Oxygen-ordering superstructures in underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ studied by hard x-ray diffraction

High-energy x-ray diffraction is used to investigate the bulk oxygen-ordering properties of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}.$ Four different superstructures of Cu-O chains aligned along the b axis and ordered with periodicity $ma,$ along the a axis have been observed. For $x<\mathrm{}0.62,$ the only observed superstructure is ortho-II with $m=2.\mathrm{}$ At room temperature, we find ortho-III $\mathrm{}(m=3\mathrm{})\mathrm{}$ for $0.72<~x<~0.82,$ ortho-V $\mathrm{}(m=5\mathrm{})\mathrm{}$ in a mixed state with ortho-II at $x=0.62,$ and ortho-VIII $\mathrm{}(m=8\mathrm{})\mathrm{}$ at $x=\mathrm{0.67.}\mathrm{}$ Ortho-II is a three-dimensional ordered structural phase, the remaining ones are essentially two-dimensional. None of the superstructures develops long-range ordering. The temperature dependence of the observed superstructure ordering is investigated explicitly and a structural phase diagram is presented.