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Secondary emission from a semi-infinite crystal is considered. The contribution to the emission amplitude originating from structural factor singularities is analyzed. Poles of the structural factor determine the main contribution to the emission amplitude. The energy and angular distributions of the emission depend on the crystallographic orientation of the crystal surface and are characterized by a set of allowed vectors of the reciprocal lattice. It is shown that emission anisotropy related to the crystallographic directions is due to the coherent character of the photoabsorption process, and diffraction scattering leads only to relative change in the emission intensity in allowed low-index directions. The concrete calculations are performed for (100) and (111) surfaces of a diamond-like lattice. [ABSTRACT FROM AUTHOR]