  The simple alkali metal Na, that crystallizes in a body-centred cubic
structure at ambient pressure, exhibits a wealth of complex phases at extreme
conditions as found by experimental studies. The analysis of the mechanism of
stabilization of some of these phases, namely, the low-temperature Sm-type
phase and the high-pressure cI16 and oP8 phases, shows that they satisfy the
criteria for the Hume-Rothery mechanism. These phases appear to be stabilized
due to a formation of numerous planes in a Brillouin-Jones zone in the vicinity
of the Fermi sphere of Na, which leads to the reduction of the overall
electronic energy. For the oP8 phase, this mechanism seems to be working if one
assumes that Na becomes divalent metal at this density. The oP8 phase of Na is
analysed in comparison with the MnP-type oP8 phases known in binary compounds,
as well as in relation to the hP4 structure of the NiAs-type.
