UNRAVELLING POWDER DIFFRACTION PATTERNS - ISOMORPHOUS REPLACEMENTS, CENTRAL ROWS AND SOME WARNING IN THE TRICLINIC CASE

G. Ferraris¹, A. Pavese² and M. Prencipe¹

¹Dpt. Sci. Mineral. Petrol., Univ. Torino, Italy - ferraris@dsmp.unito.it
²Dpt. Sci.Terra, Univ. Milano, Italy

Keywords: Powder patterns, indexing, isomorphous replacements, central rows

The contribution deals with (i) information which can be obtained by comparing patterns from substituted compounds and (ii) some problems which can arise in indexing triclinic powder diffraction patterns

Isomorphous replacements

An anisotropic effect which modifies the lattice dimensions can be used to detect the subset of reflections which in a powder diffraction pattern belong to the same central row because Dd/d is peculiar and constant along each of such rows, i.e. along a row with indexes nhnknl. In general, the changes in position and intensity shown by the Bragg reflections belonging to the patterns of two different members of an isomorphous series are useful for obtaining hints to index and unfold. If the isomorphous replacement takes place in a special crystallographic site which contributes only to reflections with peculiar parities of the indexes, an analysis of the largest changes in intensities can lead to detect such type of reflections. Besides, the variation of intensities produced by isomorphous replacements can be used for structure determination according to the method indicated by Burger and Prandl (1997) for anomalous scattering in the case of powder data. Simulated powder patterns of olivine, (Fe, Mg)₂SiO₄, are discussed as an example.

Triclinic patterns

Because of experimental errors, in the indexing of a triclinic powder pattern the discrimination between two cells which differ only for having supplementary angles (type I and type II cells) might meet some difficulties in the following cases: (a) reflections with at least one index null are dominant in the large d_hkl region or/and (b) one interaxial angle is close to 90°. In case (a), e.g. for l = 0, d*_hk0 = (h²a*² + k²b*² + 2hka*b*cos g*)^1/2 can exactly match the relevant d_obs's both with all positive indexes and g* > 90° and with one negative index and g*  < 90°. In case (b), e.g. if a*~ 90°, d*_hkl (h²a*² + k²b*² + l²c*² + 2hla*c*cos b* + 2hka*b*cos g*)^1/2 can match, within experimental errors, the relevant d_obs's both for positive h with b* and g* > 90°, and negative h, with (b*)' = 180° - b* < 0 and (g*)' = 180° - g* < 0. In the described cases, a (low-accuracy) powder diffraction pattern has some chance to be acceptably indexed both with a type I and a type II cell. In fact, since in a triclinic lattice 9 independent reflections with indexes only equal to ±1 or 0 (at least one) are possible, and the total grows up to 24 if one index with values ±2 is allowed, the chance that no general hkl reflections are present in the crucial subset of the 15-20 largest d_hkl' s is quite high.

Burger; K., Prandl, W. Z. Kristallogr., 212, 493-505 (1997).