Asymmetric Cation Coordination in Oxide Materials:  Influence of Lone-Pair Cations on the Intra-octahedral Distortion in d⁰ Transition Metals

Abstract

The oxides that contain both a d 0 transition metal (Ti 4+ , Nb 5+ , W 6+ , etc.) and a lone-pair cation (Sn 2+ , Se 4+ , Te 4+ , etc.) are examined to investigate the influence of the lone-pair cation on the intra-octahedral distortion of the d 0 transition metal. The direction and magnitude of the out-of-center distortion are also examined. When an intra-octahedral distortion is observed, at least one of the d 0 transition metal-oxide bonds needs to either be terminal or should link to another d 0 transition metal. With respect to the direction of the out-of-center distortion, Ti 4+ , V 5+ , and Nb 5+ usually displace toward an edge (local C 2 direction) or corner (local C 4 direction), whereas Mo 6+ and W 6+ are observed distorting toward an edge (C 2 ) or face (local C 3 direction). Finally, the magnitude of the distortion scales as

Unusual High‐Temperature Structural Behaviour in Ferroelectric Bi2WO6

“…[20] Off-centre octahedral distortions are a general feature of the structural chemistry of d 0 metal cations, a phenomenon which is generally ascribed to covalency effects (i.e., second-order Jahn-Teller effects); the specific preference of W 6 + for edge-or face-directed displacements rather than vertex-directed is discussed by Halasyamani. [21] In the HT phase, there is no net polarisation, but within each edge-sharing dimer the W atom is once again off-centredin this case away from the shared edge, as may be expected due to inter-cation repulsions; the W-W contact within the dimeric pair is still short, at 3.32 . Regarding communication between the Bi 2 O 2 and WO 4 layers, the environments of the two crystallographically distinct Bi sites in this phase are significantly different than in the Aurivillius phases, as in this case Bi1 and Bi2 lie above a "gap" or above a "shared edge", respectively in the WO 4 layer.…”

First-principles studies of lone-pair-induced distortions in epitaxial phases of perovskiteSnTiO3andPbTiO3

“…62 Finally, we point out that, for both compounds, the stable P 4mm phase is exempt from the "minimal Q" rule, having a lone-pair charge that is 0.01-0.02e higher than that of the preferred tensile phase. This exemption may be explained when, in addition to the lone pair activity, we consider distortions inside the TiO 6 unit, where Ti displacements along the [001] direction, i.e., toward a corner of the octahedron, are always heavily favored 63 (note that Ti and Pb off-centerings happen in lockstep). Therefore, minimization of the repulsive Coulomb interactions between the A-site cation lone pair and the negatively charged oxygen cage surrounding it becomes more important only when Ti is forced to off-center along a sub-optimal direction, such as toward an edge (Amm2) or a face (Cm) of the octahedral unit.…”

Noncentrosymmetric Inorganic Oxide Materials: Synthetic Strategies and Characterisation Techniques

“…The lone-pair 'pushes' the oxide ligands toward one side of the metal cation resulting in a noncentrosymmetric coordination environment. The lone-pair cation coordination environment may be considered as pre-distorted, [38] as these cations are almost always found in local NCS environments. Halasyamani et al, [38][39][40][41][42][43][44][45][46][47][48][49][50] Norquist et al, [51][52][53] and others [54][55][56][57][58][59][60][61][62][63] have used SOJT-distorted cations in the design and synthesis of new NCS materials.…”

“…Thus, the lone-pair polyhedra serve to reinforce the SOJT distortion of the d 0 cation. [38] Additionally, with the octahedrally coordinated d 0 cations, a continuous symmetry measures approach [65][66][67] has been used to quantify the magnitude and direction of the distortion. [68] They were able to divide the d 0 transition metals into three categories: strong (Mo 6þ and V 5þ ), moderate (W 6þ , Ti 4þ , Nb 5þ , and Ta 5þ ), and weak (Zr 4þ and Hf 4þ ) distorters (see Figure 1.4).…”