Table of contents

Positron lifetime studies in cadmium disclose a pattern of temperature dependence similar to that previously found in angular correlation and Doppler broadening studies. A value of 0.47+or-0.03 eV for the monovacancy formation energy is deduced.

In an earlier paper (see ibid., vol.6, p.337) the authors described a Monte-Carlo simulation of various thermodynamical properties of Na at 293 and 361K using the interionic potential of Rasolt and Taylor (1975). The authors have subsequently discovered and corrected a small error in their Na pseudopotential. This correction does not affect low T properties but does give significantly better results for the high T value of C₄₄.

The transverse magnetoresistance in a monocrystalline Au+105 at ppm Fe alloy has been measured at 1.7K with the applied magnetic field along the (110), (111) or (001) directions. The negative component is markedly anisotropic, being greatest when the cyclotron motion is confined to a (100) plane. Two possible causes are discussed: a preferred alignment of the localized moments, such as previously indicated by Mossbauer measurements, and an anisotropic s-d exchange coupling between the electrons and the virtual bound state.

The Hall coefficient of two ternary alloys Cu-Ni-Ge and Cu-Au-Ge, measured at 4.2K, 78K, and 293K, has been found to be independent of temperature. This is entirely in accordance with predictions from measurements of the de Haas-van Alphen effect from which it had been deduced that electron scattering in such alloys should be isotropic.

Some initial measurements are presented of the electrical resistivity of a nominal 1.0 at.% MoFe alloy between 1.2 and 40K in the pressure range 0-67 kbar. It is found that the temperature of the resistance maximum decreases by about 35 mK kbar^-1 which is a dramatic pressure shift compared with that found in other spin glass alloys such as AuFe and AuMn.

It is pointed out that electronic states at the top of the d band in FCC transition metal are localized in atomic layers perpendicular to the cubic axes. This leads to a model with three sub-bands, each having two-dimensional magnetic properties, coupled by Hund's rule exchange. The spin-wave spectrum for a ferromagnetic metal is calculated and is shown to have low-lying flat modes close to the cubic axes in q space. The energy of these modes is proportional to the magnetization and they drive the phase transition at the Curie temperature T_c. Experimental evidence for this behaviour in nickel and Pd₃Fe is quoted. The main branch of the spin-wave spectrum renormalizes only slightly with temperature and does not change at all above T_c, in agreement with the observations of Mook et al. (1973, 1974) on nickel. The thermodynamical consequences of the model are discussed and, in particular, the susceptibility of nickel above T_c is found to be in good agreement with experiment.

Vacancy formation energies at constant volume for the alkali metals (Na and K) have been calculated using the local pseudopotential formalism. The authors have considered terms up to the third order in the perturbative calculations and adopted two kinds of model potentials for bare electron-ion interactions i.e. (i) a simplified Heine-Abarenkov (HA) potential with two unknown parameters and (ii) the Ashcroft empty core potential with a core parameter. The parameters were determined to reproduce the equilibrium lattice constant and bulk modulus for HA potential and the core parameter for the Ashcroft one through only the former. A lattice-statics method has been also used to estimate the lattice distortions around the vacancy. It was found that the vacancy formation energies calculated using the HA form for both metals did not deviate largely from the corresponding experimental values. On the other hand the results from the Ashcroft scheme tend to give more unreliable values than the ones above.

The trace of the force-dipole tensor (A+2B) as well as the components A and B of hydrogen interstitials in niobium were determined from measurements of the lattice parameters of the alpha , alpha ' and beta phases. It is shown that the orthorhombic structure of the beta phase is due to a direct hydrogen-hydrogen interaction. A parameter H, analogous to A or B and representing the strength of this direct interaction, is deduced assuming a central force model. It is shown that the concentration dependence of the structural parameters is correctly predicted by this model. The values of A, B and H are 2.88, 2.75 and 0.05 eV or 2.88, 2.84 and -0.05 eV respectively depending upon whether the nearest-neighbour direct hydrogen-hydrogen interaction is repulsive or attractive.

The ultrasonic longitudinal sound wave attenuation coefficient and the nuclear spin relaxation rate have been calculated for a superconducting alloy containing paramagnetic impurities with local states within the gap. The Green's function given by Shiba (1968) or Rusinov (1969), which is appropriate for the case of a strong exchange interaction between the conduction electron spin and the magnetic impurity spin is used. For temperatures near T_c and for a low impurity concentration the authors also include the Kondo effect in their calculations. They find significant deviations from calculations based on the Green's function given earlier by Abrikosov and Gor'kov (1961).

