Practical Electron Microscopy and Database

An Online Book, Second Edition by Dr. Yougui Liao (2006)

Practical Electron Microscopy and Database - An Online Book

Chapter/Index: Introduction | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | Appendix

Angular/Polar Distribution of X-ray Generation in Electron Microscopy

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]
         Angular/Polar Distribution of X-ray Generation in Electron Microscopy ----------------------- [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)
Figure 1001. Polar diagram of the angular distribution of the x-ray continuum generated in Al (left) and Au (right). [1]


         

 

 

 


         
           

 

 

 

 

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