  The relation between the properties of a specific crystallographic site and
the properties of the full crystal is discussed by using spherical tensors. The
concept of spherical tensors is introduced and the way it transforms under the
symmetry operations of the site and from site to site is described in detail.
The law of spherical tensor coupling is given and illustrated with the example
of the electric dipole and quadrupole transitions in x-ray absorption
spectroscopy. The main application of the formalism is the reduction of
computation time in the calculation of the properties of crystals by band
structure methods. The general approach is illustrated by the examples of
substitutional chromium in spinel and substitutional vanadium in garnet.
