Classification of octahedral tilting phases in the perovskitelikeA2BX4structure

The possible lower symmetries (subgroups) of the ${A}_{2}$${\mathrm{BX}}_{4}$ structure (space-group symmetry ${D}_{4h}^{17}$) due to rigid octahedral tiltings at phase transitions are investigated. The method for obtaining subgroups determined by reducible representations (i.e., coupled order parameters) is described. This method depends upon subgroup information for irreducible representations (i.e., single uncoupled order parameters). All subgroup symmetries which are allowed by the coupling of two simple octahedral tiltings are listed for this structure.