Table of contents

The Jahn-Teller theorem is established directly by using a particular case of the Frobenius reciprocity theorem.

The previously published (Schmid and Holzl 1972) semi-analytic method for the exact computation of the Green function for regular polymers can be generalized to an arbitrary number of degrees of freedom per unit cell, such that there is no essential increase in the computation difficulties compared to a simple polyethylene backbone.

Recently published series expansions of Griffiths and Wood (1973) for the Ising model with pure triplet interactions on the triangular lattice are found to be inconsistent with the exact solution of Baxter and Wu (1973). The necessary corrections are given.

The specific heat at constant pressure of small single crystals of thallium monoselenide has been measured by applying a heat pulse technique in the temperature range 3-300K and a differential calorimetric measuring method in the temperature range 190-600K.

Within the framework of a one-electron theory, the behaviour of metal-semiconductor junctions has been studied for some III-V and II-VI zincblende compounds. Although very good agreement has been found with the experimental data for the compounds of the covalent group, large discrepancies arise for those of the ionic group.

The Morin phase transition in haematite is investigated theoretically by the use of a model hamiltonian. The critical temperature was determined by calculating the temperature dependence of the renormalized magnon energy. It is shown that two kinds of spin configurations are stable near the Morin temperature T_M in the temperature range T_M to T_M(1+H_a/2H_e), where H_e denotes the exchange field and H_a the dipolar anisotropy field.

¹⁸²W Mossbauer quadrupole splittings in W_1-xTa_xSe₂ have been measured for x=0, 0.08 and 0.50, and found to be virtually independent of x. In is inferred that at the concentrations studied the perturbation caused by a tantalum impurity is largely screened within one metal-metal distance. The experimental results are inconsistent with a rigid band model.

The magnetic circular dichroism of KCl:Tl and KI:Tl has been measured after X-irradiation at 77K. The results support earlier assignments of some optical absorption bands in the irradiated crystals to Tl⁰ and Tl²⁺ ions; these valence states result from the capture of electrons and holes by Tl⁺ ions.

A quantitative analysis is given for the charge transfer when organic bases are intercalated into layer-structure transition metal chalcogenides. Some degree of consistency is found for the charge transfer from a given intercalate in different compounds.

Far-infrared absorption lines have been observed in Mn-doped Al₂O₃ at 9 and 50 cm^-1. These values are inconsistent with those expected for Mn³⁺ in a substitutional site and provide further evidence that Jahn-Teller effects are present in this system. Comparison is made with a recent analysis for Cr²⁺ in Al₂O₃ by Bates et al (1973).

The high-frequency part of the impurity-induced infrared absorption in liquid argon can be accounted for by binary collisions between impurity and argon atoms.

'Shake-up' satellite peaks have been observed for 2s and 2p lines in the X-ray photoemission spectra of solid compounds of the d⁰ ions Sc³⁺ and Ti⁴⁺. For this configuration (and presumably for the other 3d ions) these satellites cannot arise from simultaneous transitions of electrons from 3d orbitals; the data suggest that they originate from the excitation of electrons in ligand orbitals to the metal 3d states.

The inelastic scattering of neutrons from polycrystalline reactor grade graphite has been measured at graphite temperatures of 20 degrees C, 1000 degrees C and 1920 degrees C, and for incident neutron energies of 0-0015 eV, 0.00246 eV and 0.00445 eV. With these incident energies, step changes in the cross section are clearly visible, and it can be shown that these originate from the momentum conservation condition associated with scattering from longitudinal phonons travelling normal to the graphite net planes; the position of the steps thus yield points on this dispersion curve. The data produced are consistent with sinusoidal dispersion curves, and the corresponding force constant between adjacent planes, C₃₃, can therefore be determined. This force constant decreases rapidly with increasing temperature indicating the importance of anharmonic terms in the analysis of the thermal properties of graphite.

Coloration in NaCl has been investigated by means of optical absorption and positron annihilation measurements. The lifetime and their intensities are determined and results from angular correlation obtained by magnetic quenching of the ortho-positronium state are presented. It is concluded that the positron itself introduces a considerable amount of F-centres and other defects during the measuring time, and that the results obtained depend strongly on this defect creation.

