On the Ordering of Na$^+$ Ions in Na$_x$CoO$_2$
  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. 
M. Roger, D.J.P. Morris, D.A. Tennant, M.J. Gutmann, J.P. Goff,   D.Prabhakaran, N. Shannon, B. Lake, A.T. Boothroyd, R. Col...