The investigation of the multiscale phase separation from nanoscale to micron scale, really demands powerful bulk experimental methods without any time or spatial averaging. Local structural probes with micrometer size spots such the Pair Distribution Function (PDF) or micro-X-ray Absorption Near Edge structure (m-XANES) may investigate nanoscale structuresand nanoparticles. Available data provide information on local electronic and lattice fluctuations, complementary to other techniques such as scanning mXRD.Moreover, using specific optical layouts, X-ray imaging at high spatial resolution can be combined with m-XANES spectroscopy to identify chemical changes and correlate them with 2D and 3D morphologies.

As an example I will present and discuss m-XANES data of La₂CuO_4+y, the simplest cuprate superconductor with mobile oxygen interstitials that exhibits a bulk multiscale structural phase separation. I will show that m-XANES mapping at the La L₃-edge provide the experimental support to the percolative superconductivity scenario in high temperature cuprates superconductors. The phase separation (PS) that appears in the La₂CuO_4+y near the insulator to metal transition (IMT) can be associated to a short range Charge Density Wave (CDW) order inhomogeneity coexisting with a quenched lattice disorder. Near the IMT in the La₂CuO_4+y at y=0.06 two coexisting superconducting phases appear. One at T_c1 = 16 K and one at T_c2 = 29 K. I may show that they are characterized by two different space geometries and also by two different superconducting vortex dynamics in two different complex geometrical spaces.