Scientists are normally happy to find regularities and correlations in their data – but only if they can explain them. Otherwise, they worry that those patterns might just be revealing some flaw in the data itself, so-called experimental artifacts.
That’s what scientists in Nicola Marzari’s group at the Swiss Federal Institute for Technology in Lausanne (EPFL) worried about when they noticed an unexpected pattern in two widely used databases of electronic structures, the Materials Project (MP) database and the Materials Cloud 3-dimensional crystal structures ‘source’ database (MC3Dsource).
The two collections include over 80,000 electronic structures of experimental as well as predicted materials, and in principle, all types of structures should be equally represented. But scientists noticed that around 60 percent of structures in both databases have primitive unit cells (the smallest possible cell in a crystal structure) made out of a multiple of 4 atoms. The scientists named this recurrence the “Rule of Four” and started looking for an explanation.
Initial Investigations
“A first intuitive reason could come from the fact that when a conventional unit cell (a larger cell than the primitive one, representing the full symmetry of the crystal) is transformed into a primitive cell, the number of atoms is typically reduced by four times,” says Elena Gazzarini, a former INSPIRE Potentials fellow in the Laboratory of Theory and Simulation of Materials (THEOS) at EPFL and now at DOI: 10.1038/s41524-024-01248-z