Role of the coupling between strains and order parameter gradient in crystals

The manifestation and the role of coupling between order parameter gradient and strains, or equivalently between order parameter and gradient of strains, is reviewed. Dynamical phenomena occurring in perovskites, and in particular in quantum paraelectric phases, evidenced as a coupling between phonon branches at q≠0, and also in several other systems (quartz, Sn₂P₂Se₆, Cs₂HgBr₄, and other systems satisfying the Lifshitz criterion) in relation with the formation of an incommensurate phase, are presented. Besides, the consequences in relation with domain walls, structure of incommensurate phases, and defects are also discussed.