Place: Ψk (Psi-k) Conference 2010, Berlin, Germany
Jean Crivello, Université de Paris, Jomdan, Paris, France
Taichi Abe, National Institute for Materials Science, Tsukuba, Ibaraki, Japan
Topologically Close Packed (TCP) phases, as the sigma phase, occur in steels and Ni-base superalloys. They are brittle and have a detrimental effect on the mechanical properties of these multicomponent materials.
DFT theory has show to be a useful approach to understand binary sigma phases stability (1,2).
For the first time, ternary sigma phases DFT studies were done. The selected elements are Cr,Re,Ni and Cr,Re,Mo. The enthalpies of formation at 0 K of different possible configurations (243) of the tetragonal P42/mmm with five sublattices (Wyckoff positions) in a ternary sigma phase have been calculated by using the VASP code. We include the configurational entropic contribution within the Bragg-Williams approximation, avoiding any phenomenological parameters usually used in the traditional CALPHAD approach, which is used here as a formalism allowing for the calculation of thermodynamic functions.
The present approach demonstrates very successful in predicting properties as the site occupancies in sigma phase. Miscibility gaps in ternary sigma phases are predicted and discussed. We present then calculations of prototypical phase diagrams of these ternary systems, which compare well with experimental findings. The possible extrapolation from lower order to higher order system is discussed.