Showing papers in "Journal of Physics F: Metal Physics in 1974"

Electronic properties of small silver particles: the optical constants and their temperature dependence

Abstract: Specimen size dependences of the dielectric constant and of its variations with temperature have been investigated by measuring the optical plasma resonance absorption of small silver particles embedded in glass. The following relations hold at the wavelength 405 nm: epsilon 2 (imaginary part at 300K)=0.23+2.64/R, and epsilon 2(300K)- epsilon 2(1.5K) approximately=0.07-0.08/R where R is the particle radius in nm. Agreement has been found with the free path effect but not with the quantum size effect theories of Kawabata and Kubo (1966) and of Glauberman and Adamyan (1969). The behaviour of the temperature dependence can partly be explained by thermal lattice contraction. The ratio of electron density to the optical effective mass shows no distinct changes as R varies from 10.5 nm to 1.1 nm. It may hence be concluded that normal metallic properties are present in silver particles embedded in glass which contain more than about 400 atoms.

The surface energy of a bounded electron gas

Abstract: An exact expression for the exchange and correlation energy of an inhomogeneous electron gas, as defined by Hohenberg, Kohn and Sham (1966), is derived. This expression is separated into exchange and correlation terms and a formula linking the surface exchange energy of a half space to the Kohn-Sham one electron potential follows without approximation. For an infinite barrier model, the local density approximation gives a surface exchange energy 50% greater than the exact value, a large and previously unsuspected error. An exact evaluation of the surface correlation energy is not feasible, but the authors argue that the dominant contribution, arising from the difference in zero point energy between bounded and unbounded systems, can be estimated using a simple model. Numerical results, not dependent on the introduction of arbitrary plasmon wavevector cutoffs, give surface correlation energies larger than Lang and Kohn (1970), who work from a local formula, by a factor of six.

An image force theorem for dislocations in anisotropic bicrystals

Abstract: 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.

Theory of lattice contraction at aluminium surfaces

Abstract: The authors show how the elementary concepts which govern the bulk total energy and crystal structure of sp bonded metals are also relevant at the surface. A simple model explains the observed contraction in the interlayer spacing of the (110) surface layer of aluminium compared with the (100) and (111) surfaces.

Consideration of the existence of surface wave (Rayleigh wave) solutions in anisotropic elastic crystals

Abstract: From a previous analysis it is known that a proper surface wave may always occur in a stable linear anisotropic half space provided that a certain real symmetric 3*3 matrix B is not positive definite for all velocities less than a limiting velocity nu L, the velocity at which bulk wave solutions first appear. B is also the lagrangian factor matrix for a particular straight dislocation moving uniformly in an infinite medium which is elastically identical to the half space. By examining the behaviour of the dislocation lagrangian and the eigenvalues of B at nu L, it is proved that proper surface waves may always occur except in cetain special cases. In each special case there always exists at least one bulk wave solution which satisfies the free surface condition on the half space boundary. Thus, there exist no forbidden directions for steady state propagation satisfying the free surface condition, i.e. either a proper (attenuated) surface wave and/or an unattenuated 'bulk surface wave' solution is possible. One simple numerical integration suffices to determine if a given propagation direction admits a proper surface solution.

Adsorption and surface alloying of lead monolayers on (111) and (110) faces of gold

Abstract: Auger electron spectroscopy and low energy diffraction have been used to study monolayers of lead deposited in ultrahigh vacuum on to (111) and (110) faces of gold. Comparison is made with a previous study of the (100) substrate. The succession of structure is similar on all three faces: low density arrangements followed by a compact hexagonal monolayer followed by another hexagonal arrangement which is interpreted as the intermetallic compound AuPb2. (A previous interpretation in terms of AuPb3, based on observations on the (100) face, is corrected.) The completion of the first monolayer is marked by sharp knees in the plots of the Auger signals as a function of evaporation time. Essentially the same alloy structure is found on all three faces. There are only slight differences due to differences in the substrate symmetry and structure.

