Phonon softening and the phase transition in VN

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 (3) over barm) to tetragonal (space group P (4) over bar 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)' mode, indicating that the tetragonal phase exhibits improper ferroelasticity. The effect of nonmetal vacancy composition on phase transition is also discussed.