Comment on Probability density functions of the average and difference intensities of Friedel opposites by Shmueli & Flack (2010)

Olczak, A.

doi:10.1107/S0108767311007896

Figure 2
(a) Three atoms represented by small circles and their interatomic vectors, $[{\bf R}_{jk}]$ . Movement of atom 3 to position $[{3^\prime}]$ causes a change of two vectors: $[{\bf R}_{13}]$ and $[{\bf R}_{23}]$ , which means that interatomic vectors $[{\bf R}_{13}]$ and $[{\bf R}_{23}]$ are not independent. They always have to fulfil the relation $[{\bf R}_{12} + {\bf R}_{23} + {\bf R}_{31} = 0]$ . (b) Possible collection of three randomly generated vectors. These vectors fulfil the condition $[{\bf R}_{12} + {\bf R}_{23} + {\bf R}_{31} = 0]$ and, consequently, there exists an arrangement of three atoms (the structure) for which these vectors can be interpreted as interatomic vectors [see part (a)]. (c) Another possible collection of three vectors generated randomly. These vectors do not fulfil the relation $[{\bf R}_{12} + {\bf R}_{23} + {\bf R}_{31} = 0]$ and consequently there is no configuration of three atoms for which these vectors could be interpreted as interatomic vectors. This means that they cannot be expressed as $[{\bf R}_{12} = {\bf r}_{1} - {\bf r}_{2}]$ , $[{\bf R}_{23} = {\bf r}_{2} - {\bf r}_{3}]$ , $[{\bf R}_{31} = {\bf r}_{3} - {\bf r}_{1}]$ , where $[{\bf r}_j]$ represent atom positions. These vectors should not contribute to D_E and A_E histograms, because they are not associated with any arrangement of atoms in the unit cell.

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ISSN: 2053-2733

Volume 67| Part 3| May 2011| Pages 315-317

https://doi.org/10.1107/S0108767311007896

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