Table of contents

Integrated X-ray diffraction intensities have been measured for 21 reflections from an indium crystal at 295K. Mean square amplitudes of vibration in the two principal directions have been determined and are (u_a²)=0.0318+or-0.0003 A² and (u_c²)=0.0357+or-0.0003 AA². The value of the X-ray Debye temperature is 106+or-1K.

It has been found that for simple metals the eigenvalues of the wavefunctions generated by the Herman-Skillman atomic structure programme (1963) differ from the experimental values. The use of the correct core eigenvalues in calculations with the Harrison a priori pseudopotential theory (1966) has a significant effect on the resulting phonon dispersion curves.

Orbitally-averaged electron-phonon scattering rates on the second zone Fermi surface of indium have been obtained from measurements of radio frequency size effect line amplitudes for fifteen different extremal orbits. Using an inversion scheme based on a Fourier series expansion the anisotropy of the local scattering rate as a function of wavevector has been inferred.

After subtraction of a contribution due to magnetic clusters, the magnetization of NiV alloys, as a function of the field, temperature and concentration, follows fairly well the itinerant model, on both sides of the critical concentration. In a critical alloy ( approximately 89 at% Ni) the percentage of Ni atoms in magnetic clusters probably does not exceed 10%. Special attention is focussed on the temperature dependence of the magnetization in high fields.

Pulsed NMR measurements in a 99.54 at% ⁶¹Ni enriched sample of Ni metal in the paramagnetic phase are reported for a wide range of temperatures (785-1520K). The Knight shift (K) follows an expected Curie-Weiss law K(T)=K( infinity )+A_K/(T-T_c), where K( infinity )=(1.48+or-0.05)%, A_K=-(560+or-10)%K, and T_c=(662+or-10)K. The d spin hyperfine field is found to be -(108+or-8)kG per Bohr magneton. The recovery of the magnetization following a comb of saturating pulses is (150+or-50) mu s for the entire temperature range.

Recent theories of nuclear quadrupole relaxation in liquid metals developed by Sholl (1974) and other authors are revised. It is shown that they improperly establish a connection between the electric field gradient (EFG) and the interatomic pair potential. The correct expression for the EFG is derived from the total extra-nuclear charge density. It is consistent with an expression given by Sholl in an earlier paper and shows the same asymptotic behaviour.

For original article see ibid., vol.6, no.5, p.L157 (1976). The expression for the electric field gradient derived by Schirmacher in the proceeding letter is shown to be identical to that proposed by Sholl (1967). It is shown physically why the use of the effective interatomic potential to obtain the electric field gradient is incorrect.

X-ray L₁₁₁ absorption discontinuities of neodymium, samarium and gadolinium in the pure metals and in NdCo₅, SmCo₅ and GdCo₅ respectively have been studied using a 40cm Cauchois type bent (mica) crystal X-ray spectrograph. It is observed that the L₁₁₁ absorption discontinuities of the rare earths in the compounds shift towards the high energy side. The chemical shifts have been correlated with the charges on the absorbing atoms.

Photoemission spectra from polycrystalline films of Ag are reported for the photon energy range 12 to 40 eV. A one-electron density of initial states derived using the f-sum rule is compared with calculations and high resolution XPS measurements.

Linear screening theory for the interionic interaction in simple liquid metals is extended by including pair and three-ion interactions due to the third-order perturbation term in the electron-ion interaction. Additional pair potentials, phi ₂⁽³⁾(r), of both sodium and potassium are large and attractive in the short range. The position of the sharply rising part of the pair potential moves to a smaller distance by several percent with the inclusion of phi ₂⁽³⁾(r). The role of phi ₂⁽³⁾(r) is essential if the theory of Anderson Weeks and Chandler is to give a good description of liquid structures. On the other hand, second-order calculations are rather successful when the Gibbs-Bogoliubov inequality method is employed.

The temperature dependence of peak counting rates of gamma - gamma angular correlation curves of positron annihilation has been measured for pure Cu, Cu-3.9at%Si, Cu-7.8at%Si, Cu-4.6at%Ga, Cu-8.3at%Ga, Cu-15.0 at %Ga and Cu-8.0at.%Mn. All the measurements were performed at thermal equilibrium from temperatures above the melting points to room temperature. Measured data were analyzed according to the positron trapping model and the values of the apparent formation energy of a single vacancy were found to be 1.21+or-0.02 eV, 1.13+or-0.02 eV, 0.92+or-0.02 eV, 1.10+or-0.02 eV, 1.02+or-0.02 eV, 0.88+or-0.02 eV and 1.19+or-0.02 eV, respectively. Some differences among thermal equilibrium data are considered and relations between apparent formation energies of a vacancy and melting temperatures are discussed. Evidence that the apparent formation energies of copper solid solutions are approximately proportional to the electrons per atom ratio was found.

