Journal of Physics F: Metal Physics

The surface and bulk densities of states of a solid described by the stacking of principal layers are obtained by means of an iterative procedure which allows (i) the inclusion of 2ⁿ layers after n iterations, (ii) the simultaneous calculation of the Green functions for both the 'right' and 'left' surfaces as well as for the bulk (or central) principal layer, and (iii) the use of imaginary parts eta as small as one wishes in the energy without any large increase in computing time, so that the limit eta to 0 can really be obtained. As a by-product the authors obtain (i) the 'right' and 'left' transfer matrices of the 'effective field' or continuous fraction approach and (ii) a factorisation theorem which relates the Green functions of both surfaces to the Green functions of both surfaces to the Green functions of the bulk and the free metal atom.

A new theory of the class of dilute magnetic alloys, called the spin glasses, is proposed which offers a simple explanation of the cusp found experimentally in the susceptibility. The argument is that because the interaction between the spins dissolved in the matrix oscillates in sign according to distance, there will be no mean ferro- or antiferromagnetism, but there will be a ground state with the spins aligned in definite directions, even if these directions appear to be at random. At the critical temperature the existence of these preferred directions affects the orientation of the spins, leading to a cusp in the susceptibility. This cusp is smoothed by an external field. Although the behaviour at low t needs a quantum mechanical treatment, it is interesting to complete the classical calculations down to t=0. Classically the susceptibility tends to a constant value at t=0, and the specific heat to a constant value.

(100), (110) and (111) single crystal aluminium substrates were thoroughly outgassed by heating by electron bombardment in ultra high vacuum. Fresh single crystal surfaces were prepared by autoepitaxy on these substrates and the work functions of the surfaces were determined photoelectrically. The general effect of the deposition of an aluminium film on the substrate was to reduce the work function, but annealing the film at temperatures between 473 K and 573 K caused the work function to return to a constant value which was taken to be characteristic of the ordered surface. (100) aluminium surfaces were also prepared by epitaxy on potassium chloride crystals. The effect of argon ion bombardment on a bulk (110) aluminium surface is to increase the work function towards the polycrystalline value, but the characteristic value for the (110) face may be restored by annealing the crystal. There is a linear relationship between surface atom density and work function for the three faces investigated.

Rigorous expressions for the exchange parameters and the spin-wave stiffness constant of ferromagnetic metals are obtained using a local spin-density functional formalism and the muffin-tin potential model. The calculated results for ferromagnetic iron are given as an example of the approach.

Equilibrium grain boundary segregation is assessed in terms of its measurement, theory and industrial significance. Aspects of the phenomenon of this segregation, namely the localisation, chemical system dependence, response to environmental parameters, etc., are discussed in relation to the measurement techniques for grain boundary segregation. These techniques-the interfacial energy approach, AES, XPS, STEM with X-ray analysis and the atom-probe FIM-are analysed in terms of their unique contributions. The theories of segregation are presented in a unified framework which uses analogues of the theories for gas adsorption on free surfaces. The cases of limited and unlimited numbers of sites are treated. Thus, McLean's segregation theory is seen to be the counterpart of Langmuir adsorption and a self-interacting segregant is seen to follow the analogue of the Fowler theory. The Fowler theory is extended to ternary systems and accurate methods of estimating the value of the relevant fixed parameters are presented. The kinetics of segregation and desegregation are then outlined. A range of material aspects affected by grain boundary segregation are described.

The dependence of the electrical resistivity of Pb on hydrostatic pressure is determined over major portions of the temperature and pressure ranges 1-300K and 0-10 GPa (100 kbar), respectively, and for Sn at 300K. The results are compared with a simple Bloch-Gruneisen law including volume changes due to thermal contraction. It is demonstrated that both Pb and Sn are ideally suited for use as accurate resistive manometers, enabling a reliable continuous determination of pressure over a wide temperature range. The agreement between the pressure at low temperatures indicated by both resistive and superconducting (T_c) Pb manometers is excellent. T_c(P) calibration curves are given to 22 GPa for Pb and to 5 GPa for Sn and In. A general method is presented which shows how pressure can be used to test for the presence of electron-electron scattering; in the temperature range studied, T>or=7.2K, electron-phonon scattering constitutes the dominant scattering mechanism in Pb, as expected.

The transfer matrix of a solid described by the stacking of principal layers is obtained by an iterative procedure which takes into account 2" layers after n iterations, in contrast to usual schemes where each iteration includes just one more layer. The Green function and density of states at the surface of the corresponding semi-infinite crystal are then given by well known formulae in terms of the transfer matrix. This method, especially convenient near singularities, is applied to the calculation of the spectral as well as the total densities of states for the (100) face of molybdenum. The Slater-Koster algorithm for the calculation of tight-binding parameters is used with a basis of nine orbitals per atom (4d, 5s, 5p). Surface states and resonances are first identified and then analysed into orbital components to find their dominant symmetry. Their evolution along the main symmetry lines of the two-dimensional Brillouin zone is given explicitly. The surface-state peak just below the Fermi level (Swanson hump) is not obtained. This is traced to the difficulty in placing an appropriate boundary condition at the surface with the tight-binding parameterisation scheme.

