while the axes are termed rhombohedral. The most frequently, for the convenience,
the unit cell is presented in a hexagonal coordinate. The ideal trigonal perovskites
belong to space group R-3c (167) with a center of symmetry. In case of space group
R3c, there is displacement of the B cations from the center of the octahedra which
leads to the loss of the symmetry center [30].
The main driving force of the structural distortions is a stereochemical activity of
the Bi
3+ 6s
2 lone pair, which hybridizes with 6p oxygen electrons. As the result of
the hybridization, the asymmetric wave function is achieved what leads to significant shortening of three of twelve Bi–O bonds and elongation of the opposite three
bonds. The displacement is realized along [1 1 1] direction of the ideal cubic
structure and is called as ferroelectric. On the other hand, the [FeO 6 ] octahedron is
rigid and to accommodate the displacement it needs to be tilted. The tilt counteracts
a movement of the Fe
3+ from the center of the octahedra and is called as antiferrodistortive. The combination of these two distortions lowers the total energy by
only 1 eV with respect to the cubic structure. As the consequence, BiFeO 3 adopts
the R3c structure in which Bi
3+ cation is shifted towered c-axis from the middle of
Fig. 9.4 a BiFeO 3 unit cell (red arrows indicate direction the of electric polarization, black arrows
indicate the direction of Fe
3+ magnetic moment) ; b G-type antiferromagnetic moments alignment
in BiFeO 3 ; c Bi
3+ and Fe
3+ ions displacement in coordination polyhedral; d FeO 6 octahedra tilting
and rotation. The figures were drawn by VESTA [40]
9 Mössbauer Spectroscopy of Magnetoelectric Perovskite Oxides
287
the unit cell is presented in a hexagonal coordinate. The ideal trigonal perovskites
belong to space group R-3c (167) with a center of symmetry. In case of space group
R3c, there is displacement of the B cations from the center of the octahedra which
leads to the loss of the symmetry center [30].
The main driving force of the structural distortions is a stereochemical activity of
the Bi
3+ 6s
2 lone pair, which hybridizes with 6p oxygen electrons. As the result of
the hybridization, the asymmetric wave function is achieved what leads to significant shortening of three of twelve Bi–O bonds and elongation of the opposite three
bonds. The displacement is realized along [1 1 1] direction of the ideal cubic
structure and is called as ferroelectric. On the other hand, the [FeO 6 ] octahedron is
rigid and to accommodate the displacement it needs to be tilted. The tilt counteracts
a movement of the Fe
3+ from the center of the octahedra and is called as antiferrodistortive. The combination of these two distortions lowers the total energy by
only 1 eV with respect to the cubic structure. As the consequence, BiFeO 3 adopts
the R3c structure in which Bi
3+ cation is shifted towered c-axis from the middle of
Fig. 9.4 a BiFeO 3 unit cell (red arrows indicate direction the of electric polarization, black arrows
indicate the direction of Fe
3+ magnetic moment) ; b G-type antiferromagnetic moments alignment
in BiFeO 3 ; c Bi
3+ and Fe
3+ ions displacement in coordination polyhedral; d FeO 6 octahedra tilting
and rotation. The figures were drawn by VESTA [40]
9 Mössbauer Spectroscopy of Magnetoelectric Perovskite Oxides
287