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Precipitated phases, formed by spinodal decomposition during long‐term storage in a desiccator in dry atmosphere, are found with the X‐ray diffraction (XRD) study of Fe1+yTe1−xSex crystals. Their compositions are deduced from the position of satellite Bragg reflections in the XRD pattern. In particular, in the Fe1.19Te0.58Se0.42 crystal, traces of phases with significantly higher tellurium content, namely Fe1+yTe0.9Se0.1 and FeTe, are found. The detection and analysis of side bands in the diffraction pattern of an aged crystal indicate spinodal decay. It leads to the formation of a modulated structure in the entire volume of the sample and to strain in the crystal structure. In turn, this results in a significant improvement in the superconducting characteristics. Specifically, the resistive transition narrows to 2 K at the onset temperature 14.5 K, and the superconducting volume fraction increases up to about 100%. [ABSTRACT FROM AUTHOR]