The interaction energy between two Al slabs is found as a function of separation, d. For d greater than about 6 au the van der Waals interaction predominates, given accurately by the Lifschitz formula. For d less than 1 au pseudopotential perturbation theory can be used to find the interaction, and it turns out that there is a weak maximum coming from the Friedel oscillations in the ionic screening. At intermediate d the results of Ferrante and Smith (1973) are used in which the charge densities of the separate slabs are superimposed, and the interaction energy found using a local density approximation. Using these results, the relative contributions of the short-range forces and the long-range van der Waals forces to mechanical adhesion are studied, and it is found that in general the van der Waals forces make a negligible contribution. The consequences of these interaction energy results for strength properties of materials are also considered, and a simple model for the grain boundary energy discussed.

Measurements have been made of lattice parameters residual electrical resistivities and microhardness values of AlSc alloys containing up to 3.28at%Sc. The change in lattice parameter a with concentration c is found to be (da/dc)/a=0.122+or-0.011 at%^-1, in residual resistivity rho ₀/c=3.5+or-0.5 mu Omega cm at%^-1 and in relative microhardness (d sigma /dc) sigma =1.0+or-0.1 at%^-1. Changes in lattice parameter and residual resistivity support the virtual bound state model of Al-3d alloys and changes in microhardness correlate with deviations from Vegard's law for these alloys.

The linear thermal expansion for a number of BCC solid solution alloys in the system Zr-Nb-Mo-Re has been measured at room temperature and at temperatures between 1.5 and 35K. Values of the room temperature Gruneisen parameter gamma _G(300) and the low temperature lattice, gamma _l, and electronic, gamma _e, Gruneisen parameters have been derived from the expansion data. These parameters have been applied to a discussion of model calculations for the pressure dependence of the superconducting transition temperature in this alloy system.

The free energy of a semi-infinite model binary alloy is set up. It is described essentially by two physically identifiable parameters. On minimizing this free energy under suitable constraints in a Bragg-Williams type approximation, it is shown that the composition varies as one moves in from the surface into the bulk. This 'surface segregation' of a constituent is studied under different conditions. Agreement has been obtained with the experimental results on Ni-Au alloy.

A method is developed for evaluating the electronic properties of non-simple liquid and amorphous metals their alloys and liquid semiconductors. By non-simple metals we mean those for which the nearly free electron model does not hold, such as transition, noble and rare earth metals. Explicit expressions are evaluated within a tight binding self consistent single site framework. The formalism presented effects considerable simplification of the previously encountered technical difficulties involved in a matrix generalization of the one-band equations. Numerical applications to the density of states for dilute liquid mercury are shown.

Scattering experiments on molten metals now afford the possibility of extracting valence electron correlation functions. Therefore, the theory of the pair correlation function between valence electrons in the presence of a weak electron-ion interaction nu _ie is developed by the present authors. To obtain explicit results to second-order in nu _ie. Two different approaches have been used: (i) diagrammatic analysis and (ii) density functional theory, in which the change in the electron-electron pair correlation function from its value in jellium is expressed in terms of the electron density change, for a fixed configuration of ions. While the theory is applicable both to crystalline and molten nearly-free electron metals, the theory has been pushed through further for liquid metals, and in particular the most extensive numerical results have been obtained for liquid Na.

The importance of using non-local potentials to gain an understanding of properties of simple metals has been shown by recent calculations. An expansion of the total energy to third order in the pseudopotential was derived for a local potential by Lloyd and Sholl (1968). The generalization of this expansion to a non-local potential is presented. The theory depends on a Green's function expansion of the integrated density of states and involves no approximations with regard to the interpretation of poles or the shape of the Fermi surface. Such approximations do arise in Rayleigh-Schrodinger perturbation theory. The third-order expansions from the present theory and from Rayleigh-Schrodinger perturbation theory are compared.

The Fermi surface of the Cu-Ge alloy in the HCP zeta phase field is studied by measurements of momentum distributions of annihilation photons from two single crystals at e/a=1.38 and 1.45. The Fermi surface of the alloy at e/a=1.38 lies inside the Jones zone, and has a high degree of contact with the zone faces. A normal to (10.0) and a small degree of contact with the zone faces B normal to (00.1). The overlap of the Fermi surface across the A faces is observed for the alloy at e/a=1.45. Remarkable bulges of the Fermi surface are detected along the directions towards the faces C normal to (10.1) in both the compositions. The present results reveal the correlation between the overlapping of the Fermi surface across the zone faces and the change of lattice constant. The relative stability of the HCP zeta phase is discussed in the light of the experimental results.

The energy bands and the character of conduction electrons have been studied for the equiatomic yttrium-magnesium compound YMg, following the self-consistent symmetrized augmented plane wave (SAPW) method. The convergence of energy eigenvalues has been checked towards the number of iterations and basis functions, as well as their sensitivity to changes in the Slater exchange parameter alpha . The Fermi energy is obtained as E_F=0.380 rydberg relative to the bottom of conduction band. The calculated density of states N spin up spin down (E_F) is 2.99 el/eV per unit cell. A comparison with the experimental Pauli susceptibility indicates a large exchange enhancement. The character of conduction electrons is principally of d-type within the yttrium APW sphere, the incidence on the crystal field is briefly discussed.

