Etude par diffraction X et microscopie electronique du système CaTiO3---Ca2Fe2O5

In order to check the extended defect model previously proposed for the nonstoichiometric perovskite A_nM_nO_3n−1 (n 2), the Ca₂Ti_2−2xFe_2xO_6−x solid solution has been studied by means of X-ray diffraction and electron microscope investigations. The results show the existence of a continuous evolution (0 x 1) with two different regions. Close to the CaTiO₃ composition (0 x 0.40) the oxygen vacancies seem to be randomly distributed and the symmetry remains pseudocubic. In the composition range 0.55 x 1, the electron microscope patterns show an ordering of the defects: the oxygen vacancies are ordered in the (0k0) planes in strings parallel to the [101] direction. It is concluded from these observations that perpendicular to the Oy direction isolated planes of tetrahedra arranged in rows separate planes of corner-linked octahedra. The n = 2; 2.5; 3, et 4 terms of the A_nM_nO_3n−1 series have been identified. C.S. planes characteristic of classical nonstoichiometric oxides with small cations do not appear: instead, tetrahedra planes succeed to the previous octahedra planes as the degree of nonstoichiometry increases.

Résumé

Afin de vérifier le modèle de non-stoechiométrie proposé dans un travail précédent pour les perovskites lacunaires A_nM_nO_3n−1 (n 2), la solution solide Ca₂Ti_2−2xFe_2xO_6−x a été, étudiée par diffraction X et microscopie électronique. Les résultats montrent l'existence d'une évolution continue (0 x 1) avec deux domaines différents. Pour les compositions proches de CaTiO₃ (0 x 0.40), les lacunes oxygénées semblent être distribuées statistiquement et la symétrie demeure pseudocubique. Dans le domaine de compositions 0.55 x 1, les images de microscopie électronique montrent un ordre des défauts: les lacunes d'oxygène sont ordonnées dans les plans (0k0) en rangées parallèles à la direction [101]. Ces observations ont permis de conclure que perpendiculairement à la direction Oy des plans isolés de files de tétraèdres séparent des plans d'octaèdres liés par leurs sommets. Les termes n = 2; 2.5; 3 et 4 des séries A_nM_nO_3n−1 ont été identifiés. Des plans de cisaillement rencontrés dans les oxydes non-stoechiométriques classiques de petits cations n'ont pas été mis en évidence: par contre, des plans de tétraèdres se substituent aux plans d'octaèdres initiaux lorsque le degré de non-stoechiométrie augmente.     

Some New Results for McKean’s Graphs with Applications to Kac’s Equation

The main goal of the present paper is to sharpen some results about the error made when the Wild sums, used to represent the solution of the Kac analog of Boltzmann’s equation, are truncated at the n-th stage. More precisely, in Carlen, Carvalho and Gabetta (J. Funct. Anal. 220: 362–387 (2005)), one finds a bound for the above-mentioned error which depends on (an ^Λ+ε). On the one hand, it is shown that Λ, the least negative eigenvalue of the linearized collision operator, is the best possible exponent. On the other hand, ε is an extra strictly positive number and a a positive coefficient which depends on ε too. Thus, it is interesting to check whether ε can be removed from the above bound. According to the aforesaid reference, this problem is studied here by means of the probability distribution of the depth of a leaf in a McKean random tree. In fact, an accurate study of the probability generating function of such a depth leads to conclude that the above bound can be replaced with (a′ n ^Λ).     

On several variations of the turan and ramsey numbers

We introduce several variations of the Turan and Ramsey numbers, including zero-sum and bounded-average Ramsey numbers. Some interesting relations between these concepts are presented. In particular, a generalization of the k-local Ramsey numbers is established.     

Site selective spectroscopy and structural analysis of yttria-doped zirconias

Yttria-stabilized zirconias Zr_1?xY_xO_2?0.5x (tetragonal, cubic fluorite, and cubic CLn₂O₃-type forms) are investigated by spectroscopic methods. Optically active europium ions that partially substitute yttrium ions act as a structural microprobe. Both conventional ultraviolet and dye laser (site-selective) excitation are used. The yttria-stabilized zirconias may be well described by a cationic sublattice in which tetravalent and trivalent cations are statistically distributed. The anionic sublattice accommodates vacancies at random on oxygen positions. These vacancies in turn cause complex oxygen displacements giving rise to what may be described as a “glass of anions.”     

The compound decision problem in the opponent case

The compound decision problem is considered under the assumption that Nature plays the role of an opponent. The empirical Bayes approach is a particular case of this approach. It is shown that in many instances sequential compound rules with good asymptotic properties for the fixed case have similar good properties in the opponent case.     

Central limit theorems for solutions of the Kac equation: speed of approach to equilibrium in weak metrics

This paper is part of our efforts to show how direct application of probabilistic methods, pertaining to central limit general theory, can enlighten us about the convergence to equilibrium of the solutions of the Kac equation. Here, we consider convergence with respect to the following metrics: Kolmogorov’s uniform metric; 1 and 2 Gini’s dissimilarity indices (widely known as 1 and 2 Wasserstein metrics); χ-weighted metrics. Our main results provide new bounds, or improvements on already well-known ones, for the corresponding distances between the solution of the Kac equation and the limiting Gaussian (Maxwellian) distribution. The study is conducted both under the necessary assumption that initial data have finite energy, without assuming existence of moments of order greater than 2, and under the condition that the (2 + δ)-moment of the initial distribution is finite for some δ > 0.     

Dipole Chains in Zeolite Pores: The Effects of Symmetry Breaking

Abstract

Dipole molecules become arranged in a highly ordered manner within zeolite pores. They are oriented nearly parallel to the straight channels and aligned collectively into one specific direction. They form arrangements different from the crystallization in the free bulk as well as different from arrangements in amorphous hosts. This polar arrangement results in (i) a lowering of the symmetry of the guest-host system compared to the host, (ii) nonlinear optical effects of second order such as second harmonic generation, (iii) a macroscopic polarization giving rise to pyroelectric effects and (iv) special phase transition phenomena in these one-dimensional systems.     

Ligand influence on connectivity and processing: magnetic crystals based on metalloceniums and films of TCNE-based magnets (TCNE=tetracyanoethylene)

Molecular materials built from coordination complexes exhibit properties that can be explained through intermolecular electronic interactions driven by the ligand moieties. The nature of the ligand in the precursor molecules governs the connectivity of the magnetic phases and the possibility of producing them by using a gas-phase process. Metallocenium, metal bisdithiolate materials, and solvated and solvent-free [M(tcne)2] (tcne=tetracyanoethylene) magnets illustrate such features.