2.6.4 X-ray total reflection
The reflection of x-rays can be described in a way analogous to that used for light optics. One has to consider that the interaction of the x-ray electromagnetic wave that hits a plane boundary between vacuum and a material is described by its refraction index n, which takes into account both scattering and absorption and can be calculated by quantum mechanics.
Where NA is the Avogadro number, λ is the wavelength of the incident radiation, ρ is the density of the medium, A is the atomic mass, e and m0 are the electric charge and rest mass of the electron, and c is the velocity of light.
As the bound electrons from the material follow the incident photons in the opposite phase, the real part of refraction index for x-rays (1 - δ) is slightly smaller than unit. The imaginary part β of the refraction index (usually smaller than 1 - δ) is a measure of absorption.
The so called critical angle for total reflection can be described as:
where Z is the atomic number of the element.
The dependence of total reflection critical angle and energy is depicted in the animation below.
An introduction to TXRF spectrometry has been prepared in another e-learning material available on-line at the IAEA Training Course series (CD-ROM) TCS-51.