Structure determination from powder data using anomalous scattering: difference and partial, Patterson densities, and phases of structure factors
Abstract
For structure determination from X-ray powder data, anomalous (resonant) scattering can be used to obtain difference Patterson and partial Patterson densities as well as phases of structure factors. Usually tuneable synchrotron radiation is used, and two or more powder patterns near and far the absorption edge of an atom type contained in the crystal are recorded.
The algebraic theory together with some novel and efficient approximations is given in detail. Also symmetry restrictions, experimental and scaling procedures, and the use of the Maximum-Entropy method (MEM) are discussed. The application to the structure of an iron garnet Fe2Ca3Ge3O2 is presented. This resulted in the first determination of two partial Patterson densities: of the iron atoms and of germanium atoms.
From an MEM calculation of the electron-density, using the signed structure factors F(H) together with only the absolute values |F(H)| of the remaining reflections, all atoms could be localized with good resolution and low background, whereas the ordinary Fourier calculation failed completely to show the oxygen atoms. This result is based on only 34 unique out of 83 total reflections in 0 ≤ sin θ/λ ≤ 0.494 Å−1. These successful applications open up new possibilities in the structure determination of unknown compounds.
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Artikel in diesem Heft
- Icosahedral coincidence rotations
- Localization and integration of diffraction spots from two-dimensional X-ray detector images by digital filtering
- Finite periodicity and crystal structures
- Structure determination from powder data using anomalous scattering: difference and partial, Patterson densities, and phases of structure factors
- Phase transitions of modulated Co-åkermanite, Ca2CoSi2O7
- Preparation and single crystal structure refinement of mixed orthophosphates M3Cr4(PO4)6 (M = Mg, Zn, Cu) – copper(II) in compressed octahedral coordination1
- Crystal structures of Ca5Ge3O11 and wollastonite-type GaGeO3
- One-dimensional staircase aggregates in crystals of 1,7-bis(dimethylamino)heptamethinium hexafluorophosphate, a polymethine dye
- Crystal structures of N-4-methyl phenyl)-2,2,2-trichloroacetamide, N-2,3-dimethyl phenyl)-2,2,2-trichloroacetamide and N-(2-nitro phenyl)-2,2,2-trichloroacetamide
- The structure of 6-(2-hydroxybenzylamino)purine acetic acid solvate
- Structural variations in the mercury(II) bis(1,1-dithiolate)s: the crystal and molecular structure of [Hg(S2CNMe2)2]
Artikel in diesem Heft
- Icosahedral coincidence rotations
- Localization and integration of diffraction spots from two-dimensional X-ray detector images by digital filtering
- Finite periodicity and crystal structures
- Structure determination from powder data using anomalous scattering: difference and partial, Patterson densities, and phases of structure factors
- Phase transitions of modulated Co-åkermanite, Ca2CoSi2O7
- Preparation and single crystal structure refinement of mixed orthophosphates M3Cr4(PO4)6 (M = Mg, Zn, Cu) – copper(II) in compressed octahedral coordination1
- Crystal structures of Ca5Ge3O11 and wollastonite-type GaGeO3
- One-dimensional staircase aggregates in crystals of 1,7-bis(dimethylamino)heptamethinium hexafluorophosphate, a polymethine dye
- Crystal structures of N-4-methyl phenyl)-2,2,2-trichloroacetamide, N-2,3-dimethyl phenyl)-2,2,2-trichloroacetamide and N-(2-nitro phenyl)-2,2,2-trichloroacetamide
- The structure of 6-(2-hydroxybenzylamino)purine acetic acid solvate
- Structural variations in the mercury(II) bis(1,1-dithiolate)s: the crystal and molecular structure of [Hg(S2CNMe2)2]
