The crystal scattering of two coherent neutron beams is discussed. It is found that the conventional pair correlation function used in single-beam scattering is insufficient to describe the scattering of two coherent neutron beams. A generalized pair correlation function with unequal momentum transfer is introduced. It is found that the energy exchange between vibrational quanta of the crystal and incident neutrons leads to a modification of the scattering amplitude. Through the scattering of two coherent neutron beams one is able to measure directly the phase of the scattering amplitude.