Thermodynamic analysis of phase equilibria in the Cr–Mo–B ternary system

A thermodynamic analysis of the phase equilibria in the Cr–Mo–B ternary system has been carried out by combining first-principles calculations with the CALPHAD approach. The thermodynamic descriptions of three binary systems relevant to this ternary phase diagram were taken from previous studies. The enthalpy of formation of the (Cr,Mo)2B (Al2Cu-type, tI  12, space group I4/mcmI4/mcm), (Cr,Mo)3B2 (U3Si2-type, tP  10, space group P4/mbmP4/mbm), (Cr,Mo)B (CrB-type, oC8, space group Cmcm), (Cr,Mo)3B4 (Ta3B4-type, oI14, space group Immm), and (Cr,Mo)B2 (AlB2-type, hP  3, space group P6/mmmP6/mmm) phases were obtained from first-principles calculations. The ternary thermodynamic parameters evaluated using these theoretical values, as well as the available experimental information on the phase boundaries, enabled us to calculate the phase equilibria in the Cr–Mo–B ternary system over the entire composition and temperature ranges.