Structural Studies of Superconductors with Modulated or Composite Structures, Using Powder and Single Crystal Diffraction Methods: New Treatment of the Diffraction Pattern of Twinned Crystal.

The application of X-ray powder diffraction to the polycrystalline sample in Crystallography and Materials Science has increased dramatically over the past 20 years. Recently, complicated solids, such as modulated crystal, have been synthesized in the search for new materials and some of them are prepared only in powder form. The principles of applying Rietveld method for a modulated structures are discussed and the method was applied to modulated high rm T_{c} superconductor, Li inserted rm Bi_2Sr_2CaCu _2O_{8 + y}. The structure of hydrogen reduced high T_{c } superconductor rm YBa_2Cu _3O_{6 + y} was determined using conventional Rietveld method. The difficulty of analysis of diffraction pattern of twinned crystal is well known. A strategy is described for recognition of fully and partially overlapped reflections. The fully reflections are identified by comparison of the integer Miller indices after transformation to a single basis set for all twin components. Partially overlapped reflections are rejected based on their calculated separation in the omega scanning angle. The new method is applied to twinned crystal rm (BO)_2 [ Ag(CN)_2]. A composite crystal is characterized by the presence of two or more 3-dimensional lattices, incommensurate along one or two directions. Each sublattice is considered as a modulated structure and the whole crystal is described by a superspace group. rm(ET)_4Hg _{2.88}Br_8 is the first case that a superconductor has incommensurate composite structure. At room temperature, the crystal is described by superspace group P:C2/c:-11(0, 0, gamma ). In the crystal, the Hg column is shifted because of the weak correlation between Hg columns at different cells. The shifting of Hg column causes diffuse intensity in the reciprocal space. The structure was determined with corrections of the diffuse intensity. Upon cooling the crystal underwent second order phase transition. At 19K the crystal is described by a triclinic superspace group. The crystal rm(ET)_4Hg_ {2.91}Br_8 of orthorhombic modification is coexistence with a twinned composite structure. The structure was determined by excluding fully and partially overlapped reflections.