The Falicov-Kimball model of spinless itinerant fermions and localized
classical ions, on a one-dimensional lattice and at zero temperature,
has been studied by means of restricted phase diagrams in the grand-c
anonical ensemble. Compared with earlier investigations a more efficie
nt numerical procedure has been applied and consequently more precise
phase diagrams have been obtained. For small and large values of the u
nique coupling parameter our study has confirmed the results obtained
in other works; however for intermediate values we have found new kind
s of periodic phases and structural phase transitions.