THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

On the magnetic properties of Lithium Vanadium Bronzes LixV2O5

Magnetic susceptibility of V₂O₅ and of the α-, ?-, δ- and γ-Li_xV₂O₅ bronzes prepared either at high or at room temperature has been measured between liquid helium and ambient temperature. The results are representative of the localized character of the V⁴⁺ ion d-electron and, for high enough x-values, of the existence of antiferromagnetic interactions in a low dimensional system. The intrachain exchange integral J has been determined using the Bonner/Fischer model for Heisenberg chains with S = 1/2 spin. It is larger for the γ- than for the δ-phase. This result as well as the occurrence of long range ordering below T_N ≈ 130 K in the γ-phase may be ascribed to ordering of V⁴⁺ and V⁵⁺ ions in the former bronze and to the random distribution of V⁴⁺ ions in the latter one.     

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.     

Preparation and characterization of Fully stoichiometric SrCoO3 by electrochemical oxidation

A nearly stoichiometric SrCoO₃ phase had been prepared up to now only using high oxygen pressure. A new method for preparing fully stoichiometric SrCoO₃ has been proposed using electrochemical oxidation. Brownmillerite-type SrCoO_2.50 is oxidized into a completely stoichiometric perovskite at a potential of 500 mV for 180 hours at room temperature in alkaline media (1 M KOH). The oxidized phase has a cubic unit cell (a=383.5 pm). It is metallic and, at temperatures below T=280 K, it shows ferromagnetic behavior. The magnetic moment at 0 K is 2.1 μ_B. The physical properties of SrCoO_3.00 have been explained in terms of partial occupancy of a σ*e band.     

Mechanisms and kinetics of polymerization of thermoplastic polyimides. II. Study of “bridged” dianhydride/aromatic amine systems

The aim of the present work was to identify and follow the main and side reactions involved in the ring dehydration of amic acid prepared from “bridged” dianhydrides whose central substituent is an electron acceptor or donor, and an aromatic diamine. Several isomeric structures may appear as a result of the opening reactivity and selectivity of anhydride groups towards the aromatic amine. Reaction mechanisms and kinetics were thus studied in solvent phase with HPLC and ¹³C-NMR and in solid molten phase by FTIR and solid ¹³C-NMR. The experimental conditions (liquid and solid) and the structure of the products (type of central substituent) affecting the mechanisms and kinetics of the reactions were noted. © 1993 John Wiley & Sons, Inc.