Mossbauer effect investigation of Y-Fe compounds

Abstract: Mossbauer spectra were taken of the compounds YFe2, YFe3, Y6Fe23 and Y2Fe17 at temperatures ranging from 15K to well above the Curie temperatures (Tc=540, 538, 496 and 358K, respectively). The various spectra were analysed by means of subspectra due to the different nonequivalent Fe sites occurring in these compounds. For each of these sites the temperature dependence of the hyperfine field was determined and shown to be similar for different sites within the same compound.

Thermodynamic calculations for liquid alloys with an application to sodium- potassium

Abstract: 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.

On the vacancy formation energy and volume of simple cubic metals

Abstract: A derivation of the vacancy formation energy and volume is given within the framework of local pseudopotential theory. Numerical results are presented for the alkalis and for Al. The theory is based on the previous work of Ho (1971) but with some modifications and extensions. The differences are not numerically very significant in the alkalis but are critical in Al for which the authors obtain satisfactory results while Ho's theory failed.

The energy and elastic constants of simple metals in terms of pairwise interactions

Abstract: 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.

X-ray photoelectron studies of thorium and uranium

Abstract: The X-ray induced photoemission from both clean and deliberately oxidized thorium and uranium surfaces is described. The results are compared with previously reported XPS and X-ray emission measurements of electron binding energies for the heavy elements. While agreement between photoelectron and X-ray spectroscopic results is fair for most of the electron energy levels studied large discrepancies were observed in the energies of the P1, P2 and P3 levels. The authors discuss also the effect of oxidation on the spectra and on the valence bands for the metals.

Third order perturbation theory and lattice dynamics of simple metals

Abstract: The dynamical matrix of simple metals is set up by evaluating the total electron energy to third order in the electron ion pseudopotential. In this way three body unpaired non central forces arising from the off diagonal elements of the dielectric matrix are explicitly introduced. Since the usual on Fermi sphere approximation to a nonlocal pseudopotential gives a completely unreliable estimate of third order contributions and a full non local calculation is not feasible, a procedure is given to construct an average local potential, which disposes of most of the non locality and allows for a realistic calculation of the contributions of the unpaired forces to the lattice dynamics of simple metals. The phonon frequencies and the elastic constants of Li, Na, Al and Pb are evaluated. The results show that third order corrections are very important for Pb, while for the other metals they are about 10%. This indicates that three-body central forces are essential in order to describe the lattice dynamics of lead, while for Li, Na and Al a good description is obtained by considering only a central pairwise interaction between the ions.

Quantum size effects in metal particles and thin films by an extended RPA

Abstract: The RPA is extended in the framework of linear response theory to allow for the treatment of a finite free electron gas. The dielectric function taking quantum size effects into account, is calculated and shown to be finite in the limit of small wavevectors. The theory is applied to a simple free electron model for a small metal particle and analytical expressions are obtained for the electronic polarizability of a thin film and for the optical properties in the plasma resonance region.

Critical concentration for the onset of ferromagnetism in Pd-Ni alloys

Abstract: 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.

Ferromagnetism and strong correlations in metals

Abstract: A single band description of ferromagnetism in 3d transition metals is given based on a recent formal theory of strong correlations by the author. Correlations are assumed to be important leading to 'Hubbard split bands' and localized moments. Correlations and magnetic effects of the system are calculated selfconsistently. An effective Heisenberg Hamiltonian is obtained. The magnetic excitations of the system are spin waves, their dispersion relation is derived. The spin wave stiffness constant is compared with earlier theories. At the Curie temperature Tc long range magnetic order disappears, localized moments and short range order, however, still exist above Tc. Comparison with experiment is made.

Itinerant ferromagnetism and susceptibility of nickel-platinum alloys

Abstract: The authors have studied the high field susceptibility of nickel-platinum alloys in fields up to 150 kOe, at temperatures between 4.2 and 300K. The high field susceptibility is analysed in the ferromagnetic and paramagnetic range by means of Arrott plots and Landau coefficients. The paramagnetic initial susceptibility follows a Curie-Weiss law, with a Curie constant independent of nickel concentration. The results are compared with those obtained for palladium-nickel alloys. The experimental data are discussed in the framework of recent theories on itinerant ferromagnetism.

