Table of contents

A simple model based on the synthesis of de Gennes' double exchange concept and Hubbard's treatment of correlation in narrow band systems is proposed to account for the transition from the antiferromagnetic insulating state to the metallic state observed in various transition metal compounds.

The phenomenon of a flat-topped coexistence curve in two phase fluid systems is explained in terms of electromagnetic and acoustic 'dispersion' forces across the interface. Modifications to existing scaling laws very near the critical point are indicated.

W. D. Langer's solution to the Hubbard model is shown to be incorrect to lowest order in the bandwidth. (see ibid. vol. 4, l56, 1971).

Anelastic relaxation measurements are reported for CaF₂ containing 0.45 mol percent GdF₃ as a function of heat treatment of the crystals prior to measurement. Two main relaxation modes were found whose intensities were influenced by heat treatment in the same way as were tetragonal centres observed in the EPR spectrum. Treating these centres as pairs formed of Gd³⁺ ions plus nearby F^- interstitials, a two shell relaxation mode analysis accounts quantitatively for the relaxation times observed by anelastic and dielectric relaxation and by EPR linebroadening. An additional relaxation mode, excited by <100> longitudinal stress, was observed but not identified. It was uninfluenced by heat treatment.

For Pt. I see abstr. a33218 of 1969. The 'quasi-classical' model of the electron plasma in solids, used by Das and de Alba to calculate the low field form of the shielding length, is employed to calculate the de Haas-van Alphen type of oscillatory terms in the shielding.

Following suggestions that large dipole fields are present in amorphous materials, a rough calculation is carried out of the probability distribution of potential in amorphous silica. As a result of fluctuations in interatomic distances nonzero dipole moments can be associated with each tetrahedron. Information obtained from the model of Bell and Dean (1967) for vitreous silica is used to calculate the probability distribution of the field to such dipoles, assuming the tetrahedra to be randomly distributed.

It is shown, using a simple one dimensional model, that reflection of an incident atom of thermal energy depends on the existence of a surface mode in which the incident atom is only weakly coupled to the bulk modes of the crystal. The adsorption/desorption process is also discussed and the desorption rate calculated. The results are partly generalizable to three dimensions.

The magnetic form factor of chromium ions in Al₂O₃ has been investigated using long-wavelength neutrons. The results provide an indication of the effects predicted by Hubbard and Marshall (1965) at low scattering angle arising from covalency. The feasibility of this method for the determination of covalency parameters is discussed.

The author has extended previous calculations of the energies of vacancies, ion interstitials and inert gas atoms in calcium fluoride and obtained new results for the systems Kr/SrF₂ and Xe/BaF₂.

The author has used Gaussian wavefunctions in a study of the F_t centre in MgO and CaO. It is shown that Gaussian wavefunctions are very suitable for defect centre calculations because the integrals over the Madelung potential may be obtained analytically using Ewald's method of lattice summation. The calculation of Berezin of the singlet-triplet splitting in the F_t centre has been extended. A more general wavefunction is used and the crystal field and the polarization of the lattice explicity considered. The results support the conclusion that the F_t centre is a linear trivacancy.

Optical phonon modes in MnO at room temperature have been measured using a beryllium filter detector technique. The method is shown to have good energy resolution and adequate momentum resolution for these measurements. The results are combined with earlier results and it is shown that neither the simple shell model nor the breathing shell model gives an adequate representation.

The low temperature attenuation of transverse hypersonic waves in cubic media due to the anharmonic interactions with thermal phonons is discussed. The effect of elastic anisotropy on the allowed three phonon processes is treated in detail. Allowed processes where transverse hypersonic waves interact with thermal phonons on the same acoustic branch of the phonon spectrum as themselves are predicted to exist. These processes are expected, however, to be very sensitive to lattice dispersion. This can cause a lower temperature dependence for the hypersonic attenuation than the T⁴ predicted for higher branch allowed processes in isotropic media by Landau and Rumer (1937).

