A theoretical investigation of structural,mechanical, electronic and thermoelectric properties of orthorhombic CH<Subscript>3</Subscript>NH<Subscript>3</Subscript>PbI<Subscript>3</Subscript>

The structural, mechanical, electronic and thermoelectric properties of the low temperature orthorhombic perovskite phase of CH₃NH₃PbI₃ have been investigated using density functional theory (DFT). Elastic parameters bulk modulus B, Young’s modulus E, shear modulus G, Poisson’s ratio ν and anisotropy value A have been calculated by the Voigt–Reuss–Hill averaging scheme. Phonon dispersions of the structure were investigated using a finite displacement method. The relaxed system is dynamically stable, and the equilibrium elastic constants satisfy all the mechanical stability criteria for orthorhombic crystals, showing stability against the influence of external forces. The lattice thermal conductivity was calculated within the single-mode relaxation-time approximation of the Boltzmann equation from first-principles anharmonic lattice dynamics calculations. Our results show that lattice thermal conductivity is anisotropic, and the corresponding lattice thermal conductivity at 150 K was found to be 0.189, 0.138, and 0.530 Wm^?1K^?1 in the a, b, and c directions. Electronic structure calculations demonstrate that this compound has a DFT direct band gap at the gamma point of about 1.57 eV. The electronic transport properties have been calculated by solving the semiclassical Boltzmann transport equation on top of DFT calculations, within the constant relaxation time approximation. The Seebeck coefficient S is almost constant from 50 to 150 K. At temperatures 100 and 150 K, the maximal figure of merit is found to be 0.06 and 0.122 in the direction of the c-axis, respectively.     

Static and dynamic descriptions of bond breaking/formation: a complementary view?

Ab initio molecular-dynamic simulations using density-functional theory and the recent atom-centered density-matrix propagation (ADMP) method were used to study the bond breaking and formation for a case-study substitution nucleophilic bimolecular reaction, namely, the Walden inversion. Using the atoms-in-molecule approach, we have performed a detailed analysis to investigate intra- and intermolecular charge transfer along the ADMP trajectory. These results were compared to those obtained considering a static approach, such as the intrinsic reaction path. In particular, the topological properties computed along the dynamic trajectory well evidence a stronger electron exchange tending to spontaneously maximize the rising covalent interaction. Furthermore, their analysis suggests that the bond formation mechanism involves a reactive intermediate with a bonding interaction stronger than in the final product.     

Mechanism and kinetics of the polymerization of thermoplastic polyimides. I. Study of the pyromellitic anhydride/aromatic amine system

We have synthesized model compounds representing the repeating units of a polyamic acid prepared from pyromellitic anhydride and an aromatic amine. They were characterized with HPLC, ¹H and ¹³C liquid and solid NMR and FTIR. The Kinetic study of the ring dehydration reaction of model compounds showed that the reaction paths were very different, depending on the experimental conditions (isotherms, liquid, or solid states). They could lead to a deterioration of the polyamic of the polyamic acid by the formation of side reactions. These reactions could predominate as a result of the existence of an equilibrium between the amic acid group and starting monomers.     

Synthese en milieu hydrothermal et caractérisation de l'oxyhydroxyde de vanadium V3+OOH et d'une nouvelle variété allotropique du dioxyde VO2

Vanadium oxyhydroxide containing mostly trivalent vanadium was synthesized under hydrothermal conditions at 200°C and 2 k bar by hydrolysis of NaVO₃ previously reduced under hydrogen. The structure of VOOH is of diaspore type, isotypic with A1OOH. Oxidation of VOOH at 80°C in air gives in a few days a new metastable phase of vanadium dioxide VO₂; the structure of this new phase is also of the diaspore type, the transformation VOOH → VO₂ being topotactic. Characterization of these phases was done by X-ray diffraction, thermogravimetry, and magnetic, and electrical measurements. Both phases show semiconductor behavior and no electronic transition is observed in VO₂ (diaspore) up to 200°C.     

Part IV Parallel algorithms for partial differential equations

Part IV Parallel algorithms for partial differential equations     

Bond lengths in ‘CaMn3’ (Mn4)O12: A new Jahn-Teller distortion of Mn3+ octahedra

The crystal structure of [CaMn₃] (Mn₄)O₁₂ has been refined with the Rietveld method by using neutron powder diffraction data. This compound is trigonal with the perovskite-like [NaMn₃] (Mn₄)O₁₂ arrangement. The trigonality is due to the 1:3 order between Mn⁴⁺ and Mn³⁺ on the octahedral sites. [CaMn₃] (Mn₄)O₁₂ contains two different types of Mn³⁺ Jahn-Teller distorted polyhedra: the first, which is found in all the AC₃B₄O₁₂ compounds is a rhombic prism, while the second is an apically contracted octahedron, which represents a new type of Jahn-Teller distortion for Mn³⁺ cations in oxide compounds.     

Explicit difference approximations of the one-dimensional diffusion equation,using a smoothing technique

Summary Considering the one-dimensional diffusion equation, smoothing formulas are constructed which, when applied to solutions computed by use of unstable explicit difference approximations, result in stable approximation procedures. It is then shown that more general difference approximations can be written as combinations of simpler difference equations and smoothing formulas.

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Zusammenfassung Für die eindimensionale Wärmeleitungsgleichung werden Glättungsverfahren ausgearbeitet, die bei Anwendung auf Lösungen, welche mit Hilfe unstabiler expliziter Differenzengleichungen errechnet worden sind, stabile numerische Verfahren ergeben. Im Anschluß daran wird gezeigt, daß allgemeinere Differenzenverfahren als Kombinationen von einfachen Differenzengleichungen und Glättungsverfahren geschrieben werden können.

     

Classroom note: A simple non-trivial student model of a bouncing soccer ball

When students have made some progress in studying ordinary differential equations (ODEs) during a semester, small groups are given a soccer ball and asked to determine the simplest model describing one bounce of the ball from shoulder height. To start with, they play with the ball. However, after a few weeks, they begin to ask penetrating questions and they are led to a simple model that has a non-trivial twist to the solution.