Condensed Phonon Modes in Successive Phases of WO₃

Abstract

The irreducible representations of normal modes of WO 3 are presented at the points \(\varGamma\), X , M and R in or on the Brillouin zone of the hypothetic cubic phase. The atomic displacements at each phase are decomposed into the normal modes referring to the diffraction data. The normal modes concerned with W atoms condense at all the transition points except for the orthorhombic-monoclinic transition, where a linear combination of three rotational modes of WO 6 octahedra, R 25 x + R 25 z + M 3 y , condenses. Antiferrodistortive structures in the phases above room temperature are due to the condensations of the M , X and R modes. Ferridistortive structure in the monoclinic (II) phase is due to the condensation of both \(\varGamma_{15}^{z}\) and M 3 ' z modes. WO 3 is shown to have ferridistortive structures with first-order successive phase transitions.