Showing papers in "Journal of Physics F: Metal Physics in 1977"

Theory of energy bands and related properties of 4d transition metals. I. Band parameters and their volume dependence

Abstract: The energy bands of the 4d transition metal series are computed self-consistently within the atomic sphere approximation (ASA) over a range where the volume changes by nearly an order of magnitude about the equilibrium atomic volume. The parameters defining the position and width of the s and d bands are tabulated across the series and as a function of volume. A theoretical interpretation of the trends gives a more detailed understanding of the electronic structure of transition metals. The bottom of the conduction band is accurately described by an Ashcroft empty core pseudopotential. The centre of the d band is fitted very well by an exponential, and the width approximately satisfies Heine's inverse five-thirds volume dependence. The d band occupancy to the left of the series is very sensitive to the relative ion core volume which Duthie and Pettifor show as explaining the rare earth crystal structure trend. The ASA includes explicitly the very important bonding d charge in addition to the usual renormalized atom contribution.

Energy bandstructure and Fermi surface of LaB6 by a self-consistent APW method

Abstract: Self-consistent calculations of the energy bandstructure of LaB6, which has attracted interest as an electron beam source, are carried out using the usual nonrelativistic, symmetrized APW method. A one-electron potential is constructed on the basis of the X alpha method. The calculation is repeated for two special values of the exchange parameter, i.e. alpha =1.0 and 2/3. The two calculated bandstructures do not differ significantly in their essential features. They are characterized by wide B sp bands and La sd bands. The La d bands appear near the Fermi energy, EF, and a strong hybridization of the La d and B sp bands occurs. The strong hybridization causes a large wavevector dependence of the d bands, and EF cuts one such d band. These results account well for various small effective masses observed in LaB6. The calculated density of states for the valence bands agrees well with a recent X-ray photoemission measurement.

Electrical resistivity of dislocations in metals

Abstract: The transport equation for electrons in a dislocated crystal is solved in a way which allows explicitly for a complex (many sheets, open or closed) Fermi surface. Assuming resonance scattering of Fermi electrons by the dislocation core, and assuming negligible interband scattering the author obtains simple expressions for dislocation limited resistivity in metals of arbitrary bandstructure. The dislocation limited mobility mu of electrons or holes in metals of arbitrary bandstructure and containing randomly oriented dislocations of density beta (length per unit volume) is given by the universal expression mu beta =3e/8h(cross)=5.70*1014 V-1 s-1. Experimental data on dislocation resistivity for seventeen metals from ten subgroups of the periodic table are reviewed and comparison is made with calculated values. Good overall agreement of theory with experiment, encompassing a range from 10-19 to 10-14 Omega cm3 of dislocation specific resistivity, provides strong evidence both for the existence of dislocation resonances and, for multiband metals, the minor importance of interband scattering by the dislocation core.

Self-consistent screening of a proton in jellium

Abstract: The nonlinear screening of a fixed proton in jellium for the metallic density range covering rs=1 to rs=6 has been calculated self-consistently using the density-functional formalism. A new method is introduced for achieving self-consistency in a straightforward manner. For rs>4, the screening charge near the proton is essentially hydrogenic; the interaction energy in this range of rs is nearly the same as that found for the hydrogen atom using the same formalism and differs by about 10% from the exact binding energy of the atom.

New method for the Anderson model. II. The U=0 limit

Abstract: For pt.I see ibid., vol.6, p.1375 (1976). This new method is shown to give the exact result for U=0. It is implied that the same expansion in Vkd will converge in both the large U, magnetic regime, and the small U, nonmagnetic regime.

