Table of contents

A method is developed for calculating the nonlinear elastic field of a straight dislocation, when boundary conditions on the dislocation core are taken into account. The method applies to the general anisotropic case and can be used to improve the simulation of the dislocation core by semi-discrete methods.

The temperature dependence of positron trapping at vacancies in metals is discussed taking account of the velocity dependence of the capture cross section for a freely moving positron and also the role of positron scattering in limiting the arrival rate of particles to the vicinity of a vacancy trap. The Fermi golden rule and the analogy with low-energy neutron capture by nuclei strongly suggest a temperature-independent free particle trapping rate. Simple arguments for a classical itinerant positron sweeping out volume as it moves through the crystal show that scattering only affects the trapping rate if the mean free path is less than the capture radius. Recent estimates of the positron mean free path in metals suggest that this is not the case in most situations.

A consistent picture of the electrical and optical properties of mercury in the density range 0.4-8.5 g cm^-3 is presented. In this region mercury is an intrinsic semiconductor with a theoretical gap increasing to 4.2 eV at 0.4 g cm^-3. Deviations of the apparent electrical gap and of the apparent optical gap from the theoretical gap can be understood from the density fluctuation theory. A theory for the line shape of the optical absorption coefficient is presented and is found to be consistent with the experimental phenomena.

The electrical resistivity of Pt-Mn alloys containing from 0.09 to 18% Mn has been measured. In the most dilute alloys, a clear logarithmic region of positive slope has been observed in plots of resistivity against temperature, indicating that these Pt-Mn alloys show Coles-like behaviour. In all alloys up to about 11 at% Mn a resistance minimum has been observed which is attributed to spin glass ordering, below the minimum the resistivity follows the general T^3/2 law associated with spin glasses at low temperatures. Above this concentration there is no minimum and the resistivity is found to increase monotonically with temperature.

A resistance minimum is derived from a general theory of Adkins and the author, for spin glasses with narrow band metallic hosts and sizeable valence differences between host and impurity, as observed in PtMn by Sarkissian and Taylor (see ibid., vol.4, L243 (1974)). The resistivity follows the general T^3/2 law associated with spin glasses at low temperatures.

Ultraviolet photoelectron spectra have been obtained fron clean surfaces of Ag-Au alloys using 21.22 and 40.81 eV photons. The spectra, which exhibit fine structure not previously reported, have been successfully interpretated in terms of the coherent potential approximation to the extent that currently available calculations permit.

Conflicting reports have appeared in the literature concerning the usefulness of the Born-Green equation to determine effective interionic pair potentials in liquid metals from measured structure factors. To elucidate the problem, numerical investigations of the Born-Green equation have been made. These are based on recent structure factor data for sodium and potassium. Using the linearized simultaneous equation method of Waseda and Suzuki (1973), it is found that the equations in real space are ill conditioned. Hence a unique solution cannot be found numerically. However, in Fourier space unique solutions can be determined, but these solutions are temperature dependent. It is concluded that the temperature independent pair potentials for liquid metals which have been obtained from the Born-Green equation are not reliable.

It is argued that a distinction must be made between the longitudinal and transverse sum rules and that one consequence of the difference between these is that the absorption spectrum of a metal with narrow d bands is subject to the partial sum rule. Application to liquid Hg implies that in this particular case the transfer of oscillator strength proposed by Faber (1966) is unimportant.

An order-disorder transition in a lattice model of the beta -Au_xCu_52-xZn₄₈ system has been simulated by means of the Monte Carlo technique. The transition temperature of the model as a function of Au concentration has been found to be in very good agreement with the experimental data of Bowe and Muldawer (1972).

In a computer simulation study of generalised (112) stacking faults in a body centered cubic structure representing alpha -iron a stable fault has been found which may be regarded as a twin nucleus. The twin boundary has an unexpected but characteristic, symmetrical structure which is distinct from that associated with the conventional mirror image orientation relation.

Expressions for the stacking fault energies of close packed metals are derived. The technique employs periodic boundary conditions on a crystal containing a large number of widely spaced faults. All necessary summations are performed in wavenumber space. Reasonable agreement is obtained with experiment for the metals Be, Mg, Al, Cu, Ag, and Au. Contrary to some earlier work, the electrostatic contribution to the fault energy is found to be quite significant. The noble metal calculations include an evaluation of the d state overlap energy term; and this is shown to be small in comparison to the other contributions.

A model of stopping of a low velocity heavy ion moving through an electron gas has been used to calculate the stopping power of gold and tungsten for ions (6<or=Z₁<or=54) channelled along (110) Au and (100) W directions. A comparison is the results with experimental data shows satisfactory agreement and a definite improvement over modified Firsov theory in producing deep minima for some of the projectiles.

