Redetermination de la structure cristalline du tetrafluoroantimonate III de sodium NaSbF4 - interaction liaison fluor-paire electronique libre

The crystal structure of NaSbF₄ has been redetermined by X-ray diffraction. The coordination about antimony is AX₆E with a 2.2.2.1 geometry. The units are linked by fluorine bridges and form a double layer perpendicular to the a axis. Infrared and Raman spectra were recorded and are discussed in terms of the distorted octahedral arrangement of fluorines about each antimony.     

The ferroelectric transition of dipolar hard spheres

We investigate by Monte Carlo simulation the size dependence of the variation of the polarization and the dielectric constant with temperature for dipolar hard spheres at the two densities rho sigma3=0.80 and 0.88. From the crossing of the fourth-order cumulant for different system sizes first more precise estimates of the ferroelectric transition temperatures are obtained. Theoretical approaches, when predicting an ordering transition, are shown to generally overestimate the critical temperature.     

Synthesis,structure, and magnetic properties of [MnIII(salpn)NCS]n,a helical polymer,and the dimer [MnIII(salpn)NCS]2. Weak ferromagnetism in [MnIII(salpn)NCS]n related to the strong magnetic anisotropy in Jahn-Teller MnIII (salpnH2 = N,N'-bis(salicylidene)-1,3-diaminopropane)

Dimeric [Mn(salpn)NCS](2)(1) and polymeric [Mn(salpn)NCS](n)(2) are formed by the reaction of Mn(CH(3)CO(2))(2).4H(2)O, the schiff base, and thiocyanate. The formation of the two polymorphic forms is solvent and temperature dependent. 1: orthorhombic, space group Pbca, with a = 12.573(2) A, b = 13.970(7) A, c = 18.891(9) A, and Z = 8. 2: orthorhombic, space group Pna2(1), with a = 12.5277(14) A, b = 11.576(2) A, c = 11.513(2) A, and Z = 4. The dimers in 1 are held together by weak noncovalent S...pi (phenyl) interactions leading to a chain along the a-axis. Each monomeric unit of the polymer in 2 is related to its adjacent ones by a 2-fold screw axis leading to a helix along the c-axis. The exchange coupling is nondetectable in the dimer. The magnetic susceptibility of the helical chain fits a classical chain law with J = -3.2 cm(-1) and shows a weak ferromagnetic ordering below 7 K due to spin canting effects.     

Higher-order topological sensitivity for 2-D potential problems. Application to fast identification of inclusions

This article concerns an extension of the topological derivative concept for 2-D potential problems involving penetrable inclusions, whereby a cost function J is expanded in powers of the characteristic size ε of a small inclusion. The O(ε⁴) approximation of J is established for a small inclusion of given location, shape and conductivity embedded in a 2-D region of arbitrary shape and conductivity, and then generalized to several such inclusions. Simpler and more explicit versions of this result are obtained for a centrally-symmetric inclusion and a circular inclusion. Numerical tests are performed on a sample configuration, for (i) the O(ε⁴) expansion of potential energy, and (ii) the identification of a hidden inclusion. For the latter problem, a simple approximate global search procedure based on minimizing the O(ε⁴) approximation of J over a dense search grid is proposed and demonstrated.     

Scheduling jobs with chain precedence constraints and deteriorating jobs

In this paper we consider a single machine scheduling problem with deteriorating jobs. By deteriorating jobs, we mean that the processing time of a job is a simple linear function of its execution starting time. For the jobs with chain precedence constraints, we prove that the weighted sum of squared completion times minimization problem with strong chains and weak chains can be solved in polynomial time, respectively.     

Microstructural effects in non linear stratified composites

In this paper, we analyze the microstructural effects on non linear elastic and periodic composites within the framework of asymptotic homogenization. We assume that the constitutive laws of the individual constituents derive from strain potentials. The microstructural effects are incorporated by considering the higher order terms, which come from the asymptotic series expansion. The complete solution at any order requires the resolution of a chain of cell problems in which the source terms depend on the solution at the lower order. The influence of these terms on the macroscopic response of the non linear composite is evaluated in the particular case of a stratified microstructure. The analytic solutions of the cell problems at the first and second order are provided for arbitrary local strain–stress laws which derive from potentials. As classically, the non-linear dependence on the applied macroscopic strain is retrieved for the solution at the first order. It is proved that the second order term in the expansion series also exhibits a non linear dependence with the macroscopic strain but linearly depends on the gradient of macroscopic strain. As a consequence, the macroscopic potential obtained by homogenization is a quadratic function of the macroscopic strain gradient when the expansion series is truncated at the second order. This model generalizes the well known first strain gradient elasticity theory to the case of non linear elastic material. The influence of the non local correctors on the macroscopic potential is investigated in the case of power law elasticity under macroscopic plane strain or antiplane conditions.