Evolutionary search for novel superhard materials: Methodology and applications to forms of carbon and TiO2

TL;DR

This paper introduces an advanced evolutionary algorithm-based method for predicting the hardest crystal structures in specific chemical systems, successfully identifying near-diamond hardness carbon forms and establishing hardness limits for TiO2 polymorphs.

Contribution

The authors developed a novel prediction methodology combining USPEX with an electronegativity-based hardness model, bond-valence, and graph theory, enabling accurate hardness predictions for complex crystal structures.

Findings

Identified low-energy carbon structures with hardness close to diamond.

Demonstrated TiO2 cannot surpass 17 GPa hardness in any polymorph.

Validated the method's effectiveness in predicting superhard materials.

Abstract

We have developed a method for prediction of the hardest crystal structures in a given chemical system. It is based on the evolutionary algorithm USPEX (Universal Structure Prediction: Evolutionary Xtallography) and electronegativity-based hardness model that we have augmented with bond-valence model and graph theory. These extensions enable correct description of the hardness of layered, molecular, and low-symmetry crystal structures. Applying this method to C and TiO2, we have (i) obtained a number of low-energy carbon structures with hardness slightly lower than diamond and (ii) proved that TiO2 in any of its possible polymorphs cannot be the hardest oxide, its hardness being below 17 GPa.