STRUCTURE FACTORS WITH RATIONAL INDICES. THE FIRST APPLICATIONS
1Carmelo Giacovazzo, 1,2Dritan Siliqi, 3Cristina Fernandez-Castano and 4G. Comunale
1IRMEC c/o Dipartimento
Geomineralogico, Universita di Bari, Campus Universitario, Via
Orabona 4, 70125 Bari , Italy
2Laboratory of X-ray Diffraction,
Department of Inorganic Chemistry, Faculty of Natural Sciences,
Tirana, Albania
3Departamento de Cristalografia, Instituto
de Quimica-Fisica "Rocasolano", CSIC, Madrid, Spain.
4Centro di Geodinamica, Universita della
Basilicata, Potenza, Italy
The statistics of the structure factors with rational indices has been recently derived.1,2,3,4 Their statistical properties can be quite different from the standard Wilson distributions and are shown in detail without any restriction on the type and on the number of the rational index reflections. The attention has been focused on the relation between integral index reflections and half-integral index reflections (the canonical case). In this situation the phase relationships assume a simple form and can be easily calculated. The connection between the probabilistic approach and the algebraic approach based on the Hilbert transform method and on sampling Shannon theorem are also described.5,6 The first applications involve: a) test on the intensity statistics; b) tests on the phase relationships; c) trials to extend the resolution of the measured intensities.