Origin of the quadrupole splitting in the Mössbauer 57Fe spectrum of cubic (disordered) LiFeO2

The room-temperature Mössbauer ⁵⁷Fe spectrum of polycrystalline disordered cubic α-LiFeO₂ contains a quadrupole splitting |Δ_obs| of 0.65(2) mm/sec. This value is relatively large for an Fe atom in an essentially Fe³⁺_HS state. To account for its magnitude, the distribution of the electric-field gradient (EFG) values associated with the Fe atoms was investigated by means of exact geometric analysis involving the 12 nearest cation neighbors (model A) as well as large-scale computer simulation involving more distant cations (models B to E). It is found that (1) the major contribution to |Δ_obs| comes from the distribution of +1 and +3 charges among the 12 nearest cation neighbors of a reference Fe atom; (2) this contribution by itself largely accounts for |Δ_obs|; (3) the contribution from cations beyond the seventh-nearest neighbors is marginal; (4) displacing the oxygen atoms from their lattice sites toward adjacent Fe atoms produces a significant effect on the distribution of EFG values at a reference Fe atom, while incipient cation ordering appears to have a relatively small effect; and (5) the contribution of the EFG = 0 component to model |EFG| distributions will be overemphasized unless cations beyond the first-nearest neighbors are included in the EFG summation. The 144 distinct (up to rotation and reflection) Li¹⁺_12?kFe³⁺_k configurations on the coordination cuboctahedron of nearest cation neighbors (required for the examination of model A) are listed, together with their symmetries and multiplicities, and it is shown that the 144 configurations engender only 17 distinct |EFG| values. Observations are also made on various geometric aspects of calculating EFG at ⁵⁷Fe³⁺_HS on cubic lattices.