The similarity calculation begins with computing a crystal site fingerprint, vsite, for each site in the two structures. The fingerprint is a 12-dimensional vector in which an element at position k (e.g., 4) provides the percentage of how much the given site should be considered k-fold coordinated (i.e., w(CN=4)):
So, we are testing the coordination percentages up to 12-fold coordination.
The fingerprints from sites in a given structure are subsequently statistically processed to yield the minimum, maximum, mean, and standard deviation of each coordination percentage. The resultant ordered vector defines a structure fingerprint, vstruct:
Finally, structure similarity is determined by the distance, d, between two structure fingerprints vistruct and vjstruct:
A small distance value indicates high similarity between two structures, whereas a large distance (around 1) suggests that the structures are very dissimilar. Note that the structure fingerprint vectors are normalized before calculating the distance measure.
- Diamond (mp-66) vs. GaAs (mp-2534) d = 0
- Diamond (mp-66) vs. Rocksalt (mp-22862) d = 1.4
- Diamond (mp-66) vs. Perfect CaTO3 Perovskite (mp-5827) d = 1.4
- Rocksalt (mp-22862) vs. Perfect CaTO3 Perovskite (mp-5827) d = 1.1
- N. E. R. Zimmermann, A. Jain, in preparation (2018)
- N. E. R. Zimmermann, M. K. Horton, A. Jain, M. Haranczyk, Front. Mater., 4, 34, (2017)
Nils Zimmermann, Donny Winston