Oxygen Ordering in Yba 2 cu 3 o z at Low Temperature
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OXYGEN ORDERING INYBa 2 Cu3Oz AT LOW TEMPERATURE G. CEDER,- M.ASTA** and D.de FONTAINE* "*Dept. of Materials Science and Minerals Engineering, University of California, Berkeley, CA 94720, and Materials and Chemical Science Division, Lawrence Berkeley Laboratory, Berkeley, CA 94720 "**Dept. of Physics, University of California, Berkeley, CA 94720 ABSTRACT A parameter-free phase diagram is derived for oxygen ordering in the YBa 2 Cu 3 Oz compound. Four phase regions are found in which the following structures are stable: Tetragonal, Ortho I, Ortho II, and anti-Ortho I. In addition, long-period quasi-one-dimensional states of order can become stable at low temperature. A simple branching algorithm allows one to predict these additional structures and their diffraction patterns. Theoretical predictions are in excellent agreement with recent experimental findings. Implications for the existence of Tc plateaus are briefly discussed. INTRODUCTION Oxygen ordering in YBa 2 Cu 3 Oz is responsible for the tetragonal to orthorhombic phase transition at high temperature [1] and gives rise to additional ordered phases at low temperature [2,3]. Although the Cu-O planes in which these configurational changes take place probably do not carry the superconducting current, the oxygen ordering may still be relevant for the phenomenon of superconductivity in this compound as ordered configurations are known [4] to produce a higher hole density in the CuO 2 planes than random oxygen distributions with the same composition. Moreover, it has been suggested recently [3] that such ordered superstructures are intimately related to the existence of "plateaus" in the Tc vs. oxygen content behavior observed by various investigators [3,5,6]. The purpose of this communication is to present a consistent theoretical model for oxygen ordering in YBCO featuring a parameter-free "pseudo-binary" phase diagram for this system and an algorithm for determining "branching phases," the predicted structures and diffraction patterns of which agree closely with experimental findings [2,3]. PHASE DIAGRAM The basic model, described in detail elsewhere [7,8], consists of a two-dimensional array of oxygen sites forming two interpenetrating square sublattices on the "basal" (or "chain") plane of YBCO. A positive (repulsive or "ordering") effective pair interaction V1 couples the two sublattices, a second-neighbor pair interaction couples oxygen sites in the 0Cu-O chain direction (V2 ) and repulsive interactions (V3 ) couple oxygen sites in the direction normal to the chains. Heuristically, it may be deduced that V2 must be negative (attractive or "clustering") and that the dominant effective pair interaction in the normal direction, V , must 3 be positive. There results a two-dimensional Ising model with isotropic nearest-neighbor and anisotropic next-neighbor interactions. Ground state analyses were performed [8,9] for all possible values of the ratios V2 /V1 and V3 /V1 and the conditions for the stability of the observed orthorhombic phases, Ortho I (stoichiometr
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