Nature is made of laws. Investigating them is the task of science, but obviously it is not always easy to explain their existence. A good example comes from a recently published study by researchers at the Federal Institute of Technology in Zurich, which describes a curious regularity discovered by its authors in the world of inorganic matter. As they explain on the pages of npj Computational Materials, in fact, most inorganic compounds have at their base a minimal structure, or rather a primitive cell, composed of a number of atoms that is a multiple of four. A discovery that could have important repercussions in the world of solid state physics, if someone in the future manages to understand why.
The intuition for the authors of the study came from the analysis of two databases that contain the crystalline structures of more than 80 thousand inorganic compounds: 60% of the compounds in question, in fact, obey what the researchers decided to call “rule of four” (rule of four), that is, they have a primitive cell – the smallest unit that repeats within their crystalline structure – composed of a number of atoms that is a multiple of four.
For specialists in the physics of matter, such a regularity represents a very tempting opportunity. Explaining the reason could in fact help to understand some essential properties that arise from this atomic configuration, and therefore, ultimately, to improve the ability to design new materials.
For this reason, Swiss researchers have tried various ways to find an explanation for the rule of four. First they checked the software used for their analyzes of the materials for errors, but found none. Then a physical or chemical law that could explain it, again without result. So they relied on an algorithm designed to group the compounds under investigation based on similarities between their atomic properties, and again this did nothing.
Using a machine learning algorithm, the researchers then asked the program to predict which of the compounds within the two databases followed the rule of four, obtaining correct answers 87% of the time. This means that there must actually be an explanation, a property of compounds that allows us to predict the presence of primitive cells multiples of four. As always in machine learning, the program is able to identify regularities, but not to explain to us which regularities it has identified. And so the search for an explanation, for now, continues.