The author develops an expression for the softening of an elastic constant of dysprosium antimonide. This softening is due to a Jahn-Teller coupling between magnetic ions whose ground manifolds are split into several levels by a crystalline field. This expression is evaluated in the molecular-field approximation and further approximated by considering only quadrupolar interactions. A good fit to the thermal variation of the elastic constant of dysprosium antimonide C_theta =¹/₂(C₁₁-C₁₂) is obtained by suitably choosing the background elastic constant, the Jahn-Teller strain coupling g_theta and the biquadratic coupling I_theta . Several physical mechanisms are discussed which give rise to the fitted values of the parameters and to the structural and magnetic phase transition at 9.5K. It is concluded that the phase transition is driven by approximately equal amounts of strain coupling g_theta and exchange interactions.

By the use of a simple model, the structure of the ground state of the strong spin-phonon interaction is studied. It is shown that the ground state of the system is very different from the state with no spin-phonon excitations. By second-order perturbation theory among degenerate states it is possible to see that the new ground state is populated by coherent running lattice waves associated to correlated spin waves. Some of the physical implications of this structure are discussed. It is suggested that the validity of the model is not limited to magnetoelastic problems.

A Monte Carlo method is given for the calculation of the configurational free energy of a crystal surface using the grand canonical ensemble. This method is then applied to nearest-neighbour models of (1,0,0) faces of simple cubic and face-centred cubic crystals and the results compared with the analytic approximations of Burton, Cabrera and Frank (1951).

The interaction potential V(v,z₀) for a classical charged particle approaching a metal surface with velocity v is discussed within the jellium approximation. A general expression for the potential is derived in terms of the retarded density response function of the bounded electron gas including effects due to acceleration of the charge. For normal incidence and the classical infinite barrier model of the surface, the asymptotic form of the potential has been determined analytically and the lowest-order finite velocity correction to the classical image potential shown to be proportional to z₀^-2 ln z₀, and not to z₀^-2 as has been suggested. Close to the surface, the potential has been determined numerically, and shows a pronounced velocity dependence. An approximate expression for V(v_z,z₀) is then derived for a more general model of the surface which takes into account the diffuseness of the electron density. For v<<v_F, the potential is essentially unchanged from its value at v=0, but for v>>v_F, finite velocity effects dominate when the charge is still some distance from the surface.

The conventional pseudopotential secular equation for the E(k) relationship in electron band theory is of order 2N, when N pseudo-plane-waves are used, and spin-orbit coupling included. However, when the crystal has a centre of symmetry it can be shown from group theory that the roots of this equation (eigenvalues) will be degenerate in pairs. It is shown that this result may be simply deduced from the form of the secular matrix, and have derived the equation of order N which contains all the distinct roots once. The result may be simply stated: the conventional equation may be written as a determinant of order 2N equated zero, whereas our equation is a pfaffian of order N equated to zero.

The matrix elements of the exact and approximate exchange operator are investigated in the frame of the pseudo-potential model. It is found that the Slater local potential and the simple modifications of it give different matrix elements in some states as the exact exchange operator.

An equation for the charge density in terms of the dielectric matrix of the crystal is used to study the valence electron distribution in covalent and partially ionic semiconductors. Through a perturbation expansion of the dielectric matrix in terms of the ion pseudopotential, the authors write the valence charge density as a series of powers of the pseudopotential. The calculated charge densities are in good agreement with the available experimental data and with the electron distributions obtained using wavefunctions from accurate band structure calculations. In particular they account for the shift towards the more electro- negative ion of the covalent charge pile-up in partially ionic compounds, indicating that perturbation theory can provide a good description of the electron distribution even in materials with an appreciable ionic character.

Ultraviolet and X-ray induced photoelectron spectroscopy studies have been carried out on single crystals of SnSe₂ and SnS₂. Basal surfaces of both materials are inert and have photothresholds of 5.35 eV and 6.3 eV respectively. The kinetic energy distributions of excited electrons are analysed in terms of existing theoretical band calculations. Good agreement exists between experiment and calculations based on the pseudopotential and tight binding methods.

For pt.I see ibid., vol.6, no.24, 3631 (1973). The energy band structures of SnS₂ and SnSe₂ are calculated by a semi-empirical tight-binding method. The band structures are discussed in relation to the optical properties of the materials and to previous calculations which have used the pseudopotential technique. Computation of the valence band density of states and of the energy distribution of the joint density of states for various photon energies is described for the case of SnSe₂. These results are used to interpret the X-ray and ultraviolet excited photoemission data.

A calculation is performed for the ground state energy of an electronic bubble in liquid neon as a function of temperature and pressure, and using experimentally determined electron-neon scattering cross sections. The density of the compressed liquid is calculated from an equation of corresponding states. It is found that the electronic bubble should collapse at temperatures near T_c with a few atmospheres of overpressure.

The magnetic effects of small quantities of V₂O₅, MoO₃ and CuO acting as impurities in a 67 mol% WO₃:33 mol% P₂O₅ semiconducting glass have been investigated. The four paramagnetic species that were produced have been attributed to W⁵⁺, V⁴⁺, Mo⁵⁺ and Cu²⁺ and the magnetic resonance spectrum of each has been characterized at low impurity concentrations. At high impurity concentrations (>1.5 mol%) a strongly exchange narrowed resonance is observed and this is related to the type of resonance observed in binary V₂O₅:P₂O₅ and MoO₃:P₂O₅ glasses. Magnetic interactions are found to occur when the paramagnetic species are at sites separated by less than 16 AA. Nuclear magnetic resonance investigations were also performed and the results for T₁ measurements on the ³¹P nuclear resonance follow a spin diffusion model in which the relaxation time depends upon the paramagnetic impurity concentration.

For pt.I see ibid., vol.6, no.24, 3661 (1973). The electrical and optical properties of semiconducting glasses made from 67 MOL% WO₃:33 mol% P₂O₅ and 0.2-8.6 mol% V₂O₅, MoO₃ or CuO have been investigated. V₂O₅ and MoO₃ reduce the conductivity sharply while CuO and most other transition metal oxides have little effect. The dominant parameter is the activation energy for conduction which varies inversely as impurity spacing at low impurity concentrations. Isolated impurity ions induce localization energies of about 0.75 eV for V ions and 0.80 eV for Mo ions. In the case of vanadium, interaction effects reduce these energies eventually resulting in direct electron hopping between impurity sites. The results may be related to properties of V₂O₅:P₂O₅ glasses. Thermopower and optical absorption measurements on undoped glasses are consistent with a small-polaron hopping mechanism, and the correlation W_opt approximately 4 W_H, where W_opt is the energy of the absorption peak, is qualitatively observed even for doped glasses. However, the conduction process cannot be described in terms of a simple form of trap-controlled drift mobility, and a model involving electrostatic interactions between impurity sites appears to be necessary.

A simplified method, based on the model proposed by Baldereschi and Lipari (1971) for investigating the energy levels of direct excitons, is used to calculate the exchange energies to first order. Contributions from second-order intra-series and inter-series terms are considered and found to be negligible for most of the materials investigated. The exchange energies so obtained, are generally in good agreement with existing theoretical and experimental values.

A generalized treatment of photoconductivity in amorphous semiconductors having an M-CEO trap distribution is presented. The problem is formulated in terms of Shockley-Read recombination- generation statistics, as distinct from ad hoc formulations of previous treatments of the problem. For the first time, self-consistent characteristics are presented of photocurrent, excess hole and electron concentrations, and lifetimes as a function of light intensity and temperature, with the activation energy and energy gap as parameters. The photocurrent characteristics are found to exhibit all the salient characteristics of existing experimental data. The physics of the photoconductivity is discussed in terms of the excess carrier lifetimes and the material parameters.

For pt.I see abstr. A24581 of 1973. Magnon energies, renormalized in a Hartree-Foch approximation, have been derived. The model includes isotropic and anisotropic exchange interactions, a crystal field of HCP symmetry, magnetoelastic interactions and dipolar interactions. The novel feature of the theory is a modification of magnon renormalization by the ellipticity of spin precession that is a characteristic of highly anisotropic ferromagnets.

