Table of contents

The crack extension force has been obtained by representing the crack with a suitable distribution of infinitesimal dislocations and using the concept of force on a dislocation. The method is sufficiently general to enable the energy release rate for a crack deviating from its original crack plane to be obtained and, as an example, it is applied to the problem of a long straight slit like crack in a general uniaxial stress field.

Pressure induced variations in the electron-phonon coupling constant lambda of cesium are calculated from first principles. The authors find that lambda increases with pressure and predict that cesium should be superconducting with an observable transition temperature T_c at 36 kbar.

Anisotropy of the magnetostriction of Mo and W is attributed to anisotropic strain dependence of the orbital paramagnetism. The magnetostriction of V is almost isotropic.

For a system of atoms interacting via two body forces a suggestion is made, using a matrix formulation of the problem, construction of a coherent potential. Considering the average behaviour of atomic clusters it is possible to include the effects of the off diagonal elements of the interaction matrix.

The change in positron density due to the presence of a dislocation in a metal is calculated. The resultant change in positron lifetime is found using both the Sommerfeld independent particle model and the local screening theory of Micah and Young. The lifetime change is calculated in the case of aluminium and found to be about 1% compared with the experimentally observed change of 15%. The angular correlation function, which is a measure of the degree of positron localization, is also calculated. It is found that the experimental angular correlation can be equally well interpreted on the basis of dislocation or vacancy trapping.

Iron films were made by evaporation in a technical vacuum on amorphous carbon substrates at 20 degrees C and 120 degrees C. The structure and stability of the films were strongly affected by the quality of the vacuum during deposition. The films prepared in a vacuum of 2*10^-4 Torr (O₂) on the substrate at 20 degrees C exhibited an amorphous like halo pattern of electron diffraction but careful analysis revealed that they consisted of very fine grains having fcc structure. Films prepared on the substrate at 120 degrees C in the same vacuum were a mixture of wustite and a small amount of amorphous like iron which transformed to the defective magnetite structure by exposure to the air for a short period.

The scattering from impurities in copper is analysed in terms of s, p and d partial waves. The (anisotropic) transition probability between points on the Fermi surface is calculated in terms of scattering phase shifts characterizing the impurity. Maps of the calculated scattering are presented for each phase shift and the corresponding Dingle temperatures are calculated for a variety of orbits seen in the de Haas-van Alphen effect. A procedure developed to calculate the impurity resistivity and anisotropy of the corresponding relaxation time demonstrated the need to use a vector mean free path in such a calculation. The calculated scattering is compared with experimental values in the Cu(Ni), Cu(Fe) and Cu(Al) systems and values derived for the scattering phase shifts.

Variations of the band structure and Fermi surface of Ir with various crystal potentials, including one recently proposed by Hedin-Lundqvist, is investigated by means of the relativistic APW method. A perturbationally based analysis of the difference between crystal potentials is carried out and the radial components of spherically expanded wave-functions are studied. The band structure at the Fermi energy is found to be quite sensitive to the exchange and correlation term, due to a strong localization of d type band electrons at this energy.

The calculated transverse frequencies agree very well with the experimental results but there is some divergence at a few points in the longitudinal branches. The computed value of the electrical resistivity using the exchange and correlation gives a better agreement with experimental values than those obtained by other workers previously reported using the model potential. It has been observed that although the calculated numerical values of the resistivity differ noticeably when the two exchanges and correlations are used, the calculated phonon frequencies differ insignificantly. The disagreement between the calculated and experimental result is considered to be linked with the form of screening used.

The free electron exchange approximation is studied by the method of many body perturbation theory. It is found that screening reduces exchange much below the Slater value. A formula is given for a k dependent exchange potential which includes screening. A method for its use in band structure calculations is suggested.

For pt. I see ibid., vol.2, 1055-61 (1972). The use of the k dependent potential is described. The band structure of Ca and its Fermi surface are computed with this potential and it is shown that the results are a marked improvement on those given by conventional potentials. The energy eigenvalues are computed for symmetry points for Al and it is shown that fair agreement is obtained with results obtained from a pseudopotential. It should be stressed that the potential used is entirely a priori, with no adjustable parameter.

A selfconsistent single site effective Hamiltonian is derived within the multiple scattering theory to describe a disordered tight binding binary alloy for which both constituent bandwidths and site potentials are different. The total density of states and the constituent partial density of states are calculated and discussed. It is shown that the multiple scattering approach provides a suitable formalism for investigating problems such as (i) the extension of the Koster-Slater formula when impurity and host have different bandwidths, (ii) the appearance of a satellite-peak structure in the broader bandwidth component density of states when the difference in bandwidths is great enough, (iii) the generalization of the theory to a two band model relevant for transition and noble metal alloys.

