  Spectral singularities that spoil the completeness of Bloch-Floquet states
may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here
an equivalence is established between spectral singularities in complex
crystals and secularities that arise in Bragg diffraction patterns. Signatures
of spectral singularities in a scattering process with wave packets are
elucidated for a PT-symmetric complex crystal.
