Difference between revisions of "Structure Similarity"
(→Examples) |
(→Examples) |
||
Line 37: | Line 37: | ||
* Diamond ([https://materialsproject.org/materials/mp-66 mp-66]) vs. Rocksalt ([https://materialsproject.org/materials/mp-22862 mp-22862]) <math>\rightarrow</math> ''d'' = 1.4 | * Diamond ([https://materialsproject.org/materials/mp-66 mp-66]) vs. Rocksalt ([https://materialsproject.org/materials/mp-22862 mp-22862]) <math>\rightarrow</math> ''d'' = 1.4 | ||
− | * Diamond ([https://materialsproject.org/materials/mp-66 mp-66]) vs. Perfect | + | * Diamond ([https://materialsproject.org/materials/mp-66 mp-66]) vs. Perfect CaTiO<sub>3</sub> Perovskite ([https://materialsproject.org/materials/mp-5827 mp-5827]) <math>\rightarrow</math> ''d'' = 1.4 |
− | * Rocksalt ([https://materialsproject.org/materials/mp-22862 mp-22862]) vs. Perfect | + | * Rocksalt ([https://materialsproject.org/materials/mp-22862 mp-22862]) vs. Perfect CaTiO<sub>3</sub> Perovskite ([https://materialsproject.org/materials/mp-5827 mp-5827]) <math>\rightarrow</math> ''d'' = 1.1 |
== References == | == References == |
Revision as of 00:00, 8 March 2018
Contents
Introduction
The similarity between two structures i and j is assessed on the basis of local coordination information from all sites in the two structures. [1] [2]
Site Fingerprints
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.
Structure Fingerprints
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:
Structure Distance
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.
Examples
References
- ↑ 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)
Authors
Nils Zimmermann, Donny Winston