Polarized Raman scattering measurements have been performed on Na0.5CoO2 single crystal from 8 to 305 K. Both the A(1g) and E-1g phonon modes show a softening below T-c1 approximate to 83 K. Additionally, the A(1g) phonon mode, which is forbidden in the scattering geometry of cross polarization for the triangular CoO2 layers, appears below T-c1. In contrast, the metal-insulator transition at T-c2 approximate to 46 K has only secondary effect on the Raman spectra. The phonon softening and the forbidden Raman intensity follow closely magnetic order parameter and the gap function at the Fermi surface, indicating that the distortion of CoO6 octahedra at T-c1, instead of the Na ordering at similar to 350 K, is the relevant structural component of the 83 K phase transition.
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