The crystal structure of the non-stoichiometric Na _x Si ₁₃₆ silicon clathrate has been refined using the Rietveld method, in order to determine accurately the distribution of the sodium atoms within the two available sites. In agreement with the previous data, it was found that for x≤8, the alkali atoms occupy exclusively, and not only preferentially the eight larger Si ₂₈ sites. For 8<x<24, the filling of the sixteen smaller Si ₂₀ cages occurs gradually with increasing x, and a slight increase of the unit cell parameter is then observed. The crystal structure of the stoichiometric Na ₈ Si ₄₆ clathrate, which is present as impurity in the studied samples, has also been refined.