A TEM and RUM study of the inherent displacive flexibility of the fresnoite framework structure type

Abstract

A careful electron diffraction study has been made of the incommensurately modulated room-tem- perature phases of the fresnoites Ba2TiGe2O8 (BTG) and Ba2TiSi2O8 (BTS) and used to determine their (3+1)- and (3+2)-dimensional superspace group symmetries. The primitive primary modulation wave vectors in both materials are found to occur close to the same position in the parent Brillouin zone, near � 0:3h110i � þ 1=2c �. A rigid unit mode (RUM) analysis of the inherent dis- placive structural flexibility of the ideal fresnoite framework structure type is then carried out in an at- tempt to understand the significance of this particular modulation wave vector. Six zero-frequency RUM modes and two close to zero frequency quasi-RUM (Q-RUM) modes are found to exist for any modulation wave vector. These RUM modes are all primarily associated with rotations of the constituent TO4 (T ¼ Si or Ge) tetrahedra and TiO5 square pyramids around in-plane i.e. perpendicular to c rotation axes. A seventh RUM mode involving rotation of the constituent rigid polyhedra around c combined with shifts in the basal plane is found but only at a very specific modulation wave vector q � 0:30h110i �, in close agreement with the condensed RUM mode found in the electron diffraction study. It is the condensation of just such a RUM mode that appears to play a major role in the various incommensurately modulated structures ob- served in Ba2TiGe2O8 ,B a 2TiSi2O8 and Sr2TiSi2O8, re- spectively.