Tolerance Factor and Phase Stability of the KCoO₂-Type AMN₂ Nitrides

In order to help understand the structural stability of KCoO2-type ternary nitrides AMN(2), referring to perovskite structure, a tolerance factor t is proposed to describe the size effect on the phase/symmetry options of the experimentally accessible AMN(2) nitrides. This leads to a range of t values above 0.946 for structurally stable KCoO2-type AMN(2) nitrides with t values around 0.970 for the orthorhombic and tetragonal phase boundary. In contrast, most of AMN(2) nitrides exhibit alpha-NaFeO2-type structure with t similar to 0.898-0.946 and cations ordered or disordered rocksalt structure while t below 0.898. Employing the proposed criterion, the structure formation for other ternary AMN(2) compositions with lanthanum and alkaline earth cations for the A sites were predicted, which was testified through the synthesis attempts and complemented by formation energy evaluations. The efforts to synthesize the ternary Lanthanide and alkaline earth-based AMN(2) nitrides were unsuccessful, which could associate the structural instability with the large formation energies of lanthanide nitrides LaMN2 and the greater tolerance factor of 1.048 for BaTiN2. The experimentally already synthesized AMN(2) nitrides could be categorized into three types with different tolerance factors, and scarce AMN(2) nitrides with lower formation energies would be accessible using different synthetic routes beyond the traditional solid-state synthesis method.