Barium titanate BaTiO3 goes through several polymorphic phase transitions with temperature : Rhombohedral Orthorhombic Tetragonal Cubic Below - 80C - 80C to 5C 5 C to 120 C Above 120 C The structure of all of these polymorphs is very similar to that of the cubic compound and the nature of phase transformations can be visualized by assuming that the only changes in the structure are displacements of the Ba atom. (Actually, Ti and O atoms move as well). Cubic BaTiO3 has the perovskite structure with the space group Pm3m and each cell has one formula unit (5 atoms) with: Ba: Ti: 000 0:00h 070 200 Although the coordinates given here for Ba and Ti seem to be different from those in the notes, they nevertheless merge to the ones in the notes if we take the origin as hy in this problem. a) Draw the cubic BaTiO3 structure and determine the point symmetry at each kind of atom as well as the coordination of Ba by O, Ti by O and Ba by Ti. b) If the displacement of the Ba atom along a rotational axis removes symmetry from the structure, but can not remove rotational symmetry about the displacement vector, how might you displace the Ba atom (the same way in each cell) to form the three lower symmetry ordered BaTiO3 structures? c) If the actual phase transformations only involved displacement of atoms, would these transformations be rapid or sluggish