  We extend the Weak Crystallization theory to the case of metallic alloys. The
additional ingredient -- itinerant electrons -- generates nontrivial dependence
of free energy on the angles between ordering wave vectors of ionic density.
That leads to stabilization of FCC, Rhombohedral, and icosahedral
quasicrystalline (iQC) phases, which are absent in the generic theory with only
local interactions. The condition for stability of iQC that we find, is
consistent with the Hume-Rothery rules known empirically for majority of stable
iQC; namely, the length of the primary Bragg peak wavevector is approximately
equal to the diameter of the Fermi surface.
