J. MATER. CHEM., 1991, 1(3), 477-478 Madelung Energy and Hole Location in YBa,Cu,O, Sheela K. Ramasesha"and K. Thomas Jacob* "Materials Science Division, National Aeronautical Laboratorx Bangalore 560 0 17, India Department of Metallurgx Indian Institute of Science, Bangalore 560 0 12, India The Madelung energy of YBa,Cu,O, has been computed for different locations of the hole in the structure. The lowest-energy configuration corresponds to partial localization of the hole on 0(1)and O(11) sites. Keywords: Coulomb interaction; Madelung potential; Valence fluctuation; Mixed valence; Hole location Although there has been significant effort, both theoretical and experimental, to understand the location of holes in YB~,CU,O,-~, very little attention has been focussed on the nature of charge carriers in YBa2Cu408 (124).Madelung energy computations provide a simple method for exploring the sites for hole localisation in complex structures. Earlier calculations on the YBa,Cu307 (1 23) compound' indicated that the most probable sites for hole localisation are Cu(1) and O(4) following the nomenclature of Siegriet et aL2 In this communication we explore the minimum-energy locations for holes in the 124 compound. In order to maintain charge neutrality in the 124 compound, a hole has to be localised on copper, oxygen or copper- oxygen ligand. The structure of the 124 compcund is similar to that of the 123 compound except that there is an extra Cu-0 chain in 124. The crystal structure and site descrip- tions are given in Fig.1. Madelung potentials are computed using the Ewald method. Potential around an ion i due to all other ions in the crystal is given by where A is the unit cell volume, G is the reciprocal lattice vector, qi is the charge of the ion around which potential is calculated, qr is the charge of other ions in the crystal, rl is the distance between the ith ion and other ions, S(G) is the structure factor given by S(G)=&,exp(-iG*r,) (2)t and F (x)is the error function of the form The value of the constant q is chosen such that the summations in eqn.( 1) converge rapidly. The computer pro- gram used in this study was checked initially on simple compounds such as NaCl and CsCl. The program was further verified by computing the Madelung potential of YBa2Cu3O7 with holes localized on chain Cu sites.The value of -335.9843 eV obtained compares well with -335.996 eV reported by Tsay et aL3 Atomic positions and cell parameters of the unit cell are 63 Ba @Y 0 cu 00 Fig. 1 The unit cell of YBa,Cu,O, with site description of all the atoms taken from Marsh et aL4 Since the number of formula units per unit cell is two for this compound, potentials have to be calculated around 30 atoms. Symmetry considerations reduce the number of unequal positions to 16. Then by proper multiplicity factors, the Madelung energy, EMad,of the unit cell is calculated. There is one hole per formula unit of YBa2Cu408. The Madelung energy is calculated by localising the hole at different sites in the unit cell.Calculations for hole localisation on the four copper sites [Cu(l), Cu(ll), Cu(2), Cu(21)] and eight oxygen sites [O(l), 0(1 l), 0(2), 0(21), 0(3), 0(31), 0(4), O(41)J are carried out. Since in these high T, superconductors, there is a possibility of hybridi~ation,~-' partial localisation of the hole on several combinations of oxygen sites, copper sites and mixed copper-oxygen sites is considered. A few cases in which hole is localized on three of four sites are also J. MATER. CHEM., 1991, VOL. 1 Table 1 Madelung energy (EMa& and energy of formation (E,) of YBa,Cu,O, from isolated ions Y3+, Ba2+, Cu2+ and 0,-in the gas phase for different locations of holes EMad Ef EMad Ef EMad Ef hole location /eV /eV hole location /eV lev hole location ~~ -737.52 -663.86 -739.29 -665.63 -690.19 -662.1 1 -741.85 -668.19 -658.43 -675.93 -691.39 -663.3 1 -717.60 -643.94 -649.09 -666.59 -691.23 -663.15 -644.84 -662.34 -645.03 -662.53 -690.2 1 -662.13 -652.23 -669.83 -650.78 -668.28 -690.24 -662.16 -643.82 -661.32 -653.08 -670.58 -663.44 -635.36 -617.28 -634.78 -691.93 -663.85 -684.48 -656.39 -645.43 -662.93 -693.26 -665.1 8 -662.55 -634.47 -620.1 1 -637.61 -690.67 -662.59 -681.15 -653.07 -648.17 -665.67 -696.46 -668.38 -690.18 -662.10 -653.15 -670.65 -691.0 -662.92 -687.85 -659.77 atomic sites on which the holes are localized are identified.considered.In such situations, one hole per unit cell is localized on the copper sites and another hole on the oxygen sites. The