Based on an analysis of phonon modes and the results of first-principles total-energy calculations for the cubic, tetragonal, and orthorhombic phases of VN, a possible mechanism of the cubic (space group $Fm\overline{3}m$) to tetragonal (space group $P\overline{4}2m$) phase transition at 205 K is proposed. The mechanism suggests that spontaneous volume and shear strains, $e_A={\epsilon }_{xx}+{\epsilon }_{yy}+{\epsilon }_{zz}$ and $e_{E1}=2{\epsilon }_{zz}-{\epsilon }_{xx}-{\epsilon }_{yy}$, are induced indirectly by the collapse of the $X_3^{\prime }$ mode, indicating that the tetragonal phase exhibits improper ferroelasticity. The effect of nonmetal vacancy composition on phase transition is also discussed.

• Received 16 September 2008

DOI:https://doi.org/10.1103/PhysRevB.78.224113