Diffraction streaks due to phase disorder in one-dimensional displacive modulation

It can be proved mathematically that the initial phase disorder in the wave of a one-dimensional displacive modulation introduces additional variations in the structure of reciprocal space and, as a result, causes characteristic diffraction streaks. Using a simple two-dimensional model, the occurrence of such streaks is confirmed in optical diffraction patterns. Electron diffraction streaks from two crystals with incommensurately modulated structures are presented and explained as the diffraction effect of the phase disorder.