Table of contents

By consideration of a selfconsistent calculation of electronic charge density for the lithium (001) surface, it is shown that crystalline effects can easily be as large as, or larger than, uniform background contributions to the contraction of the outermost interlayer spacing of sp bonded metals.

Quantitative measurements have been made of the motion of tungsten doublets and triplets on the (211) plane of tungsten. It is shown that these clusters diffuse by the movement of one atom at a time. The activation energy (35 kJ mol^-1) and prefactor (10^-11 cm ² s^-1) of the diffusion coefficient are the same for both doublets and triplets, but differ substantially from the parameters characteristic of single-atom motion. This behaviour is interpreted in terms of strong attractive interactions between pairs of atoms.

Specimens of finely divided aluminium have been prepared which do not exhibit the anomalously high values of NMR second moment previously reported. This long-standing anomaly is attributed to quadrupolar interactions introduced by cold working.

Contributions to the broadening of the lithium soft X-ray emission and absorption edges are discussed. In the literature both the direct coupling of the core hole to the host ions and the apparent width due to changes in the core level energy caused by fluctuations in the electron density in the vibrating lattice have been considered. It is found that contrary to assertions of Dow, Robinson and Carver (1973) the two effects are only apparently different and should not be added. The discrepancy between the estimate made by Bergersen, McMullen and Carbotte (1971) and that of Dow et al. is analysed and found to be at least in part due to conceptual errors and approximations made by the latter authors. The Auger width of the lithium core level is estimated and found to be small, at least in lowest order.

The lanthanum M_IV and M_V X-ray emission spectra have been studied. These spectra indicate the existence of highly localised 4f states near the Fermi level.

The diffuse scattering of X-rays (CuK_{alpha 1}) and the change of the electrical resistivity has been investigated at single crystals of copper after low temperature electron irradiation (defect concentrations between 3 and 6*10^-4). The X-ray measurements were made near the (200), (400), and (220) Bragg reflections in directions parallel and perpendicular to the scattering vector. The data taken immediately after the irradiation showed all the characteristic features predicted by the theory for scattering from point defects with weak displacement fields (Huang scattering).

For pt. I see ibid., vol.4, no.10, 1575 (1974). After low temperature electron irradiation of copper single crystals the thermal recovery behaviour has been investigated by measurements of the diffuse scattering of X-rays close to the Bragg reflections and by measurements of the electrical resistivity change. At the end of recovery stage I an increase of the scattering intensity per interstitial was observed. This gives direct evidence that the interstitials agglomerate during their free migration. In recovery stage II a further increase of the scattering intensity per interstitial suggests an increase of the average interstitial cluster size throughout this stage. The mean number of interstitials per cluster can be estimated. These results can be compared with observations in the electron microscope.

The authors have formulated the lattice statics method for hexagonal close packed metals and applied it to a vacancy in magnesium. Both near neighbour and asymptotic displacements have been calculated and compared. The results indicate that, as in cubic metals the elastic limit is achieved far from the defect and that the asymptotic displacements are very anisotropic. The calculated relaxation energy indicates that in Mg, as is the case in Al, the relaxation contribution to the vacancy formation energy is small. To describe the interatomic interactions the authors have used two different methods: force constants deduced from the neutron scattering data and interatomic potentials calculated from Shaw's nonlocal model potential.

Measurements of broadening of X-ray diffraction peaks were made for splat cooled pure aluminium samples, and some splat cooled aluminium-tin and aluminium-nickel solid solutions. A Fourier analysis was made of the shape of the peaks and the instrumental broadening was corrected by using the peaks of annealed material. It was found that in all examined samples the major source of broadening are strains. In Al-Sn and Al-Ni solid solutions, obtained by quenching from the melt, microstrains increased with increasing concentration of solute atoms. There are indications that strains are smaller in larger coherent regions.

Using a formalism developed by Stroh (1962), a simple image force theorem for a dislocated anisotropic bicrystal is derived. An extension of the Stroh formalism, shows that the prelogarithmic energy factors depend only on the crystallographic directions of the dislocation line and its Burgers vector relative to each medium constituting the bicrystal. In addition, a formula is developed which allows one to obtain the prelogarithmic energy factor by simple numerical integration. A previous result of Dundurs and Sendeckyj (1965) for the net integrated tractions on any plane parallel to the interface of a dislocated bicrystal is extended to the anisotropic case. Finally, an intimate relation between dislocations moving parallel to the bicrystal interface and Stoneley waves in anisotropic bicrystals is developed.

Using Rogula's theory of the elastic pseudocontinuum which takes into account nonlocal interactions (Kunin 1966, Kroner 1967) and the discreteness of the atomic structure the self and interaction energies of jogs in dislocation lines are calculated. The theory includes the effect of the core structure of the dislocation, of the form of the jog and of the dispersion (k dependence of elastic moduli). The results deviate remarkably from results obtained by using ordinary elasticity theory.

Second order perturbation theory enables the author to write U, the energy of a simple metal, as a large volume dependent part F(V) plus a small term which is the sum over pairs of ions of the central interaction Phi (R; rho ), R being the ion-ion distance. It is noted that Phi is a density dependent pair potential; hence the additional argument. The physics of this representation is discussed. Expressions for the pressure P and bulk modulus B are derived. The author derives formulae and gives numerical results to show a violation of the Cauchy relations and a correction to the conventional lattice dynamical theory of B. Without reference to a particular model an estimate of this correction is obtained.

The low frequency band modes associated with interstitial hydrogen in the alpha phase of two Pd-Ag alloys containing 10 and 20 at% of silver have been studied at a number of temperatures over the range 428-623K by cold neutron inelastic scattering. The frequency distribution functions obtained from the scattered neutron distributions have been compared with the reported normal mode frequency distribution of pure palladium.

A theoretical calculation is described for the anisotropic relaxation time due to impurity scattering on the Fermi surface of simple metals. The calculation is based on a multiple plane wave scattering formalism using pseudopotentials and phase shifts. The pseudowavefunctions and the Fermi surface are obtained from a four orthogonalised plane wave calculation while the scattering pseudopotentials are taken from form factors which are locally rescreened and corrected for lattice distortion around impurities. Detailed results are presented for impurity in Al. Calculated Dingle temperatures are in reasonable agreement with experimental results. A phase shift model is introduced which allows the Dingle temperature to be expressed in terms of impurity phase shifts and pseudowavefunction amplitudes. These amplitudes have been calculated for several orbits on the Fermi surfaces of Al, In and Pb. The influence of impurities on the low field Hall effect is also discussed.

A unique solution to the screening problem in an alloy can be constructed by solving Thomas-Fermi equations throughout the interstitial region, subject to field continuity conditions on the boundaries of spheres containing the atomic cores. A simple mathematical approximation to the general solution involves only the one dimensional TF equation, with end conditions corresponding to selfconsistent charge transfers between the Wigner-Seitz spheres occupied by different components. Preliminary calculations for typical binary alloys show that the method is simple to apply and can give physically significant results.

A formalism is presented for the calculation, in liquid alloys, of the partial structure factors, the free energies and associated thermodynamic properties. An application is made to NaK alloys with encouraging results.

Measurements of the phonon limited mean free path have been made in zinc and previous measurements in cadmium have been extended. In both metals a fairly extensive investigation of the lens part of the Fermi surface has been made. A less detailed study of the vertical monster arms has also been made. The electron-phonon scattering is compared in the two metals and estimates made of the ratio of the differential scattering cross section. A comparison is also made between values of the electron mean free path obtained using the limiting point method and values obtained using the parallel field method. Finally the temperature dependence of the mean free path has been discussed in terms of diffusive and catastrophic scattering.

The electrical resistivity is obtained exactly for a model of a dilute alloy that incorporates two isotropic (corresponding to impurity and normal phonon) and one anisotropic (corresponding to Umklapp phonon) additive electron scattering probabilities. The deviations from Matthiessen's rule are found to have a weak dependence on the residual resistivity rho ₀ similar to the ln rho ₀ behaviour recently observed at low temperatures in several metals for a wide range of concentrations and variety of nonmagnetic impurities. An interesting aspect of the exact solution is that the Umklapp scattering contribution to the resistivity is much smaller than the normal scattering contribution in contrast to the results given by the variational principle with the simplest trial function where the opposite is true to polyvalent metals; this result suggests that phonon drag may play an important role in the low temperature resistivity of polyvalent metals.

The specific heat of high purity gadolinium, prepared by solid electrotransport processing, has been measured in the temperature range 1.5 to 14K, and the data analysed for electronic, Debye and magnetic contributions to the total specific heat. The electronic coefficient gamma was found to be 3.7+or-0.2 mJ mol^-1 K^-2 and the magnetic specific heat, assumed to be of the form C_M=BTⁿ, yielded B=1.94+or-0.04 mJ mol^-1 K^-(n+1) with n=1.75+or-0.05. The Debye temperature between 1.5 and 5K was calculated to be 187+or-3K, while for temperatures in excess of 5K it was found to decrease with temperature to a constant value of 160+or-3K above 12K.

The frequency dependent conductivity is considered within a memory function framework. In a detailed example of the use of this formalism the authors assume the ions to scatter the electrons by means of an energy independent pseudopotential, evaluating the memory function to second order in the pseudopotential, electron-electron interactions being in principle included exactly. The result so obtained for the conductivity, is shown to agree with a direct calculation in powers of the pseudopotential, corresponding to the summation of an infinite subset of terms in this series. In the limit of zero frequency, the Baym formula for the resistivity with a screened pseudopotential is regained, without assuming independent particle behaviour in any way.

