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We present high energy X-ray diffraction studies on the structural phases ofan optimal high-$T_c$ superconductor La$_{2-x}$Sr$_x$CuO$_{4+y}$ tailored byco-hole-doping. This is specifically done by varying the content of two verydifferent chemical species, Sr and O, respectively, in order to study theinfluence of each. A superstructure known as staging is observed in allsamples, with the staging number $n$ increasing for higher Sr dopings $x$. Wefind that the staging phases emerge abruptly with temperature, and can bedescribed as a second order phase transition with transition temperaturesslightly depending on the Sr doping. The Sr appears to correlate theinterstitial oxygen in a way that stabilises the reproducibility of the stagingphase both in terms of staging period and volume fraction in a specific sample.The structural details as investigated in this letter appear to have no directbearing on the electronic phase separation previously observed in the samesamples. This provides new evidence that the electronic phase separation isdetermined by the overall hole concentration rather than specific Sr/O contentand concommittant structural details.

Staging superstructures in high-$T_c$ Sr/O co-doped La$_{2-x}$Sr$_x$CuO$_{4+y}$