The structural behavior of ${\mathrm{mm}}^3$-sized single crystals of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$ with oxygen concentrations close to the metal-insulator transition is studied as a function of temperature, using 95-keV synchrotron x-ray diffraction. At x=0.36, no evidence is found of a room-temperature phase separation into tetragonal and orthorhombic phases, nor of a phase boundary between Ortho-II and tetragonal. Instead, we observe two distinct phase transitions: tetragonal to Ortho-I with a critical temperature ${\mathit{T}}_{\mathit{O}\mathrm{I}}$=246(2) °C and Ortho-I to Ortho-II with ${\mathit{T}}_{\mathit{O}\mathrm{II}}$=85(10) °C. Measurements of the spontaneous strain show the O/T transition to be nearly continuous with a critical exponent β=0.34(2), consistent with a 3D Ising model driven weakly first order, presumably by the strain. A memory effect is observed, where relics of the twin domains—possibly related to tweed formations—continue to exist in the tetragonal phase when the temperature is increased above ${\mathit{T}}_{\mathit{O}\mathrm{I}}$. Corresponding measurements for x=0.35 gave similar results—with ${\mathit{T}}_{\mathit{O}\mathrm{I}}$=181(2) °C, ${\mathit{T}}_{\mathit{O}\mathrm{II}}$=95(10) °C, and β=0.35(2)—but with the appearance of a small tetragonal component at room temperature. This component is interpreted as a nonequilibrium feature. In both cases the Ortho-I to Ortho-II transformations are very broad with a characteristic temperature dependence of the widths of the superstructure peaks that are similar to results obtained in a previous study for x=0.50. By comparison of the Ortho-II correlation lengths along a, b, and c with the corresponding data for x=0.50 we find evidence for a strong x dependency of ASYNNNI-type effective interaction parameters. The present results cannot be explained in terms of prevalent lattice gas models of the oxygen ordering and emphasizes the need for a theoretical basis that incorporates the strain and charge degrees of freedom. © 1996 The American Physical Society.

• Received 19 December 1995

DOI:https://doi.org/10.1103/PhysRevB.53.15335