Представлена новая модель для прогнозирования твердости материалов.

The findings of the research are presented in the journal Physical Review Materials. Hardness is a crucial property of materials that determines their ability to resist deformation and other damage (such as dents and scratches) caused by external forces. Typically, hardness is assessed by pressing an indenter into the test sample, where the indenter must be made of a harder material, usually diamond.

In this context, hardness is defined based on the relationship between the maximum indentation force and the impression left on the sample. Modern industry requires new hard and superhard materials with enhanced mechanical properties compared to traditional materials. One solution to this challenge is the use of contemporary computational methods for high-throughput screening of materials with improved characteristics.

“Today, computational methods are sufficiently advanced to accurately predict the structure and properties of various compounds and materials. However, it is essential not only to predict the material's structure but also to accurately calculate its mechanical properties, such as hardness, which are necessary for the experimental synthesis of materials with predetermined characteristics.

Existing empirical models for predicting hardness are based on the strength of chemical bonds, the degree of ionicity, the electronegativity of crystals, and the elastic moduli of materials. We have proposed a simple and accurate model based on material properties such as the shear modulus and the derivative of the bulk modulus with respect to pressure. Both properties can be obtained through experiments or atomistic modeling,” explained Faridun Jalolov, the first author of the study and a graduate student in the “Materials Science” program at Skoltech.

The importance of utilizing the shear modulus in the hardness model arises from its dependence on the directions of deformation within the crystalline structure—this enabled the calculation of the spatial dependence of hardness for a range of materials, taking into account the anisotropy of crystal structures. The derivative of the elastic modulus with respect to pressure, derived from the equation of state, allowed for the consideration of temperature's impact on hardness.

“We demonstrated that the hardness model works for hard and superhard materials using examples of rhenium diboride (ReB₂) and boron carbide (B₄C). The obtained temperature dependence of hardness aligns well with existing experimental measurements and predictions from machine learning-based models. All parameters in our model can be directly obtained from calculations or experiments, making the model suitable for practical application,” added Alexander Kvashnin, a professor at the Skoltech Energy Transition Project Center, co-author, and scientific supervisor of the work.