The lattice dynamics of indium is studied using pseudopotential theory. It is found that experimental results for neutron scattering, elastic constants, and specific heat are well fitted by using the nonlocal optimized model potential of Shaw (1968) to second order in the pseudopotential and by setting the effective mass equal to 0.8. Calculations with local pseudopotentials to second order do not fit as well. Corrections for exchange and correlation increase the frequencies of a given mode but do not change the overall shape of the dispersion curves. The inclusion of third-order terms in the pseudopotential according to the method of Bertoni, Bortolani, Calandra, and Nizzoli (1974) and according to modifications of their method lead to significant changes in the dispersion curves with all modes along symmetry directions being unstable.

The author generalizes the solution of the independent boson model to take the finite lifetime of the core hole into account. The generalized solution is compared to the conventional convolution of the infinite lifetime spectral function with a Lorentzian lifetime broadening function. The generalized solution reduces to the conventional convolution in two limits. However, the new solution predicts appreciable phonon broadening for simple metals. Rough estimates of this new effect are compared with recent experimental results on XPS lines.

The model potential method is reformulated for d band metals. The (non-local and energy-dependent) ionic model potential v₀(E) is written as w₀(E)+U(E-E). w₀(E) is a standard Heine-Abarenkov-like model potential which behaves as -Ze²/r outside the model region (w₀ is approximated in this work by a local potential). The resonance part U/(E-E) takes care of the d resonance; U is a finite range Hermitian operator which acts only on d states and is separable in each m channel. The metal pseudopotential is Sigma _ionsv₀(E)+V_e( rho _sc) where V_c( rho _sc) is the potential due to the screening density rho _sc(r) which is equal to the true (d+sp) electronic density outside the region where the true and model potential are not equal. A first-order calculation of the screened form factor is carried out. The resonant-part energy parameter E is first renormalized to E, which turns out to be similar to the mean d band energy E_d of Harrison (1969) and Moriarty (1970), and a consistent procedure to expand a physical quantity in terms of the renormalized potential is proposed. The screening density is calculated to first order using a recent formula for the integrated density of states appropriate for a singular resonant potential. The depletion charge density problem is considered.

The model potential proposed differs from the Heine-Abarenkov (1964) or Shaw (1968) model potential in as much as it replaces the constant potential in the core region (r<r_m, model radius) by a parabolic form. The model parameters are determined by matching the logarithmic derivatives at the boundary (r=r_m). The local version of the model potential is used to study the phonon spectra and electrical resistivity of sodium, potassium and rubidium. The calculated results agree well with the experimental values.

Measurements of the de Haas-van Alphen effect in polycrystalline dispersions of metallic lithium are described. X-ray studies indicate that the low-temperature martensitic transformation is suppressed in samples of this form, and that the room temperature BCC structure is retained down to liquid helium temperatures. The de Haas-van Alphen amplitude shows a characteristic beat structure arising from the Fermi surface anisotropy. The radial distortion of the BCC Fermi surface is estimated to be 2.6+or-0.9%. The method of analysis is verified by similar measurements in dispersion of sodium. The results for lithium are consistent with the most recent positron annihilation, Compton scattering and optical absorption data, but yield a Fermi surface distortion which is significantly less than that given by typical bandstructure calculations. This discrepancy lends support to the suggestion of Rasolt, Nickerson and Vosko that non-local exchange and correlation effects may cause a substantial reduction of the Fermi surface anisotropy (see Solid State Commun., vol.16, p.827 (1975)).

The temperature dependence of the peak counting rates of gamma - gamma angular correlation curves of positron annihilation has been measured for the alloy Cu 50.0 at.% Au and anomalous changes in the peak counting rates near the order-disorder transition temperature have been observed. The peak counting rates of the disordered phase were fitted to the trapping model to make it apparent how ordering phenomena affected positron annihilation. The reasons for such effects have been proposed. In particular, the abnormal increase of the peak counting rates just below the temperature at which the transition between the disordered state and CuAuII occurs suggests the formation of new trapping sites for positrons.

