Thermodynamic Stability of Co-Al-W L12 \gamma'
  Co-based superalloys in the Co-Al-W system exhibit coherent L12 Co3(Al,W) \gamma' precipitates in an fcc Co \gamma 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 1173K. Here, we perform an extensive series of density functional theory (DFT) calculations of the \gamma' 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(Al0.5W0.5) \gamma' at 0K with respect to HCP 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 SQS. 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 Ni3Al. However, in contrast to the Ni3Al system, we find that substituting Co on Al sites is thermodynamically favorable at 0K, consistent with experimental observation of Co excess and Al deficiency in \gamma' with respect to the Co3(Al0.5W0.5) composition. Lastly, we consider vibrational, electronic, and magnetic contributions to the free energy, finding that they promote the stability of \gamma', 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 \gamma' decomposition products, B2 CoAl, effectively destabilizing the Co, CoAl, and Co3W three phase mixture, thus stabilizing the \gamma' phase. 
James E. Saal and Chris Wolverton
cond-mat.mtrl-sci