Electronic-structure calculations for amorphous solids using the recursion method and linear muffin-tin orbitals: Application to Fe80B20

Penta-lanthanum zinc diplumbide, La5Zn1-x Pb2+x (x ≃ 0.6)

The title non-stoichiometric penta-lanthanum zinc diplumbide, La5Zn1-x Pb2+x (x ≃ 0.6), was prepared from the elements in an evacuated silica ampoule. It adopts the Nb5Sn2Si-type structure (space group I4/mcm, Pearson symbol tI32), a ternary ordered superstructure of the W5Si3 type. Among the four independent crystallographic positions, three are fully occupied by La (Wyckoff 16k), La (4b), and Pb (8h) and one is occupied by a statistical mixture [occupancy ratio 0.394 (12):0.606 (12)] of Zn and Pb (4a). The structure is constructed by face-sharing 10-vertex polyhedra around the unmixed Pb sites. These fragments enclose channels of trans-face-sharing tetra-gonal anti-prisms occupied by the disordered Zn and Pb sites.

The Muffin-Tin-Orbital Point of View

We review the interpretation of multiple-scattering theory in terms of muffin-tin orbitals. The use of slightly overlapping muffin-tin wells is justified rigorously. It is shown that the structure constants may be screened for a useful range of positive and negative energies, and that the screening may be chosen to yield desirable properties of the KKR matrix. Energy linearization and the linear muffin-tin-orbital method are discussed.

Third-Generation TB-LMTO

We describe the screened Korringa-Kohn-Rostoker (KKR) method and the third-generation linear muffin-tin orbital (LMTO) method for solving the single-particle Schrödinger equation for a MT potential. In the screened KKR method, the eigenvectors CRL,i are given as the non-zero solutions, and the energies εi as those for which such solutions can be found, of the linear homogeneous equations: , where Ka (ε) is the screened KKR matrix. The screening is specified by the boundary condition that, when a screened spherical wave is expanded in spherical harmonics YR′L′ (ȓR′) about its neighboring sites R′, then each component either vanishes at a radius, rR′=aR′L′, or is a regular solution at that site. When the corresponding “hard” spheres are chosen to be nearly touching, then the KKR matrix is usually short ranged and its energy dependence smooth over a range of order 1 Ry around the centre of the valence band. The KKR matrix, K (εν), at a fixed, arbitrary energy turns out to be the negative of the Hamiltonian, and its first energy derivative, K (εν), to be the overlap matrix in a basis of kinked partial waves, φRL (εν, rR), each of which is a partial wave inside the MT-sphere, tailed with a screened spherical wave in the interstitial, or taking the other point of view, a screened spherical wave in the interstitial, augmented by a partial wave inside the sphere. When of short range, K (ε) has the two-centre tight-binding (TB) form and can be generated in real space, simply by inversion of a positive definite matrix for a cluster. The LMTOs, χRL (εν), are smooth orbitals constructed from φRL(εν, rR) and φRL(εν, rR), and the Hamiltonian and overlap matrices in the basis of LMTOs are expressed solely in terms of K (εν) and its first three energy derivatives. The errors of the single-particle energies εi obtained from the Hamiltonian and overlap matrices in the φ(εν)- and χ(εν) bases are respectively of second and fourth order in εi – εi. Third-generation LMTO sets give wave functions which are correct to order εi – εν, not only inside the MT spheres, but also in the interstitial region. As a consequence, the simple and popular formalism which previously resulted from the atomic-spheres approximation (ASA) now holds in general, that is, it includes downfolding and the combined correction. Downfolding to few-orbital, possibly short-ranged, low-energy, and possibly orthonormal Hamiltonians now works exceedingly well, as is demonstrated for a high-temperature superconductor. First-principles sp3 and sp3d5 TB Hamiltonians for the valence and lowest conduction bands of silicon are derived. Finally, we prove that the new method treats overlap of the potential wells correctly to leading order and we demonstrate how this can be exploited to get rid of the empty spheres in the diamond structure.

Analysis of the electronic structure of liquid rubidium by the methods of ab initio molecular dynamics, linear muffin-tin orbitals and recursion

It is well known that liquid rubidium shows some unusual properties at low densities. The ab initio SIESTA package and the supercell technique within the linear muffin-tin orbital method were used to investigate this phenomenon. Electronic structures of liquid rubidium at different temperatures from the melting point up to the critical point were obtained. The atomic structure for the supercell technique was simulated for a cluster of 4000 atoms by the Schommers method on the basis of experimental structure factors of Rb obtained by Tamura and co-workers at different temperatures (from 373 up to 1973 K). The Kubo-Greenwood formula was applied for the calculations of the melt conductivity. The results obtained indicate that the metal-nonmetal transition in liquid rubidium is not connected to the gap at the Fermi energy in the density of electronic states, but, more likely, with electron localization on some kind of atomic cluster.

Local structure studies of Fe-Nb-B metallic glasses using electron diffraction

Local atomic structures in Fe(84)Nb(7)B(9) and Fe(70)Nb(10)B(20) amorphous alloys were examined by means of electron diffraction with the help of computer calculation. Electron diffraction patterns were taken by using energy-filtered transmission electron microscopy (TEM) to eliminate inelastic scattering. We constructed structure models with 5000 atoms fitting to experimental interference functions. Voronoi polyhedral analyses were performed for the obtained final structure models. Local atomic structures of the alloys were closely related to those of the crystalline phases that appeared on annealing. A difference of stability of two amorphous phases was discussed on the basis of structure models.