  The determination by powder neutron diffraction of the ambient temperature
crystal structures of compounds in the NaxCoO2 family, for 0.3 < x <= 1.0, is
reported. The structures consist of triangular CoO2 layers with Na ions
distributed in intervening charge reservoir layers. The shapes of the CoO6
octahedra that make up the CoO2 layers are found to be critically dependent on
the electron count and on the distribution of the Na ions in the intervening
layers, where two types of Na sites are available. Correlation of the shapes of
cobalt-oxygen octahedra, the Na ion positions, and the electronic phase diagram
in NaxCoO2 is made, showing how structural and electronic degrees of freedom
can be coupled in electrically conducting triangular lattice systems.
