An optimal shape design formulation for inhomogeneous dam problems

In this paper, the flow problem of incompressible liquid through an inhomogeneous porous medium (say dam), with permeability allowing parametrization of the free boundary by a graph of continuous unidimensional function, is considered. We propose a new formulation on an optimal shape design problem. We show the existence of a solution of the optimal shape design problem. The finite element method is used to obtain numerical results which show the efficiency of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Planar nets of Ti atoms comprising squares and rhombs in the new binary antimonide Ti2Sb

The new binary antimonide Ti(2)Sb was found to crystallize in a distorted variant of the La(2)Sb type, which contains a square planar La net with short La-La bonds. In the Ti(2)Sb structure, the corresponding Ti net is deformed to squares and rhombs in order to enhance Ti-Ti bonding, as proven by single-crystal X-ray investigation in combination with the real-space pair distribution function technique utilizing both X-ray and neutron powder diffraction data. Electronic structure calculations revealed a lowering of the total energy caused by the disorder, the major driving force being strengthened Ti-Ti interactions along the diagonal of the Ti(4) rhombs.     

Crystal structure and physical properties of the new chalcogenides Ba3Cu(17-x)(S,Te)11 and Ba3Cu(17-x)(S,Te)11.5 with two different Cu clusters

The sulfide-tellurides Ba(3)Cu(17-x)(S,Te)(11) and Ba(3)Cu(17-x)(S,Te)(11.5) were synthesized from the elements in stoichiometric ratios heated to 1073 K, followed by slow cooling to 873 K over 100 h. Ba(3)Cu(17-x)(S,Te)(11) is isostructural to Ba(3)Cu(17-x)(Se,Te)(11) when [S] > [Te], space group R ?3m, with lattice dimensions of a = 12.009(1) ?, c = 27.764(2) ?, V = 3467.6(5) ?(3), for Ba(3)Cu(15.7(4))S(7.051(5))Te(3.949) (Z = 6). The structure is composed of Cu atoms forming paired hexagonal antiprisms, capped on the two outer hexagonal faces, where each Cu atom is tetrahedrally coordinated by four Q (= S, Te) atoms. The new variant is formed when [Te] > [S]; then Ba(3)Cu(17-x)(S,Te)(11.5) adopts space group Fm3?m with a = 17.2095(8) ?, V = 5096.9(4) ?(3), for Ba(3)Cu(15.6(2))S(5.33(4))Te(6.17) (Z = 8). This structure consists of eight Te-centered Cu(16) icosioctahedra per cell interconnected by cubic Cu(8) units centered by Q atoms. Electronic structure calculations and property measurements illustrate that these compounds behave as extrinsic p-type semiconductors-toward metallic behavior for the latter compound. With standard oxidation states Ba(2+), Cu(+), and Q(2-), the electron precise formulas are Ba(3)Cu(16)Q(11) and Ba(3)Cu(17)Q(11.5).     

The first semiquinone-bridged bisdithiazolyl radical conductor: a canted antiferromagnet displaying a spin-flop transition

The alternating ABABAB π-stacked bis-1,2,3-dithiazolyl radical 2a (2, R(2)=Ph) has a conductivity σ of 3×10(-5) S cm(-1) at 300 K, and orders as a spin-canted antiferromagnet (T(N)=4.5 K) which undergoes a spin-flop transition to a field-induced ferromagnetic state saturating (at 2 K) at H ～20 kOe.     

Non-linear eigenvalue problems for <Emphasis Type="Italic">p</Emphasis>-Laplacian with variable domain

In this work we consider some eigenvalue problems for p-Laplacian with variable domain. Eigenvalues of this operator are taken as a functional of the domain. We calculate the first variation of this functional, using the obtained formula investigate behavior of the eigenvalues when the domain varies. Then we consider one shape optimization problem for the first eigenvalue, prove the necessary condition of optimality relatively domain, offer an algorithm for the numerical solution of this problem.     

Crystal structure, electronic structure, and physical properties of Ti1-deltaMo1+deltaAs4 and Ti1-deltaMo1+deltaSb4

The new ternary pnictides, Ti(1-delta)Mo(1+delta)Pn4 (Pn = As, Sb), were uncovered during our search for novel thermoelectric materials. Both compounds crystallize in the OsGe2 type in the monoclinic space group C2/m, with lattice dimensions of a = 10.1222(9) A, b = 3.6080(3) A, c = 8.1884(8) A, beta = 120.230(2) degrees , and V = 258.38(7) A3 (Z = 2) for Ti(0.79(1))Mo(1.21)Sb4 and a = 9.1580(2) A, b = 3.3172(1) A, c = 7.6666(1) A, beta = 119.496(1) degrees , and V = 202.720(4) A3 (Z = 2) for Ti(0.86(2))Mo(1.14)As4. The electronic structure calculations predicted metallic behavior for these compounds, which was in agreement with the measured temperature dependence of the electrical conductivity and Seebeck coefficient.     

