Fast integral equation methods for the modified Helmholtz equation

We present integral equation methods for the solution to the two-dimensional, modified Helmholtz equation, u(x) ? α²Δu(x) = 0, in bounded or unbounded multiply-connected domains. We consider both Dirichlet and Neumann problems. We derive well-conditioned Fredholm integral equations of the second kind, which are discretized using high-order, hybrid Gauss-trapezoid rules. Our fast multipole-based iterative solution procedure requires only O(N) operations, where N is the number of nodes in the discretization of the boundary. We demonstrate the performance of our methods on several numerical examples, and we show that they have both the ability to handle highly complex geometry and the potential to solve large-scale problems.     

Numerical and perturbative computations of solitary waves of the Benjamin–Ono equation with higher order nonlinearity using Christov rational basis functions

Computation of solitons of the cubically-nonlinear Benjamin–Ono equation is challenging. First, the equation contains the Hilbert transform, a nonlocal integral operator. Second, its solitary waves decay only as O(1/∣x∣²). To solve the integro-differential equation for waves traveling at a phase speed c, we introduced the artificial homotopy H(u_XX) ? c u + (1 ? δ)u² + δu³ = 0, δ ∈ [0, 1] and solved it in two ways. The first was continuation in the homotopy parameter δ, marching from the known Benjamin–Ono soliton for δ = 0 to the cubically-nonlinear soliton at δ = 1. The second strategy was to bypass continuation by numerically computing perturbation series in δ and forming Padé approximants to obtain a very accurate approximation at δ = 1. To further minimize computations, we derived an elementary theorem to reduce the two-parameter soliton family to a parameter-free function, the soliton symmetric about the origin with unit phase speed. Solitons for higher order Benjamin–Ono equations are also computed and compared to their Korteweg–deVries counterparts. All computations applied the pseudospectral method with a basis of rational orthogonal functions invented by Christov, which are eigenfunctions of the Hilbert transform.     

An oxygen permeable membrane La0.8Sr0.2(Ga0.8Mg0.2)1 − xCrxO3 − δ for a reduced atmosphere

Mixed electron hole and oxide ion conducting perovskite-type oxides, La_0.8Sr_0.2(Ga_0.8Mg_0.2)_1 ? xCr_xO_3 ? δ (0 ≤ x ≤ 1.0)_, were prepared by solid state reaction. The phase stability and the oxygen permeation properties of the oxides were examined as a function of the content of Cr. La_0.8Sr_0.2(Ga_0.8Mg_0.2)_1 ? xCr_xO_3 ? δ has a perovskite related tetragonal phase with x = 0.1 to 0.8. The total electrical conductivity of La_0.8Sr_0.2(Ga_0.8Mg_0.2)_1 ? xCr_xO_3 ? δ increases with increasing x. The oxygen permeation flux across the La_0.8Sr_0.2(Ga_0.8Mg_0.2)_1 ? xCr_xO_3 ? δ membranes at higher temperatures increases with x up to x = 04. The maximum oxygen permeation flux of 1.6 × 10^? 7 mol^? 1 cm^? 2 at 1100 °C in a oxygen activity gradient of air/10^? 2 Pa is observed in La_0.8Sr_0.2(Ga_0.8Mg_0.2)_0.6Cr_0.4O_3 ? δ. This perovskite-type oxide is stable under an oxygen partial pressure of 7 × 10^? 10 Pa at 1000 °C.     

Oxygen-rich Ti1−xO2 pillar growth at a gold nanoparticle–TiO2 contact by O2 exposure

In-situ gas-injection transmission electron microscopy revealed that a pillar grew at the edge of the interface of a gold nanoparticle and a TiO₂ substrate during exposure to O₂ gas at 100 Pa. The pillar was found to have a titanium-deficient chemical composition of Ti_1 ? xO₂ (x > 0) by electron energy loss spectroscopy (EELS). The spectra showed a chemical shift of oxygen and titanium ions to have ionic states of Ti³⁺ and O^y? (y < 3/2). The formation of the Ti_1 ? xO₂ at the contact edge of gold–Ti_1 ? xO₂ interface is discussed from the perspective of an O₂ affinity, which plays an important role in CO oxidation process of supported gold particle.     

