Hydrogen absorption in transition metal silicides: La3Pd5Si-hydrogen system

Pressure-composition isotherm measurements show that the ternary lanthanum palladium silicide phase La3Pd5Si absorbs reversibly up to 5 hydrogen atoms per formula unit at 550 K and 14 bar hydrogen pressure. In-situ synchrotron and neutron powder diffraction reveals three phases, an alpha-phase having the limiting composition La3Pd5SiD approximately 1.6 at low deuterium pressure (at up to 9.5 bar D2 and 550 K), a beta-phase La3Pd5SiD approximately 2.30-4 at intermediate deuterium pressure (<9.5 bar D2 and 550 K), and a relatively unstable gamma-phase La3Pd5SiD approximately 5 at high deuterium pressure (obtained at 75 bar D2 and 293 K). While the alpha and beta phases retain the symmetry of the H-free La3Pd5Si (space group Imma), the gamma-phase undergoes a symmetry lowering (a(gamma) approximately a(beta), b(gamma) approximately 3b(beta) and c(gamma) approximately c(beta), V(gamma) approximately 3V(beta), space group Pmnb). The structure of the alpha-phase contains isolated [Pd-D-Pd] fragments, which are joined into polymeric (-Pd-D-Pd-)n zig-zag chains in the beta-phase. In the gamma-phase some D sites depopulate, while new D sites are occupied, thus leading to a partial interruption of the zig-zag chains and the formation of isolated [D-Pd-D-Pd] and [D-Pd-D-Pd-D] fragments. This unexpected behavior can be attributed to the onset of repulsive Si-D and D-D interactions (Si-D > 3.0 A, D-D > 2.1 A) that divide the structure into Si-poor slabs that absorb hydrogen and Si-rich slabs that do not. The competition between silicon and deuterium which act as a transition metal ligand is further underlined by the fact that Pd atoms having one Si ligand are capable of forming Pd-D bonds, whereas Pd atoms having two Si ligands are not.     

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.     

Spectroscopic and ab initio characterization of the [ReH9]2- ion

The dynamics and bonding of the hydrido complex Ba[ReH9], containing the D3h face-capped trigonal prismatic [ReH9]2- ion, have been investigated by vibrational spectroscopy and density functional theory (DFT). The combination of infrared, Raman, and inelastic neutron-scattering (INS) spectroscopies has enabled observation of all the modes of the [ReH9]2- ion for the first time. We demonstrate that calculations of the isolated [ReH9]2- ion are unable to reproduce the INS spectrum and that the complete unit cell must be considered with periodic DFT to have reliable results. This is shown to be a consequence of the long-range Coulomb potential present. Analysis of the electronic structure shows that the bonding between the rhenium and the hydrogen is largely covalent. There is a small degree of covalency between the prism hydrides and the barium. The counterion is crucial to the stability of the materials; hence, variation of it potentially offers a method to fine-tune the properties of the material.     

Une méthode combinée d'éléments finis à deux grilles/bases réduites pour l'approximation des solutions d'une E.D.P. paramétrique

In the frame of mathematical optimization procedures or parameter fitting the same problem, modeled with partial differential equations depending on a parameter has to be solved many times for different sets of parameters. The reduced basis method may be successful in this frame and recent progress have permitted to make the computations reliable thanks to a posteriori estimators and to extend the method to non linear problems thanks to the “magic points” interpolation. However, in an industrial context, it may not be possible to use the code (for example of finite element type that allows for evaluating the elements of the reduced basis) to perform all the “off-line” computations necessary for an efficient performance of the reduced basis method. We propose here an alternating approach based on a coarse grid finite element the convergence of which is accelerated through the reduced basis. To cite this article: R. Chakir, Y. Maday, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

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).