Bilbao Crystallographic Server Structure Utilities Help COMPSTRU

Comparison of crystal structures of the same symmetry [COMPSTRU]

Often a quantitative comparison of two structural models of the same phase, coming from different sources, is difficult because the models, although postulating the same space group symmetry, are described using different sets of atoms in the asymmetric unit, or different equivalent choices of origin or cell orientations. The program COMPSTRU compares two structure descriptions of the same compound characterizing the similarity of the two structure models by different quantitative descriptors.

First, the program transforms the Structure 2 to the most similar configuration of Structure 1. The difference between the two models is quantified by evaluation of (i) the global distortion decomposed into a spontaneous strain (lattice deformation) and atomic displacement field representing the distances between the pared atoms of the two structures; (ii) the measure of similarity as introduced by Bergerhoff (Bergerhoff et al., 1999).

The determination of the transformation matrix that transforms Structure 2 to the most similar configuration to Structure 1 is done in two steps:

  1. If originally the two structural models are referred to settings (although standard) that differ in the choice of the unit cell (with axes interchanged in the orthorhombic case or more general cell transformations in the case of monoclinic or triclinic structures), the program searches for a transformation that maps best the lattice parameters of Structure 2 to those of Structure 1. The transformation should belong to the affine normaliser of the structure space group.

  2. The transformation of the modified Structure 2 to the most similar configuration of Structure 1 is determined by the best pairings of the atomic positions of the two structures. The program uses the Euclidean normalizer of the common space group for exploring all possible equivalent descriptions of the (modified in Step (i)) structure 2.

The initial structures should be described with respect to the standard (default) settings of the structure space group. If transformation of the structures into standard settings is necessary, then the program SETSTRU on this server can be used.

The program is also helpful for the recognition of similar atomic arrangements of different compounds that is essential for the classification of crystal structures into isoconfigurational structure types.

Bilbao Crystallographic Server
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