The response function of a uniform extended system of noninteracting fermions, and thus the energy of a weakly perturbed system of this kind, is computed exactly and in the von Weizsacker approximation; it is thus shown that (a) the original von Weizsacker coefficient leads to an upper bound to the energy which becomes asymptotically exact for short wavelength perturbations and (b) the coefficient reduced by a factor of 9 leads to a lower bound which becomes asymptotically exact for long waves. Generalisations of these results are discussed for the case when the fermions are interacting electrons.

A theoretical discussion is given of the energy loss processes relevant to hopping of localized carriers in amorphous semiconductors in high electric fields. The differences between high field steady and alternating fields are pointed out. The results are applied to the discussion of the experimental results on high field ac conduction in SiO and it is shown that a high effective temperature may be reached in this mode of operation. The concept of effective temperature in high field dc conduction-the Poole-Frenkel process-is also discussed and it is shown that the effective temperature should be a function of lattice temperature only and not of the electric field-in agreement with experimental results.

Measurements are reported for the first time of electronic conduction in silicon monoxide films under alternating fields of high amplitude-sufficiently high to cause a significant lowering of the coulombic barriers at donor-like sites in the material. This ac Poole-Frenkel effect has an entirely different dependence on temperature and frequency from the familiar dc effect and offers insight into the dynamics of relaxation of carrier energy in hopping motion at high electric fields. The interpretation of these results is given in the light of the theoretical model of a modified Poole-Frenkel effect, involving hopping motion of carriers in localized traps between emission and capture at donor sites.

Experiments are described which provide conclusive evidence for space charge conduction in homogeneous single crystals of trigonal selenium. From measurements of thermal activation energies for both ohmic and space charge limited currents over a broad temperature range localized levels have been calculated to lie at approximately 0.09, 0.21 and 0.47 eV from the valence band. Supporting data on thermally stimulated currents and ac conductivity have further established that conduction processes in this elemental semiconductor must be understood in terms of the normal energy band picture.

The microscopic dielectric function epsilon (q) of germanium was calculated using a pseudopotential scheme. Fifteen bands and 23040 points were included in the sampling of the Brillouin zone 14.67+or-0.4 was obtained from the simple Penn model. The Fourier components of the charge density and the histogram of the density of states are also presented. The comparison with experiment gives good agreement.

Bloch's selfconsistently renormalized spin wave approximation is rederived in a way which clarifies its relationship to higher order calculations-as the sum of all bubble corrections to the free spin wave propagator. Resulting formula for the renormalization, magnetization and specific heat are more general than those presented in previous works, accommodating many-neighbour interactions, external magnetic field and uniaxial anisotropy. A detailed numerical study is made of the characteristic properties of the approximation, for example, the spin and lattice dependence in the vicinity of the Curie temperature leads to a more comprehensive view than hitherto available, the free energies of the double valued solutions found in the simplest case show that one of them is unstable.

A theoretical expression for the coefficient U of the higher order electron-nuclear interaction term U(S³_xS³_yI_y+S³_zI_z-¹/₅ (S.I)(3S(S+1)-1)) in the spin Hamiltonian is derived for V²⁺ in MgO. Racah formalism is used in order to include in the calculation the effects of interactions between the ground ⁴F state and the low lying excited ²G and ⁴P states. The calculated value of U is then compared with the experimental value obtained from ENDOR data. It is found that the discrepancy between theoretical and experiment values of U is removed. The contribution of the ²G state to U is found to be an order of magnitude larger than that of the ground ⁴F state, but the effect of the ⁴P state is insignificant in comparison. The same expression can be applied to Cr³⁺ in MgO and to Co²⁺ in CaF₂, and it is shown that the contribution of the ²G state is also important for these ions.

The effects are considered of finite conduction electron lifetime and finite deep hole mass on the form of the singularity at the threshold of optical absorption in metals and semiconductors. An approximation is obtained for all orders of perturbation theory. The dependence of the energy range over which the singularity is spread on the electron lifetime, the hole mass, the Fermi momentum and the phase shift of the electron scattering by a deep hole is obtained.

