Table of contents

We examine the modification of the low temperature thermopower of dilute nonmagnetic alloys due to phonon drag induced electron diffusion. Deviations from the usual expression are found to be proportional to those in the resistivity predicted by Dworin.

A semiempirical pseudopotential for crystalline mercury has been determined using a fitting procedure to experimental dimensions of the Fermi surface. Three separate classes of pseudopotential were found to be consistent with measured calipers of the Fermi surface. One pseudopotential is equivalent to the Evans's pseudopotential used for liquid mercury.

An analysis of recent experiments on aluminium shows that in a high magnetic field the resistivity has a temperature dependence proportional to T³, similar in form and magnitude to that of an impure sample in zero field, and markedly different from the T⁵ behaviour of pure material in zero field. The idea of momentum nonconservation at electron-phonon collisions, which was introduced to explain the impurity effect, is extended to account for the temperature dependent part of the magnetoresistance.

The Compton profile of polycrystalline scandium has been measured with MoKα x rays. In the medium and high momentum regions the observed profile is in good agreement with that calculated from Hartree-Fock free atom wavefunctions for the valence-electron configuration 3d4s². At small momentum values the experimental profile lies between those computed for the conduction-electron configurations 3d4s² and 3d²4s.

Although the large cohesive energies of the transition metals have been successfully explained by the tight binding (TB) method, the corresponding TB wavefunctions are shown not to satisfy the virial theorem. The consequences, especially as regards the shape of the wavefunction, the mechanisms of binding, and the nature of the repulsive force, are discussed with the help of analogous results for molecular bonds.

The Anderson model Hamiltonian has been used to study the binding energy at finite temperature between a magnetic impurity and the conduction electrons. By employing the extended Hartree-Fock approximation to a cluster variational calculation we have derived a critical temperature which gives an upper limit for binding in such a system.

The resistivity (ρ) at temperatures below 4.2 K of palladium alloys with 2 to 6 at% nickel has been measured and fitted to the expression ρ - ρ0 = ATⁿ. The behaviour of A clearly indicates the critical concentration for the para- to ferromagnetic transition at 2.32 ± 0.03 at% nickel. Well away from this composition n is close to 2.0, but decreases on approaching it from either side.

We determine the interaction energy between two impurities in the transition matrix using a realistic `d' band structure. We study the variation and the validity of the asymptotic form of the interaction energies of transitional impurities with `d' band filling.

We make the calculation for ferromagnetic nickel based alloys in detail.

A detailed study of the diffuse scattering in the neutron diffraction patterns of single crystals of γ MnCu alloys containing 10, 15, 25 and 40 at% Mn has shown that diffuse peaks occur at the 1½0 type positions, and are due to both atomic and magnetic short range ordering.

Analysis of the diffuse scattering has yielded the atomic and magnetic short range order parameters and a value of S = 2.0 ± 0.3 for the localized spin on the manganese site.

Neutron diffraction measurements of polycrystalline specimens have also confirmed that dilute γ MnCu alloys containing 3, 8, 15 and 25 at% Mn show no evidence of co-operative magnetic ordering at temperatures down to 4.2K. It is suggested that earlier results from Mössbauer and electron spin resonance experiments can be reconciled with the neutron diffraction results by invoking a model in which there is a non-zero temporal average of the spins rather than long range spatial magnetic ordering.

In a previous paper it was shown that if a high phosphorus-containing stainless steel is quenched directly from solution treatment temperatures of 1100 and 1300°C to ageing temperatures in the range 400 to 750°C, a complex series of precipitates and quenching defects is formed. The present paper describes a transmission electron microscope study of some of these defects. Specifically, an attempt has been made to characterize their nature and geometry using diffraction contrast analysis.

