This article is concerned with the mechanisms by which type II superconductors can carry currents. The equilibrium properties of the vortex lattice are described and the generalized driving force in gradients of temperature and field is derived using irreversible thermodynamics. This leads to expressions for thermal cross effects which can include pinning forces. The field distributions which occur in a range of situations are derived and a number of useful solutions of the critical state given. In particular, the distribution in a longitudinal field is obtained, and the conditions under which force-free configurations can break down by the cutting of vortices discussed. The effects of lattice rigidity on the summation of pinning forces is considered and it is shown that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument. Theoretical expressions are derived for the vortex pinning interaction to a number of different metallurgical...

Flux vortices and transport currents in type II superconductors

The manipulation of magnetic properties by an electric field in magnetoelectric multiferroic materials has driven significant research activity, with the goal of realizing their transformative technological potential. Here, we review progress in the fundamental understanding and design of new multiferroic materials, advances in characterization and modelling tools to describe them, and the exploration of devices and applications. Focusing on the translation of the many scientific breakthroughs into technological innovations, we identify the key open questions in the field where targeted research activities could have maximum impact in transitioning scientific discoveries into real applications. Magnetoelectric multiferroics, where magnetic properties are manipulated by electric field and vice versa, could lead to improved electronic devices. Here, advances in materials, characterisation and modelling, and usage in applications are reviewed.

Advances in magnetoelectric multiferroics.

Steam Reforming and Graphite Formation on Ni Catalysts

Interaction of hydrogen with solid surfaces

Publisher Summary This chapter discusses statistical exchange-correlation in the self-consistent field. There are two sides to a self-consistent field calculation: the determination of the potential and the solution of Schrodinger's equation for the one-electron problem. The solution of Schrodinger's equation has fortunately advanced far enough through the application of the electronic digital computer so that it can be regarded for most purposes as being a standardized technique. The main point of the method of Gaspar, Kohn, and Sham is that they derive the approximate exchange correction from an approximate Hamiltonian for the system by varying the spin-orbitals to minimize the average value of this Hamiltonian for the ground state. The approximate Hamiltonian has many important and valuable features that are described in the chapter.

Statistical Exchange-Correlation in the Self-Consistent Field

Calculated low-energy electron diffraction spectra for $c(2\ifmmode\times\else\texttimes\fi{}2)$ overlayer structures of O, S, Se, and Te on Ni(001) show very good agreement with experiment for fourfold coordinated bonding sites and displacements of 0.90, 1.30, 1.45, and 1.90 \ifmmode\pm\else\textpm\fi{} 0.1 \AA{}, respectively, from the center of the first layer of nickel atoms. These adsorbate-atom locations correspond to Ni-chalcogen bond lengths smaller than occur in bulk compounds, but comparable to those found in divalent Ni-chelate complexes.

Chemisorption Bonding of c(2×2) Chalcogen Overlayers on Ni(001)

Elastic low-energy-electron-diffraction intensity-energy spectra are calculated for Ni (001), (110), and (111) surfaces between 10 and 220 eV by the layer-Korringa-Kohn-Rostoker method and compared with recent room-temperature experimental results The calculation uses the Wakoh self-consistent muffin-tin potential, retains eight phase shifts, and includes finite temperature effects (assuming a Debye spectrum) An effective Debye temperature of 335\ifmmode^\circ\else\textdegree\fi{}K is found from the temperature dependence of spectral intensities, an energy-dependent imaginary potential roughly of the form $\ensuremath{\beta}=085{E}^{\frac{1}{3}}$ for electron energy $E$ (in eV) is determined by matching features of the calculated spectra to experiment, and the best values of the first interlayer spacing are found to be 176 \AA{} (the bulk spacing) +002 \ifmmode\pm\else\textpm\fi{} 002 \AA{} on the (001) surface, 124 - (006\ifmmode\pm\else\textpm\fi{}002) \AA{} on the (110) surface, and 203 - (0025\ifmmode\pm\else\textpm\fi{}0025) \AA{} on the (111) surface With these parameters, excellent agreement with observed spectra is obtained in positions and shapes of peaks for several beams and a large number of incident angles For all faces a small systematic deviation in peak positions is found with a constant 11-eV inner potential, suggesting an inner potential varying from the expected static value of 135 at low energies to about 9 eV near 220 eV Comparison of relative intensities between calculation with the above $\ensuremath{\beta}(E)$ and experiment suggests that excitation of $3p$ electrons from Ni significantly enhances electron absorption above 65 eV

Analysis of low-energy-electron-diffraction intensity spectra for (001), (110), and (111) nickel

Determination of the structure of ordered adsorbed layers by analysis of LEED spectra

The degree to which the surface atomic arrangement influences the bonding geometry of sulfur atoms on (001), (110), and (111) Ni surfaces is investigated by an analysis of experimental low-energy electron diffraction data. For all surfaces, the sulfur atoms reside in high-coordination sites---the atomic hollows of the surface; all nearest-neighbor Ni-S bond lengths are less than those of stable bulk compounds.

P. M. Marcus

Papers

Chemisorption Bonding of c(2×2) Chalcogen Overlayers on Ni(001)

Analysis of low-energy-electron-diffraction intensity spectra for (001), (110), and (111) nickel

Determination of the structure of ordered adsorbed layers by analysis of LEED spectra

Crystallographic Dependence of Chemisorption Bonding for Sulfur on (001), (110), and (111) Nickel

Low-Energy-Electron-Diffraction Spectra from [001] Surfaces of Face-Centered Cubic Metals: Theory and Experiment