On the magnetic and electrical properties of nearly equiatomic ordered FeRh alloys

Abstract: Results of measurements on a number of ordered FeRh alloys in the range 49.5-52 at % iron and on the ternary alloys Fe50Rh47Pd3 and Fe49.5Rh44Ir6.5 are reported. The magnetization and the electrical resistivity were measured at 4.2 K in semicontinuous magnetic fields up to 370 kOe and the electrical resistivity in zero field from 4.2K to 1300K. The results show that minor deviations from stoichiometry have a drastic influence on the properties. In particular, the high temperature resistivity decreases rather fast as a function of iron concentration at both sides of stoichiometry. This along with a large magnetoresistance suggests that FeRh has the character of a semimetal.

A calculation of the Coulomb correlation energy, U, for transition metals in Hubbard's model

Abstract: The intra-atomic electron-electron Coulomb correlation energy U, which appears in the Hubbard Hamiltonian (1963), is shown to be well approximated by the change in eigenvalue of a localized Hartree-Fock state that occurs when the occupation of that state is changed. A selfconsistent calculation of all the Hartree-Fock states within a neutral Wigner-Seitz cell is made for three electronic configurations of each of the transition metals. Values of U are deduced from the differences in the d electron eigenvalues of the configurations. It is found that the ratios U/W, where W is the bandwidth, show a trend across the transition metals which is in excellent agreement with the known magnetic properties of their ground states.

Investigation of Frenkel defects in electron irradiated copper by Huang scattering of X-rays. I. Results for single interstitials

Abstract: The diffuse scattering of X-rays (CuKalpha 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).

Anisotropic relaxation times for impurity scattering on the Fermi surface

Abstract: 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.

Ferromagnet or spin glass? Magnetic ordering in Au-Fe alloys

Abstract: Bulk magnetization measurements on Au-Fe alloys are widely held as indicating the onset of long range ferromagnetism in alloys with Fe concentration above about 12 at.%. The 'ordering' temperatures deduced from these measurements appear to be in reasonable agreement with temperatures of the maxima of d rho /dT in the resistivity of the alloys but are considerably higher than the values obtained from Mossbauer effect measurements for alloys in the concentration range between 12 and 20 at% Fe. Magnetization measurements on a Au-15at% Fe alloys are presented which, contrary to the above, show a behaviour usually associated with spin glass alloys and indicate a spin freezing temperature close to the 'ordering' temperature expected from Mossbauer effect measurements. The results show that the apparent ferromagnetic behaviour and higher ordering temperatures obtained by previous workers in their magnetization measurements have a simple physical explanation based on the intrinsic properties of the alloys.

Band structure and optical properties of gallium

Abstract: The optical properties of clean, evaporated films of gallium have been studied at several temperatures. The observed spectra were interpreted on the basis of a pseudopotential calculation of the band structure. The position of characteristic peaks in the spectra agreed well with the predictions from the optimized model potential for gallium recently published by Appapillai and Williams (1973). The shift of the peaks with temperature was too large to be accounted for by shifts in the atomic form factor alone; the Debye-Waller factor must be included to explain the observations.

Nuclear quadrupolar relaxation in liquid metals

Abstract: The theory of nuclear quadrupolar relaxation in liquid metals is formulated in terms of the Van Hove functions and two approximations (A and B) are suggested for the correlation functions of the field gradient that are involved. The ion-ion potentials required are taken as those due to Appapillai and Williams (see abstr. A36507 of 1973). Detailed calculations are performed for Rb, Hg, Ga, In, Sb and Bi and the experimental data for Na, Cu and Al are also discussed. It is argued that approximation A underestimates and approximation B overestimates the cancellation between the two and three particle terms in the correlation functions and that the use of the Appapillai-Williams potential coupled with the ionic Sternheimer antishielding factor underestimates the field gradients involved. The temperature dependence of the relaxation rates is predicted to be somewhat less than that of D-1 where D is the diffusion constant, which agrees qualitatively with the experimental data.

