Short-pitch helicoidal modes in antiferroelectric liquid crystals and scattering of resonant X rays

The structure of antiferro-and ferroelectric phases in chiral smectic liquid crystals is studied on the basis of the theory of modes with a short pitch. The existence of ferroelectric phases is explained both by the characteristic incommensurability of short-pitch modes with respect to the thickness of the smectic layer and by distortions of the short-pitch antiferroelectric structure of a long-wavelength mode. It is pointed out that the details of the short-pitch order can be observed in resonant x-ray scattering. The fundamental features of the pattern of such scattering in the phases considered are predicted.