Table of contents

X-ray transmission measurements of the structure factor of liquid caesium have been carried out for temperatures between 30 degrees C and 150 degrees C. From these measurements the radial distribution function, the pair potential and the electrical resistivity are derived.

A numerical calculation of the surface magnetization of a paramagnetic metal is given within a finite barrier potential model of the metallic surface. It is found that there exists a ferromagnetic instability at the surface for large enough values of the barrier height V.

High-quality copper single crystals have been quenched from temperatures between 750 and 1050 degrees C. The analysis of the quenched-in resistivities gives a vacancy formation energy of (1.27+or-0.05) eV in good agreement with the monovacancy formation energy of (1.29+or-0.02) eV found by positron annihilation. Isochronal annealing of quenched copper shows two recovery stages, one centred at 0 degrees C and one above 200 degrees C. In the first stage, nearly 35% of the quenched-in resistivity is annealed out. Vacancies migrate in this stage with an activation energy of (0.74+or-0.08) eV. The sum of the measured vacancy formation and migration energies is (2.01+or-0.13) eV and agrees well with the monovacancy self-diffusion energy Q_SD^1V=(2.06+or-0.05). The data can be explained within the vacancy annealing model for stage III in electron-irradiated copper as elaborated by Schilling and co-workers (1973 and 1976).

Results are presented for the velocity of ultrasound in liquid ⁶Li-⁶Li alloys of composition 4.5, 49.7 and 99.9 at.% Li for temperature up to 700 degrees C. At the melting point the ratio of the velocity of sound in ⁶Li to that in ⁷Li was found within experimental error to equal (M₇/M₆)¹2/, the result expected for classical liquids which differ only in the isotopic mass M. In the alloy of 49.7 at.% ⁷Li the sound velocity exceeded 0.6% the value expected for a thermodynamically ideal alloy. This result is discussed in terms of the theoretical treatment by Parrinello, Tosi and March (1974) of collective excitations in binary isotopic fluids.

Local effective electron-ion potentials for metals are constructed from a priori calculations of the electron density around an ion embedded in an electron gas. These effective potentials fold certain higher order contributions to the cohesive energy into a lower order calculation. The dynamical matrix is evaluated to second and third order in the effective potential. When band structure effects are included in the energy denominators of the response functions, the lithium phonon frequencies calculated with no empirical input are in excellent agreement with experiment.

A simple semi-empirical model is presented which explains observed positron momentum distribution p(k) in alkali metals as well as large apparent positron effective mass m** defined by p(k) varies as exp(-k²/2m**k_BT). It is shown that p(k) can be taken as a Boltzmann-type distribution only when the lifetime broadening Gamma (k,E) of a positron quasi-particle increases with the energy as approximately E¹2/. Such an energy dependence of Gamma (k,E) is actually expected for phonon effects in both solid and liquid metals. The deviation of m** from the true effective mass m* is directly related to the magnitude of Gamma (k,E) and m**/m* is calculated as a function of Gamma (k,E).

A system of rare-earth atoms with mixed valency is viewed as an alloy A_1-nB_n, where n denotes the probability of finding the rare-earth atom in the state with valence three and (1-n) is the probability of finding the rare-earth atom in the state with valence two. The coherent potential approximation (CPA) used in alloy theory is then applied to determine the d and f electron configuration in such systems. Thus, the various properties of systems with mixed valency can be determined. The theory also includes local environment effects. An explanation is offered for various properties observed for rare-earth compounds.

Results are presented for a semi-empirical pseudopotential model for the Fermi surface of indium which was developed during a study of the effect of alloying on indium by Holtham and Parsons (see Proc. Int. Conf. on Low Temp. Phys., vol.4, p.222 (1972) and ibid., vol.6, p.1481 (1976)). The authors find U₁₁₁=-0.0550(95), U₀₀₂=-0.0229(93) and U₂₀₀=0.0179(72) Ryd, with lambda _4p=0.0309(57) and epsilon _F=0.6377(28) Ryd. The model is similar to that proposed by Hughes and Shepherd (1969) although a different form for the spin-orbit interaction is used and the symmetry of the basis states is fully taken into account. The model predicts no connectivity of the second zone hole surface near T or W and predicts no swelling at the junctions of the third zone beta -arm electron surface. Hughes and Shepherd's conclusion that spin-orbit effects are needed to describe the third zone electron surface accurately, is confirmed, and the recent contrary finding of van Weeren and Anderson (1973) is discussed. The viability of the present model is investigated by computing Fermi surface calipers, effective masses and Sondheimer oscillation frequencies. These results, together with the variation of extremal cross sections under either hydrostatic pressure or uniaxial stress, are then compared with experiment.

A detailed study has been made of the third zone electron beta -arm Fermi surface of dilute indium-lead and indium-thallium alloys. Precise experimental measurements of the change with alloy composition have been made using the de Haas-van Alphen effect. Theoretical calculations of the Fermi surface changes have been computed using an extension of a pseudopotential model developed for pure indium. The effect of variations in valence, lattice parameter, pseudopotential and the spin-orbit interaction have been examined separately. Good agreement between theory and experiment is obtained for the indium-lead alloys, but the agreement for the indium-thallium system is less satisfactory. The determination of accurate values of the solute concentration is also briefly discussed.

