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