Evaluation of phase relationship in W-Fe-C ternary system through symmetry principles and first-principles calculation

Solid state phase reactions are complicated and sometimes a black box because of the copious reactants and versatile pathways. In this work, the phase relationship in W-Fe-C ternary system is systematically studied by means of the symmetry principles in crystal chemistry and first-principles thermodynamics. According to group-subgroup relation, ternary carbides FexWxC (x = 6, 3, and 2) are likely to form via the intermediate W2C and FeW3C phases at C-rich condition. At C-poor condition, those ternary carbides are prone to be transformed from Fe7W6 with residual C element in the matrix or C from Fe3C in steel. Based on percolation theory, we find the direct phase transition from Fe6W6C to Fe3W3C undergoes with transient Fe2W2C. The calculated Gibbs reaction free energy is in good agreement with various experimental observation and clarifies the discrepancies and controversaries among different experiments in the literature. The success in predicting the phase relationship of W-Fe-C ternary system suggests that the symmetry principles in crystal chemistry combined with first-principles calculations not only unravel the intrinsic mechanism behind the phase reaction, but also should be incorporated into future designs of covalent materials, such as carbides, nitrides, and oxides.