Hydrogen-induced atomic rearrangement in MgPd3

The hydrogenation behavior of MgPd₃ has been studied by in situ X-ray powder diffraction and by neutron powder diffraction. At room temperature and p ≈500 kPa hydrogen pressure its structure is capable of incorporating up to one hydrogen atom per formula unit (α-MgPd₃H_≈1), thereby retaining a tetragonal ZrAl₃-type metal atom arrangement. Upon heating to 750 K in a hydrogen atmosphere of 610 kPa it transforms into a cubic modification with AuCu₃-type metal atom arrangement (β-MgPd₃H_≈0.7). Neutron diffraction on the deuteride reveals an anion deficient anti-perovskite-type structure (β-MgPd₃D_0.67, a=398.200(7) pm) in which octahedral sites surrounded exclusively by palladium atoms are occupied by deuterium. Complete removal of hydrogen (480 K, 1 Pa) stabilizes a new binary modification (β-MgPd₃, a=391.78(2) pm) crystallizing with a primitive cubic AuCu₃-type structure. Mechanical treatment (grinding) transforms both α and β modifications of MgPd₃ into a cubic face-centered solid solution Mg_0.25Pd_0.75 showing a random distribution of magnesium and palladium atoms.     

Analysis of a part design procedure

Summary. In this paper we analyze and illustrate a new "ab initio" part design procedure, in which, given a cost function which reflects performance, materials, and manufacturing considerations, the topology and the geometry of the part are automatically produced. The analysis is based on demonstration of, first, the compactness of the metric space over which the cost function is defined, and, second, lower semi-continuity of the cost function. Examples include beams and elastic supports. Received November 15, 1993     

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).     

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.     

Error bars and quadratically convergent methods for the numerical simulation of the Hartree-Fock equations

Summary. This paper presents an a posteriori error analysis of the discretization methods used in computational quantum chemistry on the Hartree-Fock equations. Upper and lower bounds for the energy are obtained from any discrete approximation strategy of the solution and the estimator proposed is shown to possess further approximation virtues.     

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.