Table of contents

The authors show how to calculate the momentum distribution function N(p) for electrons within the KKR-CPA band theory method for random alloys. As an example, they evaluate N(p) for momenta along the directions defined by p=(0,0,p_z); 0<or=p_z<or=2 and p=(1,1,p_z+1); 0<or=p_z<or=1 for an Ag_0.2Pd_0.8 random alloy. They argue that a well defined Gamma -centred sheet of Fermi surface and possibly also smeared out d-like X-centred 'ellipses' and a multiply connected 'jungle gym' should be observable in a positron annihilation experiment.

The U(Fe_xCo_1-x)₂ compounds with x<0.62 are non-magnetic and show an exchange-enhanced paramagnetism. In this composition range the values of magnetic susceptibilities are temperature independent and increase gradually when substituting cobalt by iron. For an iron content greater than x=0.62 the compounds are ferromagnetic. The temperature dependence of their magnetic susceptibility can be described by considering a Pauli paramagnetic term in addition to a Curie-Weiss behaviour. The local susceptibility of non-magnetic iron atoms is analysed in the local environment model.

Measurements of AC susceptibility and electrical resistivity show the onset of magnetic order at about 5K and the onset of superconductivity at about 1.5K in samples of Y₄Co₃ which are believed to be single phase. Interpretations are considered which take into account the characteristic structure of the compound and different possible types of magnetic ordering.

The structure and the thermal motion of ions in liquid rubidium are simulated for six states including the critical point along the saturated vapour-pressure curve using the molecular dynamics method. The effective pair potential between rubidium ions in expanded liquid states is calculated by extrapolating the optimised model potential parameters proposed by Cowley (1976) and the screening parameters of Singwi et al. (1970). It becomes deeper and softer at lower densities. The calculated structure factor, S(Q) and the pair distribution function, g(r) are found in better agreement with the measured ones than those calculated by Mountain (1978) using the empty-core pair potential of Price (1971). The calculated short-range orders for an expanded state close to the critical point are significantly different from those of liquid argon near the critical point, which is mostly due to softening of repulsion between rubidium ions. The self-diffusion constant is calculated and fits Tⁿ law with n=1.65 along most of the saturated vapour-pressure curve, in contrast to the case of fluid argon where it fits the Arrhenius-type formula.

The phonon shake-up that occurs when the linear and quadratic phonon potentials both change during X-ray absorption is considered. Full account of all quadratic terms and the competition between linear and quadratic shake-up effects is made. Many previous studies of quadratic phonon shake-up have used a wavefunction approach. The phonon matrix elements have been determined by explicit evaluation of the overlap integrals. The author however, uses an equations of motion approach to transform the time evolution operator to a form that allows an exact evaluation of the phonon matrix elements needed to describe the spectra. They use this theory to determine the strengths of the phonon shake-up satellites in X-ray absorption spectra at zero temperature. An exact expression is obtained for the strength of each satellite. During quadratic shake-up, two phonon transitions and phonon frequency shifts occur. Both effects significantly change the strength of a satellite from that predicted for linear shake-up alone. Inclusion of the two phonon transitions enhances the high-energy satellites. Inclusion of the frequency shifts can either broaden the spectra or increase the strength of the zero phonon lines depending on the sign of the frequency shift.

Certain physical properties, or differences of two physical quantities, oscillate in sign depending on how far the energy bandstructure is filled. The authors show how a theorem of Ducastelle and Cyrot-Lackmann (1971) concerning the number of such zeros for the case of a tight-binding band can be extended to quantities expressible in terms of Green functions. One application is to the relative ease of formation of different structures or magnetic configurations in transition metals; another application is to the Landau theory of phase transitions. The authors show the relation between the theorem and Friedel oscillations.

