Skoltech Researchers Proposed A New Model For Predicting Hardness Of Materials

Moscow, 16 January 2025

Skoltech researchers have presented a new simple physical model for predicting the hardness of materials based on information about the shear modulus and equations of state of crystal structures. The model is useful for a wide range of practical applications — all parameters in it can be determined through basic calculations or measured experimentally. The results of the study are presented in the Physical Review Materials journal.

Hardness is an important property of materials that determines their ability to resist deformations and other damages (dents, scratches) due to external forces. It is typically determined by pressing the indenter into the test sample, and the indenter must be made of a harder material, usually diamond. In this case, the hardness is determined based on the ratio between the maximum indentation force and the imprint that remains on the sample. Modern industry needs new hard and superhard materials with improved mechanical properties compared to traditional materials. One of the solutions to this problem is the use of modern computational methods for high-throughput search (screening) of materials with improved properties.

“Today, computational methods are sufficiently advanced to accurately predict the structure and properties of various compounds and materials. However, it is important not only to predict the structure of a material, but also to accurately calculate its mechanical properties, such as hardness, which are necessary for the experimental synthesis of a material with predefined properties. The existing empirical models for predicting hardness are based on the strength of chemical bonds, the degree of ionization, the electronegativity of crystals, and the elastic moduli of materials. We proposed a simple and accurate model based on material properties such as the shear modulus and pressure derivative of bulk modulus. Both properties can be obtained through experiments or atomistic simulations,” said the lead author of the work, Faridun Jalolov, a PhD student in the Materials Science and Engineering program at Skoltech.

The shear modulus is important in the hardness model because it depends on the direction of deformation of the crystal structure, which enabled the authors to calculate the spatial dependence of hardness for a number of materials with the anisotropy of the crystal structure in mind. By obtaining the pressure derivative of bulk modulus from the equation of state, the team took into account the impact of temperature on hardness.

“We used the examples of rhenium diboride (ReB2) and boron carbide (B4C) to demonstrate that the hardness model works for hard and superhard materials. The hardness obtained is consistent with the experimental measurements and predictions made by machine learning models. All values in our model can be obtained directly from calculations or experiments, so the model is suitable for practical use,” added Professor Alexander Kvashnin from the Skoltech Energy Transition Center, a co-author and the scientific supervisor of the study.

About Skoltech

Skoltech is a private international university in Russia, cultivating a new generation of leaders in technology, science, and business. As a factory of technologies, it conducts research in breakthrough fields and promotes technological innovation to solve critical problems that face Russia and the world. Skoltech focuses on six priority areas: life sciences, health, and agro; telecommunications, photonics, and quantum technologies; artificial intelligence; advanced materials and engineering; energy efficiency and the energy transition; and advanced studies. Established in 2011 in collaboration with the Massachusetts Institute of Technology (MIT), Skoltech was listed among the world’s top 100 young universities by the Nature Index in its both editions (2019, 2021). On Research.com, the Institute ranks as Russian university No. 2 overall and No. 1 for genetics and materials science. In the recent SCImago Institutions Rankings, Skoltech placed first nationwide for computer science. Website: https://www.skoltech.ru/.

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