Material Hardness Descriptor Derived by Symbolic Regression
Hardness is a materials' property with implications in several industrial fields, including oil and gas, manufacturing, and others. However, the relationship between this macroscale property and atomic (i.e., microscale) properties is unknown and in the last decade several models have unsuccessfully tried to correlate them in a wide range of chemical space. The understanding of such relationship is of fundamental importance for discovery of harder materials with specific characteristics to be employed in a wide range of fields. In this work, we have found a physical descriptor for Vickers hardness using a symbolic-regression artificial-intelligence approach based on compressed sensing. SISSO (Sure Independence Screening plus Sparsifying Operator) is an artificial-intelligence algorithm used for discovering simple and interpretable predictive models. It performs feature selection from up to billions of candidates obtained from several primary features by applying a set of mathematical operators. The resulting sparse SISSO model accurately describes the target property (i.e., Vickers hardness) with minimal complexity. We have considered the experimental values of hardness for binary, ternary, and quaternary transition-metal borides, carbides, nitrides, carbonitrides, carboborides, and boronitrides of 61 materials, on which the fitting was performed. The found descriptor is a non-linear function of the microscopic properties, with the most significant contribution being from a combination of Voigt-averaged bulk modulus, Poisson's ratio, and Reuss-averaged shear modulus. Results of high-throughput screening of 635 candidate materials using the found descriptor suggest the enhancement of material's hardness through mixing with harder yet metastable structures (e.g., metastable VN, TaN, ReN$_2$, Cr$_3$N$_4$, and ZrB$_6$ all exhibit high hardness).