text: In a crystal, the constitutive particles are arranged periodically, with translational symmetry forming a lattice. The crystal structure can be described as a Bravais lattice with a group of atoms, called the basis, placed at every lattice point; that is, [crystal structure] = [lattice]  [basis]. If the lattice is infinite and completely regular, the system is a perfect crystal.  For such a system, only a set of specific values for  can give scattering, and the scattering amplitude for all other values is zero.  This set of values forms a lattice, called the reciprocal lattice, which is the Fourier transform of the real-space crystal lattice.
  In principle the scattering factor  can be used to determine the scattering from a perfect crystal; in the simple case when the basis is a single atom at the origin (and again neglecting all thermal motion, so that there is no need for averaging) all the atoms have identical environments. Equation () can be written as
  : and    .
  The structure factor is then simply the squared modulus of the Fourier transform of the lattice, and shows the directions in which scattering can have non-zero intensity. At these values of  the wave from every lattice point is in phase. The value of the structure factor is the same for all these reciprocal lattice points, and the intensity varies only due to changes in  with .