Trends in formation energies and elastic moduli of ternary and quaternary transition metal nitrides

The paper deals with characteristics of a wide range of ternary and quaternary metal nitrides (M = Ti, Zr, Hf, V, Nb or Ta) of various compositions obtained by ab initio calculations. We focus on the formation energies (E (form)), bulk moduli (B), shear moduli (G) and a difference of B and G from the weighted average of B and G of binary metal nitrides (a dagger B and a dagger G). We show numerous monotonous dependencies, and identify exceptions to them. For elastic moduli of (MMN)-M-1-N-2 we find that a dagger B decreases (down to -19 GPa) and a dagger G increases (up to 20 GPa) with increasing difference between atomic radii of M-1 and M-2. In parallel, low a dagger B and high a dagger G correspond to high E (form) and |E (form)|, respectively. E (form) of (MMN)-M-1-N-2 increases with increasing difference between atomic radii and electronegativities of M-1 and M-2. The lowest E (form) values were observed for Ta-containing compositions, and the difference between E (form) of (TaMMN)-M-1-N-2 and (MMN)-M-1-N-2 is more significant for lower atomic radius and higher electronegativity of M-1 and M-2. Overall, we present trends which allow one to use fundamental arguments (such as atomic radii and electronegativities) to understand and predict which compositions form (nano)composites, which compositions form (stable) solid solutions, and which materials exhibit enhanced elastic moduli. The phenomena shown can be tested experimentally, and examined for even wider range of materials.