L. M. Falicov

Crystal chemistry and band structures of the group V semimetals and the IV-VI semiconductors

Some simple facts regarding crystal structures and semiconducting vs semimetallic behavior of the Group V elements and the related Group IV–VI compounds are summarized. The simple chemical interpretation of these facts (based on three perpendicular p-bonding orbitals) is reviewed. This picture is reinterpreted in terms of a simple pseudopotential band model, which provides a deeper basis for understanding the simple chemical notions. The results of various band structure calculations are presented in detail in order to make explicit the direct relation between band and bond pictures as well as between crystal structures and semimetallic vs semiconducting behavior. The calculations also provide information as to probable locations of valence and conduction band edges.

Theory of valence mixing for rare-earth compounds

Abstract A theory for the mixed valence state of rare-earth compounds is presented. It includes the following features: (1) two types of electronic states-localized, highly correlated states and itinerant, non-correlated states; (2) a very strong Coulomb repulsion between localized states in the same site; (3) a Coulomb interaction between localized and itinerant states which drives the phase transition; and (4) hybridization between localized and itinerant states which produces the mixed valence state. It is shown that this model produces (a) at T = 0, a variation in the number of localized electrons which may vary in a smooth or in a discontinuous fashion as a function of pressure or alloying; (b) transitions at finite temperature which terminate in a classical critical point. Qualitative agreement with experiment is an encouraging feature of the model.

The electronic potential in a metal close to a surface edge

Abstract An approximate solution of the Schrodinger-Poisson-Hartree equation for a 90° metallic wedge shows that the Friedel oscillations get sizeably enhanced because of the two dimensional discontinuity. Such a result may have profound chemical effects in a transition metal, with level rearrangement and charge transfers which may explain the different chemical reactivity of metallic edges and steps.

Model calculation of the electronic structure of a (111) surface in a diamond-structure solid

The authors present exact results for a model calculation of the surface electronic structure of a (111) face of a diamond-type solid. The model contains only one s-state per atom, but allows for surface rearrangement both at the outer layer and at the outer bounds. Two kinds of surface states are found. The first kind are localized at the outer bounds and split off the bulk bands as the bond potential increases beyond a critical value. The second kind are intrinsic surface states and exist independently of the surface rearrangement but only in a restricted domain in the Brillouin zone where structure factors are smaller than 1. These intrinsic states have not been discussed before; they exist also in more realistic hybrid models of diamond-structure solids.

New theoretical method to study densities of states of tetrahedrally coordinated solids

Abstract A new simple method is proposed to calculate local densities of states of arbitrary tetrahedrally coordinated solids. It involves the selection of a finite cluster of atoms connected to an infinite Bethe lattice of coordination four. The method is accurate, is easily handled numerically, and converges fast. Low-order approximations yield sufficient information which is susceptible to consistent physical interpretation. This has been made for the diamond, BC-8 and ST-12 structures in terms of the ring topology around a given atom. Comparison with exact calculations is very good and the ring interpretation is physical and conceptually appealing.

Hyperfine field at a point interstitial impurity in ferromagnetic nickel

Abstract A simple model for the spin polarization around a charged interstitial impurity in ferromagnetic nickel is presented. It is based on screening of the charge by only s -electrons, while d -electrons, considered to be correlated and localized, are responsible, through an exchange mechanism, for the s -electron spin polarization. Agreement with recent experiments on μ + precession in Ni, as well as neutron diffraction data is satisfactory.

Electronic structure of the transition-metal monoxides

A model for the electronic structure of the transition-metal monoxides is presented. It consists of: (a) A criterion based on 4s bandwidths and spectroscopic term values to decide on the metallic versus insulating character; (b) A quantitative description for the insulating oxides which includes itinerant metal 4s and oxygen 2p states and correlated localized ionic levels arising from the 3d electrons. Optical properties are studied in detail; comparison with experiment is reasonably good.

Ferromagnetism and spatial long-range order in binary alloys

Ferromagnetism and chemical long-range order in binary alloys are studied within the mean-field approximation. The ordering process is driven by pairwise interatomic forces and the magnetic interactions are of the Ising type. Only nearest-neighbour forces are included. It is found that there is a strong influence of one phenomenon on the other, with either the critical order-disorder transformation temperature or the Curie temperature appreciably altered from the corresponding isolated values. The interplay of the two phenomena yields in some cases unusual sequences of phases as a function of temperature. The case of CoxFe1-x alloy is examined along these lines and it is found that the phase diagram can be well reproduced for 0.3

The Band Structure and Fermi Surface of Magnesium

A calculation of the band structure of magnesium metal is performed by means of the orthogonalized plane wave method, in a similar way to that done by Heine for aluminium. The various contributions to the lattice potential are carefully analyzed and computed in order to obtain a final accuracy of about 0.035 Ry, including the errors due to convergence of the secular equation. Group theory methods are used to evaluate the energy levels at points of symmetry and to test the accuracy of the numerical methods. The Fermi energy is obtained by comparison with the free-electron model. The Fermi surface is then described with emphasis on its geometrical and topographical properties to allow for direct comparison with experiment.

STERIC PROPERTIES OF THE TRANSITION-METAL IONS ON STEPPED SURFACES

Simplified model calculations are presented for the steric properties of the transition metal ions in various crystalline geometries on stepped surfaces. Results derived from these calculations are consistent with available experimental data of catalytic properties of Pt and Au stepped surfaces.