The authors used the atomic sphere approximation (ASA) to implement the Korringa-Kohn-Rostoker-coherent potential approximation (KKR-CPA) program in order to investigate the electronic structure of Ag_cPd_1-c alloys. In contrast with previous tight-binding calculations and in agreement with experiments the authors find that there is a split-off impurity band in the Pd-rich as well as the Ag-rich alloys. This reflects the fact that random hybridisation and random overlap played an important role in their calculation while they have been neglected in previous work. In addition to the averaged density of states and the specific heat they discuss the evolution of the individual bands and their lifetimes with changing concentration in terms of the Bloch spectral functions.

With the aim of studying the characteristics of the electronic states at the Fermi energy, the authors have investigated the electronic structure of NiH by means of an ab initio augmented plane wave calculation. The d band holes of the pure Ni metal are filled in the hydride, in agreement with magnetisation measurements and as suggested by a comparative study of the K absorption edges of Ni and NiH. This feature is qualitatively similar to that found for PdH; however, the Fermi level in NiH is much closer to the top of the d bands than in PdH. The bandstructure results are used in conjunction with recent experimental estimates of the Debye and Einstein temperatures for the acoustic and optic modes respectively, to calculate the electron-phonon coupling parameter lambda using the model of Gaspari and Gyorffy (1972). A large decrease of the electronic contribution to lambda is found from PdH to NiH. This contributes, together with the hardening of the optic modes evidenced by electrical resistivity measurements, to a drastic lowering of the superconducting transition temperature, T_c and should lead to the non-occurrence of superconductivity in NiH above 1.5K. A site and angular momentum density-of-states analysis of the occupied energy bands is also presented which hopefully will stimulate photoemission and X-ray emission experiments.

Develops a relativistic version of the KKR-CPA method and points out that it is a tractible scheme for studying the electronic structure of random metallic alloys containing constituents with large atomic number. Taking Pt_cNi_1-c as an example the authors demonstrate the necessity of such an approach without, however, presenting a full calculation in the present paper.

Accurate measurements of the de Haas-van Alphen effect amplitudes in mercury show departures from the theory of Lifshitz and Kosevich (1956). These departures are in accordance with the theory of Engelsberg and Simpson (1970), and are due to the breakdown of the quasiparticle picture of the electrons in the presence of electron-phonon interactions.

X-ray form factors have been calculated for metallic vanadium by the APW method. The charge asphericity is estimated using ratios of the integrated intensities of the X-ray scattering for reflection pairs having the same value of sin( theta / lambda ). The charge asphericity obtained from a state-dependent potential, which was made to reproduce the dimensions and shape of the Fermi hole pocket at N-points, is larger than that obtained from state-independent potentials. The ratios of the integrated intensities obtained by the state-dependent potential are in reasonable agreement with the experimental ones determined by Weiss and Demarco (1965) and Diana and Mazzone (1974) and are in excellent agreement with a recent experiment performed by Ohba et al. (1981).

Extends the self-consistent energy-independent model pseudopotential theory, developed previously for the binary allows of simple metals, to the calculation of the interionic pair potentials in the K-Rb, Na-K, Na-Cs, Li-Na, Li-Mg, Li-In and Li-Tl liquid alloys for a number of different concentrations. Then the authors determine, for these alloys, the hard-sphere diameters from the calculated interionic pair potentials for use in the determination of the partial structure factors in the Percus-Yevick approximation. Finally, the partial structure factors thus obtained are applied to calculate the electrical resistivities. It is found from the comparison of the calculated electrical resistivities with experiment that (a) the values proposed in this work for the hard-sphere diameters are reasonable and (b) the concentration dependence of the electrical resistivity in the liquid binary alloy, in which the electronegativity difference between two components is significant, is primarily dependent upon the partial localisation of the valence electrons on the electronegative ions in the alloy.