Ionic and electronic conductivities,stability and thermal expansion of La10 − x(Si,Al)6O26 ± δ solid electrolytes

Apatite-type La_10 − xSi_6 − yAl_yO_{27 − 3x/2 − y/2} (x = 0–0.33; y = 0.5–1.5) exhibit predominant oxygen ionic conductivity in a wide range of oxygen partial pressures. The conductivity of silicates containing 26.50–26.75 oxygen atoms per formula unit is comparable to that of gadolinia-doped ceria at 770–870 K. The average thermal expansion coefficients are (8.7–10.8) × 10^− 6 K^− 1 at 373–1273 K. At temperatures above 1100 K, silicon oxide volatilization from the surface layers of apatite ceramics and a moderate degradation of the ionic transport with time are observed under reducing conditions, thus limiting the operation temperature of Si-containing solid electrolytes.     

A ceria layer as diffusion barrier between LAMOX and lanthanum strontium cobalt ferrite along with the impedance analysis

A thin interlayer of samarium doped ceria (SDC) is applied as diffusion barrier between La_1 ? xSr_xCo_yFe_1 ? yO₃ x = 0.1–0.4, y = 0.2–0.8 (LSCF) cathode and La_1.8Dy_0.2Mo_1.6W_0.4O₉ (LDMW82) electrolyte to obstruct Mo–Sr diffusion and solid state reaction in the intermediate temperature range of SOFC. We demonstrate the effectiveness of the diffusion barrier through contrasting the clearly defined interfaces of LSCF/SDC/LDMW82 against a rugged growing product layer of LSCF/LDMW82 in 800 °C thermal annealing, and analyze the product composition and the probable new phase. In addition, the measured polarization resistance is considerably lower for the half-cell with a diffusion barrier. Therefore, the electrochemical performance of the LSCF cathode is investigated on the SDC-protected LDMW82. The cell with LSCF (x = 0.4) persistently outperforms the one with x = 0.2 in polarization resistance because of its small low-frequency contribution. The activation energy of polarization resistance is also lower for La_0.6Sr_0.4Co_yFe_1 ? yO₃ (112–135 kJ/mol), than that for La_0.8Sr_0.2Co_yFe_1 ? yO₃ (156–164 kJ/mol). La_0.6Sr_0.4Co_yFe_1 ? yO₃ y = 0.4–0.8 is the proper composition for the cathode interfaced to SDC/LDMW82.     

Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: High-order image approximations for reaction fields

As a sequel to our previous paper on extending the Fast Multipole Method (FMM) for charges inside a dielectric sphere [J. Comput. Phys. 223 (2007) 846–864], this paper further extends the FMM to the electrostatic calculation for charges inside a dielectric sphere immersed in an ionic solvent, a scenery with more relevance in biological applications. The key findings include two fourth-order multiple discrete image approximations in terms of u = λa to the reaction field induced by the ionic solvent, provided that u = λa < 1 where λ is the inverse Debye screening length of the ionic solvent and a is the radius of the dielectric sphere. A 10⁻⁴ relative accuracy in the reaction field of a source charge within the sphere can be achieved with only 3–4 point image charges. Together with the image charges, the FMM can be used to speed up the calculation of electrostatic interactions of charges in a dielectric sphere immersed in an ionic solvent.     

