Table of contents

The equation of state of a liquid metal (described by volume and pairwise forces only) is investigated using a hard sphere reference system. The pressure can be written either (i) as that due to the hard spheres, but with the density dependence of the diameters ignored, plus a rather complicated term due to the perturbation or (ii) as that obtained by using the correct pressure expression but with the true radial distribution function replaced by the hard sphere one.

A pseudopotential calculation of the resistivity of copper alloys in the 'dirty limit' has been performed. Reasonable agreement with experiment is obtained.

It is shown that the resistivity data of AuV and possibly other dilute alloys with high T_K can be explained within the framework of the theory of localized magnetic moments.

The authors show how the elementary concepts which govern the bulk total energy and crystal structure of sp bonded metals are also relevant at the surface. A simple model explains the observed contraction in the interlayer spacing of the (110) surface layer of aluminium compared with the (100) and (111) surfaces.

Simple one dimensional models of anharmonic lattice potentials are used to investigate the effect of anharmonicity on the electron-phonon coupling constant lambda . It is found that if the phonon energy is interpreted as the first excitation energy then anharmonicity will have little influence except to diminish slightly the size of lambda .

The Kondo mass enhancement is related to that predicted by Brinkman and Rice (1970) for a highly correlated gas. The significance of the quantity E in the formula ( Delta /h(cross))exp(-E/ Delta ) for the Kondo frequency is discussed.

It is shown that there exists an exact transformation of the functional integral expression for the partition function which allows one to map the Anderson model into an effective s-d exchange model. In the extreme magnetic limit (U/ Delta >>1) this leads to a Schrieffer-Wolff type of interaction and clarifies the manner in which S^z sigma ^z and S^+or- sigma ^+or- terms arise.

The magnetic entropy of ZrZn₂ is evaluated by comparing its low temperature heat capacity data to that of nonmagnetic ZrCu_1.1Al_0.9. It is found to be finite but small, indicating that ZrZn₂ is very much an itinerant electron ferromagnet.

A CW NMR study of Fe rich FeCr alloys indicates that there is a long ranged perturbation of the hyperfine fields at Fe sites around a Cr impurity, consistent with the Mossbauer effect results. In addition there is evidence of the ordering of two Cr impurities as second near neighbours. The average hyperfine field change per Cr impurity is found to be not inconsistent with the value determined by the Mossbauer effect.

The author shows that the nuclear magnetic resonance experiments on dilute heavy transition metal impurities embedded in cubic ferromagnetic hosts can be explained with the help of an electric field gradient resulting from the spin-orbit effect.

The optical absorption spectra of colloidal solutions of Cu with gelatin as a stabilizer are studied. One characteristic absorption peak is found at 2.14 eV (580 nm) which is attributed to surface plasmons of Cu particles. This result agrees with previous measurements of energy loss of electrons transmitted through thin Cu films.

Measurements have been made of the positron annihilation coincidence counting rate at the peak position in aluminum and in an Al-0.27 at% Si alloy as a function of temperature from 25 degrees C to 600 degrees C. The results were analysed according to the positron trapping model to yield the vacancy formation energy, E_f, and the vacancy-silicon binding free energy. The thermal expansion of the sample and the temperature dependence of the Si solubility were taken into account, and the trapping rate assumed to be temperature independent. For pure aluminum it is found that E_f=0.67+or-0.03 eV. For the Al-Si alloy a least squares analysis based on the Lomer expression for the vacancy concentration of a dilute alloy shows that the vacancy-silicon binding free energy is 0.12 eV. This is smaller than the binding free energy of 0.20 eV found by Burke and King (1970) from length and lattice parameter thermal expansion measurements.

A derivation of the vacancy formation energy and volume is given within the framework of local pseudopotential theory. Numerical results are presented for the alkalis and for Al. The theory is based on the previous work of Ho (1971) but with some modifications and extensions. The differences are not numerically very significant in the alkalis but are critical in Al for which the authors obtain satisfactory results while Ho's theory failed.

An effective Hamiltonian method is developed for relativistic band structure calculations where resonances are present such as in the heavy d band transition metals and noble metals. The method, which is a generalization of the nonrelativistic one of Hubbard (1969) is used nonrelativistically for Cu and relativistically for Au in comparisons with previous calculations by the APW method. The overall agreement with these calculations is satisfactory, i.e. an RMS difference of 0.008 Ryd in the case of Au for the 36 energy levels compared.

The volume dependence of the width of the d 'resonance' in some transition metals is calculated using the Mattheiss prescription for the crystalline electron-ion potential. This information is then used in a single scatterer approximation to estimate the variation of eta , the electronic part of the electron-photon mass enhancement, with volume. The results agree well with empirical analyses of the pressure dependence of the superconducting transition temperature in transition metals. The authors also discuss the volume dependence of the width of the d band.

The band structure of lithium has been calculated by the OPW method using the Seitz potential for the ions and the selfconsistent Hartree potential due to the conduction electrons. Use of the same potential for the 'core state' as for the conduction-electron states is found to be of some importance. A novel method is presented to transform the OPW generalized eigenvalue problem into standard eigenvalue form. The band structure so obtained agrees with previous calculations, particularly that of Rudge (1969). The calculated Fermi surface distortions are less than 4%, while the density of states and optical masses are 1.50 and 1.47 respectively. The direct interband optical conductivity has also been calculated; its overall magnitude is in reasonable agreement with measurements by Mathewson and Myers (1973). The calculation predicts a sharp absorption edge at 3.4 eV, in agreement with the measurement by Hodgson (1966), and in contrast to the much slower rise in the optical conductivity beginning at 2.4 eV reported by Mathewson and Myers.

