Non-consistent approximations of self-adjoint eigenproblems: application to the supercell method

In this article, we introduce a general theoretical framework to analyze non-consistent approximations of the discrete eigenmodes of a self-adjoint operator. We focus in particular on the discrete eigenvalues laying in spectral gaps. We first provide a priori error estimates on the eigenvalues and eigenvectors in the absence of spectral pollution. We then show that the supercell method for perturbed periodic Schrödinger operators falls into the scope of our study. We prove that this method is spectral pollution free, and we derive optimal convergence rates for the planewave discretization method, taking numerical integration errors into account. Some numerical illustrations are provided.     

Die Kristallstruktur der Subcarbide von Übergangsmetallen

Ohne ZusammenfassungMit 4 Abbildungen     

Charge transfer and valence electron concentration in Chevrel phases

Single crystal X-ray diffraction measurements on M_xMo₃S₄ compounds (M = Cu, Ag, Sn, In) yield evidence for the existence of a charge transfer from the interstitial element M to the Mo₆S₈ building blocks. The importance of this transfer was estimated from the contraction of the Mo₆ octahedron as a function of the valency and the concentration of the cations. It is suggested that this effect stabilises the structure and has a strong influence on the superconducting transition temperature. Bonding is discussed using a simple valence bond model which is based on the electron requirement of the Mo₆ octahedron to form 12 covalent bonds.     

Tetragonal rare earth (R) Iron borides,R1+εFe4B4 (ε≅0.1), with incommensurate rare earth and iron substructures

Crystallographic and magnetic properties of a new structural series of ternary borides with composition R_1+εFe₄B₄ (R = Ce, Pr, Nd, Sm, Gd, Tb, 0.11(Pr) ≤ε≤ 0.15(Tb) are reported. The compounds are built of incommensurate substructures of rare earth atoms (linear strings ?? c?), iron atoms (chains of edge sharing tetrahedra ?? c?),and boron atom pairs. A single crystal X-ray diffraction study of one representative (Sm_1.13Fe₄B₄) based on a commensurate structure model (composition : Sm₁₇(Fe₄B₄)₁₅, a = 7.07 Å, c ≡ 17c_Sm ≡ 15c_Fe= 58.69 Å, space group P4₂/n) revealed a periodic twist modulation of the Fe tetrahedra chains around c?. Magnetic susceptibility measurements on single crystals of another representative (Nd_1.11Fe₄B₄) revealed ferromagnetic ordering at T_c = 13 K. Above this temperature the magnetic properties are dominated by ferromagnetic inclusions (Fe₂B, Nd₂Fe₁₄B).     

The distribution of the deuterium atoms in the deuterated cubic laves-phase ZrV2D4·5

A neutron diffraction analysis at room temperature of ZrV₂D_4·5 has been made. The deuterium atoms are found to occupy two types of tetrahedral interstices in the metal atom host structure. One is formed by 1 Zr and 3 V atoms and has an occupancy of 39%, whereas the other one is formed by 2 Zr and 2 V atoms, having an occupancy of 25%. Together these interstices can be considered as forming a three-dimensional infinite network of diffusion paths which is similar to that observed in the deuterated hexagonal Laves-phase ZrMn₂D₃. The adjacent D atom sites in this network are about 1.3 åA apart and the average Zr-D and V-D distances are 2.10 and 1.77 åA, respectively.     

Tandem immunoaffinity and reversed-phase high-performance liquid chromatography for the identification of the specific binding sites of a hapten on a proteic carrier

Immunoaffinity (IA) and reversed-phase (RP) high-performance liquid chromatography were combined for the identification of the specific binding sites of benzylpenicilloyl (BPO) groups on human serum albumin (HSA). Tryptic hydrolysates of BPO-HSA were loaded on the IA column. BPO-peptides were desorbed and concentrated directly on the RP column, coupled via a switching valve, then separated by using gradient elution and identified by the amino acid sequences. This single-step procedure permitted more than 95% recovery of the BPO-peptides present in minute amounts, with good specificity.