[Image above] Superhard materials are in high demand for many industrial applications, such as the diamond-coated drill bits above. Data-driven approaches to materials discovery can help identify new superhard materials. Credit: Junkyardsparkle, Wikimedia (CC0 1.0)

When it comes to developing new materials, the process is traditionally slow and painstaking. Yet in the past decade, development of new materials has advanced rapidly, due in large part to increased use of data-driven approaches to materials discovery.

Data-driven approaches to materials discovery augment existing experimental methods by identifying promising compositions to explore, thus reducing the number of samples that must be experimentally made and tested before finding a desirable composition. Previous studies covered on CTT have used such methods to identify materials based on their phase stability and glass transition temperature, among other properties.

One material property that researchers have tried to predict using data-driven approaches is hardness. Superhard materials, or materials with hardness above 40 GPa, are in high demand for many industrial applications, including cutting, drilling, and polishing technologies.

Over the past several decades, researchers have devoted significant efforts to developing superhard materials. (Diamond remains the hardest known material to date, though.) And data-driven approaches are used regularly in these efforts.

Last year, Skolkovo Institute of Science and Technology full professor Artem R. Oganov co-wrote an overview article with senior research scientist Alexander Kvashnin and doctoral candidate Zahed Allahyari on the use of computational models to help identify possible superhard materials in the past few years. Notably, none of these models calculate hardness and fracture toughness directly from the crystal structure.

“Unfortunately, there are no accurate theoretical models that could be used to calculate the hardness and fracture toughness from the crystal structure,” Oganov and doctoral candidate Efim Mazhnik write in a new paper. “The main reason is that the underlying physical principles are complex and include both elastic and plastic effects. Another reason is that the properties itself are ill-defined and can depend on the different experimental factors including the applied load, surface roughness, concentration of defects in the sample, loading time, shape of the indenter, degree of elastic recovery, etc.”

Instead of crystal structure, models use other properties of the crystal to estimate hardness and fracture toughness—such as elastic properties, which are the basis for a model Oganov and Mazhnik described in a September 2019 paper they published following the overview article.

In that paper, they explain previous models used elastic properties to estimate hardness, but the specific elastic properties chosen for those models led to limitations. Instead, Oganov and Mazhnik used Young’s modulus E and Poisson’s ratio ν because “these properties are less correlated with each other and thus expected to form simpler expressions.”

They concluded their new model had very good agreement with experimental results. However, using the model to screen large databases was difficult because, in cases where elastic property values needed to be determined through quantum mechanical calculations, the process was time-consuming.

To speed up the process, Oganov and Mazhnik explored combining their elastic properties-based model with machine learning. And their recently published paper on this attempt did more than speed up the process—it opened a doorway to develop a model that allows direct calculation of hardness and fracture toughness from the crystal structure.

In the recent paper, Oganov and Mazhnik note that the main idea of machine learning models is to use a dataset with already known values and to expand it to unknown data. “By passing the dataset through the model, we can optimize its internal parameters to reduce the error and to obtain reasonable results,” they write.

In their case, they wanted to expand from calculating hardness and fracture toughness values for crystal structures with known elastic properties to crystal structures for which the elastic properties were unknown. To do so, they trained a neural network to predict Young’s modulus and Poisson’s ratio from crystal structure using information from the database of crystal structures by The Materials Project obtained via the Python Materials Genomics package. From there, they input the predicted values into their elastic properties-based model to estimate hardness and fracture toughness.

After performing checks to verify the accuracy of both predicted elastic property values and the estimated hardness and fracture toughness, the researchers used their model to estimate hardness and fracture toughness for crystals structures with unknown elastic properties.

The model predicted more borides would be superhard than carbides or nitrides, “confirming conclusions of Ref. 2 that very hard materials are more likely to be found among metal borides than metal carbides or nitrides.” Though some of the suggested superhard structures were likely untrue due to underrepresentation of similar crystal structures in the database, overall many of the structures looked promising, suggesting “this method can be used with other data or algorithms to produce even better results.”

In an email, Oganov says their new model is not the first to allow a direct calculation of hardness and fracture toughness from crystal structure. “But the combination of speed and reliability is remarkable,” he says.

Oganov says they want to develop the model more so the neural network can predict the entire elastic constants tensor (not just averaged moduli), and the same for hardness and fracture toughness. In addition, Oganov says these machine learning models “can and will be incorporated into USPEX, to enable superquick prediction of these properties.”

USPEX is the acronym for the Universal Structure Predictor: Evolutionary Xtallography, a novel method for computational materials discovery being developed in Oganov’s laboratory since 2004. The acronym is a play off the Russian word “uspekh,” which means “success.” The USPEX code, which allows researchers to predict crystal structure by knowing only the chemical composition of a material, has so far lived up to its name—more than 6,000 researchers worldwide use the code today, according to the laboratory website.

The 2019 paper, published in Journal of Applied Physics, is “A model of hardness and fracture toughness of solids” (DOI: 10.1063/1.5113622).

The 2020 paper, published in Journal of Applied Physics, is “Application of machine learning methods for predicting new superhard materials” (DOI: 10.1063/5.0012055).