A.I. Improves the Search for Next Generation Superhard Materials


Hardness is a critical mechanical property for modern applications. Traditionally, empirical design rules based on known materials such as diamond have been employed to find superhard materials with Vickers hardness exceeding 40 GPa. Consequently, 3D network of high valence electron density and short covalent bonds can improve the material hardness as per the findings of the previous studies. Researchers have used these qualitative ideas together with quantitative computational methods like density functional theory (DFT) to discover new superhard materials. Despite the good progress, computational approaches are expensive, time-consuming, and generally impractical for some systems. The simple DFT-derived mathematical models also fail to correctly establish the relationships between material’s hardness property, physical and chemical structure, and chemical composition.

Recently, machine learning, a promising alternative that overcomes many of these limitations, was demonstrated to find new superhard materials by modeling their elastic moduli properties. Even though machine learning techniques are generally suitable for rapid material screening in terms of speed and accuracy, this approach relied on computational methods that only estimate the Vickers hardness as a single value. They also fail to accurately predict the response of materials to plastic deformation that yields hardness. In addition, due to the poor understanding of the underlying mechanism behind the indentation size effect, these machine learning approaches are less likely to accurately capture the material’s load-displacement response even if they accurately predict the hardness as a single load. This remains a key challenge in the design of superhard materials.

To address the challenges above, University of Houston researchers: Ms. Ziyan Zhang, Dr. Aria Mansouri Tehrani, Mr. Blake Day, and Professor Jakoah Brgoch, in collaboration with Professor Anton Oliynyk from the Manhattan College, proposed an ensemble machine-learning method capable of finding superhard materials by directly predicting the load-dependent Vickers hardness based only on chemical composition. “Our group is creating methods that circumvent the need for using proxies like elastic moduli as a stand-in for hardness. Instead, we are going right at predicting Vickers hardness,” Brgoch explained. They started by gathering sufficient training data, including 1062 experimentally measured load-dependent Vickers hardness and 532 unique compositions extracted from the literature alongside their chemical compositions. The data covered 59 elements excluding halogens, alkali metal and noble gases that are not common with materials analysis based on the Vickers micro-indentation. The model was tested by predicting the load-dependent hardness of eight different disilicides and then synthesizing and measuring the hardness to validate their approach. Finally, the trained model was used to screen for superhard materials from a sample of 66000 compounds in different crystal structure databases. The work is published in the research journal, Advanced Materials.

From the 66000 compounds examined, the team identified 68 materials that should exhibit a Vickers hardness exceeding 45 GPa at an applied for of 0.5N. Additionally, only ten materials exceeded 45 GPa at an applied load of 5N. “Superhard materials are incredibly rare, and these machine learning results prove it” the professor explained. It was worth noting that although the transition metal borocarbides are underexplored in the literature, they provide a promising space for finding new superhard materials. For instance, over ten thermodynamically suitable compositions with a potential hardness value above 40 GPa at 0.5N applied load were identified. “There is a lot of opportunity for borocarbides,” Brgoch said. “Now, we just need to make these materials in the laboratory.”

In summary, the authors demonstrated for the first time a new approach based on ensemble machine learning to find superhard materials by directly predicting Vickers hardness based only on chemical composition. Ensemble learning algorithms are appropriate for training because they are effective when dealing with small data sets and can maximize the speed at which phase space can be screened. As a result, the resultant model exhibited a reduced variance and bias and a quick turnaround for property prediction. Overall, the proposed ensemble machine learning model proved effective for screening new materials with outstanding properties even if the crystal structure is unknown. “Combining the scalability, transferability, and efficiency of machine learning, ensemble learning approaches would modernize material screening to search for new superhard materials,” Brgoch told Advances in Engineering,

About the author

Prof. Jakoah Brgoch is an Associate Professor in the Department of Chemistry and a Principal Investigator in the Texas Center of Superconductivity. Jakoah also has a courtesy appointment in the William A. Brookshire Department of Chemical and Biomolecular Engineering and he is a member of the Hewlett-Packard Enterprise Data Science Institute. Jakoah completed his bachelors and masters in Chemistry from Illinois State University followed by his Ph.D. from Iowa State University and Ames National Laboratory under the supervision of Gordon Miller followed by postdoctoral research at the University of California, Santa Barbara in the Materials Research Laboratory with Ram Seshadri.

Jakoah is now leading a multidisciplinary research group with research topics ranging from the development of persistent luminescent materials for bio-imaging to understanding the mechanical response in superhard materials all through a combination of materials synthesis, characterization, first-principles computation, and machine learning. He has published more than 85 peer-reviewed papers, earned a 2019 NSF CAREER research award, and is a 2020 Alfred P. Sloan Research Fellow in Chemistry.

About the author

Ms. Ziyan Zhang studied Macromolecules Materials and Engineering at Sun Yet-san University, where she obtained her bachelor’s degree in 2017. She is currently a Ph.D. student studying Inorganic Chemistry at the University of Houston in the Department of Chemistry, under the supervision of Prof. Jakoah Brgoch. Her main research focus is on applying machine-learning methods to model materials properties and guide the search of novel inorganic materials.



Zhang, Z., Mansouri Tehrani, A., Oliynyk, A., Day, B., & Brgoch, J. (2020). Finding the Next Superhard Material through Ensemble LearningAdvanced Materials, 33(5), 2005112.

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