In-Plane Cation Ordering and Sodium Displacements in Layered Honeycomb Oxides with Tetravalent Lanthanides: NaLnO (Ln = Ce, Pr, and Tb).

The detailed structural characterization of "213" honeycomb systems is a key concern in a wide range of fundamental areas, such as frustrated magnetism, and technical applications, such as cathode materials, catalysts, and thermoelectric materials. NaLnO (Ln = Ce, Pr, and Tb) are an intriguing series of "213" honeycomb systems because they host tetravalent lanthanides. "213" honeycomb materials have been reported to adopt either a cation-disordered 3̅ subcell, a cation-ordered trigonal (312), or monoclinic (2/ or 2/) supercell. On the basis of analysis of the average (synchrotron diffraction) and local [pair distribution function (PDF) and solid-state NMR] structure probes, cation ordering in the honeycomb layer of NaLnO materials has been confirmed. Through rationalization of the Na chemical shifts and quadrupolar coupling constants, the local environment of Na atoms was probed with no observed evidence of cation disorder. Through these studies, it is shown that the NaLnO materials adopt a 2/ supercell derived from symmetry-breaking displacements of intralayered Na atoms from the ideal crystallographic position (in 2/). The Na displacement is validated using distortion index parameters from diffraction data and atomic displacement parameters from PDF data. The 2/ supercell is faulted, as evidenced by the increased breadth of the superstructure diffraction peaks. DIFFaX simulations and structural considerations with a two-phase approach were employed to derive a suitable faulting model.