Charge modulations versus strain waves in resonant x-ray scattering

A method is described for using resonant x-ray scattering to separately quantify the charge (valence) modulation and the strain wave associated with a charge density wave. The essence of the method is a separation of the atomic form factor into a raw amplitude f(R)(omega) and a valence-dependent amplitude f(D)(omega) which in many cases may be determined independently from absorption measurements. The advantage of this separation is that the strain wave follows the average quantity parallel to f(R)(omega)+< v > f(D)(omega)parallel to(2), whereas the charge modulation follows only parallel to f(D)(omega)parallel to(2). This allows the two distinct modulations to be quantified separately. A scheme for characterizing a given CDW as Peierls-like or Wigner-like follows naturally. The method is illustrated for an idealized model of a one-dimensional chain.