Calculations of the electronic band structure of metals have been performed using the Shaw optimized model potential (1968). The parameters defining the potential have been evaluated specifically for this work without using the tables of Shaw, and this has permitted iteration back through the evaluation of the parameters. In this way a self-consistency has been imposed between parts of the theory previously linked only through parameterization. The vibrational excitations are also computed with the same potentials and with the effective mass deduced from the band structure calculations thus providing electron properties and vibrational properties corresponding to the same model. In most cases this procedure produced results in reasonable agreement with other theories for the band structure. For the vibrational properties however a large increase in the effective mass m* was necessary to reconcile the model with experiment. Results are presented in detail for potassium, tin and antimony.

The electrical resistivities, rho , of Eu, Yb and Ba have been measured at high temperatures. In solid Yb and Ba rho varies linearly with temperature. This is contrary to some previous results. Both metals show a large percentage increase of rho on melting. The temperature dependence of rho in Eu is nonlinear and there is a smaller percentage change on melting. The resistivities of liquid Eu and Ba are larger than those of any other liquid metals. Negative temperature coefficients of resistivity are observed for all three metals in the liquid state. These results and those obtained in our earlier measurements on alloys of rare earth metals are discussed in the context of existing theories. The authors suggest that even in the liquid rare earth metals and their alloys an interpretation involving the liquid structure factors and the effective valences of the components may still provide a reasonable qualitative explanation of the behaviour of the resistivity. The occurrence of negative temperature coefficients in other disordered metallic systems is also commented on.

The applicability of a simplified energy surface, similar to the one used to explain the Hall coefficient of beryllium in a previous paper (Shiozaki 1975), to the other hexagonal close packed metals, zinc and cadmium, has been examined. A simplified Fermi surface has been constructed of the doughnut-like ring and ellipsoid pieces, its overall dimensions being chosen to resemble those of the experimentally determined surface. Good agreement is obtained with the simple model for the anisotropy and the sign of the Hall coefficients. It is found that the contribution from the second zone hole 'monster' is very considerable and it appears that the results are further improved only if the author improves the approximation for the 'monster'. It is concluded that the anisotropy of the relaxation time plays no important role.

A new approach is given to describe the superconducting properties of the A-15 compounds. Using the notion of charge transfer and local character of the constituents of an alloy, an attempt is made to give a coherent picture of the superconducting properties of different A₃X alloys. A correlation is found between the difference of the density of electrons at the limits of the Wigner-Seitz cell of the atoms in an alloy and its physical properties. If the transfer is proportional to this difference, the T_c variations of different A-15 alloys can be described. This model also predicts high T_c for 'hypothetical' A-15 alloys like Nb₃Si, Nb₃Te or Nb₃Bi.

The superconducting energy gap of gallium has been determined along the three principal crystallographic axes from the temperature dependence of the attenuation of longitudinal ultrasonic waves with frequencies in the range 10-150 MHz. Like many other physical properties of gallium, the gas was found to be highly anisotropic. A self-consistent method was developed and used in order to determine the part of ultrasonic attenuation caused by electron-phonon interactions. An abnormal peak of attenuation, for which no explanation can be given, was observed for propagation along b axis. Finally, the investigation of transition temperature against magnetic field has allowed the discontinuity of specific heat at the critical temperature to be estimated.

Paramagnetic susceptibility, high field magnetization and Mossbauer measurements are reported for the Be_xFe_1-x intermetallic compounds (x=0.671 to 0.774) which have the Be₂Fe crystal structure, the excess Be atoms occupy the Fe sites. The data show a rather strong decrease in the iron magnetic moments for the Be substitution which is localized around the excess Be atoms and it is attributed to the decrease in the magnetic splitting of the iron 3d bands while the electron density at the iron sites remains substantially unchanged.

Amplitude modulating the microwave field and monitoring delta M_z/ delta t by means of a coil coaxial to the static field and close to the sample, are shown to constitute an original technique for studying conduction electron spin resonance. A calculation of the line shape is derived for both cases of normal and anomalous skin effect. The method is shown to provide several favourable features when compared to conventional spectrometry. Experiments on lithium are reported as an example, and results are compared to theoretical calculations.

The optical properties of Au and Ag are measured between 0.5 and 5.4 eV for temperatures ranging from 40 to 840K. The analysis of these spectra-also extended to the case of Cu-permits the assessment of energy separations associated with interconduction-band transitions in the vicinity of L over a wide temperature range. Notably the L_4- to L₄₊ (nonrelativistic: L₂' to L₁) energy gap at 295K is found to be 4.81 eV for Cu, 4.11 eV for Ag and 4.20 eV for Au. The temperature dependence of this gap (around 295K) typically is -6.5*10^-4 eV K^-1 for all noble metals, i.e., considerably larger than predicted on the basis of band calculations. The present analysis also shows the interband absorption edge of Ag to arise from transitions in extended regions of the Brillouin zone. A comparison of experimental and theoretical spectra suggests lattice expansion to be the major source of temperature dependence of the band structure. It also yields information regarding the influence of dipole matrix elements on the epsilon ₂ spectra.

Soft X-ray appearance potential spectra were recorded for a series of Fe/Ni alloys whose compositions in the surface region were determined by means of Auger electron spectroscopy. The L₃ appearance potentials (correlated with the binding energies of 2p_3/2 electrons) of Ni increase by 0.5 eV between 0 and 30% Fe and then at even higher Fe concentrations remain constant. The corresponding values for Fe are practically unaffected by alloying. This effect is tentatively ascribed to a local intra-atomic reorganization process of the Ni valence electrons. A quantity derived from the intensities of the APS peaks which is correlated with the (local) densities of unfilled states above E_F varies linearly with the alloy composition.