Nature of e(g) electron order in La(1-x)Sr(1+x)MnO(4)

X-ray scattering measurements of the low-temperature structure of La(1-x)Sr(1+x)MnO(4) ( 0.33< or =x< or =0.67) indicate the existence of three distinct regions: a disordered phase (x<0.4), a charge-ordered phase (x> or =0.5), and a mixed phase (0.4< or =x<0.5). For x>0.5, the modulation vector associated with the charge order is incommensurate with the lattice and depends linearly on the concentration of e(g) electrons. The primary superlattice reflections are strongly suppressed along the modulation direction and the higher harmonics are weak, implying the existence of a largely transverse and nearly sinusoidal structural distortion, consistent with a charge-density wave of the e(g) electrons.