CALPHAD description of the Mo–Re system focused on the sigma phase modelling
R. Mathieu, N. J. Dupin, J. C. Crivello, K. Yaqoob, A. A. H. Breidi, J.-M. Fiorani, N. David, J. M. Joubert.
CALPHAD, 43, 18-31, (2013)
The phase equilibria and thermodynamic properties of the Mo–Re system are studied by combining first-principle and CALPHAD approach. The mixing enthalpies in the bcc and hcp solution phases are estimated by first-principle calculations using the special quasirandom structures. The liquid, bcc and hcp phases are described by a substitutional solution model. The intermetallic phases, σ and χ, are described with the compound energy formalism with, respectively, 5 and 4 sublattices (SL) using the formation enthalpies of all the end-members directly from ab initio calculations. A phase diagram in agreement with the available experimental knowledge is obtained thanks to a least square procedure involving a limited number of parameters. Introducing all the elements in all the sublattices of the structure allows a proper description of the configuration of the intermetallic phases. Different simplifications of the description of the σ phase are considered. The ideal 4SL simplification is equivalent to the full description. The 3SL and 2SL models require excess parameters in order to fit reasonably the experimental phase diagram. Among these, only the (Mo,Re)10(Mo,Re)12(Mo,Re)8 model allows to closely approximate the low temperature thermodynamic properties of the full description.
Keyword(s): thermodynamic discription; calphad; mo-re; dft-cef; sqs; σ phase