Gold-iron spin glasses in low DC fields. I. Susceptibility and thermoremanence

Abstract: Detailed studies of low-field susceptibility chi (T), thermoremanence and isothermal remanence in gold-iron alloys containing 0.25, 2, 4, 7at% Fe are presented. The susceptibilities show sharp but not discontinuous reversals of slope at Tf. Below the maximum in chi (T), the zero-field cooled susceptibility shows a marked shoulder at 0.6Tf which coincides with a maximum in the incremental isothermal remanence as a function of temperature. Below Tf the total magnetisation decreases slowly, flattening out to a constant value of approximately 0.9M(Tf). Thermoremanence increases almost linearly with decreasing temperature from zero at Tf. Both total magnetisation M(T)/M(Tf) and TRM/M(Tf) follow functions of temperature which are almost independent of composition. The results suggest a finite susceptibility at T=0, approximately 0.35 chi (Tf) indicating the presence of a reversible component to the magnetisation at absolute zero. Analogies with the behaviour of rock magnetism are indicated and the variation of TRM is analysed in terms of a spectrum of blocking temperatures deduced from isothermal remanence experiments.

The electronic structure of some A15 compounds by semiself-consistent band calculations

Abstract: The LMTO method has been used for band calculations on V3Si, V3Ge, V3Ga, Cr3Si and Cr3Ge. Within the unhybridised, canonical scheme of Andersen (1973, 1975) which has been extended to the case of several atoms per unit cell, self-consistent potentials have been obtained and subsequently used in LMTO calculations. Gross features of the density of states seem to be well described, and the agreement with XPS, SXE and X-ray diffraction measurements is very satisfactory. A correct treatment of the Madelung contribution to the potential is found to be essential for the self-consistency procedure.

On the temperature dependence of the electrical resistivity of amorphous metals

Abstract: The temperature dependence of the electrical resistivity of amorphous metals is calculated using two complementary models of the lattice vibrations. The model which describes uncorrelated Einstein oscillators leads to a very satisfactory fit of the experimental data for CuSn alloys at T>or approximately=10K. The negative temperature coefficients are explained by the temperature dependence of the elastic scattering. The results are interpreted as an indication of strong vibrational disorder. For very low temperatures (T

Magnetic properties and structures of some ordered (FeMn)3Si alloys

Abstract: Magnetic and crystallographic properties of the (FeMn)3Si system have been studied by X-ray and neutron diffraction magnetization resistivity and magnetoresistivity measurements. The single-phase alloys have been found to crystallize in the L21A structure and to have ferromagnetic properties at low Mn concentrations. At higher concentrations the alloys exhibit a more complex behaviour, having antiferromagnetic components below a temperature TR which is almost concentration independent. The resistivity showed anomalies at TR as well as at the Curie point. The variation of the magnetic moment on each site has been determined as a function of concentration and is discussed in terms of environmental changes occurring as a result of Mn additions.

A theory of Fano effects in the electronic structure of d band metals and alloys

Abstract: The electronic structure of d band metals and alloys is studied by using the concept of the Fano effect which is commonly used in solid state optics. A simple theory based on the Anderson model is presented to explain the asymmetry in the local density of states (DOS) of s and p symmetry in a d band metal. A prescription is given for calculating the parameters in the Anderson model from first principles and some simple example calculations are carried out to illustrate AR. An antiresonance (AR) dip position in a local DOS at a given site is quite insensitive to a change in the potential at the site, while the d band at the surrounding sites is shifted due to the potential change. It is pointed out that this shift of the d band results in AR in a generalised phase shift Delta NL, that is, a change in the number of occupied states due to the potential change. The significance of AR in Delta NL in several phenomena is discussed.

Volume change in some substitutional alloys using Morse potential function

Abstract: Volume changes in some low-concentration substitution alloys are calculated using the Morse potential function. The potential parameters for the unlike interactions are calculated using a simple interpolation formula. The relaxation of the distant ions is calculated in a consistent way so that both the 'force balance' and 'energy minimum' conditions are satisfied simultaneously. It is observed that the simple model predicts values which are in good agreement with the experimental values in most cases. But a major discrepancy is found to occur in two cases where silver is substituted in copper and lithium.

The optical surface modes of metal spheres

Abstract: A theoretical study of optical surface plasmon modes of metal spheres is made within the framework of a free-electron spatially dispersive dielectric function model which includes retardation effects. Dispersion equations for homogeneous and inhomogeneous spheres are derived for the lth spherical harmonic. The radiative properties of the modes are investigated as a function of l and surface structure which is included by means of a double step-function profile. The real part of the frequency has the same magnitude, and trend with sphere radius, as the current experimental results.