At 3K the calculated change in the resistivity obtained by Hayman and Carbotte (see ibid., vol.2, p.915 (1972)) using Ziman's one-iteration approximation (1961) to the solution of the linearised Boltzmann equation is three times as large as that obtained by Ekin and Bringer (see Phys. Rev. B., vol.7, p.4468 (1973)) using the variational technique with a rather simple trial function. In an attempt to resolve the discrepancy between two widely used techniques, the Boltzmann equation was iterated to convergence to determine accurately the anisotropic relaxation time tau (k) as a function of position on the Fermi surface. It was found that the variational result for tau (k) is in good agreement with the accurate one except on those parts of the Fermi surface that are least heavily weighted in a calculation of the electrical resistivity; on the other hand, the Ziman one-iteration solution is much too anisotropic, at least for the temperature range considered. The electrical resistivity calculated with the accurately determined anisotropic relaxation times is only marginally better than the variational result. The same applies to the effective number of carriers in the Hall effect.

Low-field Hall coefficient R and transverse magnetoresistance Delta rho / rho ₀ were measured in Al single crystals. A definite defect structure (statistically distributed Frenkel pairs) was created in the specimens by low-temperature electron irradiation. This defect structure could then be changed in a controlled way by annealing at different temperatures. Eliminating the influence of defect concentration with the aid of the Kohler representation thus allowed the dependence of R and Delta rho / rho ₀ on the defect structure to be investigated. Various effects of the Fermi surface geometry and of the scattering mechanism on R and Delta rho / rho ₀ are discussed on the basis of simple equations for the low-field Hall coefficient and magnetoresistance.

Two expressions for the inverse relaxation time tau (nk)^-1 have been derived for the scattering of a Bloch electron by an impurity which may induce charge transfer and lattice distortion. The muffin-tin model was used. The first expression is based on the treatment of scattering by individual centres in the distorted system and is exact if the lattice distortion is not too large. In the derivation of the second expression the impurity with its distorted environment has been treated as a whole, so that cluster phase shifts are used. This expression is exact if the muffin-tin radius is small. If the muffin-tin radius is kept reasonable neither the first nor the second expression is exact for large lattice distortion. The theory is applicable to vacancy scattering as well.

The normal mode Gruneisen gamma parameters have been measured for several modes of vibration of potassium at 4.5K over the pressure range 0.001 to 4.1 kbar, by means of coherent inelastic neutron scattering experiments. The results are compared with six different theoretical calculations based on a variety of screened pseudopotential models for the interionic forces in this simple metal, including a very recent calculation described in the following paper by Taylor and Glyde (ibid., vol.6, no.10, p.1915 (1976)). There is overall qualitative agreement between several theories and experiment, but significant discrepancies exist for four particular normal modes. Significant differences are also found between the present results for certain low frequency transverse modes and the analogous gamma values derived from the pressure dependence of the elastic constant C₄₄ at room temperature.

For pt.I see ibid., vol.6, no.10, p.1899 (1976). The mode Gruneisen parameters, gamma , in potassium have been computed employing the Dagens, Rasolt and Taylor (1975) description of the effective ion-ion interaction in metallic potassium. Comparison with the observed gamma of Meyer et al. in pt.I shows some significant discrepancies between theory and experiment. A comparison with previous calculations shows these discrepancies are common to all calculation of gamma employing the pseudopotential method. Particularly the discrepancy at low wavevector for the longitudinal mode along (q,q,O) suggests a possible contribution to gamma (qL) depending explicitly on the volume which is not included in an effective ion-ion interaction.

The classical model of a spin glass, consisting of dipoles arranged in random positions and experiencing random forces is directly quantised assuming the dipoles have a moment of inertia I. The ground state of this system presents a similar problem to that of the thermal behaviour of the classical system in that quantum fluctuations compete with the potential energy of the system. It is shown that a spin glass exists provided that the dimensionless parameter J₀I/h² is greater than a critical value, where NJ₀ is the classical ground state energy and N the number of dipoles. When the parameter is less than this value the ground state is not a spin glass, the dipoles being approximately in s states so that no spin glass can exist.

For pt.I see ibid., vol.5, p.965 (1975). The paper continues the study of dilute magnetic alloys using the model of a randomly-sited solution of dipoles with distance-dependent and hence randomly-signed forces. The time dependence of the system is studied above and below the critical temperature and the self-correlation time of a dipole is shown to tend to infinity as T to T_c from above. Comparable results are obtained from below, where it is shown that the system settles into one of many states of equilibrium. The behaviour near T=0 is shown to be dominated by domain structure.

