Thermodynamic stability of Co-Al-W L12 γ′

James E. Saal*, C. Wolverton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

73 Scopus citations


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 0.5W0.5) 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(Al0.5W 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.

Original languageEnglish (US)
Pages (from-to)2330-2338
Number of pages9
JournalActa Materialia
Issue number7
StatePublished - Apr 2013


  • Cobalt-base superalloys
  • Density functional theory
  • Finite-temperature free energy
  • Phase stability
  • Point defects

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Ceramics and Composites
  • Polymers and Plastics
  • Metals and Alloys


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