Table of contents

A quantitative theoretical explanation is given of the different temperature variations found for the thermal conductivity of solid helium parallel and perpendicular to the c axis.

As in the theory of electron tunnelling a transfer hamiltonian formalism is proposed to describe phonon transmission through a solid-liquid ⁴He interface. Such an approach allows a systematic evaluation of the effects of phonon scattering processes on the Kapitza resistance.

The Andrew's second moment correction formula as reconsidered for an experimental setup where an untuned wide-band lock-in amplifier which responds to the odd harmonise as well as the fundamental of the input signal is used. The calculation shows that the contribution due to the presence of the odd harmonics is only one ninth of the Andrew's term and therefore the Andrew's correction formula can still be used without introducing excessive error.

F centre production by ionizing radiation in MgF₂ has a character which changes markedly with temperature; below approximately 50K and above approximately 200K essentially unsaturating defect production occurs while between approximately 50K and approximately 200K the concentration of F centres quickly saturates. Detailed measurements of the effect of irradiation intensity at 5K, 80K, and 300K have been made, together with measurements at constant intensity as a function of temperature. These results are interpreted in terms of a model in which the radiation creates close pairs of F centres and H centres which are stable at low temperatures, recombine at intermediate temperatures and dissociate at higher temperatures. Other evidence is presented for this model, including the fact that the observed F band is rather wider for F centres created at 5K than for centres created at 300K and measured at 5K.

A theory is presented for the diffusion coefficients of electrons in a single valley or multivalley semiconductor in a high electric field. The valleys may be isotropic or anisotropic and the coefficients describe diffusion transverse and longitudinal to the field. Generalized Einstein relations are found for a single valley semiconductor and for transverse diffusion in a semiconductor with two types of isotropic valleys. The general method is applied to gallium arsenide and silicon.

Specific heat measurements have been made between 0.2 and 4 K on NdNi₂, NdAl₂ and NdCo₂ and also on LaAl₂. Hyperfine contributions have been identified in the neodymium compounds, and the ionic moments deduced, giving 1.63 mu _B, 2.39 mu _B and 2.63 mu _B respectively. These moments, the known Curie temperatures and paramagnetic susceptibilities, can all be interpreted in terms of a common model to represents crystal field and exchange effects. All three compounds have 'electronic' specific heats which are far larger than the electronic specific heat of LaAl₂ ( gamma =12.1 mJ mole^-1 K^-2).

Measurements between 1 and 10 K show that CeNi₂ and CeCo₂ have large electronic specific heats represented by gamma =24.9 and 38.2 mJ mole^-1 K^-2 respectively. Possible origins of these large values are discussed. A small specific heat anomaly is found at 5.9 K in all specimens, and is believed to be due to uncombined cerium, possibly in the cubic gamma form.

Measurements of the linear coefficients of thermal expansion of TlCl and TlBr are reported between 25 and 260 K. The results are believed to be accurate in an absolute sense to within 2% down to 50K, falling to 6% at 25K. The Gruneisen parameters gamma have been calculated using earlier data on the specific heats and elastic constants, between 260 and 80K. Within this range it is concluded: (i) Any variation of gamma with temperature is within the limits of experimental uncertainty. (ii) Any variation of gamma with ionic mass ratio is within the limits of experimental uncertainty. (iii) The mean room temperature value of gamma for TlCl and TlBr, 2.4₅+or-0.1₈, exceeds the corresponding mean value for CsCl, CsBr and CsI, 2.0₄+or-0.1₂. Estimates of gamma ₀ based upon the pressure derivatives of the elastic constants at room temperature suggest that for TlBr statement (i) may be extended to T=0, but for TlCl( gamma ₀- gamma _infinity ) may exceed unity. Moments of the vibrational frequency spectra of the two crystals have been calculated and varying degrees of consistency with different theoretical models have been observed.

A model is presented for calculating trajectory deflections of sputtered particles due to the incident beam electrostatic field. The resultant deflection of particles prior to detection makes the sputtering current density a significant parameter in analysis of the angular distribution and energy of sputtered particles. Thus it is probable that the higher average energies of sputtered ions generally found (in comparison with neutral particle energies) is partially a result of detector discrimination against particles of a few eV. Angular corrections are given for the most important sputtered energy range up to 20 eV.

Bands of localized states have been calculated for the ideal (100), (110), and (111) surfaces of silicon. The three-parameter local pseudopotential method has been used to calculate energy bands for complex wavevectors normal to the surface, and the corresponding wavefunctions and their normal derivatives are matched to appropriate vacuum functions. Interpolation between the states calculated at points of high symmetry is provided by the approximate description of the energy bands in the bulk material developed by Heine and Jones (1969). Two bands of surface states occur in the neighbourhood of the energy gap, though there are notable differences between the results for the three faces. In particular, the glide plane present in the (110) surface leads to a doubly degenerate band along an edge of the two dimensional Brillouin. Consequences of the results for the interpretation of experimental data, and the validity of the model as a guide to surface states at real surfaces are discussed.

The local density theory is developed by Hohenberg, Kohn and Sham is extended to the spin polarized case. A spin dependent one- electron potential pertinent to ground state properties is obtained from calculations of the total energy per electron made with a 'bubble' (or random phase) type of dielectric function. The potential is found to be well represented by an analytic expression corresponding to a shifted and rescaled spin dependent Slater potential. To test this potential the momentum dependent spin susceptibility of an electron gas is calculated. The results compare favourably with available information from other calculations and from experiment. The potential obtained in this paper should be useful for split band calculations of magnetic materials.

