On the Ordering of Na$^+$ Ions in Na$_x$CoO$_2$ - Roger, M; Morris, D; Tennant, D; Gutmann, M; Goff, J; Prabhakaran, D; Shannon, N; Lake, B; Boothroyd, A; Coldea, R; Deen, P (2005)
The influence of electrostatic interactions on the ordering of sodium ions in Na$_x$CoO$_2$ is studied theoretically through Monte-Carlo simulations. For large $x$ small di- or tri-vacancy clusters are stable with respect to isolated Na vacancies. At commensurate fillings these small clusters order in triangular superstructures. These results agree with recent electron diffraction data at $x=1/2$ and 3/4. We have performed neutron La\"ue diffraction experiments at higher $x$, which confirm the predictions of this simple model. The consequences on the properties of the electronic charges in the Co layers are discussed.