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.

• Temperature corrections at the typical sintering temperature were addressed properly. • A strong correlation between actual formability of o-MAX phases and the DOS at the Fermi level were found. • Using an updated linear programing optimization algorithm, results of the preparation of o-MAX phase in the existing experiments can be predicted well. • New non-conventional synthetic routes were suggested, expected to improve purity and yield. The reaction thermodynamics for synthesizing the "312" and "413" o-MAX phases using the powder metallurgy 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. [Display omitted] [ABSTRACT FROM AUTHOR]