Starting from the master equation of Glauber (1963), for the Ising system of N spins, and working in the Bragg-Williams approximation, a Fokker-Planck equation is derived for the probability that the system has an overall magnetization. The expansion of the master equation is discussed in powers of N^-1/2 and it is shown that a certain choice of transition probability has to be made to get the correct width of the probability distribution. This is in contrast to the recent work of Goldstein and Scully (1973), which though starting from a Liouville equation effectively works only to the molecular field approximation which is not as satisfactory as the Bragg-Williams approximation. The dynamic magnetic susceptibility is also calculated.

The calculation of the magnetic neutron cross section is discussed for transition metal compounds and the general formulae are used to calculate cross-sections for three compounds of current interest. Scattering from V₂O₃ is shown to be highly anisotropic and indicative of a widely spread moment distribution, given the ground state wavefunction proposed by Rubenstein (1970). Detailed calculations are given also for FeF₂ and FeCO₃, and it is shown that the aspherical moment distribution induced by the crystal field contributes to the scattering at the nominally purely nuclear Bragg reflections. The magnetic contribution at all other Bragg peaks is dominated by the spherical moment distribution. Consequently the spherical and aspherical components can be measured in detail using polarized neutrons although the observed moment will also contain covalent contributions, which are not included in the present calculations.

The effects of the geometry of the cubic lattices on the properties of a Heisenberg antiferromagnet with first- and second-nearest-neighbour interactions are investigated. Both the Neel temperature and the quantum defect are calculated using temperature-dependent Green function theory and the random phase approximation (RPA) for all values of the exchange constants leading to antiferromagnetic order. Special attention is given to the properties of the phase transitions which occur when the exchange constraints are varied. Graphs of the Neel temperature and the quantum defect are presented to aid comparison between theory and experiment.

The Nd monopnictides NdP, NdAs and NdSb are simple cubic type I antiferromagnets in which the crystal-field splitting is larger than the exchange energy. The magnetic properties are calculated by means of a mean-field theory including crystal-field and magnetoelastic effects. The calculations are based on energy levels determined by inelastic neutron diffraction. Exchange constants are derived by comparing the theoretical paramagnetic susceptibility with experiments over a large temperature range. The temperature dependence of the sublattice magnetization deviates significantly from the usual molecular field curve (for J=⁹/₂) which neglects crystal-field effects. Theoretical high-field magnetization curves are presented. The observed tetragonal distortion below the Neel temperature T_N is explained by the theory. The effect of biquadratic exchange interaction is investigated.

The electron paramagnetic resonance spectra at 4.2 K of trivalent ytterbium, erbium and dysprosium in silver chloride are described. The symmetry and g-values of the spectra are used to derive the lattice sites, ground states and environments of the rare earth ions. Each ion is assumed to be associated with two charge-compensating silver cation vacancies at low temperatures. The majority of the Yb³⁺ ions enter the lattice substitutionally in association with two next-nearest cation vacancies arranged in a line along a cube axis. Er³⁺ is found in a number of different centres. Dy³⁺ is substitutionally incorporated probably in association with two nearest cation vacancies such that the lines joining them to the Dy³⁺ ion are at 90 degrees . The centres described are compared with those reported previously for the transition ions of the iron group and for Eu²⁺ in silver chloride.

A theoretical study is made of the nuclear electric quadrupole spin-lattice relaxation in solids, for the case where the quadrupole interaction is small compared with the Zeeman interaction. It is shown that, provided the external magnetic field H₀ has no effect on the lattice motions which cause the relaxation, the principle of time reversal invariance implies that the nuclear quadrupole spin-lattice relaxation tensor is real and the relaxation probabilities W₁ and W₂ are invariant with respect to reversal of H₀. If the magnetic field does influence the 'lattice', it is found that W₁ and W₂ are still invariant with respect to reversal of H₀ even though the relaxation tensor is not necessarily real. A simple, classical model is presented to illustrate the results obtained quantum mechanically. Finally, it is shown that the anomalous orientation dependence of W₂/W₁ recently observed for ²³Na in NaNO₃ cannot be attributed to failure of the principle of time reversal invariance.