The morphology of small planar aggregates has been investigated by computer simulation. Clusters of as few as six vacancies have been found to collapse to form loops or stacking fault tetrahedra. This is consistent with the theory that vacancy loops are nucleated directly in individual neutron cascades. Larger triangular clusters collapse and dissociate to form stacking fault tetrahedra by the Silcox-Hirsch mechanism. Hexagonal clusters show a more complex rhombohedral relaxation with extensive dissociation of the Frank dislocation on (111) planes. This may explain the fine structure observed recently in electron microscope images of vacancy loops in copper.

The effect of a large magnetic field on phonon lifetimes in a metal is discussed for the situation in which the phonon wave vector is perpendicular to the magnetic field. It is concluded that for a general surface geometry the effect is unobservable with practical spectrometer resolution. However, for metals with large, nearly flat areas of Fermi surface an effect may be detectable when the phonon wave vector spans the flat areas of Fermi surface and when the latter are parallel to the applied field. An experiment to test this idea in niobium metal suggests the existence of an oscillation in the peak intensity of a (111)LA phonon as a function of applied field. The period of the oscillation gives a cyclotron mass of (1.3+or-0.3)m for the jungle gym part of the Fermi surface of Nb.

It is shown that the variation of the Debye-Waller factor of aluminium with temperature can be adequately described in terms of nearest neighbour central force pair interactions. An expression for the Debye temperature is obtained in the form theta _D(T)=413(1-0.000461T)¹2/K and a pair potential is deduced as phi (r)=(1.02 exp (-4.23r)-9.83 exp (-0.44r))*10^-20J. Good agreement is obtained between the observed and calculated values of the thermal expansion. The anharmonic contribution to the high temperature specific heat, C_V, is discussed.

Specific heat measurements have been performed on TBe₂ and (T,T')Be₂ beryllium compounds, where T and T' are neighbour transition metals of the first series. The temperature range investigated is 1.5. to 4.2K. For the paramagnetic alloys with 5<e/a<7, there is a regular behaviour of the electronic specific heat coefficient gamma with a minimum at e/a=6.12 and, the two half d bands with opposite spin directions are equally unfilled in agreement with the paramagnetic behaviour of the compounds. In the electronic concentration range, 7<e/a<7.6, the large peak of gamma at about e/a=7.16 is mainly ascribed to clustering effects due to the appearance of ferromagnetism. Above e/a=7.6, gamma decreases down to a minimum at e/a=8 where there is a transition from weak to strong ferromagnetism.

It is shown that the consideration of size effect by Swalin (1957) to explain impurity diffusion in solids is inconsistent and cannot be used to predict activation energies.

The extended Huckel molecular orbital theory is applied to linear eight atom Ni-Cu alloy chains of varying composition. The results obtained are qualitatively in agreement with recent experiments and with the results of the CPA theory. The work functions of pure Ni and Cu and the magnetic dead layer of pure Ni are discussed in relation to the charge oscillation due to the influence of the surface.

The band structure of beryllium has been calculated with the APW method using a local exchange-correlation potential. Comparisons between measured spectroscopic properties and quantities derived from the band structure indicate that the energy eigenvalues are correct within 0.5 eV or better in a region of 5 eV around the Fermi level.

A band calculation has been made for hexagonal close packed ( epsilon phase) iron in order to investigate whether a ferro- or antiferromagnetic state might be expected theoretically. For this purpose the Stoner criterion and a similar one for the occurrence of antiferromagnetism were applied and it was found that neither magnetic state would be predicted by these because of a low value for the density of states at the Fermi energy. Because of the width of the relevant dip in the density of states curve rigid band theory failed to explain the occurrence of antiferromagnetism in alloys of epsilon -Fe with Mn, Os and Ru as observed.

A relation between the internal electron chemical potential, the electron density on the Wigner-Seitz cell boundary and the pressure on a metal is derived in the quantum corrected Thomas-Fermi approximation. Some examples of the significance of this relation for the theory of metals are discussed. It is tested using the internal electron chemical potential values given by Heine and Hodges (1972).

A method for calculating accurate positron wavefunctions and energies for metals is presented which is based on a pseudopotential picture for the thermalized positron. The approach used involves systematically correcting a positron Wigner-Seitz wavefunction and energy using perturbation theory. The results of calculations for Al are presented and these indicate that first order perturbation corrections lead to satisfactory wavefunctions and second order corrections to good energies. An unsatisfactory feature of the wavefunction near the nuclei present in earlier results calculated using a truncated plane wave expansion is rectified by the positron pseudopotential approach.

Calculations are presented of the electrical resistivity using the t matrix formulation of Ziman's nearly free electron formulae. The calculated values are in good agreement with experimental values.

With the aid of a superconducting magnet the variation of the Nernst-Ettinghausen coefficient of three silver alloys has been determined over the temperature range 10-60K. The results are examined in the light of available theories and a separation is made into diffusion and phonon drag components. The latter is reduced by alloying and appears to vary with temperature as expected, but no satisfactory calculation yet exists for predicting its behaviour quantitatively.

