Spherical harmonics are good basis functions for isotropic continuum systems, for example isolated atoms. For lattices, the plane wave is already the appropriate basis function to be used in expansions. You can of course expand the plane wave into spherical harmonics, but I am not aware of any reason this would be practical in the evaluation of scattering processes.

The key geometrical ingredient in lattice calculations is symmetry. To model scattering off of lattices, one has to consider the point group of the unit cell, usually expressed in Cartesian coordinates. The calculation of scattering cross sections involves coherent sums over lattice points. These give rise to lattice structure factors, which govern the general characteristics of the scattering spectrum. In non-resonant, quasi-elastic scattering, this is essentially the entire process necessary to obtain the scattering response.

Spherical harmonics are good basis functions for isotropic continuum systems, for example isolated atoms. For lattices, the plane wave is already the appropriate basis function to be used in expansions. You can of course expand the plane wave into spherical harmonics, but I am not aware of any reason this would be practical in the evaluation of scattering processes.

The key geometrical ingredient in lattice calculations is symmetry. Some general characteristics of the scattering response can be immediately deduced from the point group of the unit cell. The full calculation of scattering cross sections involves coherent sums over lattice points, usually carried out in Cartesian coordinates. These give rise to lattice structure factors, which govern the general characteristics of the scattering spectrum. In non-resonant, quasi-elastic scattering, this is essentially the entire process necessary to obtain the scattering response.