J. S. Faulkner

Metallic alloys : experimental and theoretical perspectives

Preface. 1. Photoemission Spectroscopy of Alloys. 2. Experimental Studies of Alloys. 3. Theory of Alloys and Phase Transitions. 4. Theory of Surfaces and Interfaces. 5. Theory of Magnetism in Alloys and Layers. 6. Theory of Electronic States.

Electronic states in Ag-Pd alloys

Electronic densities of states functions are calculated for the random substitutional alloy system Ag-Pd for a number of compositions across the complete range of concentrations. The calculations are based on the coherent potential approximation. It was found necessary to extend the simple model Hamiltonian method previously used to describe Cu-Ni alloys because of the stronger dependence of the lattice constant on composition in the Ag-Pd system. It is shown that the results are consistent with published photoemission and optical absorption data, and low temperature specific heat and Pauli spin susceptibility experiments. The possibility of s-d charge transfer in this alloy system is discussed.

Scattering theory and cluster calculations

It is shown that a formula due to Lloyd (1967) for the density of states of a cluster of muffin-tin potentials can be derived very easily from a theorem in formal scattering theory that was proved by Krein (1953). Some questions in the usual interpretation of the formulae are discussed in the light of Kreins theorem and also the time-delay operator. Generalised Jost functions are introduced and used to furnish a picture of the limiting process in various kinds of cluster calculations.

Growth and orientation of crystallites in Y‐Ba‐Cu‐O superconductors

We have studied the orientation of crystallites in samples of the ceramic superconductor YBa2Cu3Ox using x‐ray diffraction and optical microscopy. Although none of the special techniques for developing texture in this material were employed in the synthesis of our samples, it appears from our data that there is considerable orientation of the crystallites and that the pattern of orientation extends throughout the sample. The degree of orientation increases in a predictable way with the amount of processing. We describe a mechanism for explaining these observations.

Bulk preferred orientation in superconducting YBa2Cu3Ox

Abstract We have studied the orientation of grains in a series of YBa2Cu3Ox pellets that were fabricated with the normal processing steps used in the solid state reaction method. Using x-ray diffraction, we show that the crystallites near the surface to which pressure is applied tend to be oriented with their c-axes parallel to the direction of pressure, and that the degree of orientation increases with the number of processing steps the pellet has undergone until saturation is reached. The orientations of crystallites inside the pellets are studied using polarized Raman spectroscopy on a phonon line that involves vibrations of the O(1) oxygen atom along the c-axis. These orientations are found to track the surface orientations almost exactly, demonstrating that the crystallites are aligned throughout the bulk of the pellets.

KKR structure constants for complex crystals

Abstract It is shown how all of the structure constants for complex crystals can be expressed as linear combinations of quantities which can be calculated as for crystals with one atom per unit cell.

Comparison of the electronic states of alloys from the coherent potential approximation and an order-N calculation

For historical reasons, the coherent potential approximation was originally proposed for isomorphous models of alloys in which all the atoms of a given species are assumed to have the same charge distribution. Order-N methods for density-functional theory local-density approximation calculations of the electronic structure for clusters of hundreds or thousands of atoms demonstrate that a polymorphous model, in which each atom is different, is more realistic. The predictive ability of isomorphous coherent potential approximations is studied by comparison with order-N calculations.

Energetics of alloys

Calculations on one-dimensional differential equations and simplified threedimensional tight-binding models have proved helpful in the development of a theory for the electronic states of macroscopic solids that do not have translational symmetry.1 Using modern order-N methods, it is now possible to calculate the electronic states of large clusters f atoms with realistic self-consistent density functional theory local density approximation (DFT-LDA) potentials. It has been proposed by Anderson,2 quite correctly, that certain aspects of the electronic structure of macroscopic solids must be qualitatively different from those of finite clusters of atoms, and this argument holds even if the clusters are periodically reproduced to fill all space. When coupled with other theoretical insights, however, results for large finite systems can be extrapolated to give a reliable picture of the electronic states of macroscopic disordered systems.

Single impurity calculations using the quadratic Korringa-Kohn-Rostoker method

Abstract The quadratic Korringa-Kohn-Rostoker band theory method is applied to the problem of calculating the electronic states for an impurity atom in an otherwise perfect solid. Some of the advantages of this approach are pointed out, and the results of a trial calculation on a zinc atom embedded in copper are used to demonstrate the utility of the method.

The mathematics of the polymorphous coherent potential approximation

The original coherent potential approximation (CPA) used for calculating the electronic states in substitutional solid-solution alloys contains the implicit assumption that the alloy is isomorphous. That is, all of the atoms of a given chemical type are assumed to be identical. The extension of the CPA philosophy to treat an alloy model in which all of the atoms are allowed to have distinct charges and potentials is called the polymorphous CPA (PCPA). This extension requires some interesting changes in the mathematical formalism that is used to develop the CPA equations. Aspects of the mathematical formalism of the PCPA will be discussed. In particular, the ergodic theorem from measure theory will be invoked to justify the new equations for the average Greens function.