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Oxide self-assembly is a promising bottom-up approach for fabricating new composite materials at the nanometer length scale. Tailoring the properties of such systems for a wide range of electronic applications depends on the fundamental understanding of the interfaces between the constituent phases. We show that the nanoscale strain modulation in self-assembled systems made of high-T(c) superconducting films containing nanocolumns of BaZrO(3) strongly affects the oxygen composition of the superconductor. Our findings explain the observed reduction of the superconducting critical temperature.