We have performed ab initio calculations for the cubic inverse-perovskite ${\text{Sc}}_{3}E\text{N}$ $\left(E=\text{Al},\text{Ga},\text{In}\right)$ systems to study their electronic band-structures and elastic properties. In this study, we used the accurate augmented plane wave plus local orbital method to find the equilibrium structural parameters and to compute the full elastic tensors. The obtained single-crystal elastic constants were used to quantify the stiffness of the Sc-based ternary nitrides and to appraise their mechanical stability. The site-projected density of states, Fermi surfaces, and the charge-density plots have also been used to analyze the chemical bonding between the ${\text{Sc}}_6\text{N}$ cluster and the surrounding metallic lattice of either Al, Ga, or In atoms. Our calculations show that ${\text{Sc}}_3\text{GaN}$ has the largest covalent Sc-N bonding-type character with the highest Young, shear, and bulk moduli. Compared with the other two isoelectronic systems, it also behaves as the most brittle material with a relatively large elastic anisotropy.

• Received 18 December 2008

DOI:https://doi.org/10.1103/PhysRevB.79.125122