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 hexagonal and cubic phases of the intermetallic compound Fe₃Ge have been investigated with the Mossbauer effect technique and magnetization measurements. In both phases the material is ferromagnetic with T_c=640K and mu _Fe=2.0 mu _B (hexagonal), and T_c=740K and mu _Fe=2.2 mu _B (cubic). In the hexagonal phase a spin-flip is observed at 380K. This transition appears to be of second order. In the cubic phase the preferred spin direction is (100). In this phase the anisotropic part of the hyperfine field at the ⁵⁷Fe nucleus is large (+18 kOe). The origin of this anisotropy is discussed.

For pt.I see Act Crystallogr., vol.B32, p.1348 (1976). The intermetallic compound Fe₃Sn₂ has been studied by neutron diffraction and magnetisation measurements. This compound is ferromagnetic (T_C=657K). At room temperature the spin direction is along the c axis. A spin rotation is observed between approximately 250 and 60K. Below 60K the spin direction lies in the (001) plane. A consistent fit of the neutron diffraction pattern is only obtained by a modification of the magnetic form factor of Shull and Yamada (1962). This modification means that the spin carriers are delocalised in the 'Fe-Sn' planes while they are localised along the c axis. The variations of the ⁵⁷Fe anisotropic hyperfine fields (from Mossbauer effect measurements) and the mechanisms which predominantly determine the tin hyperfine fields in the series Fe₃Sn-Fe₃Sn₂-FeSn are discussed.

A theoretical model is presented to explain the temperature dependence of the elastic constants of Le₃S₄. This model is based on the band Jahn-Teller mechanism and explains the behaviour of c' and c₄₄ consistently. The theory has been fitted to experimental results and the physical meanings of the parameters obtained are discussed.

The authors describe a non-local positron-electron density functional theory and show how it can be used to find the correlation potential for a positron in inhomogeneous systems where non-local effects are important. The theory is applied to the image potential induced surface state at a metal surface. Here the image potential arises from interactions between the positron and its screening cloud, which become increasingly long ranged and non-local as the positron leaves the surface. They have tested the theory with calculations of the binding energy and lifetime of a positron at an aluminium surface which agree well with experimental values.

Measurements were made of X-ray diffuse scattering from quenched AgZn single crystals which are in a metastable beta '-phase state having the B2-type structure. Two notable features were found in the distributions of diffuse scattering intensity: one is intensity streaks running through the fundamental reflection points in the (110) and its equivalent directions and the other is intensity sheets extending uniformly parallel to the (111) and its equivalent reciprocal lattice (REL) planes. The former is the diffuse scattering often observed in the B2 alloys and is associated with the (110) (110) transverse acoustic phonons. The latter shows the presence of random displacements of the (111) atom rows in the (111) direction. The structural relationship between the beta ' and the stable zeta phase suggests that the displacements are a precursive fluctuation of the beta ' to zeta transition, but the temperature dependence of the intensity of the (111) sheets show that they are purely thermal in their origin.

The state of order of primary iron-rich iron-silicon single crystals has been investigated by neutron scattering. The atomic fraction c_Si of silicon was between 0.076 and 0.103; the temperatures T_A from which the specimens were quenched ranged from 723 K to 873 K. The observed (200) and (111) superlattice reflections are much sharper than those usually produced by short-range order. The experimental results are interpreted as follows. All specimens investigated have the DO₃ superlattice. The long-range order parameter is always very close to the highest value possible at given c_Si. The antiphase domains are very small. In most cases their diameter W_D is below 5 nm. Only if c_Si approaches the critical concentration, c*_Si(T_A), does W_D become large. c*_Si(T_A) describes the alpha - alpha ₂ phase boundary in the current Fe-Si phase diagram. The present results, however, preclude the interpretation of the function c*_Si(T_A) as a phase boundary; c*_Si(T_A) only has bearing on W_D.

Pinning rates of dislocations by hydrogen and deuterium have been analysed in monocrystalline tantalum samples of ultrahigh purity. For this purpose, measurements of internal friction and elastic modulus were performed down to 2 K, using a vibrating strip system. A marked pinning stage located between 8 K and 11 K was revealed for hydrogen. The authors show that it reflects the arrival of the hydrogen atoms at dislocation sites, resulting in the pinning of the dislocation kinks. The inferred jump rate of hydrogen atoms is 3*10^2+or-1 s^-1 at 8.3 K. The temperature dependence of diffusion was found to obey a power law, with a large exponent, 15+or-3. Deuterium migration was also detected, at around 14 K. The results obtained are compared with previous data at higher or similar temperatures and discussed in relation to the existing theories for quantum diffusion.

An introductory survey of quasicrystals is presented. Some experimental observations that seem typical of nonperiodic long-range order are reviewed critically. The atomic structure and crystallography are described within the framework of the strip-projection formalism, with special attention to the consequences for diffraction approaches and the event of a new kind of crystallography. Atomic decoration models are presented briefly and discussed in the light of experimental data. A few physical properties are also mentioned, or rather it is suggested what they might be.

An introduction to the theory of heavy-fermion systems is given. Emphasis is put on the physical arguments which accompany the various theoretical models rather than presenting the latter in all details. After an introduction to the subject, the ground state and the description of the heavy quasiparticles are discussed. The origin of the low-lying excitations is considered in detail. This is followed by a discussion of the quasiparticle interactions. The interaction of quasiparticles with phonons is studied rather extensively. Of particular interest is the hydrodynamic regime for which a theory of the density fluctuations is presented. Finally theoretical models for superconductivity in heavy-fermion systems are discussed. Special attention is paid to the pairing interactions and the nature of the pair state.