Calculations of
f
, the atomic scattering factor of an element for X-rays, have hitherto been made on the assumption that the value of
f
for a given value of sin θ/λ is independent of wave-length. This assumption is only justified when the frequency of the X-rays is much greater than the characteristic frequency of any of the energy levels in the scattering atom. This condition is realised when a hard radiation such as Mo Kα is used in order to investigate crystals containing only light elements, such as aluminium. Under these conditions it has been found that absolute determination of
f
made experimentally give results in excellent agreement with theory. In many investigations, however, we are dealing with an entirely different set of conditions. For example, investigations of alloys are usually carried out with Cr, Fe or Cu radiation. Often the alloys contain Cr, Mn, Fe, Co, Ni, Cu or Zn, and the K absorption edge for each of these elements is near the wave-length of the radiation employed. Under these circumstances the conditions postulated by the simple theory no longer hold. Dispersion terms must now be introduced into the scattering formula, and we get an effect which may in some degree be compared with the anomalous dispersion of light.
the atomic scattering power of iron for various X-ray wave-lengths