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January 23, 2026npj Computational Materials0 citationsOpen Access

A possible explanation for the Rule of Four in Inorganic Materials

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RPRobert G. Palgrave

Key Points

  • This research aims to explain the observed 'rule of four' in the number of atoms in primitive unit cells of inorganic materials.
  • Analyzed large databases of inorganic materials
  • Calculated the relationship between formula unit counts and unit cell structure
  • Identified most probable values for the number of formula units per primitive cell
  • Found that the number of atoms in a primitive unit cell tends to favor multiples of four
  • Demonstrated statistical backing for observed patterns
  • Provided insights into the structural tendencies of inorganic materials

Abstract

Abstract Recently, Gazzarrini et al. observed a ‘rule of four’, where the number of atoms in a primitive unit cell for inorganic materials taken from large databases has been observed to favour multiples of four 1 . The number of atoms in a primitive cell is given by the product of the number of atoms in a formula unit (n F ) and the number of formula units per primitive cell (Z). Here it is shown the rule of four can be explained by taking into account the most probable values of n F and Z in inorganic materials datasets.

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Cite This Study

Robert G. Palgrave (2026) studied this question.

synapsesocial.com/papers/69731047c8125b09b0d1ffa5https://doi.org/10.1038/s41524-025-01937-3
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