Generalized Wigner-Seitz constructions are shown to reproduce most of the essential features of the phase shifts obtained from the APW, KKR and KKRZ analyses of experimental Fermi surface data.

A calculation of the temperature dependent resistivity rho _T of aluminium in the dirty limit has been performed using a simple model Fermi surface. The values obtained for rho _T are as large as those seen by Caplin (1970) and have a similar temperature dependence (T^3.5). The basic cause of this behaviour is the temperature dependence of the electron-phonon relaxation time near the zone boundaries. In order to predict the relation between rho _T and impurity concentration, a two band model has also been used, giving results for the deviation from Mathiessen's rule which are similar to Caplin's experimental values.

The electrical resistivity of several dilute RuFe and RuCr alloys has been measured between 1.45 and 300K. The incremental resistivity for the RuCr alloys is temperature independent at low temperatures, although above about 60K deviations from Matthiessen's rule occur, and these are fitted on the basis of a two current model. For the RuFe system the incremental resistivity is found to be temperature dependent, increasing as T² below about 170K, but more slowly at higher temperatures. The origin of this temperature dependence is attributed to conduction electron scattering from localized spin fluctuations; confirmatory evidence for this assignment comes from the analysis of existing measurements on the depression of the superconducting transition temperature of Ru by Fe impurities.

Deviations from Matthiessen's rule (MR) for the thermal conductivity of polyvalent metals with nonmagnetic impurities are explained by two effects: (i) Even for a free electron model the energy dependence of the solution of the Boltzmann equation is not well approximated by the variational ansatz. Solving the Boltzmann equation for impurity and electron phonon scattering at the same time yields a deviation from MR, whose concentration and temperature dependence does not follow simple power laws. This effect is large enough to be measurable. (ii) The larger contribution is due to the angular dependence of the solution of the Boltzmann equation on a disconnected Fermi surface like that of Al where Umklapp scattering at the zone boundaries has to be taken into account. A simple theory based on a relaxation time approximation of the Boltzmann equation yields a rather large effect of the size found in experiments.

Magnetization measurements performed on lead samples at 4.2K show how the position of maximum magnetization of the hysteretic magnetic behaviour are related to shape effects. It is possible to obtain reversible or irreversible magnetization curves by modifying the sample shape. These curves are in agreement with the two stage flux penetration process into cylinders and discs already studied by other authors and recently discussed elsewhere. From this discussion, a simple model using conformal mapping leads to a formula giving the applied field at which the second stage occurs as a function of thickness over diameter ratio. The results are in good agreement with experimental values for discs and with a computation performed by other authors. Magnetization curves of altered spheres present interesting features which seem unknown in the literature and which may be roughly interpreted using the same ideas.

Structure observed in the characteristics of superconducting aluminium tunnel junctions is reported. An explanation based on the ability of quasiparticles of energy greater than 3 Delta to create extra quasiparticles on 'relaxing' towards the gap edge is shown to give quite good agreement to the form and magnitude of the observed structure.

Measurements have been made from 2K to 300K of the magnetic susceptibilities of polycrystalline specimens of six R₂Zn₁₇ and of four RZn₁₂ compounds whose resistivities have also been obtained, where R represents a rare earth. Most of the compounds order antiferromagnetically. The resistivities due to electron-magnon scattering go as T^1.38 for GdZn₁₂, T^1.45 for TbZn₁₂, T^5.9 for SmZn₁₂ and T^6.5 for ErZn₁₂, as a function of temperature T. The presence of short range order has been detected far above the Neel points of the two gadolinium compounds.

The symmetry properties of magnetoelastic waves are exploited to enable selection rules to be determined for the lifting of accidental degeneracy between a phonon and a magnon with the same value of k, the cause of the lifting of the degeneracy being the magnon-phonon interactions. The results are given in detail for ferromagnetic hcp metals and are compared with the published dispersion relations obtained from inelastic neutron scattering experiments on Gd, Tb and Dy. These results are independent of the mechanism postulated for the magnon-phonon interactions. The relation of these general selection rules to selection rules for particular mechanisms is also discussed.

The author presents new relaxation time measurements in dilute VT alloys (T:Co, Mo, Rh, Ta, W, Re, Os, Ir) and concentrated sigma VCo, VCo₃, VRh₃ and VIr₃ alloys. From these experimental results and previous bulk susceptibility and Knight shift measurements made by Devos (1972) the author calculates the various contributions to the bulk susceptibility of these alloys and particularly the Pauli and Van Vleck vanadium susceptibilities. This allows a systematic study of the magnetic behaviour of vanadium alloys with transition metals as a function of the nature and the concentration of the impurity. New NMR results (Knight shifts, line widths and relaxation rates) in concentrated V_1-cNi_c alloys (85%<or=c<or=at 87%) are presented in order to study the magnetic behaviour of vanadium up to the critical concentration for the occurrence of ferromagnetism (c_cr approximately 87.5%). The vanadium susceptibility is shown always to decrease with increasing impurity concentration and to have very low values for high impurity concentration, even in nearly ferromagnetic alloys (VCo₃ and concentrated VNi alloys).

The X-ray photoelectron spectroscopy technique has been applied to study the adsorption of oxygen on the surface of niobium metal foil. It has been found that these measurements provide a method for determining the composition of the surface and for distinguishing between different forms of oxygen present on the surface of the metal.