Question

Barium titanate (BaTiO3) exhibits a phase transition from a cubic to a tetragonal phase at 120 °C. The cubic phase has a space group of Pm3m, and the tetragonal phase has a space group of P4mm. The cubic cell parameter, a, just above 120 °C is 4.01 Å. At room temperature, the cell parameters of the tetragonal phase are a = 3.992 Å and c = 4.034 Å. Considering this, why is the phase transition likely attributed to a displacement of the Ti atom rather than rotations of the TiO6 octahedra?

a.The rotations of the TiO6 octahedra are energetically unfavorable.
b.The Ti atom is positioned at the center of the octahedra, making its displacement more significant.
c.Octahedral rotations are more common in perovskite structures with a higher coordination number.
d.Experimental evidence indicates a significant displacement of the Ti atom during the phase transition.

Answer 1

The phase transition in Barium titanate (BaTiO3) is most likely due to the displacement of the Ti atom and is supported by changes in the cell parameters a and c, which suggest a subtle internal rearrangement rather than entire TiO6 octahedra rotations. option (B)

Step-by-step explanation:

The phase transition of Barium titanate (BaTiO3) from a cubic to a tetragonal phase at 120 °C is attributed to the displacement of the Ti atom rather than rotations of the TiO6 octahedra. The cubic cell parameter, a, just above 120 °C is 4.01 Å, while at room temperature, the tetragonal phase has cell parameters of a = 3.992 Å and c = 4.034 Å. The correct answer is d.

Experimental evidence indicates a significant displacement of the Ti atom during the phase transition. Option d is the most plausible explanation because the small change between the cubic and tetragonal cell parameters (a and c) implies a subtle internal structural rearrangement, which is consistent with the Ti atom moving from the center of the octahedron. Rotations of the entire TiO6 octahedron are less likely as such changes would typically lead to larger variations in cell parameters.