Prediction model of elastic constants of BCC high-entropy alloys based on first-principles calculations and machine learning techniques

By combining first-principles electronic structure calculations and machine learning techniques, prediction models of elastic constants are constructed for BCC high-entropy alloys (HEA) containing 5 different elements chosen from 3d, 4d and 5d transition metals with equal concentration. Three independent elastic constants of randomly selected 2555 HEAs are calculated by using the full potential Korringa–Kohn–Rostoker (FPKKR) method with taking configurational disorder into account within the coherent potential approximation (CPA). From the obtained database of the elastic constants, prediction models are constructed by the linear regression using the descriptors generated by the linearly independent descriptor generation (LIDG) method. By optimizing the selection of descriptors based on the genetic algorithm (GA), prediction errors of 10.2 GPa, 4.5 GPa, 2.4 GPa and 7.7 GPa are achieved for bulk modulus $$B$$, shear moduli $$c{^{\prime}}$$, $${c_{44}}$$ and Young’s modulus $$E$$, respectively. By using the generated model we propose some HEAs with low $$E$$. It is well known that the magnitude of $$E$$ is closely related to the shape of the calculated density of states (DOS). This statement is reconfirmed within the BCC HEAs, i.e., HEAs with larger DOS at the Fermi level shows smaller Young’s modulus and vice versa.