Successive structural phase transitions inNaxWO3

Three successive phase transitions, cubic I to tetragonal I to tetragonal II to cubic II, in the perovskite ${\mathrm{Na}}_x$ W${\mathrm{O}}_3$ have been studied by neutron scattering. The softening of the $M_3$ phonon modes which correspond to a rotation of the W${\mathrm{O}}_6$ octahedra is observed in the cubic I phase, and the tetragonal I phase is confirmed to be a state resulting from a single $M_3$-mode condensation. Powder-diffraction studies have shown that the other two low-temperature phases also result from $M_3$-mode condensations, confirming the structural model proposed by Clarke. Although at the second and third transitions the axes of the resultant rotations change abruptly, the measured order parameter, which is proportional to the absolute rotation angle, does not have any appreciable discontinuity. This fact and the three successive $M_3$-mode condensations are unique compared with other successive phase transitions in insulating perovskite materials.