Theory of energy bands and related properties of 4d-transition metals. II. The electron-phonon matrix element, superconductivity and ion core enhancement

Abstract: For pt.I see ibid., vol.7, p.613 (1977). The variation of the electronic contribution eta to the electron-phonon mass enhancement is studied across the 4d transition metal series within the Gaspari-Gyorffy rigid muffin tin (RMT) approximation. The pd and df matrix elements are expressed in terms of band parameters. It is shown that hybridization enhances the p density of states for Nb, but reduces it for transition metals to the right of the series, whose superconductivity is, therefore, determined by df scattering which still remains dominant even after a 50% reduction by screening of the RMT results. The importance of the ion core in enhancing the scattering through orthogonality constraints and reduction in effective screening, is illustrated by studying the large volume dependence of eta shown by the early transition metals and rare earths.

Frenkel pair recombination radius in copper as a function of temperature

Abstract: Damage rate data for pure Cu and dilute Cu alloys with Au, Be, Pd and Sb measured between 50K and 107K under 3 MeV electron irradiation have been evaluated with regard to the correlated recombination. By applying the diffusion theory of a three-dimensionally migrating interstitial to the results, the temperature-dependent recombination radius was found as rv=13.7T-0.32 a0 and the displacement distance rp=5.9a0 as being independent of temperature. The resistivity contribution of trapped interstitials was found to be equal to that of free interstitials.

Single and multiple interstitials in FCC metals

Abstract: Configuration and activation energies and dipole tensors for single and multiple interstitials are calculated by computer simulation using three different potentials for Cu. The single interstitial forms a (100) dumb-bell. The di- and tri-interstitials consist of (100) dumb-bells on nearest-neighbour sites which are respectively parallel and orthogonal to each other. Multiple interstitials are strongly bound but like the single interstitial highly mobile. The tri-interstitial reorientates before it migrates. The binding volumes are relatively small, e.g. about 0.15 Delta V1 per interstitial atom for the tetra-interstitial. The anisotropy of the dipole tensor is only weakly affected by the choice of the potential, in contrast to the trace (i.e. the volume change). The results are in qualitative agreement with the experimental findings in Al.

Resistivity of liquid transition metals and their alloys using the t matrix

Abstract: The electrical resistivity and thermoelectric power of the liquid 3d transition metals (Ti, V, Cr, Mn, Fe, Co and Ni), Pd, Pt, Zr, Cu, Ag, Ge and Sn have been calculated using the t matrix approach and experimental structural data. Also the electrical resistivity of liquid alloys Sn-Ag, Sn-Co, Mn-Ge, Co-Ge and Mn-Cu, have been estimated in the same formulation. All the results are in good agreement with available experimental data showing that the electron transport properties of liquid transition metals and their alloys can be understood in terms of the t matrix approach.

Temperature and magnetic field dependences of the resistivity of amorphous alloys

Abstract: High-resolution resistivity measurements on a wise variety of amorphous alloys are reported for the temperature range from 0.5K to room temperature in magnetic fields up to 45 kOe. The resistivities are large. At the lower temperatures, below 20K, the resistivity is dominated by a -In(T2+ Delta 2) term with Delta approximately 0.5K. This term is unaffected by magnetic fields ruling out magnetic scattering in favour of scattering from the disordered structure. Successive thermal annealing of selected samples has no effect on the resistivity until the onset of crystallisation, after which the residual resistivity decreases and the low-temperature anomaly all but disappears.