Using a normal mode analysis analogous to that of Sawada et al. (1957), the authors show that Peuckert's expression for the interaction energy of an electron gas confined to a film can be written as the difference in zero point energy between the normal modes of the interacting and noninteracting systems. They consider separately the surface and bulk correlation energies and show that in each case the collective contribution (arising from the plasma oscillation) is small and has the opposite sign to the particle-hole contribution. In particular, the authors show that the surface correlation energy can be regarded as arising almost entirely from the change in the zero point energy of the particle-hole excitations due to the existence of the surface. Due to their omission of this effect, the work of Craig (1972), and Schmit and Lucas (1972) severely overestimates the plasmon contribution.

The effects of both anisotropic exchange and magnetoelastic coupling on phase transitions involving flat, conical and tilted spiral phases are investigated. Also the conditions under which the magnon modes in conical and flat spiral phases may soften are examined when anisotropic exchange is taken into account. It is found that both anisotropic exchange and magnetoelastic coupling can inhibit the instability of the magnon mode with q=Q in the flat spiral phase, but that the nature of the transition which occurs is quite different in each case. These results are discussed with reference to the phase transitions which occur in holmium and erbium near 20K.

Pd-Ni alloys are of special interest as a system where a critical composition for the paramagnetic to ferromagnetic transition exists. Interpretation of the magnetization as a function of the field, temperature and concentration for this system is not quite straightforward and previous measurements have not examined the low field behaviour in detail. New data on this system have been obtained and careful analysis with the help of Arrott plots yield Curie temperatures T₀ which extrapolate to the same value for the critical concentration as that found previously from the resistivity measurements. Existing susceptibility results for some paramagnetic Pd-Ni alloys appear to conform with this value for the critical concentration and in particular the specific heat data, where disagreement has been cited previously, are reanalysed and shown to be in agreement also with the authors value of 2.3+or-0.05 at% Ni.

The authors present a model theoretical calculation for the concentration dependence of the magnetic susceptibility chi and the temperature derivative (d chi ^-1/dT) as a function of concentration x in Ce_1-xNi_x liquid alloys at high temperatures (1100 degrees C). The theory describes reasonably well the experimental results, including the range of concentrations for which (d chi ^-1/dT) is negative.

The low temperature specific heat of ternary dilute alloys of carbon with f.c.c. binary nickel-cobalt and nickel-iron matrices have been measured between 1.2 and 8K. The results have been compared with former experiments on the parent alloys without carbon. The electronic specific heat coefficient is in the case of nickel increased by 35 mJK^-2 mol^-1 unit atomic carbon concentration. When iron or cobalt is added to the matrix, the effect of carbon rapidly decreases. This behaviour is attributed to the erasing of the van Hove peak at the top of the band of nickel, by addition of iron or cobalt. When the iron content reaches the border value between strong and weak ferromagnetism ( approximately=50%) the gamma increment per unit carbon concentration changes from weakly positive to strongly negative values, the increment of magnetization per metal atom changes from negative (-3 mu _B per carbon atom) to strongly positive.

The cubic Laves PrT₂ compounds, where T is a metal atom, are ferromagnets which display a variety of magnetic moments on the Pr³⁺ ion varying from 0.61 mu _B to 2.2 mu _B. Crystal field analysis shows that the free Pr³⁺ ion in some of these compounds must be in a singlet ( Gamma ₁) state. Here the authors analyse a singlet-triplet model for Pr³⁺ in which the induced moments interact with an enhanced d band in the compound. Expressions are given for the zero temperature magnetization and the Curie temperature in this model and the spin dynamics are discussed. In particular it is shown that the lowest spin modes are paramagnons or spin waves typical of an itinerant paramagnet or ferromagnet respectively. Finally in agreement with Fulde (1972) none of the excitonic modes become soft at the transition point.

The dependence of the magnetization on the temperature T for ferromagnetic metals is obtained in the random phase approximation at low temperatures. The magnetization is expressed as a sum of terms proportional to T^3/2, T^5/2 and T² for weak ferromagnets, which are derived from excitations of spin waves, interactions between spin waves and individual electrons, ordinary excitations of individual electrons and spin fluctuations. For very weak ferromagnets, it is shown that the dominant dependence of the magnetization on T comes from spin fluctuations and it is conjectured that the Curie temperature is inversely proportional to the enhancement factor of the susceptibility.

The fine structure observed in the sputtered atom ejection pattern by Dubinskii and Lebedev (1971) has been re-examined and shown to be the result of the etching of the blocking pattern of incident ions into the mylar collectors used. This supports the conclusion of Chadderton et al. (1973). The blocking patterns have then been used to measure blocking angle in the surface region and the results compared to theoretical considerations.