RESUMEN
The structures of the four phases exhibited by Na(0.74)WO(3), sodium tungstate, with a change in temperature have been refined from powder diffraction patterns obtained on the high-resolution powder diffractometer (HRPD), ISIS, Rutherford Appleton Laboratory, England. At temperatures above 430 K, the stable phase has the ideal perovskite structure, with space group Pm3;m (No. 221). Below that temperature, the octahedra are tilted about pseudocubic <100> directions; the tilts are produced by the condensation of the normal modes of vibration of the octahedra in the high-temperature cubic phase. Using Glazer's notation, the tilt system undergoes the following sequence: a+a+a+ (293K)-->a+a+a0(343K)-->a0a0a+(430K)-->a0a0a0. The structural refinements presented here confirm the sequence of the transitions first proposed by Clarke [(1977). Phys. Rev. Lett. 39, 1550-1553]. This is the first time that a structure determination of a perovskite with the tilt system a+a+a0 has been reported in the literature. In addition, we evaluate the weights, or importance, of the condensed modes in each low-temperature phase.
RESUMEN
An analysis of the normal modes of vibration of a cubic perovskite that have condensed to produce phases with tilted octahedra is presented. Only structures with octahedral tilts that double a repeat distance are considered; these involve small rotations of the octahedra about pseudocubic <100> directions. Phases with more than one octahedral tilt often possess atomic displacements in addition to those associated directly with the tilts. A Landau potential has been constructed which includes all parameters needed to describe the low-symmetry phases. In addition to the spontaneous macrostrain, seven different order parameters are required to describe the possible transitions between phases with only one type of A and one type of B cation. Arguments based on the Landau expansion suggest that structural displacements associated with some of these order parameters are unlikely to be present, and that some subsets of displacements may have a higher symmetry than required by the space group of the lower-symmetry phase. Comparison is made between these predictions and reported structural refinements. Where relevant, phases with more than one type of A or more than one type of B cation are considered.
