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 Fm3̄m) to tetragonal (space group P4̄2m) phase transition at 205 K is proposed. The mechanism suggests that spontaneous volume and shear strains, eA=εₓₓ+εyy+εzz and eE1=2εzz-εₓₓ-εyy, are induced indirectly by the collapse of the X₃^' mode, indicating that the tetragonal phase exhibits improper ferroelasticity. The effect of nonmetal vacancy composition on phase transition is also discussed.
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Иващенко et al. (2008) studied this question.
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