Synthesis and Assembly of Zinc Oxide Microcrystals by a Low-Temperature Dissolution–Reprecipitation Process: Lessons Learned About Twin Formation in Heterogeneous Reactions

Cobalt-doped zinc oxide single crystals with the shape of hexagonal platelets were synthesized by thermohydrolysis of zinc acetate, cobalt acetate, and hexamethylenetetramine (HMTA) in mixtures of ethanol and water. The mineralization proceeds by a low-temperature dissolution–reprecipitation process from the liquid phase by the formation of basic cobalt zinc salts as intermediates. The crystal shape as well as twin formation of the resulting oxide phase can be influenced by careful choice of the solvent mixture and the amount of doping. An understanding of the course of the reaction was achieved by comprehensive employment of analytical techniques (i.e., SEM, XRD, IR) including an in-depth HRTEM study of precipitates from various reaction stages. In addition, EPR as well as UV/Vis spectroscopic measurements provide information about the insertion of the cobalt dopant into the zincite lattice. The Langmuir–Blodgett (LB) technique is shown to be suitable for depositing coatings of the platelets on glass substrates functionalized with polyelectrolyte multilayers and hence is applied for the formation of monolayers containing domains with ordered tessellation. No major differences are found between deposits on substrates with anionic or cationic surface modification. The adherence to the substrates is sufficient to determine the absolute orientation of the deposited polar single crystals by piezoresponse force microscopy (PFM) and Kelvin probe force microscopy (KPFM) studies.     

Über die Struktur der in zwei Punkten homogenen,distributiven Spernerschen Räume unter besonderer Berücksichtigung ihrer Fernräume

Ohne Zusammenfassung     

Zur Darstellung Miquelscher Möbiusräume

In this paper we prove the following theorem (shown by J.TITS [7] in the case of finite dimension): LetO be a set of at least 2 points of a projective space of dimension 2 and suppose that the intersections ofO and the planes of are either empty or one point sets or Pascalian ovals. ThenO is an ellipsoid (nondegenerate quadric of index 1). As a corollary we obtain that every Miquelian Möbius-space is the geometry of the plane sections of an ellipsoid.