Electron microscopy
Octahedral Lattice
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For perovskite cell structures, octahedral oxygen (O) bonding around the atom (Mn for LaMnO3 as shown in Figure 3139a) in B-site generates the crystal field around the B-site atom. The valence states of the atoms (e.g. Mn) are fixed by charge neutrality. In the case of LaMnO3, if the parent compound is doped with Sr2+ for La3+, then Mn3+ (d3) is replaced by Mn4+ in the lattice.

Octahedral oxygen bonding around the Mn atom in LaMnO3

Figure 3139a. Octahedral oxygen bonding around the Mn atom in LaMnO3.

In some TM (transition metal) cases, the filling of orbitals with electrons may affect the local structure and thus induce geometrical distortion around the TM ion. The Jahn–Teller effect, also called Jahn–Teller distortion, describes this type of distortions. A typical Jahn-Teller ion is Mn3+ as shown in Figure 3139b. The ion in the high-spin configuration contains a single electron in the upper eg state when it is placed in an octahedral LF (ligand field). A tetragonal distortion can lower the energy of the system. The lowering in total energy is due to the lowering of one of the eg orbitals by lengthening the bond along the z axis. Note that the overall energy of the system is not further lowered by splitting the t2g state because the center of gravity is retained.

John-Teller effect for Mn3+ (3d4)

Figure 3139b. John-Teller effect for Mn3+ (3d4).

According to Radius Ratio Rule, the limiting cation-to-anion radius ratios for octahedral ionic lattices can be obtained as shown in Table 3139a.

Table 3139a. Cation-to-anion radius ratios (r+/r-) for coordination number (CN) 6.

Crystal type
Geometric shape

Material examples and their r+/r-

0.414 - 0.732
6 Octahedral Octahedral (i) Binary AB: NaCl (0.70), NiAs, KBr (0.678), MgO (0.471), SrS (0.571); (ii) Binary AB2: TiO2 (0.45); (iii) Others: Al2O3

All the ferroelectric materials today are based on corner-linked oxygen octahedral structures. The simplest configuration is the well-known perovskite structure.





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