  A series of CaxCoO2 (0.15 <= x <= 0.40) materials have been prepared by means
of ion exchange reaction from NaxCoO2. Transmission electron microscopy (TEM)
measurements revealed a rich variety of structural phenomena resulting from
cation ordering, structural distortion and twinning. Systematical structural
analysis, in combination with the experimental data of NaxCoO2 (0.15 <= x <=
0.8) and SrxCoO2 (1.5 <= x <= 0.4) systems, suggests that there are two common
well-defined cation ordered states corresponding respectively to the
orthorhombic superstructure at around x = 1/2 and the 31/2a&#61620;31/2a
superstructure at around x = 1/3 in this kind of system. Multiple ordered
states, phase separation, and incommensurate structural modulations commonly
appear in the materials with 0.33 < x < 0.5. The TEM observations also reveals
an additional periodic structural distortion with q2 = a* / 2 in materials for
x <= 0.35. This structural modulation also appears in the remarkable
superconducting phase Na0.33CoO2 1.3H2O.