The critical current of a double Josephson junction is expected to increase in an oscillatory manner as the temperature is lowered. The effect arises whenever the critical currents of the two junctions are different and/or when there is geometric asymmetry.

The green function approach is used for the calculation of the AC transverse conductivity in the hopping regime of the impurity conduction. This approach enables the author to clarify what type of absorption contributes to the Hall effect. The result is that only the direct (resonant) absorption occurs. On the other hand, he finds out what approximations are involved in Holstein's early calculations. He concludes that these approximations are not achieved by the experimental circumstances, a fact which explains the discrepancy between the Holstein theory and experiments. Another problem discussed is the way of calculation of the conductivity in the hopping regime. It is explained why it is correct to calculate the induced dipole moment rather than the current.

The theory of the transverse magnetophonon effect in weakly coupled ( alpha <<1) polar semiconductors is developed from a perturbation expansion of the Kubo formula for conductivity to include Landau level damping. The general oscillatory structure of the resistivity is shown to depend on omega _c and omega ₀, the cyclotron and optic phonon frequencies, as rho _osc approximately Sigma _r=1^infinity r^-1 exp (-2 pi r gamma )cos(2 pi r omega ₀/ omega _c) where gamma is a complicated function of the parameters of the phonon and impurity induced damping processes. For impurity broadening 2 pi gamma is proportional to omega ₀/ omega _c and of the order of unity, in agreement with experimental observations on GaAs.

High temperature series expansions have been calculated in terms of a general spin variable S, and anisotropy parameter eta , and and arbitrary lattice structure for the longitudinal version of the anisotropic Heisenberg model defined by the hamiltonian H_N=- Sigma _ijJ(S_izS_jz+ eta (S_i⁺S_j^-+S_i^-S_j⁺))- mu H Sigma _i=1^NS_iz where the initial sum extends over the set of nearest neighbour sites of a regular crystal lattice structure of N sites, situated in an external magnetic field H. This model contains the Ising model and the isotropic Heisenberg model at the points eta =0, and eta =¹/₂ respectively. The expansions of the partition function Z in zero field and the zero field susceptibility have been obtained through orders T^-7 and T^-6 respectively.

A simplified theory is given of the changes induced in the optical absorption of a small polaron by the presence of a static electric field bias ( epsilon ). Three cases are treated: a free carrier a carrier bound to an impurity center, and a carrier moving through a lattice in the presence of disorder potentials. Explicit formula are derived for weak and moderate fields ( epsilon <or=5*10⁵ V cm^-1), showing effects which are linear and quadratic in epsilon , with various temperature dependences. The symmetry properties of the optical high-field effects are discussed, and the problem of optical charge transfer in the Coulomb field of an impurity ion.

Zeeman optical absorption spectra of Er:GdAlO₃ have allowed a determination of the principal values of the Er³⁺-Gd³⁺ exchange interaction for the ground state and the lowest components of ⁴S_3/2 and ⁴F_9/2 states of Er³⁺. Using these interaction data, the highly nonlinear behaviour of the low field Zeeman spectra (H<40 kG) can be explained satisfactorily for the highest energy lines, which can be assigned unambiguously. Qualitative evidence for canting of Gd³⁺ moments which are NN to Er³⁺ ions is discussed, and a study of the angular dependence of the spin flop field provides evidence that the Gd³⁺ moments flop into the bc rather than the ab plane.

The optical properties of terbium doped soda glass have been investigated as a function of terbium concentration. The properties studied in this work were the excitation luminescence and absorption spectra and the luminescence decay times. In the case of short wavelength excitation, the absorption occurs in the glass matrix and is followed by energy transfer to the Tb³⁺ ions. At long wavelengths the efficiency of energy transfer between Tb³⁺ ions by dipole-dipole interaction is small up to quite high concentrations of terbium in the glass. However, above approximately 1 wt.%Tb the intensity of the luminescent ⁵D₄ to ⁷F_j transitions increases very rapidly with terbium concentration. It is suggested that in this range energy transfer occurs between the ions of a Tb³⁺ ion pair by means of an exchange-dipole interaction.

Photoluminescence spectra of refined epitaxial indium phosphide and gallium arsenide show clearly a close correspondence of bound exciton transitions. Classified in both materials are emissions due to excitons bound to neutral acceptors and donors, free exciton peaks and various types of phonon coupling. Excitons bound to neutral acceptors in both materials give rise to a sharp doublet emission which readily reveals the presence of strain in the sample. The magnitude of the strain is estimated to be approximately 10^-3 in certain regions of typical epitaxial layers. Reflectivity experiments provide new estimates of the exciton gaps-1.4182 eV in indium phosphide and 1.5150 eV in gallium arsenide.

The authors report the first observation of certain weak transitions which occur as sidebands of electron spin resonance hyperfine structure due to the protons of a methyl group executing tunnelling rotation at 4K. The transitions involve an electron spin flip and a simultaneous change in the torsional oscillator tunneling state of the methyl group. The transitions were observed in free radicals generated by gamma irradiation of crystals of methyl malonic acid. They enable the tunnelling splitting to be measured to 2% and the minimum energy orientation of the methyl group to be located to 4 degrees . The transitions were found after their position and intensity had been predicted from electron nuclear double resonance measurements. They were positively identified through their angular dependence and the fact that they disappear at higher temperatures.