Partial information about structures with the aid of convolutions
Abstract
In X-ray structure analysis a number of rules are known for the extraction of particular aspects of a structure from the interference pattern, such as a periodicity or its projection onto a plane for instance. It is demonstrated in this paper that these and other examples of partial information can be expressed by a convolution of the actual electron-density distribution ϱ (x) with appropriate “modifying functions” μ(x). With the aid of the convolution theorem of Fourier transforms a simple relationship to Fourier space is established. A common mathematical formulation of apparently different methods is thereby obtained. This provides a clear understanding of the conclusions which may be drawn from certain properties of the interference function, and facilitates an extension of the basic ideas to less familiar applications.
Articles in the same Issue
- Rules governing the layer organization of inorganic crystal structures *
- Condensed models of structures based on loose packings*
- Crystal data for β naphthyl and some substituted phenyl maleamic acids
- Dipole-dipole van der Waals interaction in alkali halides
- Some properties of alkaline earth chalcides and heavy metal halides
- The crystal structure of dithiobismorpholine (C4H8NOS)2
- Partial information about structures with the aid of convolutions
- The crystal structures of germanate micas, KMg2.5Ge4O10F2 and KLiMg2Ge4O10F2
- Optical microscopic examination of orthorhombic Na2SO4 (III) in relation to its transformation to Na2SO4(I) hexagonal*
- Elastic, thermoelastic, piezoelectric, linear electrooptic, dielectric, and pyroelectric properties of trigonal Ca3(VO4)2 single crystals
- Refinement of the structure of thiourea: A neutron diffraction study at 293 K
- Zur Kristallstruktur von Natriumnitrat
- Types of sphere packings for crystallographic point groups, rod groups and layer groups
- X-ray powder data and crystallographic data of copper-salicylaldehyde-s-methylthiosemicarbazone and copper-8-quinolinealdehyde-s-methyltliiosemicarbazone complexes
- An X-ray study of cadmium bromate dihydrate
- Crystal data for 4-4′-tetramethyl-diamino-azobenzene
- An X-ray study of 2-mercapto benzimidazole
- Crystallographic data for the mesogenic material cholesteryl methyl carbonate
Articles in the same Issue
- Rules governing the layer organization of inorganic crystal structures *
- Condensed models of structures based on loose packings*
- Crystal data for β naphthyl and some substituted phenyl maleamic acids
- Dipole-dipole van der Waals interaction in alkali halides
- Some properties of alkaline earth chalcides and heavy metal halides
- The crystal structure of dithiobismorpholine (C4H8NOS)2
- Partial information about structures with the aid of convolutions
- The crystal structures of germanate micas, KMg2.5Ge4O10F2 and KLiMg2Ge4O10F2
- Optical microscopic examination of orthorhombic Na2SO4 (III) in relation to its transformation to Na2SO4(I) hexagonal*
- Elastic, thermoelastic, piezoelectric, linear electrooptic, dielectric, and pyroelectric properties of trigonal Ca3(VO4)2 single crystals
- Refinement of the structure of thiourea: A neutron diffraction study at 293 K
- Zur Kristallstruktur von Natriumnitrat
- Types of sphere packings for crystallographic point groups, rod groups and layer groups
- X-ray powder data and crystallographic data of copper-salicylaldehyde-s-methylthiosemicarbazone and copper-8-quinolinealdehyde-s-methyltliiosemicarbazone complexes
- An X-ray study of cadmium bromate dihydrate
- Crystal data for 4-4′-tetramethyl-diamino-azobenzene
- An X-ray study of 2-mercapto benzimidazole
- Crystallographic data for the mesogenic material cholesteryl methyl carbonate