A spherical cell model is proposed in which a one-electron, self-consistent potential is constructed in either the Hartree-Fock or local density approximation depending on the nature of the cellular state in question. Analysis of the calculated eigenenergies in terms of an effective cellular Hamiltonian leads to numerical estimates of the intra-cellular Coulomb correlation energies existing between a 4f electron and either a second 4f electron or an electron in a 5d or 6s conduction band Wannier state in cerium. A simplified criterion for configurational instability is derived, and it is found that within the uncertainty inherent to the calculation, the relative position of the 4f level and particularly its behaviour under pressure are consistent with the configuration crossover model of the alpha - gamma transition in cerium.

Measurements of the absorption of high frequency longitudinal phonons in the superconducting and intermediate states of aluminium are reported. From the position and the width of the absorption edge that occurs when pair breaking ceases to be effective, the energy gap and its anisotropy can be determined. The variation of the attenuation coefficient in the intermediate state reveals non-local effects when the electron mean free path is greater than the lamina thickness.

From magnetization measurements M(T, theta )_H on erbium doped yttrium single crystals the crystalline electric field parameters and the energy levels of the erbium groundstate ⁴I_15/2 have been determined. The experimental results can be explained if the influence of the conduction electrons on the crystalline electric field is considered. Using a modified orthogonalized-plane-wave technique the contribution from the conduction electrons due to their 4f character has been calculated and the degree of 5d admixture has been determined from the experimental crystal field parameters A₂⁰(r²).

For pt.I see ibid., vol.5, p.2343 (1975). The method of calculating the susceptibilities in the spin-density-wave state of an itinerant-electron antiferromagnet introduced in the previous paper is extended to the two-band incommensurate case. The model Hamiltonian used is the Feeders and Martin two-band model in which electrons in different bands are coupled. Both longitudinal and transverse susceptibilities are calculated within the random phase approximation and explicit expressions which do not make any approximation for the form factors are given. The susceptibilities contain both intraband and interband parts. The Coulomb interaction is shown to contribute only to the interband part of the longitudinal susceptibility. The differences between the commensurate and incommensurate spin-density wave states are discussed as well as the collective modes arising from the susceptibilities.

The theoretical basis for the two-band model with spin-mixing which has been widely applied to the analysis of the transport properties of ferromagnetic metals is discussed in detail. This model is shown to have much more general validity than the original presentation suggested. The model is then applied to resistivity data in Ni and Fe based alloys to obtain a consistent set of parameters for the scattering within each spin band for various impurities, together with temperature dependent pure metal scattering rates.

The single crystal elastic constants of erbium were determined by means of an ultrasonic pulse technique as a function of temperature (10-300K) and magnetic field strength (0-3.9 T) along the c axis. Pronounced anomalies for most of the constants were observed in zero field at the Neel (85K) and Curie (20K) temperatures, as well as at 53K, at which temperature magnetic ordering in the basal plane sets in. Application of a field tries to restore the values of C₁₁ and ¹/₂(C₁₁-C₁₂) to what one would expect for a 'non-magnetic' crystal, while in the case of C₃₃ and C₄₄ it leads to very large softenings of the constants near 53K. A qualitative comparison is made with the predictions of Southern and Goodings (1973) which is based on single-ion anisotropic magnetoelastic terms.

See also ibid., vol.5, p.1385 (1975). Calculations of the wavevector dependent susceptibility chi (q) and dielectric functions epsilon (q) for paramagnetic nickel are reported. The calculations are based on a simple interacting band model described earlier. Owing to the highly anisotropic nature of the nickel Fermi surface, different Houston averaging schemes have been studied with the view to obtaining convergence in chi (q). It is shown that a nine-directional Houston averaging scheme is appropriate for paramagnetic nickel. The calculated chi (q) shows a broad hump around q=0.5 au which is attributed to Umklapp processes. Inclusion of matrix elements weakens this hump. The calculated xi (q) and epsilon (q) are not in agreement with those of earlier workers. The reasons for this disagreement are critically discussed.

The electronic structure of the Ni₃Fe alloy, in the ordered and disordered phases, has been investigated by soft X-ray emission and X-ray photoelectron spectroscopy. The densities of states deduced from these two types of experiment are compared with those of the pure elements and related to the current discussion on transition metal alloys, with emphasis on the order-disorder transition. It is found that transition effects predicted by density of states calculations are not confirmed by the experimental spectra.

A complete Hamiltonian formulation is presented of optical and ultraviolet emission from thin and thick metal foils irradiated by electrons. While the classical theory is limited to the treatment of emission by high energy electrons, the present treatment does not suffer from that limitation. It is shown how one can incorporate into the theory the effects of the crystal potential. Explicit results are given for a very simple model of crystal potential and show that quantum corrections are necessary to avoid unphysical divergences which would occur if one neglected these effects.