Sodium ion ordering ofNa0.77CoO2under competing multivacancy cluster, superlattice, and domain formation

Abstract

Hexagonal superlattice formed by sodium multivacancy-cluster ordering in ${\text{Na}}_{0.77}{\text{CoO}}_{2}$ has been proposed based on synchrotron x-ray Laue-diffraction study on electrochemically fine-tuned single crystals. The title compound sits closely to the proposed lower end of the miscibility gap of $x\ensuremath{\sim}0.77--0.82$ phase-separated range. The average sodium vacancy-cluster size is estimated to be 4.5 Na vacancies per layer within a large superlattice size of $\sqrt{19}a\ifmmode\times\else\texttimes\fi{}\sqrt{19}a\ifmmode\times\else\texttimes\fi{}3c$. The exceptionally large Na vacancy-cluster size favors large twinned simple hexagonal superlattice of $\sqrt{19}a$, in competition with the smaller divacancy, trivacancy, and quadrivacancy clusters formed superlattices of $\sqrt{12}a$ and $\sqrt{13}a$. Competing electronic correlations are revealed by the observed spin-glasslike magnetic hysteresis below $\ensuremath{\sim}3\text{ }\text{K}$ and the twin domain, triple domain, and monodomain transformations during thermal cycling between 273 and 373 K.