Superstructures in superconductors: The case of YBCO

Superstructures characterized by {\bf q}=(q$_x$, 0, 0) are observed throughout the phase diagram of yttrium-barium cuprates (YBa$_2$Cu$_3$O$_{6+x}$, YBCO); {\bf q} decreases with doping from $\frac12$ (2-unit-cell) in the heavily un-derdoped compound to $\frac15$ in the overdoped material. A 4-unit-cell superstucture is stable in the vicinity of optimal doping. The superstructures in YBCO correspond to short-range ordered regions of coupled atomic displacements on neighboring CuO, BaO, and CuO$_2$ planes, respectively. T-dependent measurements suggest that these ``nanodomains'' experience anharmonic thermal motion. These regions induce a long-range strain in the host, which manifests as ``bow-tie''-shape Huang diffuse scattering below $\sim$200 K. X- ray diffuse scattering results will be presented within the context of the oxygen ordering and the phase diagram.