Electrical conductivity and thermal expansion of the oxy-cuspidine Gd4Al2O9 substituted with Ca and Sr

The series of Gd_4 ? xM_xAl₂O_9 ? x/2 (M = Ca, Sr) with x = 0, 0.01, 0.05, 0.10 and 0.25 was prepared by the citrate complexation method. Both Gd_4 ? xCa_xAl₂O_9 ? x/2 and Gd_4 ? xSr_xAl₂O_9 ? x/2 show the monoclinic cuspidine structure with space group of P2₁/c up to 0.05–0.1 and 0.01–0.05 mol for Ca and Sr, respectively. Beyond the substitution limit of Gd₄Al₂O₉, GdAlO₃ and SrGd₂Al₂O₇ appear as additional phases. The highest electrical conductivity obtained at 900 °C yielded σ = 1.49 × 10^? 4 S/cm for Gd_3.95Ca_0.05Al₂O_8.98. In comparison, the conductivity of pure Gd₄Al₂O₉ was σ = 1.73 × 10^? 5 S/cm. The conductivities determined are in a similar range as those of other cuspidine materials investigated previously. The thermal expansion coefficient of Gd₄Al₂O₉ at 1000 °C was 7.4 × 10^? 6 K^? 1. The phase transition between 1100 and 1200 °C reported earlier changes with increasing substitution of Ca and Sr.     

Thermal expansion behavior and chemical compatibility of BaxSr1−xCo1−yFeyO3−δ with 8YSZ and 20GDC

Perovskite oxides of the composition Ba_xSr_1−xCo_1−yFe_yO_3−δ(BSCF) were synthesized via a modified Pechini method and characterized by X-ray diffraction, dilatometry and thermogravimetry. Investigations revealed that single-phase perovskites with cubic structure can be obtained for x ≤ 0.6 and 0.2 ≤ y ≤ 1.0. The as-synthesized BSCF powders can be sintered in several hours to nearly full density at temperatures of over 1180 °C. Thermal expansion curves of dense BSCF samples show nonlinear behavior with sudden increase in thermal expansion rate between about 500 °C and 650 °C, due mainly to the loss of lattice oxygen caused by the reduction of Co⁴⁺ and Fe⁴⁺ to lower valence states. Thermal expansion coefficients (TECs) of BSCF were measured to be 19.2–22.9 × 10^− 6 K^− 1 between 25 °C and 850 °C. Investigations showed further that Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3−δ is chemically compatible with 8YSZ and 20GDC for temperatures up to 800 °C, above which severe reactions were detected. After being heat-treated with 8YSZ or 20GDC for 5 h above 1000 °C, Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3−δ was completely converted to phases like SrCoO_3−δ, BaCeO₃, BaZrO₃, etc.     

Luminescent properties of red-emitting LiSr4B3O(9−3x/2)Nx:Eu2+ phosphor for white-LEDs

An Eu²⁺-activated oxynitride LiSr_(4?y)B₃O_(9?3x/2)N_x:yEu²⁺ red-emitting phosphor was synthesized by solid-state reactions. The synthesized phosphor crystallized in a cubic system with space group Ia–3d. The LiSr₄B₃O_(9?3x/2)N_x:Eu²⁺ phosphors exhibited a broad red emission band with a peak at 610 nm and a full width at half maximum of 106 nm under 410 nm excitation, which is ascribed to the 4f⁶5d¹→4f⁷ transition of Eu²⁺. The optimal doped nitrogen concentration was observed to be x=0.75. The average decay times of two different emission centers were estimated to be 568 and 489 ns in the LiSr_3.99B₃O_8.25N_0.5:0.01Eu²⁺ phosphors, respectively. Concentration quenching of Eu²⁺ ions occurred at y=0.07, and the critical distance was determined as 17.86 Å. The non-radiative transitions via dipole–dipole interactions resulted in the concentration quenching of Eu²⁺-site emission centers in the LiSr₄B₃O₉ host. These results indicate LiSr₄B₃O_(9?3x/2)N_x:Eu²⁺ phosphor is promising for application in white near-UV LEDs.     