The total spin state S=2 belonging to the pair V²⁺-F^--V² in V-KMgF₃ (s^A=s^B=³/₂ for V²⁺) has been investigated by epr techniques. The other total spin states, S=1 and S=3, are not observed because of excessive broadening of the lines. The principal interactions are described by the Hamiltonian Js^A, S^B+D_f(3s^A_s^B₇- s^A,s^B) where the isotropic exchange interaction is J=4.5+or-1.0 cm^-1 and the anisotropic interaction is D_e=-0.0339+or-0.0002cm^-1. D_e is 35% larger than the dipolar interaction calculated on a simple ionic model. Part of this discrepancy is attributed to covalent transfer of the V²⁺ spin on to the F^- ligands which can increase the dipolar interaction by up to about 20% in the present case. The contribution from pseudodipolar exchange is shown to be negligible.

The exchange interaction between pairs of V²⁺ ions occupying substitutional cation sites in magnesium oxide has been studied by electron paramagnetic resonance. For next nearest neighbour pairs coupled via an intervening oxygen ion, transitions within the total spin state S=2 only are observed. Transitions within the S=1 and S=3 levels are broadened by interactions which leave the S=2 level unaffected. The exchange-induced fine structure splitting, D_e, is almost a factor of two larger than the dipolar term D_d. Although lattice distortion, covalent spin transfer to the ligands and anisotropic exchange interactions may contribute to this discrepancy a significant part must come from so far undetermined mechanisms. The nearest neighbour pairs, which are at right angles with respect to an intervening anion, have been studied in less detail. The interaction is found to be ferromagnetic with J=-7.5+or-3 cm^-1.

Details are given of an empirical method of calculating paramagnetic resonance line shapes, based on a modification of the usual statistical theory. When applied to the calculation of the line shape functions g( omega ) for a cubic lattice of spins S=¹/₂, and of the corresponding free-induction decay functions G(t), the method gives results differing from those obtained experimentally by less than 6%, and usually less than 2% of the respective maximum values g(0), G(0).

From an analysis of the room temperature nuclear resonance of ²⁷Al principal values are obtained for the electric field gradient eq V_zz/h and the anisotropy constant eta at an aluminium site for GdAlO₃ (0.589+or-0.01 MHz and 0.878), TbAlO₃(0.890+or-0.01 MHz and 0.01 MHz and 0.613) and DyAlO₃ (1.30+or-0.03 MHz and 0.655). The directions of the principal axes of the electric field gradient relative to the crystal axes are obtained. At low temperatures the nuclear resonance of ²⁷Al is measured in GdAlO₃ in the paramagnetic region (T>3.87 K) and the antiferromagnetic region (1.4 K<T<3.87K). The results obtained are shown to agree with a simple model based on the currently held view of the ordered magnetic structure of this salt. There remains a large discrepancy between the magnitude of the observed internal magnetic field at an ²⁷Al site and that calculated assuming classical magnetic dipole coupling. The possibility of a large anisotropic transferred hyperfine interaction is discussed.

A relatively simple model is described for the random flipping of a Hamiltonian between two generally noncommuting forms. The flipping is assumed to be sudden and is further taken to be Markovian in nature. Under these assumptions an explicit derivation is given of an equation for the averaged density matrix. Two simple cases are discussed. Firstly, the formalism is shown to give previous results when the two forms of the Hamiltonian commute. Secondly, the jumping of a spin-one nucleus between two similar quadrupole Hamiltonians is discussed. Other simple problems are also tractable.

A systematic approach is developed for the improvement of the line narrowing efficiency of multipulse cycle sequences. This is based on the symmetrization of pulse cycles and exploits the useful properties of reflection symmetry subcycles. An example of a new pulse sequence is given which removes the dipolar interaction to third order in the time expansion of the logarithmic operator. Ways are discussed for compensating multipulse cycles for the effects of finite rf pulse width and rf inhomogeneity and a fully compensated version of the new pulse sequence is given.