Si extraction from silica in a basic polychalcogenide flux. Stabilization of Ba4SiSb2Se11, a novel mixed selenosilicate/selenoantimonate with a polar structure

An unusual compound, Ba4SiSb2Se11, was discovered from a reaction of Ba/Th/Sb/Se. It is assumed that Si was extracted from the silica reaction tube. It forms as silver needlelike crystals in the polar space group Cmc2(1) with a = 9.3981(3) A, b = 25.7192(7) A, c = 8.7748(3) A, and Z = 4. A rational synthesis has been devised at 600 degrees C. The compound is composed of Ba2+ ions stabilized between infinite one-dimensional [SiSb2Se11]8- chains running parallel to the a axis. Each chain is composed of a [SbSe2]- infinity backbone with [SiSe4]4- tetrahedra chelating every other Sb atom from the same side of the backbone. The V-shaped triselenide groups, (Se3)2-, are attached to the rest of the Sb atoms in the chain through one of their terminal Se atoms. The compound has a band gap of 1.43 eV. The Raman spectrum shows a broad shift at 247 cm-1 and a shoulder around 234 cm-1, which are related to the Se-Se vibration of the triselenide groups and/or the Si-Se vibrations of the [SiSe4]4- groups. The compound decomposes at 522 degrees C.     

On the Discrete Hardy Inequality

Necessary and sufficient conditions for the boundedness of thediscrete Hardy operator of the form , from to when 0 < q < 1 <p , is given.