The effect of chemical pressure in rutheno-cuprates

We have studied the effect of negative chemical pressure in the RuGd_1.5(Ce_0.5?xPr_x)Sr₂Cu₂O_10?δ with Pr content of 0.0 ? x ? 0.2. This is also investigated using the bond length results obtained from the Rietveld refinement analysis. The c parameter and cell volume increase with x for 0.0 ? x ? 0.15. The width of the resistivity transition also increases with Pr concentration, indicating higher inhomogeneity and oxygen deficiency. The difference in the ionic valences of Pr^3+,4+ and Ce⁴⁺ causing different hole doping, the difference in the ionic radii, and oxygen stoichiometry affect the superconducting transition. The magnetoresistance shows a cusp around 135 K which lies between the antiferromagnetic and ferromagnetic transition temperatures, which is probably due to the presence of a spin glass region. There exist two magnetic transition temperatures for 0.0 ? x ? 0.2 which respectively change from T_M = 155 K to 144 K and from T_irr = 115 K to 70 K. The magnetization versus applied magnetic field isotherms at 77 K and 300 K show that the remanent magnetization and coercivity are lower for samples with higher Pr content.     

Effect of Ge4+ and Mg2+ doping on superconductivity,fluctuation induced conductivity and interplanar coupling of TlSr2CaCu2O7−δ superconductors

Substitution of Ge⁴⁺ in place of Cu in Tl_0.85Cr_0.15Sr₂CaCu_2?xGe_xO_7?δ (x = 0–0.6) showed initial increase in zero critical temperature value, T_{c zero} from 98 K (x = 0) to 100 K (x = 0.1) and in the range of 85–86 K for x = 0.2–0.3. The slow decrease in T_{c zero} is unexpected as tetravalent Ge⁴⁺ substitution is expected to strongly reduce hole concentration in the samples and suppress T_{c zero}. Excess conductivity analyses of resistance versus temperature data based on Asmalazov–Larkin (AL) theory revealed that the substitution induced 2D-to-3D transition of fluctuation induced conductivity with the highest transition temperature, T_2D–3D observed at x = 0.1. FTIR spectroscopy analysis indicates Ge⁴⁺ substitution cause reduction in CuO₂/GeO₂ interplanar distance while our calculation based on Lawrence–Doniach model revealed highest superconducting coherence length, ξ_c(0) and interplanar coupling, J at x = 0.3. On the other hand, substitution of divalent Mg²⁺ for Ca²⁺ in (Tl_0.5Pb_0.5)(Sr_1.8Yb_0.2)(Ca_1?yMg_y)Cu₂O₇ (y = 0–1.0), which is not expected to directly vary hole concentration, surprisingly caused T_{c zero} to increase from 89.6 K (y = 0) to an optimum value of 95.9 K (y = 0.6) before decreasing with further increase in y. Excess conductivity analyses showed 2D-to-3D transition of fluctuation induced conductivity for all samples where the highest T_2D–3D was at y = 0.4. Similar calculation revealed highest values of ξ_c(0) and J also at y = 0.4. FTIR analysis of the samples indicates inequivalent Cu(1)O(2)Pb/Tl lengths and possible tilting of CuO₂ plane as a result of Mg²⁺ substitution. The increased ξ_c(0) and J as a result of the Ge⁴⁺ and Mg²⁺ substitutions are suggested to contributed to sustenance of superconductivity above 80 K in the samples.     

Relationship between structural phase transition and carrier concentration in La2−x−ySrxRyCuO4 (R = Ce or Tb)

We have studied the relationship between the crystal structure and the carrier concentration in La_2?x?ySr_xCe_yCuO₄ by low-temperature X-ray diffraction method. The analysis for the [1 1 0]_t peak of the tetragonal index confirms that the high-temperature tetragonal phase changes to the low-temperature orthorhombic one in both La_1.89Sr_0.11CuO₄ and La_1.88Sr_0.11Ce_0.01CuO₄. We have also examined the effects of Tb substitution for La-site on the superconductivity and the structure in La_2?x?ySr_xTb_yCuO₄. A dip of the critical temperature T_c(x) due to the 1/8 anomaly and a maximum of T_c(x) at the optimum carrier concentration do not depend on the Tb concentration. This result suggests the possibility that Tb is introduced as the trivalent ion for x = 0.07–0.18.     