Hard sphere structure factors for liquid metals

Abstract: The Gibbs-Bogoliubov inequality is used to calculate approximate hard sphere structure factors for liquid metals. The two essential assumptions are (i) second order pseudopotential perturbation theory is valid and (ii) the hard sphere structure factors are adequately described by the Percus-Yevick theory. The results, obtained for many simple metals and for varying conditions of temperature and pressure, are encouraging.

Positron annihilation in disordered binary alloys

Abstract: Measurements of the concentration dependence of the form of the long slit angular distributions for solid solutions of the PbIn, MgIn, CuAl and CuNi alloy systems are reported. A simple theoretical model provides an interpretation of the results in terms of the spatial distribution of positron and electron density within the alloy, and suggests a basis for the qualitative prediction of positron behaviour in any alloy system.

A Mossbauer study of iron precipitates in CuFe alloys

Abstract: The Mossbauer effect has been used in a study of CuFe alloys containing up to 4.6 at% iron over the temperature range 4.2 to 300K. It is found that face centred cubic gamma -Fe is not retained in CuFe alloys quenched sufficiently rapidly from the solid solution region but that the spectra of the solution quenched alloys are consistent with a model in which the iron atoms tend to form clusters. After allowing for the alpha -Fe content in a concentrated alloy a value of 3.1+or-0.2 at% is obtained as the solubility limit for Fe in Cu at 1000 degrees C in agreement with values obtained by other techniques. The precipitation of gamma -Fe and the subsequent development of alpha -Fe has been observed in alloys heat treated at 650 degrees C. At low temperatures gamma -Fe is known to be antiferromagnetic and a value of TN=63+or-4K is obtained for the Neel temperature of gamma -Fe precipitates in copper and a value of 2.7+or-0.3T for the magnetic hyperfine field at 4.2K. By applying an external magnetic field of 8T at 4.2K the magnetic hyperfine spectrum of theta -Fe has been resolved in a composite spectrum.

On the effects of spin-orbit coupling on impurity atoms in cubic ferromagnetic alloys

Abstract: Recent studies on heavy transition metal impurities embedded in cubic ferromagnetic hosts have suggested the existence of a certain amount of unquenched orbital angular momentum on the impurity site. The effects of spin-orbit coupling on the electron states around heavy impurities in band ferromagnets are examined using an extension of the Wolff-Clogston (1962) approach. Model calculations are performed for cases determined by the relative sizes of the impurity spin-orbit coupling parameter lambda , the crystal field splitting, and the exchange splitting of the impurity spin states which gives rise to the local moment. The results are compared with hyperfine anomaly and Mossbauer data on Au and Ir impurities in ferromagnetic Fe, Co and Ni.

Investigation of Frenkel defects in electron irradiated copper by Huang scattering of X-rays. II. Thermal annealing

Abstract: 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.

Vacancy formation energies and Faber's formula

Abstract: A formula due to Faber for the energies of formation of vacancies in metals is investigated from the general theoretical and numerical viewpoints. It is shown that the effective interatomic potential involved is of larger amplitude and longer range than that obtained by pseudopotential theory. Numerical success can be expected for monovalent and divalent metals. For higher valence cases it seems that non local electron-ion potentials or pseudopotential theory beyond second order (or both effects) must necessarily enter a successful formulation.

Studies of conduction electron scattering in copper using the de Haas-van Alphen effect

Abstract: Comprehensive measurements of the orbitally averaged scattering rate characterized by the Dingle temperature have been carried out for a number of orbits in dilute alloys of copper containing nickel, germanium or gold as solute. By combining the data for orbits traversing different regions of the Fermi surface and using a Fourier series inversion scheme, characteristic maps depicting the anisotropy of the local electron-impurity scattering rate 1/ tau *(k) over the Fermi surface have been deduced for each type of impurity scattering centre. The maps show a pronounced anisotropy which is different for each of the three solutes. The results may be understood in terms of the partial wave scattering model of Coleridge, and enable the differences Delta eta 1 between the phase shifts characterizing the host and impurity potentials to be determined.