A note on least-squares mixed finite elements in relation to standard and mixed finite elements

^** Email: brandts{at}science.uva.nl The least-squares mixed finite-element method for second-orderelliptic problems yields an approximation u_h V_h H₀¹() of thepotential u together with an approximation p_{h h} H(div ; )of the vector field p = – Au. Comparing u_h with the standardfinite-element approximation of u in V_h, and p_h with the mixedfinite-element approximation of p, it turns out that they arehigher-order perturbations of each other. In other words, theyare ‘superclose’. Refined a priori bounds and superconvergenceresults can now be proved. Also, the local mass conservationerror is of higher order than could be concluded from the standarda priori analysis.     

Effect of citric acid concentration as emulsifier on perovskite phase formation of nano‐sized SrMnO3 and SrCoO3 samples

In this study the effects of citric acid concentration, used as organic emulsifier, on the perovskite phase formation of the nano strontium manganite or cobaltite samples were studied. Stoichiometric perovskites in the absence and presence of citric acid were prepared by drying a solution containing molar ratio of Sr(NO₃)₂/Mn(NO₃)₂·4H₂O and Sr(NO₃)₂/Co(NO₃)₂·6H₂O = 1 followed by calcination at 900 °C for 5 h. Citric acid concentration, selected to be 0.0, 0.3, 0.6, 1.0, 1.3, 2.5 and 5 times of the total number of moles of the nitrate ions. The results revealed that increase in the citric acid concentration, larger than number of moles of the nitrate ions equivalent, deteriorates the perovskite phase formation. Instead, a new phase of carbonates and metal oxides are appeared. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural,optical and dielectric studies on K1‐x(NH4)xH2PO4 mixed crystals grown from z‐cut seeds

Mixed crystals of K_1‐x(NH₄)_xH₂PO₄(KADP) were grown from KDP (KH₂PO₄) dominated mixed solutions with varying molar proportion of ADP (NH₄H₂PO₄) addition. It was found that, as the increase of ADP molar concentration, the growth rate along z‐axis of KADP crystal decreased rapidly. The structure of KADP crystals was investigated by powder XRD and the lattice parameter was calculated. The results showed that the lattice parameter c of KADP crystal increased with the molar concentration of ADP. The optical homogeneity of grown KADP crystals was determined with a differential phase‐shifting interferometry. Frequency dependences of the dielectric constant and dielectric loss of KADP crystals were measured at room temperature (290 K). The dielectric constants of KADP crystals were almost invariant with the increase of frequency. In the region of 10²∼10⁴Hz, the values of the dielectric loss reduced with the increase of frequency. The piezo‐resonance coupling effect still exists in KADP crystals at room temperature, but shifted to low frequency band. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Preparation, characterization and photocatalytic performance of TiO2/CexZr1−xO2 toward the oxidation of gaseous benzene

Increasing environmental pollution caused by the volatile organic compounds due to their toxicity makes their removal imperative. So it is crucial to develop processes which can degrade these compounds effectively. The paper demonstrates that the photocatalytic activity of TiO₂ toward the decomposition of gaseous benzene in a batch reactor can be greatly enhanced by loading TiO₂ onto the surface of Ce_xZr_1−xO₂ (x ≥ 0.25) using sol-gel technology. This research investigated the relationship between x amount and the photocatalytic activity of TiO₂. The prepared photocatalysts were characterized by BET, XRD, UV-vis diffuse reflectance and XPS analyses. The specific surface area of photocatalyst decreases as x decreases. XRD results reveal the no peaks of titania were detected. Among the five catalysts prepared, only the binding energy values of Ti2p_3/2 of TiO₂/Ce_0.5Zr_0.5O₂ shift toward lower value. The order of photocatalytic activity is TiO₂/Ce_0.5Zr_0.5O₂ > TiO₂/Ce_0.75Zr_0.25O₂ > TiO₂/CeO₂ ≈ TiO₂/Ce_0.25Zr_0.75O₂ > TiO₂/ZrO₂ ≈ TiO₂. The mechanism role of Ceria-Zirconia mixed oxides in photocatalytic reaction was speculated.