Scattering factors

Relevant section in the xraylib documentation.

Included from the xraylib documentation: In this section, we introduce the momentum transfer parameter q, which is used in several of the following functions. It should be noted that several definitions can be found of this parameter throughout the scientific literature, which vary mostly depending on the community where it is used. The crystallography and diffraction community for example, use the following definition:

\[q = \frac{4\pi \times sin(\theta)}{\lambda}\]

with θ the angle between the incident X-ray and the crystal scattering planes according to Bragg’s law, and λ the wavelength. xraylib (and dxraylib) uses however, a different definition, in which θ corresponds to the scattering angle , which in case of Bragg scattering is equal to twice the angle from the previous definition. This new definition has the advantage of being useful when working with amorphous materials, as well as with incoherent scattering. Furthermore, our definition drops the 4π scale factor, in line with the definition by Hubbell et al in Atomic form factors, incoherent scattering functions, and photon scattering cross-sections, J. Phys. Chem. Ref. Data, Vol.4, No. 3, 1975:

\[q = Ehc \times sin(\frac{\theta}{2}) \times 10^{8}\]

with E the energy of the photon, h Planck’s constant and c the speed of light. The unit of the returned momentum transfer is then Å⁻¹.