities of the 0.790, 0.795 and 0.969 eV lines relative to the total intensities of their associated bands, are given in the temperature range 25 to 75 K. These data are discussed in terms of the theory of linear and quadratic electron-phonon coupling in the adiabatic approximation, using Debye spectra of coupled phonons and, for the 0.790, 0.795 and 0.969 eV lines, densities of coupled phonons derived from the emission band shapes. The theory gives a selfconsistency between the spectral band shapes and the widths and energies of the zero phonon lines, but does not satisfactorily fit the temperature dependence of the intensities of the zero phonon lines. It is not known whether the failure of the theory is due to a Jahn-Teller effect (no absorption at the centres has been detected), or to the coupling by the electron-phonon interaction of electronic states whose energies are not greatly separated compared with the phonon energies involved.