The resonant model potential. II. Total energy: Theory and application to copper, silver, gold and calcium

Abstract: For pt.I see ibid., vol.6, p.180 (1976). The resonant model potential theory of a d band metal discussed by the author previously is used to calculate the total energy and its structural dependence. Only completely full or empty d band metals are considered; for these metals, the Harrison Gamma / mod Ed-EF mod expansion can be used ( Gamma and Ed are the d bandwidth and mean position). The total energy Etot is consistently expanded up to second order of the renormalized model potential. The resulting Etot (up to second order) is written as a sum of five terms: a homogeneous electron gas energy, a structure-independent first- and second-order contribution, a d electron energy, a bandstructure energy, an electrostatic energy and a 'non additivity' correction. The result of Shaw is generalized here to a resonant (singular) model potential. The method is applied to the calculation of the binding energies, the T=0K stable phases and the elastic constants of four metals (Cu, Ag, Au and Ca).

Stoner theory support for the two-state hypothesis for γ iron

Abstract: Stoner theory investigations of the FCC phase of transition metals have revealed the existence of two stable electronic spin states, both ferromagnetically ordered in the region of iron. Findings concerning the energetics of the two states have been substantiated by fully self-consistent band calculations within the atomic sphere approximation using the local spin density functional treatment of exchange and correlation. This provides the first theoretical support, within the itinerant electron theory of magnetism, for the two- gamma -state hypothesis of Weiss (1963).

A dislocation model of grain boundary electrical resistivity

Abstract: Grain boundary electrical resistivities are calculated on the assumption that the scattering is due primarily to the dislocations which constitute these boundaries. Dislocation densities in grain boundaries have been estimated using Frank's formula as modified to take account of lattice symmetry. Dislocation resistivities are calculated ab initio assuming resonance scattering at the Fermi surface, and measured dislocation resistivities are also used where these are available. The calculated grain boundary resistivities are in satisfactory agreement with experimental data for thirteen of the fourteen metals from seven subgroups of the periodic table, for which data is available.

Fast neutron radiation damage in aluminium studied by interstitial trapping at 57Co Mossbauer atoms

Abstract: A description is given of Mossbauer studies of interstitial atom trapping at 57Co impurities in Al after fast neutron irradiation at 4.6K with doses from 0.2*1018 n cm-2. Trapping and detrapping during irradiation and during subsequent isochronal annealing was detected directly by the appearance and development of an additional Mossbauer line due to 57Co atoms with trapped interstitials. Simultaneous electrical resistivity measurements on the Mossbauer samples allowed the novel information from the Mossbauer studies to be correlated with the well known annealing stages of the resistivity. The isomer shift of the additional Mossbauer line was +0.42 mm s-1 relative to 57Co on substitutional sites, its small quadrupole splitting was 0.17 mm s-1. From irradiation dose and annealing temperature dependence it was concluded that trapping starts during irradiation at 4.6K and continues when interstitials are freely mobile (stage IE). Detrapping occurs by vacancy migration to the trapped interstitials (stage III).

Small-angle neutron scattering from superparamagnetic assemblies in binary CoGa alloys

Abstract: Small-angle diffuse neutron scattering measurements have been performed upon Co-rich CoGa alloys using the D11 diffractometer at ILL, Grenoble. These measurements, in conjunction with a re-investigation of the magnetic properties of the alloys, have revealed the existence of superparamagnetic behaviour associated with regions of correlated spins extending over approximately 60 AA. A relationship between the superparamagnetic assemblies and groups of Co atoms on the Ga sublattice is suggested by the differences in the observed scattering from alloys in the quenched and slow cooled conditions. Beyond a critical concentration of 55 at.% Co the onset of ferromagnetism is observed in the quenched alloys, although superparamagnetic behaviour is found to persist well into the ferromagnetic region.

Studies of defects at thermal equilibrium and melting in Cu and Ni by positron annihilation

Abstract: Peak counting rates in the angular correlation were measured as a function of temperature above room temperature in the solid and liquid phases of Cu and in the solid phase of Ni. The peak counting rates in Cu increased about 17% upon melting. Temperature dependence of the peak counting rates in the liquid phase shows a hump at 1150 degrees C. Two possible explanations were proposed for this anomaly. The data in the solid phases were numerically analysed by the trapping model in which it was assumed that only single vacancies and divacancies are effective. The data at lower temperatures, where the effect of divacancies is sufficiently small, were analysed by the conventional trapping model of single vacancies. The results of both analyses are consistent. The characteristic temperature Tc in the trapping model was defined. It was demonstrated that Tc is proportional to E1VF. The experimental values of Tc were plotted against E1VF for various FCC metals and linear relationship between E1VF and Tc was also experimentally found.

