Stacking fault energies in the AlNbTaTiV BCC high entropy alloy, calculated using density functional theory and analyzed with inferential statistics

Due to their unusual structure and composition, BCC high entropy alloys (HEAs) are generally refractive and have favorable properties such as high service temperatures, strength, and ductility, making them desirable for high performance applications. In the present work, first-principles calculations using density functional theory were used to analyze stacking fault energies (SFE) in the AlNbTaTiV BCC HEA system. Special quasi-random structures and the GGA-PBE exchange correlation functional were used. “Twinning-sense” and “non-twinning-sense” stacking faults on the (112) plane, with ABCDEFA stacking, were investigated. Additionally, a method for predicting the error bars on calculations from the approximations to a random solution based on inferential statistics was introduced and analyzed. Quinary calculations show excellent results for HEA SFE calculations with ranges and ratios comparable to the verified single element SFE values. Inferential statistics and sampling are introduced to deal with the large number of possible permutations, 120 for a quinary. Inferential statistics allows the properties of the total population to be predicted from a sample set of calculations. The results indicate that a sample of only 20 values are required for precise calculations. Inferential statistics are then used to place predictive error bars on the HEA SFE calculations and sampling procedure. All sample SFE values were well within the predictive error bars when compared to the SFE calculated from the total population.