Data-driven discovery of ultraincompressible crystals from a universal correlation between bulk modulus and volumetric cohesive energy.

Bulk modulus and cohesive energy are two important quantities of condensed matter. From the interatomic energy landscape, we here derived a correlation between the bulk modulus (B) and the volumetric cohesive energy (ρe), i.e.B= 2(ln2)2ρe/9ϵs2=kρe, whereϵsandkare the strain-to-failure of interatomic bonds and the factor of proportionality, respectively. By analyzing numerous crystals from first principles calculations, it was shown that this correlation is universally applicable to various crystals including simple substances and compounds. Most interestingly, it was found thatϵsof crystals with a similar structure are almost a constant, resulting in a linear relationship betweenBandρe. Furthermore, we found that the value ofkfor any compound can be determined based on the rule of mixtures, i.e.k= ∑xiki, wherexiandkiare the atomic fraction and the factor of proportionality for each element in this compound, respectively. Finally, this correlation was used to predict the bulk moduli for a vast number of crystals with knownρein databases. After first principles verification of the top 50 crystals with the highest predicted bulk modulus, 25 ultraincompressible crystals with a bulk modulus greater than 400 GPa that can rival diamond (436 GPa) were discovered.

Atomic stiffness for bulk modulus prediction and high-throughput screening of ultraincompressible crystals.

Determining bulk moduli is central to high-throughput screening of ultraincompressible materials. However, existing approaches are either too inaccurate or too expensive for general applications, or they are limited to narrow chemistries. Here we define a microscopic quantity to measure the atomic stiffness for each element in the periodic table. Based on this quantity, we derive an analytic formula for bulk modulus prediction. By analyzing numerous crystals from first-principles calculations, this formula shows superior accuracy, efficiency, universality, and interpretability compared to previous empirical/semiempirical formulae and machine learning models. Directed by our formula predictions and verified by first-principles calculations, 47 ultraincompressible crystals rivaling diamond are identified from over one million material candidates, which extends the family of known ultraincompressible crystals. Finally, treasure maps of possible elemental combinations for ultraincompressible crystals are created from our theory. This theory and insights provide guidelines for designing and discovering ultraincompressible crystals of the future.