Tantalum Clusters in Oxidic Matrices — Synthesis,Crystal Structure and Magnetic Properties of Eu1.83Ta15O32

The mixed‐valent oxotantalate Eu_1.83Ta₁₅O₃₂ was prepared from a compressed mixture of Ta₂O₅ and the metals in a sealed Ta ampoule at 1400 °C. The crystal structure was determined by means of single crystal X‐ray diffraction: space group R3¯, a = 777.2(6) pm and c = 3523.5(3) pm, Z = 3, 984 symmetrically independent reflections, 83 variables, R_F = 0.027 for I > 2σ (I). The structure is isotypic to Ba₂Nb₁₅O₃₂. The salient feature is a [Ta(+8/3)₆O₁₂ⁱO₆^a] cluster consisting of an octahedral Ta₆ core bonded to 12 edge‐bridging inner and six outer oxygen atoms. The clusters are arranged to slabs which are sandwiched by layers of [Ta(+5)₃O₁₃] triple octahedra. Additional Ta(+5) and Eu(+2) atoms provide the cohesion of these structural units. Twelve‐fold coordinated Eu(+2) atoms are situated on a triply degenerate position 33 pm displaced from the threefold axis of symmetry. A depletion of the Eu(+2) site from 6 to 5.5 atoms per unit cell reduces the number of electrons available for Ta‐Ta bonding from 15 to 14.67 electrons per cluster. Between 125 and 320 K Eu_1.83Ta₁₅O₃₂ is semi‐conducting with a band gap of 0.23 eV. The course of the magnetization is consistently described with the Brillouin function in terms of a M_mol/(N_Aμ_B) versus B/T plot in the temperature range 5 K — 320 K and at magnetic flux densities 0.1 T — 5 T. At moderate flux densities (< 1 T) the magnetic moment agrees fairly well with the expected value of 7.94 μ_B for free Eu (2+) ions with 4f⁷ configuration in ⁸S_7/2 ground state. Below 5 K, anisotropic magnetization measurements at flux densities B < 1 T point to an onset of an antiferromagnetic ordering of Eu spins within the layers and an incipient ferromagnetic ordering perpendicular to the layers.     

Thermodynamic properties of two metal-rich tantalum sulfides: Ta2S and Ta6S

The incongruent vaporization reactions of Ta₂S and Ta₆S have been investigated by mass-loss effusion in the temperature range 1576 to 1902 K. By extrapolation of P_S(obs) to equilibrium the enthalpies of the reactions $\text{3}\text{2}\text{Ta}{}_2\text{S(s)}\text{=}\text{1}\text{2}\text{Ta}{}_6\text{S(s) + S(g)}$ and Ta₆S = 6 Ta(s) + S(g) were found to be $\text{ΔH}{}^0{}_{298}\text{R}\text{= 53.0(0.3) · 10}{}^3\text{K}$ and $\text{ΔH}{}^0{}_{298}\text{R}\text{= 58.1(0.4) · 10}{}^3\text{K}$, respectively. Comparison between the above values, determined by a 2nd law treatment, and 3rd law values was used to derive fef (“free energy function”) values for Ta and S in the compounds. These postulated fef's, which apply only to the elements as present in the compounds measured, are compared to tabulated quantities for the pure solid elements to provide a criterion for 2nd and 3rd law evaluation.     

Crystal Structure of LiRh-type IrZn Determined by Powder X-ray and Selected Area Electron Diffraction

The LiRh-type crystal structure of the equiatomic intermetallic compound IrZn turns out to be a competitor to the otherwise energetically favored CsCl-type structures of congeneric transition metal zinc phases, thus enlightening the structural impact of element-specific factors beyond the Hume-Rothery concept.     

Wavelet formulation of the polarizable continuum model

The first implementation of a wavelet discretization of the Integral Equation Formalism (IEF) for the Polarizable Continuum Model (PCM) is presented here. The method is based on the application of a general purpose wavelet solver on the cavity boundary to solve the integral equations of the IEF‐PCM problem. Wavelet methods provide attractive properties for the solution of the electrostatic problem at the cavity boundary: the system matrix is highly sparse and iterative solution schemes can be applied efficiently; the accuracy of the solver can be increased systematically and arbitrarily; for a given system, discretization error accuracy is achieved at a computational expense that scales linearly with the number of unknowns. The scaling of the computational time with the number of atoms N is formally quadratic but a N^1.5 scaling has been observed in practice. The current bottleneck is the evaluation of the potential integrals at the cavity boundary which scales linearly with the system size. To reduce this overhead, interpolation of the potential integrals on the cavity surface has been successfully used. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Improved trial methods for a class of generalized Bernoulli problems

The aim of this article is to develop improved trial methods for the solution of a generalized exterior Bernoulli free boundary problem. At the free boundary, we prescribe the Neumann boundary condition and update the free boundary with the help of the remaining Dirichlet boundary condition. Appropriate update rules are obtained by expanding the state's Dirichlet data at the actual boundary via a Taylor expansion of first and second order. The resulting trial methods converge linearly for both cases, although the trial method based on the second order Taylor expansion is much more robust. Nevertheless, via results of shape sensitivity analysis, we are able to modify the update rules such that their convergence is improved. The feasibility of the proposed trial methods and their performance is demonstrated by numerical results.     

