X-ray scattering measurements of the low-temperature structure of La1-xSr1xMnO4 (0.33 less than or equal to x less than or equal to 0.67) indicate th
e existence of three distinct regions: a disordered phase (x < 0.4), a char
ge-ordered phase (x <greater than or equal to> 0.5), and a mixed phase (0.4
less than or equal to x < 0.5). For x > 0.5, the modulation vector associa
ted with the charge order is incommensurate with the lattice and depends li
nearly on the concentration of e(g) electrons. The primary superlattice ref
lections are strongly suppressed along the modulation direction and the hig
her harmonics are weak, implying the existence of a largely transverse and
nearly sinusoidal structural distortion, consistent with a charge-density w
ave of the e(g) electrons.