Hydrothermal synthesis of perovskite and pyrochlore powders of potassium tantalate

Potassium tantalate powders were hydrothermally synthesized at 100 to 200 °C in 4 to 15 M aqueous KOH solutions. A defect pyrochlore, Kta_(2)O_(5)(OH). nH2O (n ≈ 1.4), was obtained at 4 M KOH, but at 7–12 M KOH, this pyrochlore was gradually replaced by a defect perovskite as the stable phase. At 15 M KOH, there was no intermediate pyrochlore, only a defect perovskite, K_(0.85)Ta_(0.92)O_(2.43)(OH)_(0.57) 0.15H_(2)O. Synthesis at higher KOH concentrations led to greater incorporation of protons in the perovskite structures. The potassium vacancies required for charge compensation of incorporated protons could accommodate water molecules in the perovskite structure

Hydrothermal synthesis of KNbO_3 and NaNbO_3 powders

Orthorhombic KNbO_3 and NaNbO_3 powders were hydrothermally synthesized in KOH and NaOH solutions (6.7–15 M) at 150 and 200 °C. An intermediate hexaniobate species formed first before eventually converting to the perovskite phase. For synthesis in KOH solutions, the stability of the intermediate hexaniobate ion increased with decreasing KOH concentrations and temperatures. This led to significant variations in the induction periods and accounted for the large disparity in the mass of recovered powder for different processing parameters. It is also believed that protons were incorporated in the lattice of the as-synthesized KNbO_3 powders as water molecules and hydroxyl ions

Multivariate Anisotropic Interpolation on the Torus

We investigate the error of periodic interpolation, when sampling a function on an arbitrary pattern on the torus. We generalize the periodic Strang-Fix conditions to an anisotropic setting and provide an upper bound for the error of interpolation. These conditions and the investigation of the error especially take different levels of smoothness along certain directions into account

Lightweight Bamboo Double Layer Grid System

The paper presents the structural and environmentally sustainable aspects of bamboo as a valid construction material. A special PVC joint designed for bamboo double layer grids (DLG) is presented and implemented in a 2.3x2.3x0.9m DLG module. Experimental results obtained from evaluating two bamboo species, proof loading of the proposed PVC joint and loading of the DLG module are presented and compared to numerical predictions. The results indicate that the proposed DLG system can be used in practice for constructing lightweight medium-span bamboo structures with excellent structural, aesthetic and environmental attributes

Electronic Structure of LuRh2Si2: "Small" Fermi Surface Reference to YbRh2Si2

We present band structure calculations and quantum oscillation measurements on LuRh2Si2, which is an ideal reference to the intensively studied quantum critical heavy-fermion system YbRh2Si2. Our band structure calculations show a strong sensitivity of the Fermi surface on the position of the silicon atoms zSi within the unit cell. Single crystal structure refinement and comparison of predicted and observed quantum oscillation frequencies and masses yield zSi = 0.379c in good agreement with numerical lattice relaxation. This value of zSi is suggested for future band structure calculations on LuRh2Si2 and YbRh2Si2. LuRh2Si2 with a full f electron shell represents the "small" Fermi surface configuration of YbRh2Si2. Our experimentally and ab initio derived quantum oscillation frequencies of LuRh2Si2 show strong differences with earlier measurements on YbRh2Si2. Consequently, our results confirm the contribution of the f electrons to the Fermi surface of YbRh2Si2 at high magnetic fields. Yet the limited agreement with refined fully itinerant local density approximation calculations highlights the need for more elaborated models to describe the Fermi surface of YbRh2Si2.Comment: 12 pages 10 figure

Well-posedness of the shooting algorithm for control-affine problems with a scalar state constraint

We deal with a control-affine problem with scalar control subject to bounds, a scalar state constraint and endpoint constraints of equality type. For the numerical solution of this problem, we propose a shooting algorithm and provide a sufficient condition for its local convergence. We exhibit an example that illustrates the theory.Comment: arXiv admin note: substantial text overlap with arXiv:1411.171