Abstract
Now that first-principles calculations of ordering transformations are becoming increasingly accurate, the deficiencies of earlier mean field methods are becoming increasingly apparent. New techniques, based on cluster expansions, are now alleviating many of the earlier problems and are producing very satisfactory results. These ideas will be illustrated for the case of oxygen ordering in the YBa2Cu3Oz superconducting compound, for which a very simple two-dimensional Ising model has been developed. The model features nearest-neighbor repulsive effective pair interactions and anisotropic (attractive/repulsive) next-nearest-neighbor interactions. CVM (cluster variation method) calculations based on this model have produced a phase diagram in remarkable agreement with experimentally determined phase boundaries. Monte Carlo simulations have confirmed the validity of the model and have provided a rationalization for the influence of oxygen order on the value of Tc (superconducting transition temperature) in off-stoichiometric compounds.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Sanchez, J. M., Ducastelle, F. and Gratias, D. Physica (Utrecht), 1984, 128A, 334.
Asta, M., Wolverton, C., de Fontaine, D. and Dreyssé, H., Phys. Rev. B (in press).
Wolverton, C., Asta, M., Dreyssé, H. and de Fontaine, D. Phys. Rev. B (in press).
Sanchez, J. M., private communication to D. de F.
Dreyssé, H., Berera, A., Wille, L. T. and de Fontaine, D. Phys. Rev. B. 1989, 39, 2442–2452.
Kikuchi, R. Phys. Rev., 1951, 81, 988–1003.
Sluiter, M., de Fontaine, D., Guo, X Q., Podloucky, R. and Freeman, A. J. Phys. Rev. B. 1990, 42, 10460–10476.
Khachaturyan, A. G., Theory of Structural Transformations in Solids. John Wiley & Sons, New York, 1983, p. 68.
Ducastelle, F. and Gautier, F. J. Phys. F. 1976, 6, 2039.
de Fontaine, D., Wolverton, C., Ceder, G. and Dreyssé, H. To be published in NATO ASI Series.
de Fontaine, D. Acta Metall., 1975, 23, 553–571.
Sanchez, J. M. and de Fontaine, D. Phys. Rev. B, 1980, 21, 216–228.
Sanchez, J. M. Physica. 1982, 111A, 200.
Solal, F., Caudron, R., Ducastelle, F., Finel, A. and Loiseau, A. Phys. Rev. Lett., 1987, 58, 2245–2248.
Finel, A., Contribution à l’ étude des effets d’ordre dans le cadre du modèle d’Ising: Etats de base et diagrammes de phase. Doctoral dissertation, Université Pierre et Marie Curie, Paris, 1987 (unpublished).
Sluiter, Marcel H. F., On the first principles calculation of phase diagrams. Ph.D. dissertation, University of California, Berkeley, 1988 (unpublished).
Ceder, Gerbrand, Alloy theory and its applications to long period superstructure ordering in metallic alloys and high temperature superconductors. Ph.D. dissertation, University of California, Berkeley, 1991 (unpublished).
Inden, G. and Pitsch, W., Atomic ordering. In Materials Science and Technology, Vol. 5, ed. Peter Haasen, VCH Press, Weinheim, 1991, pp. 497–552.
Wu, M. K. et al. Phys. Rev. Lett., 1987, 58, 908–911.
de Fontaine, D., Wille, L. T. and Moss, S. C. Phys. Rev. B. 1987, 36, 5709–5712.
Sterne, P. A. and Wille, L. T. Physica C. 1989, 162, 223–224.
Wille, L. T. and de Fontaine, D. Phys Rev. B. 1988, 37, 2227–2230.
de Fontaine, D. J. Less-Common Metals. 1990, 160, L5 - L8.
Fu, W. T. et al. J. Less-Common Metals. 1989, 151, 213–220.
Wille, L. T., Berera, A. and de Fontaine, D. Phys. Rev. Lett., 1988, 60, 1065–1068.
Zubkus, V. E., Lapinskas, S. and Tornau, E. E. Physica C. 1989, 159, 501–509.
Kikuchi, R. and Choi, J. S. Physica C, 1989, 160, 347–352.
Ceder, G., Asta, M. Carter, W. C., Kraitchman, M., de Fontaine, D., Mann, M. E. and Sluiter, M. Phys. Rev. B. 1990, 41, 8698–8701.
Sanchez, J. M., private communication to D. de Fontaine.
Ceder, G., unpublished work at U.C. Berkeley.
Bartelt, N. C., Einstein, T. L. and Wille, L. T. Phys. Rev. B. 1989, 40, 10759–10765.
Andersen, N. H., Lebech, B. and Poulsen, H. F. J. Less-Common Metals. 1990, 164–165, 124–131.
Reyes Gasga, J. et al. Physica C 1989, 159, 831–848.
de Fontaine, D., Ceder, G. and Asta, M. Nature. 1990, 343, 544–546.
Hubbard, J. Phys. Rev. B. 1978, 17, 494–505.
Beyers, R. et al. Nature. 1989, 340, 619–621.
Beyers, R. et al. Nature. 1989, 340, 619–621.
Zubkus, V. E., Lapinskas, S. and Tomau, E. E. Physica C. 1990, 166, 472–475.
Farneth, W. E. et al. Solid St. Comm., 1988, 66, 953–959.
Lambin, Ph., Tight-binding investigation of the electronic properties of ordered and disordered defects in the YBaCuO system. In Oxygen Disorder Effects in High Tc Superconductors, ed. J. L. Morán-López and Ivan K. Schuller, Plenum Press, New York, 1990, pp. 101–116.
Veal, B. W. et al. Phys. Rev. B. 1990, 42, 4770–4773.
Jorgensen, J. D. et al. Physica C. 1990, 167, 571–578.
Jorgensen, J. D. et al. Physica C. 1990, 167, 571–578.
Latgé, A., Anda, E. V. and Morán-López, J. L. Phys. Rev. B. 1990, 42, 4288–4297.
Poulsen, H. F., Andersen, N. H., Andersen, J. V., Bohr, H. and Mouritzen, O. G. Nature. 1991, 349, 594–596.
McCormack, R., Ceder, G. and de Fontaine, D. To be published.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Elsevier Science Publishers Ltd
About this chapter
Cite this chapter
de Fontaine, D., Ceder, G., Asta, M., Mccormack, R. (1992). Energetics and Statistics of Order in Alloys with Application to Oxide Superconductors. In: Yavari, A.R. (eds) Ordering and Disordering in Alloys. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2886-5_39
Download citation
DOI: https://doi.org/10.1007/978-94-011-2886-5_39
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-85166-762-8
Online ISBN: 978-94-011-2886-5
eBook Packages: Springer Book Archive