  The coherent process of particle deflection by aligned atomic strings and
planes of oriented crystals is accompanied by incoherent scattering by atomic
cores. While the coherent particle deflection, described by the axial or planar
averaged potential, becomes more and more classical at high energies, the
incoherent scattering of relativistic particles remains essentially quantum.
Though the latter reminds the scattering by atoms of amorphous medium at high
enough momentum transfers, at the smallest ones the incoherent scattering
process in crystals experiences some modification by the influence of the
inhomogeneity of the atom distribution in the plane, normal to the crystal axis
or plane. Considering the axial case as a more general example, we present a
consistent theory of high energy particles incoherent scattering in oriented
crystals. The latter takes into consideration both the quantum scattering
nature and the atom distribution inhomogeneity, revealing the limited
applicability of the scattering cross section notion. The way to incorporate
the quantum scattering features into the widely used classical trajectory
simulations is elaborated using newly introduced mean square scattering angle
definition.
