First-principles study of the effect of Al and Hf impurities on Co 3 W antiphase boundary energies

The effects of Al and Hf impurities on the (111) antiphase boundary (APB) energy of metastable FCC Co 3 W are investigated via ab initio calculations. Cluster expansions are used to predict the total energies of supercells containing non-dilute concentrations of impurities using Monte Carlo simulations at relevant temperatures, giving APB energies as a function of impurity concentration and temperature for each ternary system. The cluster expansions are validated by comparing with direct energy calculations of supercells of pure L1 2 Co 3 W and the effects of each impurity are compared. Two sets of compositions are explored for each system — constant ratio (constant ratio between Co and W) and sacrificial W (constant Co). It is found that sacrificial W compositions stabilize the L1 2 structure over a wider range of compositions than constant ratio compositions (given the restriction to the FCC lattice) in both systems and should be preferred. In sacrificial W compositions, Hf increases the APB energy far more than Al, particularly at higher concentrations of the impurity, and both systems exhibit little variation with respect to temperature. It is further shown that at higher concentrations of Hf, and most noticeably for Co 3 (W 0.5 Hf 0.5 ), Hf and W tend to segregate into alternating planes, unlike the corresponding Co 3 (W 0.5 Al 0.5 ), which explains the different impacts of the two impurities on the APB energy. Finally, the ratio of (111) to (100) APB energies is studied for sacrificial W compositions to understand cross slip behavior in both ternary systems.