text: For  a finite crystal means that the sums in equations 1-7 are now over a finite .  The effect is most easily demonstrated with a 1-D lattice of points. The sum of the phase factors is a geometric series and the structure factor becomes:
  This function is shown in the Figure for different values of .
  When the scattering from every particle is in phase, which is when the scattering is at a reciprocal lattice point , the sum of the amplitudes must be  and so the maxima in intensity are  .  Taking the above expression for  and estimating the limit  using, for instance, LHôpitals rule) shows that   as seen in the Figure. At the midpoint  (by direct evaluation) and the peak width decreases like . In the large  limit, the peaks become infinitely sharp Dirac delta functions, the reciprocal lattice of the perfect 1-D lattice.
  In crystallography when  is used,  is large, and the formal size effect on diffraction is taken as , which is the same as the expression for  above near to the reciprocal lattice points, .  Using convolution, we can describe the finite real crystal structure as [lattice]  [basis] rectangular function, where the rectangular function has a value 1 inside the crystal and 0 outside it.  Then [crystal structure] = [lattice] [basis] [rectangular function]; that is, scattering  [reciprocal lattice]  [structure factor]  [ sinc function]. Thus the intensity, which is a delta function of position for the perfect crystal, becomes a  function around every point with a maximum , a width , area .