Reaction Thermodynamics and Kinetics of Solid-State Reaction Synthesis for High-Purity Out-of-Plane Ordered Cr ₂ VAlC ₂ and Cr ₂ V ₂ AlC ₃ MAX Phases

The synthesis of phase-pure out-of-plane ordered MAX phases (o-MAX) Cr2VAlC2 and Cr2V2AlC3 is notoriously challenging and often hindered by parasitic reactions inherent to conventional elemental powder routes. This work combines thermodynamic calculations with experimental synthesis to validate the proposed solid-state reaction pathways employing Cr2AlC and VC as starting compositions to prepare high-purity o-Cr2VAlC2 and o-Cr2V2AlC3 MAX phases in the Cr–V–Al-C system. The thermodynamic formability of 312 and 413 MAX phases is evaluated by calculating the formation enthalpies and Gibbs free energies for both fully ordered o-MAX phases and their corresponding solid solutions, confirming the high thermodynamic stability of o-MAX compounds in comparison to solid solution forms from both typical elemental powder metallurgy and solid-state reaction synthesis. Combining the linear programming optimization algorithm for reaction thermodynamics and the systematic experimental verifications of phase formation kinetics, high yields of o-Cr2VAlC2 (82.0 wt %) and o-Cr2V2AlC3 (88.7 wt %) MAX phases are obtained with starting compositions as Cr2AlC/VC = 1:1.2 and 1:1.9 at the sintering temperature of 1500 °C. Using the JMAK equation, the apparent activation energies for phase nucleation and growth of o-Cr2VAlC2 and o-Cr2V2AlC3 phases are found to be 313.6 and 98.4 kJ mol–1, respectively. The calculated electronic density of states and bond orders for solid solutions and fully ordered MAX phases confirm that the stabilization of higher-order o-MAX phases in the Cr–V–Al-C system is mainly attributed to the significant reduction of Cr–C and V–C bond orders for those antisite atoms in disordered structures. This work elucidates a new pragmatic strategy to precisely tailor both reaction thermodynamics and kinetics for the synthesis of o-MAX phases in general.