Defects in crystals may form a regular array, rather than a random distribution. The lattice of voids produced in irradiated molybdenum is a remarkable example of this. We give a general method of calculating the energy per defect in the array which exploits the periodicity of the defect lattice. The existence of the void lattice depends on the elastic interaction between voids. The present approach can treat both arbitrarily anisotropic elastic continua and discrete lattices, and is readily extended to discuss the stability of the defect lattice. The results predict that a void lattice should occur in molybdenum, and compare a number of models for the void. Stability against shear of the void lattice is not discussed in the present paper. The ratio of the void lattice spacing to void radius predicted is 2.2 to 4.5 and is smaller than the value of about 10 observed. The results are in general agreement with the more approximate Malén-Bullough treatment.

Phonon frequencies in zinc at 80 K have been determined for all symmetry lines in wavevector space, using a neutron crystal spectrometer. The results, which are complete and of good accuracy, are presented as dispersion curves and in table form

The conduction bands for Ca have been computed with a Slater-type potential and it is found that for less than 20% or more than 75% of the exchange term there is no overlap between the first and second band. The conduction and core bands, density of states, Fermi energy and Fermi surface are computed for an optimum value of the exchange. It is found that the Fermi surface is connected and agreement with all the known results of the de Haas-van Alphen effect is obtained. Although this is in apparent disagreement with the results of Vasvári et al. who obtain an unconnected Fermi surface, their Fermi level was wrongly located and when the error is corrected a connected surface should almost certainly be obtained. The effect of pressure on the Fermi surface and conductivity of Ca is discussed.

A high resolution point detector geometry has been applied to the study of the angular correlation spectra from positron annihilation in Cu₈₅Zn₁₅ single crystals. Strong anisotropies are observed and some features are interpreted in terms of the alloy Fermi surface. A value for the [111] neck diameter is obtained which is 50% greater than that for pure copper. Considerable smearing of the expected slope discontinuity in the neighbourhood of the Fermi momentum is interpreted as evidence for Stern's theory of charging. A large anisotropy in the higher momentum contribution to the annihilation is also observed.

Isotropy relations more extensive than, but containing, those usually quoted are obtained by considering structure-independent contributions to the energy of a crystal in a formalism involving a first order elastic constant. These lead to relations between Brugger elastic constants of different orders. The results are applied to the kinetic, exchange and correlation energies of free electrons and to the first order perturbation band-structure energy. In all cases the full set of first, second and third order elastic constant contributions follow from a single quantity.

Fallacious statements concerning the bulk modulus of the electron gas are exposed.

Results are presented on the low field Nernst-Ettinghausen coefficient of silver over the temperature range of 4-200 K. The coefficient shows a strong peak near 20 K and still exhibits a peak when divided by the thermal conductivity. The latter fact suggests the peak is to be identified with the presence of a phonon drag contribution. Although the Sondheimer-Wilson two band model is shown to be capable of producing a phonon drag term of the correct order of magnitude, the sign of the expected contribution is opposite to that observed.

In Li, at high temperature, the constant volume resistivity becomes larger than the zero (atmospheric) pressure value. This is contrary to what is observed in the other alkalis. It has been suggested that it is a result of an increase in the distortions of the lithium Fermi surface with application of hydrostatic pressure. We show that the effect can be understood much more simply and naturally on the basis of a spherical Fermi surface and a simple electron-ion pseudopotential form factor. The form factor is used to evaluate the absolute value and the volume dependence of the thermoelectric power. the thermal conductivity and the electron-phonon mass renormalization.

Using the KKRZ method, the selfconsistent band structures of the alkali metals have been calculated. The calculations give good agreement with experimental Fermi surface measurements, except for caesium where contact with the Zone boundary is predicted. It is also found that the effects of the actual interstitial potential, compared with assuming it to be constant, are negligible.

Measurements on photoemitted electron distributions from Cu, Zn and β'-CuZn up to 21 eV photon energy are reported. It is found that the Cu d-band is 0.9 eV lower relative to the Fermi level in β'-CuZn than in pure Cu and the width is only slightly smaller. The Zn d-band however has essentially the same position in both Zn and β'-CuZn. It is shown that the Cu d-states are responsible for the yellow colour of β'-CuZn rather than the conduction states as has been previously proposed.

