  The single crystal elastic constants, polycrystalline elastic moduli and
related properties of orthorhombic MgSiN$_{2}$, MgGeN$_{2}$ and MgSnN$_{2}$
have been calculated using density functional theory and compared to the
related wurtzite structured AlN, GaN and InN. Since there are no experimental
studies of single crystal elastic properties of neither MgSiN$_{2}$,
MgGeN$_{2}$ or MgSnN$_{2}$, we have established the accuracy of the
calculations by comparison with experimental data for AlN, GaN and InN. The
calculated polycrystalline elastic moduli of MgSiN$_{2}$ are found to be in
good agreement with available experimental elastic moduli. It will be shown
that MgSiN$_{2}$ and MgGeN$_{2}$ have a small $xy$-plane lattice mismatch with
AlN and GaN, respectively, while at the same time being significantly softer
than both AlN and GaN. This shows that MgSiN$_{2}$ and MgGeN$_{2}$ should be
possible to be grown on AlN and GaN without significant lattice mismatch or
strain.