A study has been made of the true low field Hall coefficient, R_H, of four samples of pure aluminium between 4.2 and 77K. All samples exhibited a low-temperature maximum in the temperature range 7-10K and the three purest samples possessed a minimum between 25 and 30K. An analysis of the low-temperature results is given using a three group model. It is found that, despite the dominance of impurity scattering, the low-temperature maximum may be explained if the mean free paths due to phonon scattering of second-zone holes and third-zone electrons have different temperature dependences. The experimental results on the four samples are found to obey the theoretical prediction that a single function exists when ((R_H-R_H(T=0))/(R_H^max-R_H(T=0))) is plotted against (T/T_max). The theory also enables the anisotropy of mean free paths for phonon scattering of the second-zone free electrons and the third-zone electrons to be deduced from the Hall results and is found to agree with that deduced from radio frequency size effect and surface Landau level experiments.

Electron-phonon mean free paths deduced from measurements of the low-field Hall coefficient of aluminium (see ibid., vol.10 p.2739, 1980) have been employed in a calculation of the temperature-dependent part of the electrical resistivity rho _T of dilute Al alloys. The independent group model is capable of explaining the minimum observed in the rho _T/T³ versus T variation of nominally pure Al.

It is suggested that the contribution to the conductivity from the 'lens' Fermi sheet is obtained separately when the longitudinal magnetoresistance is measured in the principal crystallographic symmetry directions. The high-field saturation value of the longitudinal magnetoresistivity, rho _zz( infinity ), almost equals the zero-field conductivity rho _zz¹(0) of the lens. In very dilute ZnAl alloys, rho _zz( infinity ) has been measured as a function of concentration at 4.2K, rho _zz( infinity ) is proportional to concentration in each symmetry direction. From the comparison with the calculated value from a simple model of lens with a two-wave approximation, it has been estimated that the change of inverse relaxation time, delta _tau ^-1 approximately=(1.2+or-0.1)*10¹¹ s^-1 for 1 PPM of Al.

Measurements of the low-temperature thermopower of several dilute RH-Fe alloys show that the giant negative peak due to localised spin fluctuations occurs at a temperature of approximately 3K. The authors show that this peak is a diffusion and not a drag effect, and deduce the characteristic thermopower for iron impurities in rhodium.

A general theory to count the number of local minimum states in an Ising spin glass is developed. The problem is reduced to finding the partition function of an interacting non-random spin system with an imaginary spin weight function. For the infinite-ranged spin glass with Gaussian bond distribution, the authors find (g₀)=2^0.28743N for the average number of the local minimum states. The distribution function for the energies of these states is also studied. The upper limit of the average ground state energy per spin of the infinite-ranged spin glass is found to be -J/ square root 2 pi .

For pt.I see ibid., vol.10, no.12, p.2769 (1980). The general theory, developed in the preceding paper to study the ground state properties of spin glasses, is applied to two-component spin systems. As an extension of the Edwards-Anderson model (1975) a system of the two-component spins, each spin of which can take only n directions in a plane ('discrete planar model'), is introduced to count (g_n)-the average degeneracy in the ground state. This procedure allows the authors to see how the fundamental properties change by the spin symmetry. For n=2, the theory reproduces the previous results for the Ising model. They can study the XY model as a limit of n to infinity . Precise calculations are performed for the infinite-range exchange interactions. They find (g_infinity )=e^0.51691N.

The antiferromagnetic structures of Cr-Si solid solutions in the range 1.5-6.0 at.% Si have been studied by neutron powder diffraction. The results confirm that the commensurate antiferromagnetic structure is stabilised at around 1.8 at.% Si. Both the magnetic moment and the Neel temperature are found to decrease with increasing silicon content and tend to zero at about 7.2 at.% Si. There is some evidence that the magnetic electrons are of E_g symme-ry and it is suggested that the reduction of magnetic moment is due to the stabilisation of the I_2g relative to the E_g electrons in the chromium band brought about by the formation of covalent bonds with silicon.

Polarised and unpolarised neutron measurements have been carried out on a YCo₅ single crystal. These have allowed the crystal structure to be refined and the magnetisation density distribution of this compound to be determined. The analysis of these results indicates that the moment of one of the two cobalt sites (Co₁) has a very large orbital contribution as well as an important asphericity. These features are discussed in terms of the well known and unusually large magneto-crystalline anisotropy of Co in YCo₅.