The low-field magnetoresistance of single crystals of some dilute copper-and silver-based alloys has been measured at 1.5 K and 4.2 K. The alloys studied were CuAu and AgAu (homovalent impurity): CuZn and CuGe (heterovalent impurity); and CuNi and AgPd (transition metal impurity). The results, in conjunction with previously measured Hall coefficients, were interpreted under the assumption that an anisotropic relaxation time can be defined which has a different anisotropy for each impurity. By describing the anisotropy in terms of `relaxation time models' a possible variation in the relaxation time over the Fermi surface has been deduced for the CuAu, AgAu, CuNi and AgPd alloys, but the magnetoresistance of the CuZn and CuGe alloys cannot be interpreted in terms of the models described here.

New experimental data for deviations from Matthiessen's rule for the electrical resistivity, Δ(T, c), for NiFe and NiCr alloys for temperatures 4 K <or= T <or= 300 K and solute concentrations 0.1 <or= c <or= 4 at% are discussed in terms of a popular two-current model, which includes momentum-conserving spin-flip scattering processes, ρ₁₂(T). It is first established that for this model, deviations obey a Kohler-Sondheimer-Wilson (KSW) relation, (ρ₀(c)/Δ(T, c)) = a + b(ρ₀(c)/ρ_ideal(T)) where ρ₀(c) is the solute resistivity at 0 K and ρ_ideal(T) is the resistivity of the pure solvent. The KSW coefficients (a, b) depend only on the two-current scattering anisotropies and on a reduced spin-mixing resistivity r(T) (=ρ₁₂(T)/ρ_ideal(T)). Experimental data for Δ(T, c) conform quite well to a KSW description; however, the experimental coefficients (a, b)_Cr and (a, b)_Fe are not compatible with the familiar spin-flip scattering model. The major discrepancies occur in the temperature range (T <or= 50 K) in which the model would most likely be valid. The discrepancies between data and model predictions are discussed in terms of residual impurities, of zero temperature spin-mixing processes, and for an alternate spin-mixing mechanism.

The depression of the superconducting transition temperature (T_c) of AIMn and ThU alloys decreases with pressure. To the extent that localized spin fluctations are responsible for the depression of T_c in these alloys, it is inferred that the lifetime of the spin fluctuations decreases with pressure.

Measurements of the room temperature lattice parameter, the superconducting transition temperature and the magnetic susceptibility over the temperature range 1.5 to 300 K have been made on the pseudo-binary alloy system CeRu_2-xCo_x. T_c is depressed from the values for the terminal compounds and superconductivity could not be detected above similar 0.33 K for 0.2 < x < 1.7. From the form of the variation of T_c with Co substitution and the susceptibility measurements it is concluded that the destruction of the superconductivity in CeRu₂ is due to localized spin fluctuations associated with the Co. The effects of transition metal and rare earth substitution into CeRu₂ are compared and discussed.

In this paper the consequence of using the magnetic field dependent dielectric function of Hebborn and March in the calculation of susceptibility is considered. The change in the susceptibility arising from this is calculated and the general result evaluated for the alkali metals. The change for these metals is small, being the largest for lithium.

The magnetic susceptibilities (χ) of a series of single-phase Ti-Al alloys have been measured in the temperature range 74-400 K. In addition, the susceptibility temperature dependences, χ_parallel(T) and χ_{perpendicular}(T), of single crystal specimens of pure Ti and the intermetallic compound Ti₃Al were measured and correlated with the results of lattice-parameter (c, a) thermal expansion studies. In pure Ti, both χ_parallel(T) and χ_{perpendicular}(T) (4.2-400 K) are relatively temperature independent below about 70 K, the range within which the volume thermal expansion coefficient is practically zero; and increase linearly above about 130 K, in which region c and a both expand linearly. For Ti₃Al, changes of slope of χ_parallel(T) and χ_{perpendicular}(T) (78-400 K) occurring near 200 K and 300 K were accompanied by distinct changes in the rates of thermal expansion of c and a.

