Symmetry Considerations and the Vanadium Dioxide Phase Transition

Some consequences of the symmetry change associated with the vanadium dioxide metal-semiconductor transition are derived. A free-energy expansion in the ionic displacements has been used. The effect of a $〈101〉$ zone-edge phonon instability and strain effects have been included. The symmetry arguments have been carried out using multiplier representations of the symmetric phase space group ${D_{4h}}^{14}$. It is found that a first-order transition from the symmetric phase to the monoclinic phase, ${C_{2h}}^5$, is compatible with such a free-energy expansion. Domain structure is predicted, which agrees with observations available. The dependence upon the spontaneous distortion of the dielectric tensor is derived. While the results are compatible with only one $〈101〉$ zone-edge phonon becoming unstable, the possibility of more than one such phonon participating in the transition cannot be ruled out.