total Madelung potential, EMvlad,of the unit cell with holes localised on different sites is tabulated in Table 1. The Madelung potential gives the energy associated with building an ionic lattice from constituent ions in the gas phase. In order to determine which configuration has the lowest energy, it is important to refer the energies to a common reference +frame. For convenience one may consider ions of Y ,Ba2+ , Cu2+, 02-in the gas phase at infinite separation as the starting point for the synthesis of different configurations. In cases in which the hole is localised on oxygen sites, two 02-ions have to be converted per unit cell to 0-ions in the gas phase before assembling the ions to form a unit cell in the lattice. When the hole is localised on the copper sites, two Cu2+ ions per unit cell have to be converted to Cu3+ ions before building the lattice.Where the hole is partially localised on both oxygen and copper sites, one 02-ion has to be converted to 0-and one Cu2+ to Cu3+. Total energy of formation, Ef, of different configurations, calculated using a value of 36.83 eV for the third ionisation energy of Cu and -8.75 eV for O2-+O-+e in the gas phase, are also summar- ised in Table 1. Since the core-repulsion energy is a constant for a given composition, it does not influence the relative stability of the different configurations for YBa2Cu408.The lowest-energy configuration according to the calcu- lation is that for which the hole is partially localised on 0(1) and O(1 1) sites. It is interesting that complete hole localisation on either O(1) and O(1 1) sites gives a high energy of formation. Partial localisation on 0(1) and O(l1) sites is equivalent to oxygen valence fluctuation along two planes containing these ions. Both these planes contain a barium atom. The onset of superconductivity probably arises from phase synchronization of valence fluctuations along these planes. The second lowest-energy configuration corresponds to holes localisation on O(41). Partial localisation on 0(1)and O(41) sites also gives comparable values. However, these configurations have energies of formation that are more than 5 eV higher and are therefore unlikely to represent the hole distribution at low temperatures. All other possible locations for holes give rise to higher energies of formation.The YBa2Cu408 has a structure similar to that of YBa2Cu307 except for the extra Cu-0 chain which causes the unit cell to be doubled. In YBa2Cu307, from Madelung potential calculations, it was found that the holes were local- ised on the Cu(1) and O(4) sites. The holes being localised on the O(1) and O(11) sites with the introduction of another Cu-0 chain is rather surprising. Other evidence for the importance of the 0(1) site in the superconductivity of YBa2Cu408 is provided by high-pressure studies. Kaldis et aL8 have shown that the apical oxygen [O(l)] is dis- placed towards the CuOz plane under pressure.Eenige et al.' have found that T, increases dramatically with pressure in YBa2Cu408. In contrast, the Cu(1)-O(1) distance and T, in YBa2Cu30, are not significantly affected by pressure."-" It thus appears that the sites for hole localisation are differ- ent in YBa2Cu4o8 and YBa2Cu307. The authors are grateful to Mrs. R. Sarojini for assistance in the preparation of the manuscript. References 1 S. K. Ramasesha and K. T. Jacob, Muter. Lett., 1990, 10, 239. 2 T. Siegriet, S. Sunshine, D. W. Murphy, R. J. Cava and S. M. Zahurak, Phys. Rev. B, 1987, 35, 7137. 3 S. F. Tsay, S. Y. Wang, L. Horng and T. J. W. Yang, Phys. Rev. B, 1989, 40, 9408. 4 P. Marsh, R. M. Fleming, M. L. Mandich, A. M. Desantolo, J. Kwo, M. Hong and L. J. Martinez-Miranda, Nature (London), 1988, 334, 141. 5 L. F. Mattheiss, Phys. Rev. Lett., 1987, 58, 1028. 6 W. Weber and L. F. Mattheiss, Phys. Rev. B, 1988, 37, 599. 7 C. M. Varma, S. Schmitt-Rink and E. Abrahams, Solid State Commun., 1987, 62, 681. 8 E. Kaldis, P. Fischer, A. W. Hewat, E. A. Hewat, J. Karpinski and S. Rusiecki, Physica C, 1989, 159, 668. 9 E. N. Van Eenige, R. Griessen, R. J. Wijngaarden, J. Karpinski, E. Kaldis, S. Rusiecki and E. Jilek, Physica C, 1990, 168, 482. 10 J. D. Jorgensen, S. Pei, P. Lightfoot, D. G. Hinks, B. W. Veal, B. Dabrowski, A. P. Paulikas, R. Kleb and I. D. Brown, Physicu C, 1990, 171, 93. 11 A. Driessen, R. Griessen, N. Koeman, E. Salomons, R. Brouwer, D. G. de Groot, K. Heeck, H. Hemmes and J. Rector, Phys. Rev. B, 1987,36, 5602. Communication 1/00240F; Received 17th January, 1991