Homometric structures

Short description: Type of crystal structures

In chemistry and crystallography, crystal structures that have the same set of interatomic distances are called homometric structures.[1] Homometric structures need not be congruent (that is, related by a rigid motion or reflection). Homometric crystal structures produce identical diffraction patterns; therefore, they cannot be distinguished by a diffraction experiment.

Recently, a Monte Carlo algorithm was proposed to calculate the number of homometric structures corresponding to any given set of interatomic distances.[2]

* Example of two homometric structures (top) formed by the convolution between two non-centrosymmetric structures (bottom) with different orientations.

## See also

* Patterson function
* Arthur Lindo Patterson

## References

1. ↑ Patterson, A.L. (1939). "Homometric Structures". Nature 143 (3631): 939–940. doi:10.1038/143939b0. Bibcode: 1939Natur.143..939P.
2. ↑ Gommes C.J.; Jiao Y; Torquato S (2012). "Density of States for a Specified Correlation Function and the Energy Landscape". Phys. Rev. Lett. 108 (8): 080601. doi:10.1103/PhysRevLett.108.080601. PMID 22463509. Bibcode: 2012PhRvL.108h0601G.

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