Thermodynamics for the non-conventional synthesizing of out-of-plane ordered double-transition metal“312”and“413”MAX phases(o-MAX):A high throughput linear programing first-principles calculation

The reaction thermodynamics for synthesizing the“312”and“413”o-MAX phases using the powder met-allurgy are investigated using a linear programing optimization algorithm based on the high-throughput first principles phonon calculations.The validity and reliability of the current methodology are verified by correctly predicting the impurities in four experimentally known o-MAX systems including Cr-Ti-Al-C,Cr-V-Al-C,Mo-Sc-Al-C and Mo-Ti-Al-C.The formability of each investigated o-MAX phase is evaluated by means of formation enthalpy and formation Gibbs free energy in a temperature range from 0 K to 1700 K.It is revealed that the thermodynamic stability of the“413”o-MAX structure is no better than that of the“312”phase.The formability of“413”o-MAX is also reduced at high sintering temperature,compared to that of“312”phase.The optimal synthetic routes are predicted for all thermodynamically stable“312”and“413”o-MAX phases.It is found that most o-MAX phases considered could be prepared as the single phase using the non-conventional synthetic routes from the aspect of reaction thermodynamics.Few of them including Cr_(2)TaAlC_(2),Nb_(2)HfAlC_(2),Nb_(2)TaAlC_(2),Nb_(2)Hf_(2)AlC_(3),Nb_(2)Ta_(2)AlC_(3),Mo_(2)V_(2)AlC_(3)and Mo_(2)Ta_(2)AlC_(3)are predicted to be either destabilized at high temperature or overwhelmed by the most competing side reaction.