  The crystal structures of the NaxCoO2 phases based on three-layer NaCoO2,
with x=0.32, x=0.51, x=0.60, x=0.75 and x=0.92, determined by powder neutron
diffraction, are reported. The structures have triangular CoO2 layers
interleaved by sodium ions, and evolve with variation in Na content in a more
complex way than has been observed in the two-layer NaxCoO2 system. The highest
and lowest Na containing phases studied (x=0.92 and x=0.32) are trigonal, with
three CoO2 layers per cell and octahedral Na ion coordination. The intermediate
compositions have monoclinic structures. The x=0.75 compound has one CoO2 layer
per cell, with Na in octahedral coordination and an incommensurate
superlattice. The x=0.6 and x=0.5 phases are also single-layer, but the Na is
found in trigonal prismatic coordination. The magnetic behavior of the phases
is similar to that observed in the two-layer system. Both the susceptibility
and the electronic contribution to the specific heat are largest for x=0.6.