Synthesis and characterization of layered Li1−x(Ni0.5Co0.5)1−yFeyO2(0 ≤ (1 − x) ≤ 1 and 0 ≤ y ≤ 0.2) cathodes

Layered Li(Ni_0.5Co_0.5)_1−yFe_yO₂ cathodes with 0 ≤ y ≤ 0.2 have been synthesized by firing the coprecipitated hydroxides of the transition metals and lithium hydroxide at 700 °C and characterized as cathode materials for lithium ion batteries to various cutoff charge voltages (up to 4.5 V). While the y = 0.05 sample shows an improvement in capacity, cyclability, and rate capability, those with y = 0.1 and 0.2 exhibit a decline in electrochemical performance compared to the y = 0 sample. Structural characterization of the chemically delithiated Li_1−x(Ni_0.5Co_0.5)_1−yFe_yO₂ samples indicates that the initial O3 structure is maintained down to a lithium content (1 − x) ≈ 0.3. For (1 − x) < 0.3, while a P3 type phase is formed for the y = 0 sample, an O1 type phase is formed for the y = 0.05, 0.1 and 0.2 samples. Monitoring the average oxidation state of the transition metal ions with lithium contents (1 − x) reveals that the system is chemically more stable down to a lower lithium content (1 − x) ≈ 0.3 compared to the Li_1−xCoO₂ system. The improved structural and chemical stabilities appear to lead to better cyclability to higher cutoff charge voltages compared to that found before with the LiCoO₂ system.     

Structure,stability and electrical properties of the La(2−x)SrxMnO4±δ solid solution series

Single phase materials of the La_(2−x)Sr_xMnO_4±δ (0.6 ≤ x ≤ 2.0) solid solution series were prepared via solid state reaction. The structure of each material was examined at room temperature and determined to be tetragonal for all phases examined. An expansion in lattice volume was observed on increasing lanthanum content. The stability and thermal expansion of each member of the solid solution series was determined via the use of in situ high temperature X-ray diffraction. It was found that all materials remained stable up to a temperature of 800 °C. Thermal expansion coefficients were found to be in the region of 15 × 10^− 6 K^− 1 for La_(2−x)Sr_xMnO_4±δ compounds where x > 1.4. The electrical conductivity of each phase was also determined over a similar temperature range with a maximum value of ∼6 Scm^− 1 at 900 °C for the x = 1.8 phase.     

Improving La0.6Sr0.4Co0.2Fe0.8O3 − δ cathode performance by infiltration of a Sm0.5Sr0.5CoO3 − δ coating

La_xSr_1 ? xCo_yFe_1 ? yO_3 ? δ (LSCF) represents one of the state-of-the-art cathode materials for solid oxide fuel cells (SOFCs) due primarily to its high ionic and electronic conductivity. In this study, a one-step infiltration process has been developed to deposit, on the surface of a porous LSCF cathode, a thin film (50–100 nm) of Sm_0.5Sr_0.5CoO_3 ? δ (SSC), which is catalytically more active for oxygen reduction. Electrochemical impedance spectroscopy reveals that the SSC coating has dramatically reduced the polarization resistance of the cathode, achieving area-specific resistances of 0.036 Ω cm² and 0.688 Ω cm² at 750 °C and 550 °C, respectively. It has also maintained the stability of LSCF cathodes. In particular, the peak power densities are increased by ~ 22% upon the infiltration of SSC onto the porous LSCF cathodes of our best performing cells. These results demonstrate that a conductive backbone (e.g., LSCF) coated with a catalytic film (e.g., SSC) is an attractive approach to achieving an active and stable SOFC cathode for low-temperature solid oxide fuel cells.     

