Intensity of Diffraction: the Structure Factor Equation 
Intensity of Diffraction: the Structure Factor Equation
If the previous two sections answer the question when?, this section starts to address the question how much? The concepts of Ewald sphere and reciprocal lattice or Bragg's law predict when diffraction will occur but give no indication of the intensity of a given diffraction event.
If we start with the scattering formula as seen earlier:
F(S) = 
Σ n 
f_{n}e^{2π i S.rn} 
r = xa + yb + zc 
F(S) = 
Σ n 
f_{n}e^{2π i S.(xa + yb + zc )} = 
Σ n 
f_{n}e^{2π i (S.ax + S.by + S.cz)} 
F(S) = 
Σ n 
f_{n}e^{2π i (hx + ky + lz )} 
F(S) = 
Σ x 
Σ y 
Σ z 
f_{n}e^{2π i (hx + ky + lz )} 
If Bragg's equation is the most wellknown equation, then the structure factor equation must be the second most wellknown. As much of crystallography is involved with determining atomic structure from the intensity of diffraction spots/peaks, then this equation acts as the basic computational link between the two. At first it might appear to be quite complex given the summations and use of complex numbers. However this is not so; even if students cannot understand its derivation, the Structure Factor equation is relatively easy to use as we will show later.
© Copyright 19972006.
Birkbeck College, University of London.

Author(s):
Paul Barnes Martin Vickers 