A simple model is presented in which only the 4s electrons are considered to take part in the screening, the 3d electrons being assumed to be correlated and localised on the iron sites. The model is used to calculate the hyperfine field at the impurity nucleus and, assuming a positive polarisation of the 4s electrons and about one 4s electron per atom in the pure matrix, the impurity hyperfine field is found to cross from negative to positive values as the impurity potential becomes strong enough to form a bound state at the bottom of the band. Such a change in sign is observed experimentally between Al and Si in iron and recent measurements of the soft X-ray emission spectrum of an Fe 8 at% Al alloy confirm the presence of a resonant bound state on an Al impurity in iron. The covalent admixture between the impurity state and neighbouring 3d states is discussed.

For pt.I see ibid., vol.6, p.233 (1976). An improved version of the Caroli-Blandin (1966) form of the effective interaction between local magnetic moments in metals is discussed. It is shown to explain some aspects of the magnetic properties of the Heusler alloy Pd₂MnSn and the dilute magnetic alloys CuFe and CuMn. In this context the ordered alloy Cu₃Mn is also discussed.

Thermal conductivity, electrical resistivity, Lorenz number and spontaneous magnetisation have been measured for spectroscopically pure, polycrystalline iron from about room temperature to above 1200K. Emphasis has been placed on the region around the Curie temperature. The rate of change in electrical resistivity with temperature diverges approximately logarithmically on either side of the Curie point, in reasonable agreement with recent theory which links its behaviour with that of the magnetic specific heat. A predicted link with the spontaneous magnetisation is not supported by the data at least in the range 8.5*10^-3<or approximately= mod epsilon mod <or approximately=10^-1. Anomalous behaviour is observed in the total thermal conductivity and is attributed partly to the critical scattering of phonons by the spin system, the lattice component of thermal conductivity being estimated at about 25% of the total. The data are also consistent with a divergence in the temperature derivative of the electronic component of the thermal resistivity, as found recently in other metallic systems.

The exchange parameters between Gd and the host magnetic ions in the Van Vleck beryllides PrBe₁₃, EuBe₁₃, TmBe₁₃ and UBe₁₃ were extracted using the electron spin resonance technique. A significant variation of the (positive) exchange across the rare-earth series was observed and was interpreted in terms of the dependence of the rare-earth-conduction electron exchange parameter on the 4f occupation number.

An expression for the electric field gradient (EFG) at a nucleus in a metal is obtained by constructing an antishielding theory specifically for the metallic situation. By being constructed on an energy basis the theory is able to clarify the interpretation of the conduction electron contributions to the total EFG. The expression obtained for the total EFG contains not only the familiar antishielding factors gamma _infinity and gamma (r) but also a new radial dependent factor which is in a sense the dual of gamma (r). The traditional expression for the total EFG in metals is revealed as an extreme simplification and possible improvements in practical calculations are suggested.

The quadrupole interactions of ¹¹¹Cd in the environments of the liquid In, InBi and In₂Bi are studied using both time-integrated and time-differential perturbed angular correlation methods. The time-averaged attenuation factor G₂ of liquid In does not change with increase of temperature, whereas those of the liquid alloys show temperature dependences. The time-dependent attenuation factor G₂(t) of liquid In₂Bi is also measured at 200 and 445 degrees C. From these results, the estimated atomic correlation time tau _c is the order of 10^-6 s which is consistent with the NMR result obtained by Seymour and Styles (1966).

Mossbauer spectra of iron-ruthenium alloys show broadening at low temperatures which is interpreted as the effect of hyperfine fields. This implies that magnetic order sets in at temperatures of 115+or-10K, 70+or-10K and 45+or-10K for alloys containing 70 at.%, 60 at.% and 50 at.% iron respectively.

The dielectric constant and optical conductivity of opaque specular lithium films have been determined using a combination of ultra-high vacuum and ellipsometric techniques. The data fall into two categories which the authors associate with the BCC and HCP phases of lithium. Results for the BCC phase are in good agreement with theoretical calculation if one assumes the presence of indirect transitions which shift the experimental absorption edge to a lower photon energy. The second category of data is compatible with what is expected from HCP lithium. For all the data the intraband absorption deviates markedly from the simple omega ^-2 dependence and the derived relaxation time shows a significant energy dependence. No evidence for any anomalous absorption band in this alkali metal is found.