Solid State Communications, Vol. 67, No. 3, pp. 287-291, 1988. 0038-1098/88 $3.00 + .00 Printed in Great Britain. Pergamon Press plc MONTE CARLO STUDIES OF OXYGEN ORDERING IN THE YBa2Cu307 a BASAL PLANE Zhi-Xiong Cai and S.D. Mahanti Department of Physics and Astronomy and Center for Fundamental Materials Research, Michigan State University, East Lansing, Michigan 48824-1116, USA (Received 3 March 1988 by J. Tauc) Using Monte Carlo simulation of a 2 - d lattice-gas model with anisotropic long range interaction, we have investigated the order-disorder transition in the basal plane of YBa2Cu307 ,~ (0 < < 1). With a suitable choice of parameters, we can explain most of the experimental observation semi-quantitively. In particular, the values of oxygen concentration at the order-disorder transition temperature suggests that the interaction between two oxygen atoms bridged by a copper ion is attractive. THE INTERRELATIONSHIP between the basal plane oxygen ordering, the lattice structure and the high superconducting transition temperature in YBa2- Cu307 ,~ has been well documented [1--3]. For exam- ple, the tetragonal (T) phase of YBa2Cu3Q 5 obtained by rapid quenching from high temperature gives T, ~ 0 K whereas a system with the same stoichiome- try obtained by gettering technique has an orthorhom- bic (O) structure and T~ ~ 60 K [2]. Thus understand- ing the nature of oxygen ordering and the defect struc- ture are prerequisites to an understanding of the superconducting properties of these high T, ceramics. Recently, there have been a number of theoretical studies of the oxygen ordering in the basal plane of YBaeCu307 ,~ (0 < c~ < 1) using 2-dimensional lat- tice gas models [4-8]. These studies assume that the oxygen ordering drives the tetragonal to orthorhom- bic structural phase transition but do not take explicit account of the coupling between the lattice gas varia- bles and elastic degrees of freedom. The lattice-gas Hamiltonians used in these studies all have nearest neighbor repulsion between oxygen atoms, but differ from each other as regards the next-neighbor interac- tions are concerned. Furthermore these theoretical investigations use either a quasi-chemical or cluster- variation approximation. In the present work, we have explored the physi- cal properties of the 2 d lattice gas model using Monte Carlo simulation with a concentration depen- dent field. The purpose of our research is fourfold: (1) although quasi-chemical and cluster variation meth- ods have been fairly accurate for nearest neighbor lattice-gas and Ising models, it is necessary to test 'hese methods for more complicated Hamiltonians as are appropriate for the problem at hand. Further- more, a more accurate calculation should tell us some- thing concrete about the values of the interaction parameters. (2) Experimentally, it is found that 6 ~ 0.5 at the T --* O phase transition temperature and is relatively insensitive to the oxygen partial press- ure (P) of the environment [1]. We would like to draw some conclusions about the nature of interaction par- ameters based on this fact. (3) Since the oxygen-defect structure is important in determining the electronic structure, it will be important to understand this de- fect structure i.e. vacancy (V) ordering, twin-plane formation and vacancy-twin plane attraction. (4) Fi- nally, we would like to see whether using a simple model, we can understand all the observed experi- mental facts about the tetragonal to orthorhombic phase transition, albeit qualitatively. As an approximation to modeling the order- disorder transition in this system, the structures of CuO basal plane can be described as a 2-dimensional square lattice consisting of Cu atoms, oxygen atoms, and oxygen vacancies. In the ordered (orthorhombic) phase the oxygen atoms and vacancies are ordered so that there are linear Cu-O chains parallel to the b-axis and Cu-V chains parallel to the a-axis of the orthor- hombic structure, as shown in Fig. I. The stoichio- merry of this arrangement is YBa2Cu307. If the oxy- gen atoms are absent from this plane, then one has YBa2Cu306 and its structure is tetragonal. The lattice-gas Hamiltonian used in our study is: HLG = VIE ninj + ~ ~ n~nj + nn nnna nnnb i 287