Structural, electronic and magnetic properties of splat-quenched FeCx alloys (x⩽0.05)

Abstract: The authors present the results of a combined investigation of splat-quenched Fe-Cx (x

Electronic structure of intermetallic compounds with CsCl structure

Abstract: Susceptibility, specific heat and Knight shift measurements as well as bandstructure calculations have been made for intermetallic compounds of the CsCl structure, ScB (where B is Ag, Cu, Pd, Rh, Ir, Ru), YRh and LaAg, to study the influence of filling the d shell of atom B. An analysis is given which yields quantitative results for the local susceptibilities, as characterized for the different angular momenta and sites of origin.

Exchange interactions in dilute CrFe and CrCo alloys

Abstract: Measurements of the magnetic and transport properties on the same samples of dilute CrFe and CrCo alloys over a wide range of temperature and magnetic field have enabled us to estimate firstly the strength of the coupling between the local moments and the condensed spin-density-wave state in each system, and secondly the strength of the local moment-conduction electron interaction both above and below the Neel temperature.

Electronic structure of CsAu

Abstract: The energy bandstructures and charge distributions in CsAu, which is known to show an interesting semiconducting behaviour, are calculated using the APW method. An effect of the charge transfer is taken into account by means of a self-consistent calculation. The calculated bands are characterised by a strong hybridisation of the Cs d state and the Au sp state. They show a metallic behaviour in disagreement with experiments. It has been found that the relativistic energy shifts contribute to the formation of the energy gap between the valence band consisting mainly of the Au s state and the conduction band. The spin-orbit interaction plays a minor role. The way in which CsAu undergoes a nonmetal-metal transition under pressure is suggested.

Optical properties of gallium films between 2 and 15 eV

Abstract: The authors performed optical measurements consisting of near normal incidence reflectance (2-11 eV) and multiangle reflectance measurements (11-15 eV) on gallium films condensed on cooled glass substrates in a vacuum of 2*10-10 Torr. Optical constants were determined with the help of a Kramers-Kronig analysis of the reflectance data. The optical conductivity sigma , real part of the dielectric constant epsilon 1 and energy loss function -Im(1/ epsilon ) were deduced. epsilon 1 against 1/(h(cross) omega )2 shows a linear dependence; -Im(1/ epsilon ) peaks at (14.05+or-0.05) eV.

An investigation of the atomic arrangements in some amorphous rare earth-transition metal alloys

Abstract: The structure of thin, vapour quenched films of some Gd-Co and Ho-Co alloys has been investigated by electron diffraction. The atomic arrangement at short range in these films is discussed in terms of the radial distribution function obtained by transforming the experimental interference function. The findings are compared with published data from X-ray diffraction studies of similar alloys. At the same time attempts to explain the structure in terms of some common microcrystalline structures are shown to be fruitless. It is concluded that the films are amorphous and that in further attempts to explain their structure other models of atomic packing such as the dense random packing of hard spheres should be considered.

The random anisotropy model for amorphous metallic alloys: generalized molecular field calculations

Abstract: In an attempt to explain the anomalous low-temperature magnetic properties of some amorphous rare earth-iron alloys, the authors have generalized the random anisotropy model of Harris, Plischke and Zuckermann. The results of the investigation for spin one and the classical case of infinite spin suggest the possibility of a 'spin glass-like' ground state, whose existence is confirmed by a Monte Carlo simulation. In addition, the magnetization curves show a well defined 'spin glass-like' ground state, whose existence is confirmed by a Monte Carlo simulation. In addition, the magnetization curves show a well defined 'spin glass-like' transition temperature and a sizeable coercive field, in qualitative agreement with experiments on amorphous REFe2 compounds.