On analytical derivatives for geometry optimization in the polarizable continuum model

The present paper is dedicated to the analytical computation of shape derivatives in the polarizable continuum model. We derive expressions for the interaction energy’s sensitivity with respect to variations of the cavity’s shape by means of the Hadamard representation of the shape gradient. In particular, by using the adjoint approach, the shape gradient depends only on two solutions of the underlying electrostatic problem. We further formulate boundary integral equations to compute the involved quantities.     

Coupling of FEM and BEM in Shape Optimization

In the present paper we consider the numerical solution of shape optimization problems which arise from shape functionals of integral type over a compact region of the unknown shape, especially L ²-tracking type functionals. The underlying state equation is assumed to satisfy a Poisson equation with Dirichlet boundary conditions. We proof that the shape Hessian is not strictly H ^1/2-coercive at the optimal domain which implies ill-posedness of the optimization problem under consideration. Since the adjoint state depends directly on the state, we propose a coupling of finite element methods (FEM) and boundary element methods (BEM) to realize an efficient first order shape optimization algorithm. FEM is applied in the compact region while the rest is treated by BEM. The coupling of FEM and BEM essentially retains all the structural and computational advantages of treating the free boundary by boundary integral equations.This research has been carried out when the second author stayed at the Department of Mathematics, Utrecht University, The Netherlands, supported by the EU-IHP project Nonlinear Approximation and Adaptivity: Breaking Complexity in Numerical Modelling and Data Representation     

The valence problem of Pd4Br4Te3

Pd(4)Br(4)Te(3) was prepared from Pd, Te, and PdBr(2) at 700 K. Its structure was determined by single-crystal X-ray diffraction to be triclinic, P$\bar 1$, Pearson symbol aP22; a=842.5(2), b=845.0(3), c=864.8(3) pm; alpha=82.55(3), beta=73.36(2), gamma=88.80(2) degrees ; Z=2. The Br and Te atoms are arranged according to the motif of cubic closest-packed spheres in which every 15th position is vacant; the Pd atoms occupy 8/15 of the octahedral voids. The symmetry relations with the packing of spheres are derived. Prominent structural units are hollow cuboctahedral [(PdBrTe)(6)] units, the Pd atoms are positioned near the centers of the square faces of the Br(6)Te(6) cuboctahedra; the cuboctahedra and double-octahedral Pd(2)Br(4)Te(6) units are connected to strands by sharing triangular Te(3) faces. The strands are condensed by common Br atoms into layered assemblies. Conspicuously close Te--Te contacts in the Te(3) triangles indicate attractive Te--Te interactions. The valence puzzle is resolved by the formula Pd(+II)(4)Br(-I)(4)Te(-4/3)(3). Positive Te--Te Mulliken orbital populations and the Pd--K, Br--K, and Te--L(III) XANES spectra of Pd(4)Br(4)Te(3) referenced to the spectra of PdBr(2), K(2)PdBr(6), PdTe, and PdTe(2) are in accord with attractive Te--Te interactions. The measured semiconducting and diamagnetic properties are compatible with the derived picture of chemical bonding in Pd(4)Br(4)Te(3).     

Die Kristallstruktur von Ga5Pd13 – eine niedersymmetrische Ordnungsvariante der kubisch dichtesten Kugelpackung

The Crystal Structure of Ga₅Pd₁₃ – a Low‐Symmetrical Ordering Variant of the Cubic Close Sphere Packing Ga₅Pd₁₃ is accessible from the elements in the presence of catalytically active amounts of iodine at 520 °C. The phase decomposes at 897 °C in a peritectoid reaction. The monoclinic crystal structure was determined from the intensities of an X‐ray powder diffractogram and refined by a Rietveld profile fit: C 2/m, Z = 2, a = 2425.99(5) pm, b = 405.060(7) pm, c = 544.37(1) pm, β = 102.690(1)°, R_p = 0.069. The new structure type is described as an ordering variant of the cubic close sphere packing. The ordering pattern and the distortions in the primary coordination of the atoms reflect the definite impact of the intermetallic bonding interactions on the differentiation of the structure.