Practical Electron Microscopy and Database

Based on theoretical electrodynamics with the interaction of incident electrons on a surface, the angular distribution of generated X-rays can be give in the form of polar equation, [1]
          ----------------------- [1001]
where,
         θ -- the angle between the directions of emission and acceleration.
          -- the electron acceleration.

Equation 1001 results in a typical dipole characteristic:
         i) a maximum of emission perpendicular at θ = 90° to the dipole.
         ii) a zero emission parallel at θ = 0 and 180° to the dipole.

As shown in Figure 1001, the maximum emission of the x-ray continuum is shifted to smaller angles B because:
         i) the Coulomb field of a moving charge is not exactly radially-symmetric owing to relativistic effects.
         ii) a retardation has to be taken into account due to the finite velocity of wave propagation.

(a)	(b)

[1] Ludwig Reimer, Scanning Electron Microscopy: Physics of Image Formation and Microanalysis, 1998.