As a result of these and other experiments, several statements could be formulated relating to the susceptibility temperature dependences, χ(T), of Ti and Ti-Al alloys: (i) χ(T) was strongly responsive to thermally-induced lattice-parameter changes: (ii) for a family of Ti-Al solid solutions, χ(T) was relatively insensitive to solute concentration; (iii) the total susceptibility was anisotropic; (iv) of the total susceptibility, only about one-third could be accounted for by the calorimetrically measured Fermi density-of-states, n(E_F), the remainder being due chiefly to orbital paramagnetism; (v) curvature of n(E)]_E=EF is incapable of accounting for χ(T) in the systems under study.

To satisfy the experimental observations it was suggested that the principal mechanism for susceptibility temperature dependence in Ti and Ti-Al alloys is lattice-expansion-induced variation of the orbital paramagnetism.

Simple perturbation theory is used to estimate the magnetic polarization of the conduction electrons due to a magnetic moment placed at the origin. It is found that the component of the magnetic polarization parallel to the overall magnetic moment oscillates and is the sum of two RKKY terms of slightly different wavelength. The perpendicular component has an RKKY term whose wavevector is the average of the up and down spin Fermi wavevectors and at long range an additional RKKY term of larger amplitude and longer wavelength. The perpendicular component also has a non-oscillatory part which arises from the possibility of exciting spin waves in the palladium.

Aluminium films of 11 to 13 nm thickness have been prepared in UHV on glass substrates held at 77°K. The changes of resistance and complex refractive index on subsequent heat treatment were related to a change in the effective electron density and relaxation time consistent with the Drude-Zener theory. The optical and electrical measurements were corrected for the effects of oxide growth, which was observed to take place at all pressures. This correction was deduced from a study of the oxidation of films of similar thickness.

The Mössbauer effect in Fe^{5 7} has been used to study the relaxation associated with the transition from ferromagnetism to superparamagnetism in β Co fine particles. By observing Mössbauer absorption spectra as a function of particle size, the critical volumes for single domain particles have been estimated at 8 K, 83 K and 300 K. In this way the relaxation time may be related to particular values of the energy barrier between stable magnetic states (measured in units of kT) and the results compared with theoretical predictions.

The emission and absorption spectra of simple metals are calculated taking into account many-body correlations in the electron gas. The calculations are performed up to first order in the RPA effective electron-electron interaction as well as in the RPA potential of the core hole. The first order theory of Longe and Glick has been reformulated to take account correctly of the normalization of the many-body `golden rule'. The divergency throughout the main band is eliminated and this new theory allows an estimate of the intensity of the Fermi edge singularity arising from the transient character of the core hole. The effect depends strongly on the structure of the electron wave functions close to the ion site. Strong cancellations of terms appear in the calculation of the intensity spectrum. This helps to explain why the bands are roughly one-electron like except for the low and high energy features. The calculations presented in this paper account qualitatively for most of the observed features which do not depend on band structure. Special application is made to the L emission and absorption spectra of sodium.

It is shown theoretically that in single passage magnetic resonance studies of oriented radioactive nuclei the time dependence of the radiation pattern may always be determined from classical calculations. Measurements by radiative detection of single and multiple passage magnetic resonance of ⁶⁰Co nuclei in polycrystalline and single crystal samples of iron at temperatures from 0.006 to 0.02 K are reported. The observed signals are considerably smaller than those expected theoretically. One possible explanation of the results is obtained by allowing for the magnetic fields produced on the electrons by the nuclei together with a localized anisotropic attentuation of this disturbance by electron-electron exchange.

A study of the nuclear magnetic resonance spectrum of single crystals of three alloys of aluminium containing 0.5 at% Mg, Ga and Ge impurities respectively has revealed the presence of weak satellite lines whose dependence upon the orientation of the crystal in the magnetic field establishes that they originate at host sites which are nearest neighbours to the impurity. The Ga and Ge results contradict the earlier interpretation of Minier based upon pure quadrupole resonance studies and the new assignment is in greatly improved agreement with the theoretical calculations of Fukai and Watanabe.