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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.