We review first-principles calculations of the size effect in dilute transition-metal alloys. The calculations apply local density functional theory and a Green's function method based on the KKR multiple-scattering formalism. In each cell, the full anisotropic potential in included and the forces on the atoms are calculated by the Hellmann-Feynman theorem. The method is applied to predict the atomic positions around d+sp impurities in Cu and Al. The results compare favorably with experimental data from extended X-ray-absorption-fine-structure and lattice-parameter measurements.

A chain of impurity cells in a photonic insulator introduces impurity modes of the electromagnetic field over a narrow band of frequencies. We introduce a model of this band in the manner of a tight-binding description of impurity bands in semiconductors, and use it to describe waveguiding along the chain, and, in particular, across a corner of 90°  . We also point out the possibility of using impurity bands in photonic insulators to study wave propagation along an effectively one-dimensional disordered chain.

We present a program for the calculation of the frequency band structure of an infinite photonic crystal, and of the transmission, reflection and absorption coefficients of light by a slab of this crystal. The crystal consists of a stack of identical slices parallel to a given surface; a slice may consist of a number of different components, each of which can be either a homogeneous plate or a multilayer of spherical particles of given periodicity parallel to the surface.

We present first-principles calculations of the electronic structure and hyperfine fields of 3d and 4sp impurities on the (001) surface of Ni. The calculations are based on the local-spin-density-functional theory and employ a Korringa-Kohn-Rostoker Green's function method for impurities at surfaces. The systematic behaviour obtained for the hyperfine fields of the 4sp adatoms or impurities in the first surface layer is completely different from that found in the bulk. Instead of a single maximum with a very large hyperfine-field value at about the end of an sp series, the adatoms exhibit two maxima with a pronounced minimum in between. This behaviour can be traced back to the reduced coordination number of the adatoms which leads to a much smaller relative splitting of the bonding and antibonding peaks, and to the lower symmetry at the surface which results in an on-site s-p: hybridization. The hyperfine fields found for the 3d impurities at the surface are determined basically by the ferromagnetic or antiferromagnetic coupling of the local impurity moment to the substrate magnetization and are therefore in more or less similar to those for bulk impurities.

We present first-principles calculations of the electronic structure and hyperfine fields of 4sp  impurities on the (001) surfaces of Ni and Fe. The calculations are based on the local-spin-density-functional theory and employ a Green's function method for impurities at surfaces. The systematic behavior obtained for the hyperfine fields of adatoms or impurities in the first surface layer is completely different from that found in the bulk, mainly due to the reduction of the symmetry and the coordination number at the surface. Our results explain the surprisingly small hyperfine-field values measured for Se adatoms and provide challenging predictions to be confirmed by future experiments.

The role of the anisotropic impurity scattering in the determination of the low-field Hall coefficient of Al-4d dilute alloys is investigated by means of systematic theoretical calculations, as well as experimental measurements for AlZr and AlMo. The theoretical results, obtained without using any adjustable parameter, are in excellent agreement with the experimental data and a consistent interpretation of the systematic variation of the low-field Hall coefficient for aluminium-based dilute alloys with transition-metal impurities is given.

We report a systematic study of the spin-polarization energy of 3d impurities in monovalent simple-metal hosts, by means of self-consistent, local-spin-density-functional, impurity-in-jellium calculations, and propose a phenomenological model for the interpretation of our results.