Structures and physical properties of new semiconducting gold and copper polytellurides: Ba7Au2Te14 and Ba6.76Cu2.42Te14

The title compounds were prepared from the elements between 600 and 800 degrees C in evacuated silica tubes. Both tellurides, Ba7Au2Te14 and Ba6.76Cu2.42Te14, form ternary variants of the NaBa6Cu3Te14 type, space group P63/mcm, with a = 14.2593(7) A, c = 9.2726(8) A, and V = 1632.8(2) A3 (Z = 2) for Ba7Au2Te14 and a = 14.1332(4) A, c = 9.2108(6) A, and V = 1593.3(1) A3 (Z = 2) for Ba6.76Cu2.42Te14. The Na site is filled with a Ba atom (deficient in case of the Cu telluride) and the Cu site with 66.5(3)% Au and 61.7(8)% Cu. An additional site is filled with 9.5(7)% Cu in the structure of Ba6.76Cu2.42Te14. These structures are comprised of bent Te32- units and AuTe4/CuTe4 tetrahedra, forming channels filled with Ba cations. The BaTe9 polyhedra are connecting the channels to a three-dimensional structure. According to the formulations (Ba2+)7(Au+)2(Te32-)3(Te2-)5 and (Ba2+)6.76(Cu+)2.42(Te32-)3(Te2-)5, the materials are electron-precise with 16 positive charges equalizing the 16 negative charges. Correspondingly, both tellurides are semiconductors, as experimentally confirmed, with calculated band gaps of 0.7 and 1.0 eV, respectively.     

Crystal structure and physical properties of the new one-dimensional metal Ba2Cu(7-x)Te6

The telluride Ba(2)Cu(7-x)Te(6) was synthesized from the elements in stoichiometric ratios, heated to 1073 K, followed by slow cooling to 873 K over 120 h. Ba(2)Cu(7-x)Te(6) crystallizes in space group P2(1)/m with lattice dimensions of a = 6.8591(7) ?, b = 12.1439(12) ?, c = 9.0198(9) ?, β = 110.7509(14)°, V = 702.58(12) ?(3), and Z = 2. The structure is comprised of Cu atoms forming a six-membered ring and triangles, interconnected to an infinite ribbon of Cu atoms. The ribbons are connected to each other via Cu-Te bonds to yield a three-dimensional structure, wherein each Cu atom is tetrahedrally coordinated by four Te atoms. A special feature of this telluride is the occurrence of a quasi-linear Te atom chain, which causes one-dimensional metallic properties, in accordance with electronic structure calculations and property measurements.     

Electrochemically induced transformations of heteropolyanions: new electroactive metal oxide films studied by the electrochemical quartz crystal microbalance

New oxide films have been electrodeposited from [P₂Mo₁₈O₆₂]⁶⁻ by potential cycling in mildly acidic aqueous media. To obtain an adherent and persistent film, it is necessary that more than six electrons/molecule be fixed on the framework of the heteropolyanion. The film is then studied in pure supporting electrolyte. In this medium, a remarkable current increase is observed during the potential cycling. Whether the film is deposited on a glassy carbon electrode or on the gold electrode of an electrochemical quartz crystal microbalance (EQCM), exactly the same steady current increase up to a maximum is obtained in cyclic voltammetric measurements. The EQCM reveals a steady mass increase during the continuous cycling of the film in the supporting electrolyte. This behaviour is interpreted as featuring an irreversible water and electrolyte intake into the film, up to a maximum, after which the phenomena observed during reduction and oxidation processes are taken as featuring intercalation/deintercalation, respectively. This behaviour is much the same as described in the literature for WO₃ and MoO₃ bronzes, except that the present films seem very stable and have shown no tendency to dissolve or deactivate. Received: 2 December 1998 / Accepted: 26 January 1999     

Two new titanium molybdenum arsenides: Ti2MoAs2 and Ti3MoAs3, ternary substitution variants of V3As2 and β-V4As3

The title compounds were prepared by arc-melting pre-annealed mixtures of Ti, Mo, and As. Both Ti₂MoAs₂ and Ti₃MoAs₃ adopt structures formed by the corresponding binary vanadium arsenides, V₃As₂ and β-V₄As₃. Ti₂MoAs₂ crystallizes in the tetragonal space group P4/m, with a=9.706(4) Å, c=3.451(2) Å, V=325.1(3) Å³ (Z=4), and Ti₃MoAs₃ in the monoclinic space group C2/m, with a=14.107(3) Å, b=3.5148(7) Å, c=9.522(2) Å, β=100.66(3)°, V=464.0(2) Å³ (Z=4). In both cases, the metal atoms form infinite chains of trans edge-condensed octahedra, and the As atoms are located in (capped) trigonal prismatic voids. While most metal atom sites exhibit mixed Ti/Mo occupancies, the Mo atoms prefer the sites with more metal atom and fewer As atom neighbors. Ti₂MoAs₂ and Ti₃MoAs₃ are metallic entropy-stabilized materials that decompose upon annealing at intermediate temperatures.