Superconductivity,magnetism and crystal chemistry of Ba1−xKxFe2As2

BaFe₂As₂ is the parent compound of the ‘122’ iron arsenide superconductors and crystallizes with the tetragonal ThCr₂Si₂-type structure, space group I4/mmm. A spin-density-wave transition at 140 K is accompanied by a symmetry reduction to space group Fmmm and simultaneously by antiferromagnetic ordering. Hole-doping induces superconductivity in Ba_1?xK_xFe₂As₂ with a maximum T_c of 38 K at x ≈ 0.4. The upper critical fields approach 75 T with rather small anisotropy of H_c2. At low potassium concentrations (x ? 0.2), superconductivity apparently co-exists with the orthorhombically distorted and magnetically ordered phase. At doping levels x ? 0.3, the structural distortion and antiferromagnetic ordering is completely suppressed and the T_c is maximized. No magnetically ordered domains could be detected in optimally doped Ba_1?xK_xFe₂As₂ (x ? 0.3) by ⁵⁷Fe Mössbauer spectroscopy in contrast μSR results obtained with single crystals. The magnetic hyperfine interactions investigated by ⁵⁷Fe Mössbauer spectroscopy are discussed and compared to the ZrCuSiAs-type materials.     

Maximum magnetic entropy change modulated toward room temperature in perovskite manganites La0.7−xNdx(Ca,Sr)0.3MnO3

With Nd³⁺ doping and Ca²⁺, Sr²⁺ modulating in the sol–gel technique, a series of polycrystalline perovskite samples La_0.7?xNd_x(Ca,Sr)_0.3MnO₃ (x = 0, 0.05, 0.1, 0.15, 0.20, 0.25) was prepared, their maximum magnetic entropy changes were tuned to room temperature (ΔS_H = ?1.47 J/kg K at 298 k for La_0.45Nd_0.25(Ca,Sr)_0.3MnO₃), an enhancement of the maximum magnetic entropy change (ΔS_H = ?1.89 J/kg K at 315 k) and its refrigerant capacity (about 45.3 J/kg) had also been obtained under 9 kOe magnetic field variation for La_0.55Nd_0.15(Ca,Sr)_0.3MnO₃ contrast to La_0.7(Ca,Sr)_0.3MnO₃.     

A potential red-emitting phosphor with high color-purity for near-UV light emitting diodes

New red tungstates phosphors, Na₅La_1?xLn_x(WO₄)₄ (Ln = Eu, Sm) and Na₅Eu_1?xSm_x(WO₄)₄, were prepared by solid-state reaction technique. And their structure and photo-luminescent properties were investigated. The introduction of Sm³⁺ broadened the excitation band around 400 nm of the phosphors, and strengthened the red emission. And the possible energy transfer process from Sm³⁺ to Eu³⁺ is discussed. The single red LED was fabricated by combining InGaN chip with Na₅Eu_0.94Sm_0.06(WO₄)₄ as red phosphor, intense red light can be observed by naked eyes. Then the phosphor Na₅Eu_0.94Sm_0.06(WO₄)₄ may be a good candidate for red component of near-UV InGaN-based W-LEDs, because of efficient red-emitting with broadened absorption around 400 nm and appropriate CIE chromaticity coordinates (x = 0.65, y = 0.34).     

Structural chemistry and zeolitic properties of mixed oxalates with two open-framework types based on eight coordinate metals

Two families of open-framework materials have been obtained from the assembly of MO₈ polyhedra and oxalate groups as building blocks. The compounds can be formulated as [MM′(C₂O₄)₄]²⁻(M″_y)²⁺ · (4 + x)H₂O (y is 2 for monovalent M″ metals and 1 for divalent M″ metals), in which the sum of the valences of the two metals M and M′ involved in the anionic framework is six. The water molecules and counter cations, located in the voids of the structure, lead to zeolitic or cation dynamic properties.