Towards a unified steric stabilisation model for predicting the synthesisability of MAX phases

The MAX phases constitute a large family of atomically layered ternary carbides/nitrides with hexagonal structure (space group P6 3 /mmc ) applauded for their compositional versatility, which is demonstrated by the easy formation of solid solutions with varying chemical complexity. This work presents a generalised steric stability framework to quantify the lattice distortions of M n+1 AX n MAX phases. The derived framework was consequently used to evaluate the steric stability of 13 ternary MAX phases in the (Ti,V,Cr,Zr,Nb,Hf,Ta)-Al-C system and correlate their lattice distortions to their experimental synthesisability by spark plasma sintering. The comparative synthesisability of these M n+1 AlC n phases relates well to the magnitude of their lattice distortions, unit cell crystallography, and the Goldschmidt radius of their constituent elements. Finally, this work addresses the limitations and sensitivity of the lattice distortion calculations based on Rietveld refined X-ray diffraction data.