The Morse potential function has been applied to describe the harmonic properties of Cu₃Au and Au₃Cu alloys in the state of perfect order from first and second nearest neighbour considerations. The potential parameters for like and unlike atomic interactions have been determined in a consistent manner. In the case of unlike atomic interactions a set of combination rules has been used to determine the parameters. Utilizing these parameters the nearest neighbour distances, elastic constants, Debye temperatures and cohesive energies for the ordered Cu₃Au and Au₃Cu alloys have been calculated from the derived expressions. A fairly satisfactory agreement has been observed when compared with the available experimental values.

The author shows using Hubbard's model that transition metal impurities in a ferromagnet will tend to suppress ferromagnetism in the strong correlation limit. Secondly they show that paramagnetic impurities in an itinerant electron antiferromagnet decrease the Neel temperature in a similar fashion to paramagnetic impurities in a superconductor.

The a.c. conductivity of a thin superconducting film in the transition region is calculated using a Hartree like bilinearization of the Ginzburg-Landau theory. A single expression is obtained which reduces above T_c to the fluctuation conductivity found by Schmidt and below T_c to the low frequency limit of the Mattis-Bardeen result. Good agreement with experiment is found.

The field penetration into a metal surface is investigated in this paper. By including both short range and long range interactions it is shown that the work function increases when a high electrostatic field is applied to the metal. The nonlinearity of the response to the external field is shown and results qualitatively different from those of the random phase approximation are obtained.

Low temperature measurements of the electrical resistivity, magnetoresistivity and magnetization of Rh-Fe alloys containing 1-14 at.% Mn are reported. A comparison with the Rh-Mn alloy system in a similar concentration range shows, as expected from their dilute region behaviour, strong similarity in the susceptibility whereas the resistivity appears to be different at high concentrations-resistivity minima are obtained in concentrated Rh-Fe alloys whereas none are observed in the Rh-Mn system. Dilute alloys of both Rh-Fe and Rh-Mn show positive magnetoresistivity at low temperatures, the effect being stronger in Rh-Fe.

The quasielastic neutron scattering cross section for paramagnetic impurities in metallic hosts is shown to exhibit logarithmic anomalies. The expressions for the quasielastic cross section, as derived by a generalized perturbation calculation, are dominated by the impurity spin correlation function. The observation of these anomalies would provide direct evidence of the spin compensated picture of the Kondo effect and it is suggested that Au-V or Au-Co could be good candidates for observing the anomalies.

The spin fluctuation resistivity of paramagnetic PdNi alloys has been analysed as a function of temperature. Since a selfconsistent calculation using an analogue of the coherent potential approximation is difficult, and approach is developed using an analogue of the simpler average T-matrix approximation. Agreement with experiment is satisfactory.

Nuclear spin-lattice relaxation rates have been measured as a function of composition for ¹¹⁵In and ¹²¹Sb in liquid In-Sb and for ¹¹⁵In and ²⁰⁹Bi in In-Bi, and as a function of temperature for ²⁰⁹Bi in Bi₅₀X₅₀ where X=In, Sn, Sb, Pb, and for ²⁷Al in Al₈₉Si₁₁. For ¹²¹Sb in In-Sb and for ²⁰⁹Bi in all the alloys investigated a relaxation rate was observed in excess of that predicted by the Korringa relation. The additional rates R_1Q are attributed to an electric quadrupolar interaction with diffusing ions. The relative field gradients which must be attributed to different ions in an alloy do not bear any simple relation to their valences.

The chemical shift in the X-ray K absorption edge of nickel in a number of its compounds has been measured using a focusing spectrograph of the transmission (Cauchois) type employing a mica crystal bent to a radius of curvature of 40 cm. In all the compounds investigated, the absorption discontinuity is found to shift towards the high energy side with respect to the pure metal. These shifts have been measured and the charge on nickel atom in these compounds has been calculated.

The recoilless fraction and second order Doppler shift of the Mossbauer line in iron 57 present as an impurity in Al, Rh, Pd, V, and Mo metals was measured in the range 4-1000 K. Values of the weighted mean lattice frequencies for the iron atoms were obtained and on the basis of a central force nearest neighbour model the iron-host force constant calculated. In all cases the iron-host force constant was found to be less than the equivalent host-host force constant so that resonant band modes for the iron atoms would explain the results.