The magnetic susceptibility, magnetisation, electrical resistivity and thermopower were measured for the compounds (Gd,Y)₄Co₃, which form a complete solid solution. The localised f electrons of Gd exert a molecular field on the itinerant d electrons of Co, causing exchange splitting for the latter above about 70% Gd. Below this concentration the magnetic moment of Co is small, about 0.3 mu _B per formula unit and arises from localised d electrons on certain Co sites. The exchange integral evaluated using the model developed by Bloch et al. (1975) characterising the molecular field varies rapidly for the Y rich compounds reflecting a rapid variation of the susceptibility of Y₄Co₃ with temperature. The electrical data show clearly the profound influence of the itinerant d electrons in causing high-temperature curvatures and of the localised f electrons in causing kinks at the Curie temperatures.

Presents the experimental results of magnetisation, magnetic susceptibility (at normal pressure and under a pressure of 6 kbar), electrical resistivity and thermal expansion performed on a single sample of CeSn₃. These measurements were done over the temperature range of 1.4<T<300K. The author used an extension of the Ramirez-Falicov theory outlined by Alascio et al. (1972, 1973) to show that these and previous specific heat and thermopower results can be related by including a mixing between the two possible Ce configurations.

The volume dependence of extremal cross-sectional areas of the Fermi surface of antiferromagnetic chromium is obtained from de Haas-van Alphen experiments under pressures up to 4 kbar. The experimental data analysed in terms of a nesting-model lead to d ln(Qa)/dp=-0.49*10^-6 bar^-1 for the pressure dependence of the spin-density-wave Q vector. This value which is in good agreement with results obtained from neutron diffraction is approximately one order of magnitude larger than the calculated pressure derivative of the geometrical nesting vector. It is also much larger than the value d ln(Qa)/dp approximately=0.01*10^-6 bar^-1 obtained from oscillatory magnetostriction and de Haas-van Alphen torque measurements. This discrepancy is believed to be due to a pinning of the incommensurate spin-density-wave to the lattice. Experimental evidence for such a pinning mechanism is briefly discussed.

The elastic modulus C₃₃ of a single crystal of high-purity gadolinium has been studied as a function of temperature over the range 170-300K, and as a function of applied magnetic field of up to 2.5 T in the basal plane. Anomalies in the behaviour of the elastic constants have been observed and are used to deduce a magnetic phase diagram of the element. Two magnetic phases are present in the temperature range 225-293K and three magnetic phases in the range 170-225K. Possible structures of these phases are suggested.

The specific heat capacities over the temperature range 4-460K are reported for Fe_3-xMn_xSi compounds with x=0.6, 0.8, 1.0, 1.2 and 1.6. No gross features associated with the onset of the ferromagnetism of these compounds are found. Evidence of broad anomalies, which may be related to the ferromagnetic order is seen in the x=0.6 and 0.8 compounds. Small features in the specific heat capacity close to the ferromagnetic ordering temperatures for the x=1.0, 1.2 and 1.6 compounds are resolved as 'step-like' anomalies using data for the x=0.6 and 1.6 compounds as a background correction. Distinct cusp-shaped peaks are found at the magnetic re-ordering temperature for these compounds. Estimates of the magnetic entropy associated with the magnetic ordering indicate that the re-ordering process plays a major role in the establishment of the magnetic ground-state.

Calculates the g factor at every point of the Fermi surface of aluminium by using a classical 'four orthogonalised plane waves' scheme and by introducing the spin-orbit potential as a perturbation. An important difficulty remains, linked to the choice of the wavefunction phase. Moreover a phenomenological model is proposed based on the narrowing of the g distribution by two types of motion: a random one corresponding to the diffusion of electrons on the crystalline imperfections and a coherent one around the cyclotron orbits. A qualitative model accounts relatively well for the spin resonance experiment data.