Although the physical consequences of incommensurability upon a structure will be made manifestly observable to most experimental probes, it is scattering techniques which have proved the most valuable tools for their study. A comprehensive review of the other various experimental methods, and their development based largely on superspace methods, can be found in Cummins [30].
The nature of x-ray scattering from incommensurate crystal phases is discussed in this section, developing the necessary theoretical ground for the understanding of the experimental results presented in subsequent chapters. The starting point is the basic equation for the diffraction of x-rays by an ideal periodic crystal which is briefly introduced using the kinematical approach. Then the equations are extended to include diffuse scattering by considering the general case of deviations from the periodic. The result leads to useful approximations for two cases: (i) the dynamic fluctuation of atoms, due to thermal vibration, which describes the influence of temperature upon scattered intensities; and (ii) the description of the satellite reflections from crystals modulated by a single harmonic displacement wave.