Evaluation of quadrature schemes for the discrete ordinates method

After reviewing the presently available quadrature schemes for the discrete ordinates method, the accuracy of different schemes is analyzed and evaluated. It is shown from a comprehensive error analysis that the moment conditions have to satisfied not only for the principal coordinates directions, as it is mostly carried out, but for any arbitrary test direction. Among the schemes with approximately 50 discrete ordinates the DCT-020-2468 quadrature was found to give the best accuracy. The highest accuracy among all schemes is achieved by the LC-11 quadrature which requires 96 discrete ordinates. This scheme is rarely used up to date and deserves more attention for high accuracy predictions.     

Direct fission versus sequential evaporation mechanism of sputtered caesium iodide cluster ions

A triple stage hybrid mass spectrometer was scanned for the trapping of the reaction intermediates of the over-all loss of two CsI-moieties from size-selected caesium iodide cluster ions of the general formula Cs (CsI)⁺ _n . In addition to appropriate MS/MS/MS-methods an electrically floated collision cell has been applied to trap intermediates of unimolecular and collision-induced evaporations. In comparison with other experimental findings the features of the evaporation mechanism are discussed.     

Krichever-Novikov-like bases on punctured Riemann surfaces

Bases of holomorphic -differentials on N-punctured Riemann surfaces of arbitrary genus are constructed. The resulting extension of the Virasoro algebra on N-punctured spheres is displayed explicitly.     

Decomposition of EuPdIn and EuPtIn at high temperature and high pressure—formation of the hexagonal Laves phases EuPd0.72In1.28 and EuPt0.56In1.44

EuPd_0.72In_1.28 and EuPt_0.56In_1.44 were prepared under multianvil high-pressure (10.5 GPa) high-temperature (1500 and 1400 K) conditions from the precursor compounds EuPdIn and EuPtIn. They were investigated by X-ray diffraction on both powders and single crystals: MgZn₂-type, space group P6₃/mmc, a=578.7(1) pm, c=944.9(3) pm, wR2=0.0734, 263 F² values for EuPd_0.72In_1.28 and a=591.1(2) pm, c=933.8(2) pm, wR2=0.0853, 151 F² values for EuPt_0.56In_1.44 with 13 variable parameters per refinement. Both structures are built up from face- and corner-sharing tetrahedra of palladium (platinum) and indium atoms. The europium cations are located in cavities within the three-dimensional [Pd_0.72In_1.28] and [Pt_0.56In_1.44] networks. The 2a and 6 h positions of the tetrahedral networks show mixed Pd/In and Pt/In occupancy in EuPd_0.72In_1.28 and EuPt_0.56In_1.44, respectively. The crystal chemistry of these indides is briefly discussed.     

Structure and Magnetic Properties of Ce3Ge0.66In4.34 and Ce11Ge4.74In5.26

New indides Ce₃Ge_0.66In_4.34 and Ce₁₁Ge_4.74In_5.26 were synthesized from the elements by arc‐melting and subsequent annealing at 870 K. Single crystals were grown through special annealing procedures in sealed tantalum tubes in a high‐frequency furnace. Both compounds were investigated on the basis of X‐ray powder and single crystal data: I4/mcm, La₃GeIn₄ type, a = 848.8(1), c = 1192.0(2) pm, Z = 4, wR2 = 0.0453, 499 F² values, 17 variables for Ce₃Ge_0.66In_4.34 and I4/mmm, Sm₁₁Ge₄In₆ type (ordered version of the Ho₁₁Ge₁₀ type), a = 1199.3(2), c = 1662.0(3) pm, wR2 = 0.0507, 1217 F² values, 41 variables for Ce₁₁Ge_4.74In_5.26. The Ce₃Ge_0.66In_4.34 structure shows a mixed Ge/In occupancy on the 4c Wyckoff position. This site is octahedrally coordinated by cerium atoms. These octahedra share all edges, leading to a three‐dimensional network. The latter is penetrated by a two‐dimensional indium substructure which consists of flattened tetrahedra at In–In distances of 291 and 300 pm. The Ce₁₁Ge_4.74In_5.26 structure contains three crystallographically independent germanium sites. The latter are coordinated by eight or nine cerium neighbors. These CN8 and CN9 polyhedra are condensed to a complex network which is penetrated by a three‐dimensional indium network with In–In distances of 301–314 pm. The 16m site shows a mixed In/Ge occupancy. Chemical bonding in both compounds is dominated by the p elements. Both ternaries studied exhibit localized magnetism due to the presence of Ce³⁺ ions. The compound Ce₃GeIn₄ remains paramagnetic down to 1.72 K, whereas Ce₁₁Ge₄In₆ orders ferromagnetically at T_C = 7.5 K.