Table of contents

The hypothesis that Hume-Rothery's rules for phase stability in binary alloys are a consequence of the divergent slope of the wave-number-dependent dielectric function at 2k_F is investigated. The relative energies of the fcc, bcc, and hcp structures of the alloy systems CuAl, LiMg, and CuZn are calculated with a realistic local pseudopotential model. Striking evidence of the screening anomaly is obtained in all cases. The calculations suggest alloy phase boundaries in the three systems studied which are for the most part in excellent agreement with experiment. The only exceptions are pure Cu and pure Zn, for which an incorrect structure is predicted, the former by a remarkably small 3 × 10^-5 ryd per electron. It is suggested that both discrepancies might be rectified if the forces between d electrons on neighbouring sites were properly accounted for. In particular, it is argued that the attractive forces arising from the overlap of neighbouring d electrons and from their Van der Waals interactions provide a substantial impetus for a distorted structure in Zn. A thermodynamic instability arising from the divergent slope of the dielectric function is considered. Rough calculations are presented which indicate that when higher order terms in the electron-ion interaction are properly considered this instability will disappear, without, however, the phase boundaries being significantly altered. The principal conclusion, which is consistent with previous suggestions, is therefore that the Hume-Rothery rule arise not so much from the screening divergence itself as from the rapid variation of the dielectric function in the immediate vicinity of 2k_F.

The theory of localized spin fluctuations (LSF) in dilute nearly-magnetic alloys (e.g. AlMn) due to Hargitai and Corradi is extended to include the renormalization of the spin fluctuation lifetime capital Gamma^-1_s. In this way the mass renormalization constant, Z₁, of the localized electronic states on the impurity site and the inverse LSF lifetime capital Gamma_s can be related to the fundamental parameters of the Anderson model, viz. the width capital Gamma of the localized electronic states and the Coulomb repulsion U between localized electrons of opposite spin. A numerical calculation shows that Z₁ and capital Gamma_s show no instability at the Hartree-Fock criterion for the formation of a magnetic moment (U/πcapital Gamma = 1). Expressions for the thermodynamic, magnetic and transport properties of such alloys can be written in terms of capital Gamma_s, Z₁, U and capital Gamma. Reasonable numerical values for capital Gamma_s, Z₁, U and capital Gamma are then obtained from experimental data for dilute AlMn alloys.

Calculations have been made of the relaxation times for electrons on the Fermi surface of Ag due to scattering from dilute concentrations of Au and Cu impurities. In the case of AgAu alloys it has been found that the relaxation times are primarily determined by the mass-velocity and Darwin relativistic corrections to the potential seen by an electron. In AgCu alloys the relativistic corrections are still important and the calculated relaxation times depend critically on cancellation between `potential' scattering and `relativistic scattering' and possibly the effects of the strain field.

Linewidths of the ²⁰⁹Bi nuclear magnetic resonance in liquid bismuth-lead alloys are reported as a function of concentration and temperature. The measured widths contain two components: a part proportional to temperature due to the usual magnetic hyperfine interaction with conduction electrons, and a part which decreases with increasing temperature. The latter is attributed to relaxation produced by an electric quadrupole interaction with diffusing ions. The quadrupolar term measured at 625 K passes through a marked maximum as a function of composition at 50% lead and it is the dominant contribution to the width around this composition at lower temperatures. It is concluded from a review of data for several liquid alloy systems containing nuclei with substantial quadrupole moments that this type of concentration dependence should be regarded as normal and not a peculiarity of the Bi-Pb system.

Jones' method for calculating the band structure of a long-period superlattice structure is extended to a three-dimensional crystal. In this method the antiphase boundaries themselves appear as perturbations rather than the whole crystal potential. The band structure of CuAu II is calculated, and as the length of the antiphase domains increases the long-period superlattice band structure tends to the band structure of CuAu I. The stability of CuAu II is discussed in terms of its band structure.

Wavefunctions can exist in antiphase structures which are localized about the antiphase boundaries, and this is discussed for a one-dimensional model and also for CuAu. These localized functions give rise in the long-period superlattice alloy CuAu II to two energy bands lying in the middle of the CuAu I band gap, and it is these bands which are responsible for the crystal stability.

