  We study the effect of planar defects in phononic crystals of spherical
scatterers. It is shown that a plane of impurity spheres introduces modes of
vibration of the elastic field localized on this plane at frequencies within a
frequency gap of a pure phononic crystal; these show up as sharp resonances in
the transmittance of elastic waves incident on a slab of the crystal. A
periodic arrangement of impurity planes along a given direction creates narrow
impurity bands with a width which depends on the position of these bands within
the frequency gap of the pure crystal and on the separation between the
impurity planes. We show how a slight deviation from periodicity (one impurity
plane is different from the rest) reduces dramatically the transmittance of
elastic waves incident on a slab of the crystal.
