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

In order to help understand the structural stability of KCoO₂-type ternary nitrides AMN₂, referring to perovskite structure, a tolerance factor t is proposed to describe the size effect on the phase/symmetry options of the experimentally accessible AMN₂ nitrides. This leads to a range of t values above 0.946 for structurally stable KCoO₂-type AMN₂ nitrides with t values around 0.970 for the orthorhombic and tetragonal phase boundary. In contrast, most of AMN₂ nitrides exhibit α-NaFeO₂-type structure with t ∼ 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 AMN₂ 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 AMN₂ 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 AMN₂ nitrides could be categorized into three types with different tolerance factors, and scarce AMN₂ nitrides with lower formation energies would be accessible using different synthetic routes beyond the traditional solid-state synthesis method.