Modulated Structures Induced by Phase Transformations

Modulated structures can be found in organic, inorganic and even quasicrystalline structures. They are generally detected by diffraction from the presence of satellites surrounding the Bragg reflections. Their positions may vary continuously with temperature or pressure so that the phase can be considered as incommensurately modulated. Incommensurate phases usually transform to a periodic high symmetry phase by increasing temperature and to a commensurate lock-in phase by lowering the temperature. Their domain of stability varies with temperature, pressure and with the type of compound. Examples have been identified where the interval of equilibrium vary from a few tenths to a few hundreds of degrees. Recent progress in the field of incommensurate structure analysis has been greatly favoured by the superspace group approach which is now almost exclusively applied. In many cases, the resolution of the modulated phases by diffraction methods has contributed towards the understanding of the phase changes. In addition, microscopic models for the transition mechanisms have been developed to understand small organic systems. The methods of molecular dynamics have been able to explain the formation of various sequences of commensurate and incommensurate phases observed experimentally.