Charge modulations vs. 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, fR(w), and a valence-dependent amplitude, fD(w), which in many cases may be determined independently from absorption measurements. The advantage of this separation is that the strain wave follows the quantity |fR(w) + <v> fD(w)|^2 whereas the charge modulation follows only |fD(w)|^2. This allows the two distinct modulations to be quantified separately. A scheme for characterizing a given CDW as Peierls-like or Wigner-like naturally follows. The method is illustrated for an idealized model of a one-dimensional chain.