1. Service de Physique de l'Etat Condensé, (CNRS/MIPPU/URA 2464), DSM/DRECAM/SPEC, CEA Saclay, P.C. 135, F-91191 Gif Sur Yvette, France
   
2. Department of Physics, University of Liverpool, Oliver Lodge Laboratory, Liverpool L69 7ZE, UK
   
3. Hahn-Meitner Institut, Glienicker Strasse 100, Berlin D-14109, Germany
   
4. Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstrasse 36, Berlin D-10623, Germany
   
5. ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK
   
6. Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
   
7. H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, UK
   
8. European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble cedex, France

Correspondence to: M. Roger¹ Correspondence and requests for materials should be addressed to M.R. (Email: roger@drecam.saclay.cea.fr).

Sodium cobaltate (Na_xCoO₂) has emerged as a material of exceptional scientific interest due to the potential for thermoelectric applications^{1, 2}, and because the strong interplay between the magnetic and superconducting properties has led to close comparisons with the physics of the superconducting copper oxides³. The density x of the sodium in the intercalation layers can be altered electrochemically, directly changing the number of conduction electrons on the triangular Co layers⁴. Recent electron diffraction measurements reveal a kaleidoscope of Na⁺ ion patterns as a function of concentration⁵. Here we use single-crystal neutron diffraction supported by numerical simulations to determine the long-range three-dimensional superstructures of these ions. We show that the sodium ordering and its associated distortion field are governed by pure electrostatics, and that the organizational principle is the stabilization of charge droplets that order long range at some simple fractional fillings. Our results provide a good starting point to understand the electronic properties in terms of a Hubbard hamiltonian⁶ that takes into account the electrostatic potential from the Na superstructures. The resulting depth of potential wells in the Co layer is greater than the single-particle hopping kinetic energy and as a consequence, holes preferentially occupy the lowest potential regions. Thus we conclude that the Na⁺ ion patterning has a decisive role in the transport and magnetic properties.