Structure and thermal expansion of LiGe2(PO4)3

LiGe₂(PO₄)₃ belongs to the Nasicon-type family. Room-temperature structure has been determined on a single crystal from 3D X-ray data. Thermal evolution of this structure has been established from neutron powder diffraction data between 300 and 1000 K using the Rietveld method. The thermal expansion is positive along the c-axis, whereas shrinking is observed along the a-axis below 900 K, followed by dilatation. The atomic displacements noted with increasing temperature are consistent with a model proposed for NaZr₂(PO₄)₃.     

The New Phosphates Ln1/3Zr2(PO4)3 (Ln = Rare Earth)

The new phases Ln_1/3 Zr₂(PO₄)₃ (Ln = Rare Earth) crystallize with the Nasicon-type structure. The rare earth is located in the usually labeled M₁ site with rather ionic Ln -O bonds. The ceramics resulting from the decomposition of these phosphates have been characterized in the case of lanthanum and europium. They exhibit a very low thermal expansion between room temperature and 1340°C.     

Reagent-based, modular, tandem Michael approach for obtaining different indoline alkaloid-inspired polycyclic architectures

A modular, reagent-based approach to obtain different indoline alkaloid-inspired, tetracyclic architectures is developed. With the use of TBSOTf as a Lewis acid, we report here a tandem Michael-based approach that led to the synthesis of a diastereomeric mixture of tetracyclic derivatives with two additional six-membered rings. By simply changing the Lewis acid to TMSOTf, we were able to obtain a different tetracyclic compound having additional functionalized 5- and 7-membered rings with complete stereocontrol.     

Young's moduli of surface-bound liposomes by atomic force microscopy force measurements

Mechanical properties of layers of intact liposomes attached by specific interactions on solid surfaces were studied by atomic force microscopy (AFM) force measurements. Force-distance measurements using colloidal probe tips were obtained over liposome layers and used to calculate Young's moduli by using the Hertz contact theory. A classical Hertz model and a modified Hertz one have been used to extract Young's moduli from AFM force curves. The modified model, proposed by Dimitriadis, is correcting for the finite sample thickness since Hertz's classical model is assuming that the sample is infinitely thick. Values for Young's moduli of 40 and 8 kPa have been obtained using the Hertz model for one and three layers of intact liposomes, respectively. Young's moduli of approximately 3 kPa have been obtained using the corrected Hertz model for both one and three layers of surface-bound liposomes. Compression work performed by the colloidal probe to compress these liposome layers has also been calculated.     

Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.