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Applying the Effective Bond Energy Formalism (EBEF) to Describe the Sigma (σ) Phase in the Co-Cr-Ni-Re System



Júlio Cesar Pereira Dos Santos, Sean Griesemer, Nathalie Dupin, Ursula R. Kattner, Chuan Liu, Daniela Ivanova, Thomas Hammerschmidt, Suzana Fries, Chris Wolverton, Carelyn E. Campbell


Proper descriptions of Topologically Closed-Packed (TCP) phases in thermodynamic databases are essential to adequately design new alloys. Thus, the recently introduced Effective Bond Energy Formalism (EBEF) is used in this work to describe the sigma (σ) phase in the Co-Cr-Ni-Re system. The EBEF is applied to a five-sublattice (5-SL) thermodynamic model consistent with its crystal structure and its implementation was supported by new data from Density Functional Theory (DFT). The Matrix Inversion Method is described and used to automate the generation of the EBEF parameters. Good descriptions of the ternary systems are obtained even without any ternary parameters for any of the phases. This is the first time that an EBEF description of a quaternary TCP phase is established using the SGTE descriptions for the pure elements.
Journal of Phase Equilibria and Diffusion


Effective bond energy formalism, sigma phase, Calphad, Co-based superalloys, DFT calculation.


Pereira Dos Santos, J. , Griesemer, S. , Dupin, N. , Kattner, U. , Liu, C. , Ivanova, D. , Hammerschmidt, T. , Fries, S. , Wolverton, C. and Campbell, C. (2023), Applying the Effective Bond Energy Formalism (EBEF) to Describe the Sigma (σ) Phase in the Co-Cr-Ni-Re System, Journal of Phase Equilibria and Diffusion, [online],, (Accessed July 13, 2024)


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Created December 30, 2023, Updated May 6, 2024