Using the relativistic augmented plane wave method, the energy band structure of metallic gold has been calculated for three different exchange potentials namely (i) Slater exchange, (ii) Kohn and Sham exchange and (iii) an average of (i) and (ii). The E(k) against k curves and the density of states histograms are plotted for all the three cases. It is found that in the case of gold, Slater exchange potential gives better agreement with experimental Fermi surface data.

A calculation of the electron energy bands for antiferromagnetic γ-manganese arising from the 3d and 4s levels in the free atom has been carried out by the augmented plane wave and Hubbard's parametrized methods, obtaining good agreement between them. The bands for face-centred cubic Mn are split by the tetragonality and there is further exchange splitting due to the antiferromagnetism. The general picture is of two d bands, not completely separated and crossed by a nearly-free-electron band. The width of either d band is similar 0.3 ryd and the Fermi level occurs just above the dip between the bands, giving a value of 0.0033 J mole^-1 deg K^-2 for the electronic specific heat co-efficient γ, comparable with the experimental values obtained by extrapolation from high temperatures and from alloys but considerably smaller than the only direct measurements for γ-Mn. The calculation gives an estimated value for the atomic moment of 2.4₇ μ_B in good agreement with experiment.

The electron-phonon coupling function α²(v)F(v) has been calculated for the cubic simple metals Na, K, Al and Pb, and the effects on the coupling strength of variations in the theoretical screened electron-ion potential have been studied. The volume dependence of the coupling function has also been determined using theoretical phonon frequencies.

First principles studies of the superconducting behaviour under pressure of the simple metals Al and Pb have been made. Good agreement is obtained with the experimental volume derivative of the transition temperature in Al and, for higher compressions, upward deviations are predicted to occur from the linear relationship with volume observed at low pressures. In Pb, the relative rates of decrease under pressure of T_c, Δ₀, and 2Δ₀/κ_BT₀ show the same trends as experiment, while in Al the ratio 2Δ₀/κT_c is found not to vary significantly with compression.

Doppler-shifted cyclotron resonance is studied for a simple model Fermi surface which includes a small pocket of paraboloidal form. This model is simple enough for the field dependence of all the wave characteristics to be found analytically. The results depend on the relative distances moved by the different groups of charge carriers, in the direction of the applied magnetic field, during one cyclotron period. When this displacement is larger for the carriers on the paraboloid than for the main carriers, the helicon wave is coupled with the DSCR mode. It is found that the properties of the coupled waves depend significantly on the sign of the resonant term in the conductivity with respect to the Hall conductivity due to the main carriers. If the signs coincide, the coupling results in extrema in the wave spectrum and anomalies in the impedance of the metal. If the signs are different the helicon wave transforms smoothly into the DSCR mode at the resonance.

When the displacement of the carriers on the paraboloid is smaller than for the majority of carriers a DSCR propagating mode appears below the helicon absorption edge.

The 77 keV¹⁹⁷ Au Mössbauer resonance has been investigated at 4.2 K for all the phases of the gold manganese system which could be retained at room temperature. The isomer shift increases linearly with manganese concentration due to a transfer of electrons from the manganese atoms to the gold atoms. Quadrupole interactions are observed for ¹⁹⁷Au in βMn, Au₂Mn and AuMn₂, and the values obtained are consistent with a simple point charge model. Analysis of the hyperfine magnetic fields for the magnetically ordered alloys in terms of a model whereby the field is determined by the geometrical arrangement of nearest neighbour manganese spins, yields a field per manganese unpaired electron of approximately 55 kOe,

Results are presented which indicate that the metamagnetic behaviour of the R₃Co compounds is probably the consequence of a time dependent behaviour of the magnetization at low temperatures. Magnetization curves obtained in pulsed fields, are appreciably different from those obtained in static fields, and in general, open hysteresis loops are observed, along with much higher values of the critical fields. It appears that the critical field values may depend upon the rate of field increase.

Spin echo measurements of the ⁵⁹Co nuclear resonance in GdCo₂ have revealed a rapid decay of the spin-echo amplitude with temperature up to 40 K followed by a further growth up to 79 K and subsequent decay above this temperature.