Sign reversal of the atomic scattering factor and grazing-incidence transmission at x-ray-absorption edges

We investigate a conjecture that the atomic scattering factor may change sign as the result of strong dispersion near certain x-ray absorption edges. A corollary is that the refractive index of matter is greater than unity in such regions. We find probable examples at the LII,III edges of aluminum and silicon. In these anomalous regions total external reflection at grazing incidence, which is characteristic of x rays, does not occur at any angle. Rather, there is unusually high transmission at grazing incidence for photon energies below the edge. This localized departure from total external reflection is a sensitive probe of optical properties and may possibly find application in thin-film notch filters for vuv or x-ray photons.