Abstract. 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 Laüe 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.In the past decade, Na x CoO 2 has emerged as a system of fundamental interest because of its high thermoelectric power, unusual magnetic properties and possibility, when hydrated, to superconduct [1]. The density x of intercalated sodium atoms tunes directly the density of states of quasi-particles in the metallic CoO 2 sheets. For simple fractional fıllings, electron diffraction (ED) experiments [2,3] provide evidence for the ordering of Na + ions at room temperature. This non-trivial order is generally believed to be the consequence of intricate interactions between Na + ions, mobile electrons, and phonons. We show here that the dominant process driving this ordering is simply the Coulomb potential between Na + ions. Sodium ions can occupy sites between oxygen atoms, which form two interpenetrating triangular lattices denoted Na 1 and Na 2 . Cobalt ions lie above and below Na 1 sites, resulting in an extra energy cost ∆ = ∆ c + ∆ sr relative to an Na 2 site (∆ c in the long-range Coulomb part and ∆ sr a short range repulsion between Na and Co ions shells). Na ions are bigger than the distance between nearest Na 1 and Na 2 sites, forbidding simultaneous occupancy of nearest-neighboring sites and that makes Coulomb energy minimization highly nontrivial. Our model Hamiltonian includes: (i) a long-range Coulomb potential, e/(4πεε 0 r) (the dielectric constant, taken as isotropic, is fıxed at ε = 6 to account quantitatively for the variations of the chemical potential, in terms of x, measured in cell devices [4]); (ii) Na-Na ionshell repulsion V=0.04eV for neighbors on the same sublattice; and (iii) on-site energy ∆ sr = 0.01eV. A system of two sheets of Na ions, each containing a maximum number of 1176 ions, intercalated between two CoO 2 layers (with periodic boundary conditions in 3 dimensions) is simulated at fınite temperature and fıxed chemical potential µ through a Grand-Canonical Monte-Carlo method. The hexagonal cell parameters a=2.84Å and c=10.87Å are fıxed to those measured in the x = 0.75 phase, and elastic deformations are neglected. We maintain neutrality at each step by varying the charges in the Co layers assuming a uniform spreading.The organization of Na ions is driven by the spontaneous formation of multivacancy clusters, as illustrated in Figure 1. At large distance d, the repulsion energy between two vacancies decreases as 1/d. However neighboring vacancies can reduce their energy...