Science.-Electronic materials follow a ‘rule of four’ without explanation

MADRID, 19 (EUROPA PRESS)

Scientists have discovered an unexpected “rule” followed by 60 percent of electronic structures included in large computational and experimental materials databases.

Specifically, it has been observed that its primitive unit cells are made of multiples of four atoms.

Scientists have put forward many different explanations, considering the role of specific chemical elements as well as formation energy and symmetry, but a convincing one has yet to be found. Still, scientists could use an algorithm to predict with great accuracy whether a given compound will follow the rule of four or not.

This puzzling issue was detected by Nicola Marzari’s group at the Swiss Federal Institute of Technology in Lausanne (EPFL) when they noticed an unexpected pattern in two widely used electronic structures databases: Materials Project (MP) and Materials Cloud 3-dimensional crystal structures ‘source’ (MC3Dsource).

Both include more than 80,000 electronic structures from experimental and predicted materials and, in principle, all types of structures should be equally represented. However, the scientists noted that about 60 percent of the structures in both databases have primitive unit cells (the smallest possible cell in a crystal structure) composed of a multiple of 4 atoms. Scientists called this recurrence the rule of four and began searching for an explanation.

“A first intuitive reason could come from the fact that when a conventional unit cell (a cell larger than the primitive one, representing the complete symmetry of the crystal) is transformed into a primitive cell, the number of atoms is generally reduced four times” , says in a statement from the Swiss National Center of Competence in Research (MARVEL) Elena Gazzarini, former INSPIRE Potentials fellow at the Materials Theory and Simulation Laboratory (THEOS) at EPFL and now at CERN in Geneva.

“The first question we asked was whether the software used to ‘primitivize’ the unit cell had done it correctly, and the answer was yes.”

From a chemical point of view, another possible suspect was silicon’s coordination number (the number of atoms that can bond to its atom), which is four. “We might expect to find that all materials that follow this Rule of Four include silicon,” says Gazzarini. “But again, they didn’t.”

The formation energies of the compounds could not explain the rule of four either. “The most abundant materials in nature should be the most energetically favored, that is, the most stable, those with negative formation energy,” says Gazzarini. “But what we saw with classical computational methods was that there was no correlation between the Rule of Four and negative formation energies.”

Because the material space covered by the two databases is enormous, from small units to very large cells with dozens of different chemical species, there was still the possibility that a more refined analysis looking for a correlation between formation energies and chemical properties may provide an explanation.

Thus, the team included Rose Cernosky, a machine learning expert at the University of Wisconsin, who developed an algorithm to group structures according to their atomic properties and observe formation energies within classes of materials that share some chemical similarities. But again, this method did not provide a way to distinguish materials that met the Rule of Four from those that did not.

Similarly, the abundance of multiples of four does not even correlate with highly symmetric structures but rather with low symmetries and loosely packed arrangements.

In the end, the resulting paper in npj Computational Materials is a rare example of a scientific paper describing a negative result: the researchers could only describe the phenomenon and rule out several possible causes, without finding any.

But negative results can be as important as positive ones for scientific advancement, because they point out difficult problems, which is why scientists often complain that journals should publish more such studies.

Failure to find a convincing explanation did not prevent the group from predicting, using a Random Forest algorithm, with an accuracy of 87% whether a given compound will follow the Rule of Four or not. “This is interesting because the algorithm uses only local rather than global symmetry descriptors, suggesting that there may be small chemical groups in cells (yet to be found) that can explain the rule of four,” says Gazzarini.