The RPA is extended in the framework of linear response theory to allow for the treatment of a finite free electron gas. The dielectric function taking quantum size effects into account, is calculated and shown to be finite in the limit of small wavevectors. The theory is applied to a simple free electron model for a small metal particle and analytical expressions are obtained for the electronic polarizability of a thin film and for the optical properties in the plasma resonance region.

The pressure dependence of the superconducting transition temperature for the layer compounds h-Nb_1+xSe₂ (x=0, 0.01, 0.02, 0.05 and 0.1) and 4H-NbSe₂ has been investigated to 25 kbar. A strong enhancement of T_c is observed. A brief discussion of the influence of pressure upon the band structure and its relationship to the change in T_c is given.

The conductance associated with low lying vortex core excitations in a clean superconducting tunnel junction containing well separated flux vortices whose axes are perpendicular to the insulating barrier is calculated. The method combines the Bardeen tunnelling matrix element with the Caroli-Bardeen description of clean limit vortices. Account is taken of the anisotropy of the density of states and of the angular selectivity of the barrier as a function of its thickness and band gap. For a typical case the tunnel conductance between a vortex and a normal metal (VIM) is around one third of that predicted by inserting the vortex density of states directly into conventional tunnelling formulae. However, in tunnelling transitions between two vortices (VIV) there is also an angular momentum conservation rule which results in almost zero conductance at low bias.

Using the Mossbauer effect in ¹¹⁹Sn the hyperfine fields at the Sn sites in the Heusler alloys X₂MnSn (where X is Cu, Co, Pd and Ni) have been measured at 10K to be +196, +105, -38 and +95 kG respectively. The signs were determined unambiguously using circularly polarized gamma rays. These values of the fields at the X sites (where known) and the Curie temperatures, can be explained on the basis of a resonance scattering theory, provided the numbers of conduction electrons/atom are not restricted to those derived from simple valence considerations.

⁶³Cu NMR linewidth measurements have been performed on dilute CuMn, CuFe and CuCr alloys, from 0.34 to 150 K and between 1 and 50 kG. The data have been compared with magnetization measurements and it has been shown that the existence of interactions between impurities is reflected by the NMR results even for very dilute CuMn and CuFe samples ++++(a few tens of ppm). From the single impurity contributions to the NMR width, the sd effective exchange interactions have been deduced and are found to scale as expected from the Kondo temperatures. The amplitude of the asymptotic spin polarization as deduced from the present results have been compared with its values near the impurity given by the satellite Knight shift data of Boyce and Slichter (1974) in CuFe. It is shown that the observed slight deviations with respect to the RKY asymptotic limit can be explained with results deduced from the Hartree-Fock magnetic limit of the Anderson model.

The low temperature heat capacity of a 1% alloy of cobalt in copper in magnetic fields up to 50 kOe has been measured as a function of ageing time at 400 degrees C. The existing theory due to Hayes, Hahn and Wohlfarth (1972) based upon measurements in zero magnetic field, suggests that the excess heat capacity over that of pure copper should be of the form C_mag=A+ gamma T where gamma is a function of the applied field. The present experimental results cannot be represented by a function of this kind but are best represented by C_mag= gamma 'T+C_Schottky (H,T) where gamma ' is independent of the applied field and C_Schottky (H,T) is the heat capacity of a multilevel Schottky system in which the mean number of thermally populated levels increases from 3.25 to 5.40 as the alloy is aged.

The electric field gradient (EFG) at a nucleus in the metals Be, Mg, Zn, Cd and In has been calculated. Pseudopotential theory is used and only conduction electrons external to the ion core at the origin are considered. The conduction electrons are found to produce an EFG which partly screens the ionic contribution. Good agreement with experiment is found for Be but the calculated values in Mg, Cd and In are smaller than the experimental values and it is concluded that the conduction electrons within the ion core at the origin make a large contribution to the EFG at the nucleus in these cases.

The optical properties of clean, evaporated films of gallium have been studied at several temperatures. The observed spectra were interpreted on the basis of a pseudopotential calculation of the band structure. The position of characteristic peaks in the spectra agreed well with the predictions from the optimized model potential for gallium recently published by Appapillai and Williams (1973). The shift of the peaks with temperature was too large to be accounted for by shifts in the atomic form factor alone; the Debye-Waller factor must be included to explain the observations.

The optical properties of gallium quench condensed onto substrates at 10K, 30K and 80K have been studied. It is found that films condensed at 10K had a spectrum which could be described extremely well by the Drude equations. At higher temperatures two different spectra were observed, which the authors believe belong to the orthorhombic alpha dn and the monoclinic beta phases of gallium.