Thermodynamic stability of Co-Al-W L1₂ γ′

Co-based superalloys in the Co-Al-W system exhibit coherent L1₂ Co₃(Al,W) γ′ precipitates in an face-centered cubic Co γ matrix, analogous to Ni₃Al in Ni-based systems. Unlike Ni₃Al, however, experimental observations of Co₃(Al,W) suggest that it is not a stable phase at 1173 K. Here, we perform an extensive series of density functional theory (DFT) calculations of the γ′ Co₃(Al,W) phase stability, including point defect energetics and finite-temperature contributions. We first confirm and extend previous DFT calculations of the metastability of L1₂ Co₃(Al _0.5W_0.5) γ′ at 0 K with respect to hexagonal close-packed Co, B2 CoAl and D0₁₉ Co₃W using the special quasi-random structure (SQS) approach to describe the Al/W solid solution, employing several exchange/correlation functionals, structures with varying degrees of disorder, and newly developed larger SQSs. We expand the validity of this conclusion by considering the formation of antisite and vacancy point defects, predicting defect formation energies similar in magnitude to Ni ₃Al. However, in contrast to the Ni₃Al system, we find that substituting Co on Al sites is thermodynamically favorable at 0 K, consistent with experimental observation of Co excess and Al deficiency in γ′ with respect to the Co₃(Al_0.5W _0.5) composition. Lastly, we consider vibrational, electronic and magnetic contributions to the free energy, finding that they promote the stability of γ′, making the phase thermodynamically competitive with the convex hull at elevated temperature. Surprisingly, this is due to the relatively small finite-temperature contributions of one of the γ′ decomposition products, B2 CoAl, effectively destabilizing the Co, CoAl and Co₃W three-phase mixture, thus stabilizing the γ′ phase.