Crystal chemistry and Calphad modeling of the σ phase

A systematic review of the crystal chemical properties of the σ phase is presented, with special emphasis on the atomic order, i.e. the distribution of the atoms on the different sites of the crystal structure. The data available in the literature have been systematically assessed, and are complemented by an experimental investigation in the following systems: Al–Nb, Al–Ta, Cr–Mn, Cr–Os, Cr–Re, Cr–Ru, Co–Mo, Fe–Mo, Fe–Re, Mn–Mo, Mn–Re, Mn–V, Mo–Re, Nb–Pt, Nb–Re, Ni–V, Pd–Ta, Re–V, Rh–Ta and Ru–W. The properties are analyzed as a function of composition and the nature and atomic size of the elements involved. The possibility of an order–disorder transition has also been reviewed and completed by diffraction experiments in two systems (Cr–Mn and Ni–V). First-principles calculations on the σ phase are reviewed in line with the Calphad approach. An analysis of the literature data concerning the Calphad modeling of systems involving the σ phase has been made. The different models used are presented and discussed. The conclusions of crystal structure data analysis are used to make some recommendations about the choice of a model in the frame of a Calphad assessment.