Structural transformations and phenomenological description of the formation of phase states in elpasolites Cs$_2$RbDyF$_6$ and Rb$_2$KB'F$_6$ (B'= Ho, Dy, Tb)

The structures of the cubic and monoclinic phases of an Rb$_2$KHoF$_6$ crystal from a series of elpasolites Rb$_2$KB'F$_6$ (B' = Ho, Dy, Tb), which undergoes a trigger phase transition, have been investigated using X-ray powder diffraction. The critical and noncritical displacements of atoms in the Rb$_2$KHoF$_6$ structure have been determined from the group-theoretical analysis of the complete condensate of order parameters. It has been reliably established that a change in the symmetry due to the phase transition in this crystal can be represented in the form
$$ Fm\bar3m\frac{11-9(\Gamma^+_4)\oplus 10-3(X^+_3)}{(\varphi,\varphi,\psi)}P12_1/n1. $$
A phenomenological analysis of the conditions responsible for the formation of phase states upon the phase transitions in elpasolites Cs$_2$RbDyF$_6$ and Rb$_2$KB'F$_6$ (B' = Ho, Dy, Tb) has been carried out. Taking into account the structural data and using the phenomenological theory, it has been found that the main factor determining the formation of phase states in these and related crystals is the instability of the elpasolite structure with respect to rotational distortions of two types. It has been shown that an important role in the formation of a sequence of structural transformations in these crystals is played by the interaction of rotational order parameters and displacements of the cation from the center of a cuboctahedral hole.