InternationalReciprocal spaceTables for Crystallography Volume B Edited by U. Shmueli © International Union of Crystallography 2010 |
International Tables for Crystallography (2010). Vol. B, ch. 1.2, p. 10
## Section 1.2.3. Scattering by a crystal: definition of a structure factor |

In a crystal of infinite size, is a three-dimensional periodic function, as expressed by the convolution where *n*, *m* and *p* are integers, and δ is the Dirac delta function.

Thus, according to the Fourier convolution theorem, which gives

Expression (1.2.3.3) is valid for a crystal with a very large number of unit cells, in which particle-size broadening is negligible. Furthermore, it does not account for multiple scattering of the beam within the crystal. Because of the appearance of the delta function, (1.2.3.3) implies that **S** = **H** with .

The first factor in (1.2.3.3), the scattering amplitude of one unit cell, is defined as the structure factor *F*: