The rule of four: anomalous distributions in the stoichiometries of inorganic compounds

npj Computational Materials volume  10, Article number: 73 (2024 ) Cite this article

Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space. We highlight here the anomalous abundance of inorganic compounds whose primitive unit cell contains a number of atoms that is a multiple of four. This occurrence—named here the rule of four—has to our knowledge not previously been reported or studied. Here, we first highlight the rule’s existence, especially notable when restricting oneself to experimentally known compounds, and explore its possible relationship with established descriptors of crystal structures, from symmetries to energies. We then investigate this relative abundance by looking at structural descriptors, both of global (packing configurations) and local (the smooth overlap of atomic positions) nature. Contrary to intuition, the overabundance does not correlate with low-energy or high-symmetry structures; in fact, structures which obey the rule of four are characterized by low symmetries and loosely packed arrangements maximizing the free volume. We are able to correlate this abundance with local structural symmetries, and visualize the results using a hybrid supervised-unsupervised machine learning method.

Computational materials discovery is a fast-growing discipline leading to innovation in many fields. Within a specific technological sector (i.e., communications, renewable energies, medical), the choice of material is critical for the long-lasting success of the given product. Therefore, it is important—and of fundamental interest—to efficiently identify materials’ structural and energetic characteristics through materials’ data analysis to select structures for innovative applications. The emerging field of materials informatics has demonstrated its potential as a springboard for materials development, alongside first-principles techniques such as density-functional theory (DFT)1,2. The increase in computational power, together with large-scale experimental3 and computational high-throughput studies4, is paving the way for data-intensive, systematic approaches to classify materials’ features and to screen for optimal experimental candidates. In addition, the collection of statistical methods offered by machine learning (ML) has accelerated these efforts, both within fundamental and applied research5,6,7,8,9,10.

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