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.

为什么具有特定特性的材料比其他材料更丰富？这是材料科学中的一个基本问题，鉴于组成和构型空间的巨大性，传统上很难解决这个问题。我们在此强调无机化合物的异常丰度，其原始晶胞包含的原子数量是四的倍数。据我们所知，这种现象（此处称为“四法则” ）以前从未被报道或研究过。在这里，我们首先强调该规则的存在，尤其是在将自己限制于实验已知的化合物时尤其值得注意，并探索其与从对称性到能量的晶体结构的既定描述符的可能关系。然后，我们通过查看全局（堆积配置）和局部（原子位置的平滑重叠）性质的结构描述符来研究这种相对丰度。与直觉相反，过多的结构与低能量或高对称性结构无关。事实上，遵循四法则的结构的特点是低对称性和松散排列，从而最大化自由体积。我们能够将这种丰度与局部结构对称性相关联，并使用混合监督-无监督机器学习方法将结果可视化。