Charge ordering and elastic anomalies in NaxCoO2

We report in-plane resistivity and elastic constant C₃₃ measurements on the Na_0.8CoO₂ and Na_0.5CoO₂ systems. An ordering transition is found at T₀=280 K for Na_0.8CoO₂. The temperature dependence of the elastic constant C₃₃ propagating perpendicular to the CoO₂ layers is interpreted, in a phenomenological approach, as being due to the anharmonicity of atomic vibrations. The effective Grüneisen parameter γ_eff deduced directly from the temperature dependence of C₃₃ exhibits important changes at the charge ordering, magnetic and metal-insulator phase transitions.