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
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 dhkl 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 dobs'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 dobs'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 dhkl'
s is quite high.
Burger; K., Prandl, W. Z. Kristallogr., 212,
493-505 (1997).