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Accurate separation of X‐ray α 1 –α 2 doublets by the `substitution method'
Author(s) -
Pompa F.,
Zirilli S.
Publication year - 1982
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889882012758
Subject(s) - diffraction , reciprocal lattice , reciprocal , substitution (logic) , smoothing , separation (statistics) , variable (mathematics) , mathematics , polynomial , computational physics , optics , algorithm , physics , mathematical analysis , computer science , statistics , philosophy , linguistics , programming language
An improved `substitution method' for the separation of X‐ray diffraction α 1 − α 2 doublets is based on the possibility of refining both the proportionality constant between the α 1 and α 2 contributions to the line intensity and the doublet separation expressed in terms of the diffraction angle or of a related variable in the reciprocal space. Optimization of these two parameters, with a proper evaluation of the error, clearly shows the statistical nature of the oscillations appearing on the high‐angle side of the pure α 1 component after correction; their elimination by polynomial smoothing can therefore be performed and a procedure is suggested for achieving this result. A computer program, based on these principles, has been written and tested in many practical cases.