The underlying mechanisms of phase transitions and the emergence of complexity are long-standing fundamental subjects for which a complete and unified description is still missing. This is due to the intrinsic nature of condensed matter, which contains a very large number of interacting particles. The partial or complete resolution of these open questions will require a considerable development of the experimental and theoretical means. In this context, the newlydevelopedextremely brilliant x-ray source at the European Synchrotron Radiation Facility with its unprecedented performances will provide the scientific community with a unique tool to tackle such challenging objectives. In this review article, we will discuss, through some selected examples, the potential impact this new instrument could have in the short and long term in this field of research.
Keywords: phase transitions; structural complexity; synchrotron x-ray radiation.
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