An investigation of the sodium patterning in NaxCoO2 (0.5⩽x⩽1) by density functional theory methods

Extensive experimental work has been carried out to characterize the stable Na-vacancy ordering patterns at various compositions of layered NaxCoO2. However, contradictions and debates prevail in the literature, particularly at high Na concentrations x>0.5. Understanding of the exotic electronic properties in this system requires a thorough understanding of the Na-vacancy structural orderings. Using density functional theory in the generalized gradient approximation (GGA), combined with a cluster expansion structure prediction algorithm we have found an intricate set of Na-vacancy ordered ground states in NaxCoO2 (0.5⩽x⩽1). We demonstrate a newly predicted ordering pattern between 0.67⩽x⩽0.71. By comparing the first principles electronic structure methods within the GGA and GGA+U (Hubbard U correction) approximations, we demonstrate that at certain Na concentration the stable ordering is affected by charge localization on the Co layer through coupling between the Na and Co lattices.