Skip to main content
SpringerLink
Log in

Prediction of the unit cell edge length of cubic A 2+2 BB′O6 perovskites by multiple linear regression and artificial neural networks

  • Published:
Central European Journal of Chemistry

Abstract

The unit cell edge length, a, of a set of complex cubic perovskites having the general formula A 2+2 BB′O6 is predicted using two methodologies: multiple linear regression and artificial neural neworks. The unit cell edge length is expressed as a function of six independent variables: the effective ionic radii of the constituents (A, B and B′), the electronegativities of B and B′, and the oxidation state of B. In this analysis, 147 perovskites of the A 2+2 BB′O6 type, having the cubic structure and belonging to the Fm3m space group, are included. They are divided in two sets; 98 compounds are used in the calibration set and 49 are used in the test set. Both models give consistent results and could be successfully use to predict the lattice cell parameter of new members of this series.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F.S. Galasso (Ed.): Structure, Properties and Preparation of Perovskite-type Compounds, Pergamon Press, Oxford., 1969 (and references therein).

    Google Scholar 

  2. E.J. Baran: “Structural chemistry and physicochemical properties of perovskite-like Materials”, Catalysis Today, Vol 8, (1990), pp. 133–151 (and the references therein).

    Article  CAS  Google Scholar 

  3. P.W. Barnes: Exploring structural changes and distortions in quaternary perovskites and defect pyrochlores using powder diffraction techniques, Thesis(PhD), The Ohio State University, 2003.

  4. R.H. Butner and E.N. Maslen: “Electron difference density and structural parameters in CaTiO3”, Acta Cryst. B, Vol. 48, (1992), pp. 644–649.

    Article  Google Scholar 

  5. O. Fukunaga and T. Fujita: “The relationship between ionic radii and cell volumes in the perovskite compounds”, J. Solid State. Chem., Vol. 8, (1973), pp. 331–338.

    Article  CAS  Google Scholar 

  6. D.M. Giaquinta and H. Conrad zur Loye: “Structural predictions in the ABO3 phase diagram”, Chem. Mater., Vol. 6, (1994), pp. 365–372.

    Article  CAS  Google Scholar 

  7. N.W. Thomas: “A new global parameterization of perovskite structures”, Acta Cryst. B, Vol. 54, (1998), pp. 585–594.

    Article  Google Scholar 

  8. A.A. Bokov, N.P. Protsenko and Z.-G. Ye: “Relationship between ionicity ionic radii and order/disorder in complex perovskites”, J. Phys. Chem. Solids, Vol. 61, (2000), pp. 1519–1527.

    Article  CAS  Google Scholar 

  9. M.W. Lufaso and P.M. Woodward: “Prediction of the crystal structure of perovskites using the software program SpuDS”, Acta Cryst. B, Vol. 57, (2001), pp. 725–738.

    Article  CAS  Google Scholar 

  10. L. Chonghe, T. Yihao, Z. Yingzhi, W. Chunmei and W. Ping: “Prediction of lattice constants in perovskites of GdFeO3 structure”, J. Phys. Chem. Solids, Vol. 64, (2003), pp. 2147–2156.

    Article  Google Scholar 

  11. V. Petruševski and S. Aleksovska: “Correlations between effective crystal radii and unit cell volume in Tutton salts”, Croat. Chem. Acta, Vol. 64(4), (1991), pp. 577–583.

    Google Scholar 

  12. V. Petruševski and S. Aleksovska: “Structural correlations in alums”, Croat. Chem. Acta, Vol. 67, (1994), pp. 221–230.

    Google Scholar 

  13. S. Aleksovska, V. Petruševski and Lj. Pejov: “Crystal structures of members in isostructural series: prediction of the crystal structure of Cs2MnO4—a β-K2SO4 type isomorph”, Croat. Chem. Acta, Vol. 70, (1997), pp. 1009–1019.

    CAS  Google Scholar 

  14. S. Aleksovska, S.C. Nyburg, Lj. Pejov and V.M. Petruševski: “β-K2SO4 type isomorphs: prediction of structure and refinement of Rb2CrO4”, Acta Cryst. B., Vol. 54, (1998), pp. 115–120.

    Article  Google Scholar 

  15. S. Aleksovska, V.M. Petruševski and B. Šoptrajanov: “Calculation of structural parameters in isostructural series: the kieserite group”, Acta Cryst. B, Vol. 54, (1998), pp. 564–567.

    Article  Google Scholar 

  16. V.M. Petruševski and S. Aleksovska: “Dependence of the crystal structure parameters on the size of the structural units in some isomorphous/isostructural series”, Croat. Chem. Acta, Vol. 72(1), (1999), pp. 71–76.

    Google Scholar 

  17. I. Kuzmanovski and S. Aleksovska: “Optimization of artificial neural networks for prediction of the unit cell parameters in orthorhombic perovskites. Comparison with multiple linear regression”, Chemometr. Intell. Lab. Syst., Vol. 67, (2003), pp. 167–174.

    Article  CAS  Google Scholar 

  18. K.E. Stitzer, M.D. Smith and H.-C. zur Loye: “Crystal growth of Ba2MOsO6 (M=Li, Na) from reactive hydroxy fluxes”, Solid State Sciences, Vol. 4, (2002), pp. 311–316.

    Article  CAS  Google Scholar 

  19. Y. Izumiyama, Y. Doi, M. Wakeshima, Y. Hinatsu, A. Nakamura and Y. Ishii: “Magnetic and calorimetric studies on ordered perovskite Ba2ErRuO6”, J. Solid State Chem., Vol. 169(1), (2002), pp. 125–130.

    Article  CAS  Google Scholar 

  20. S.B. Kim, B.W. Lee and C.S. Kim: “Neutron and Mössbauer studies of the double perovskite A2FeMoO6 (A=Sr and Ba)”, J. Magn. and Magn. Mater., Vol. 242–245, (2002), pp. 747–750.

    Article  Google Scholar 

  21. J.B. Philipp, P. Majewski, L. Alff, A. Erb, R. Gross, T. Graf, M.S. Brandt, J. Simon, T. Walther, W. Mader, D. Topwal and D.D. Sarma. “Structural and doping effects in the half metallic double perovskite A2CrWO6”, Phys. Rev. B, Vol. 68, (2003), pp. 144431–144445.

    Article  Google Scholar 

  22. W.T. Fu and D.J.W. Ijdo: “On the Structure of BaTl0.5Sb0.5O3: An Ordered Perovskite”, J. Solid State Chem., Vol. 128, (1997), pp. 323–325.

    Article  CAS  Google Scholar 

  23. W. Dmowski, M.K. Akbas, P.K. Davies and T. Egami: “Local structure of Pb(Sc1/2Ta1/2)O3 and related structures”, J. Phys. Chem. Solids, Vol. 61, (2000), pp. 229–237.

    Article  CAS  Google Scholar 

  24. D.-Y. Jung, G. Demazeau and J.-H. Chof: “Iridium(III) stabilized in oxygen lattices of perovskite structure Sr2MIrIIIO6 (M=Nb, Ta)”, J. Mater. Chem., Vol. 5(3), (1995), pp. 517–519.

    Article  CAS  Google Scholar 

  25. P.E. Kazin, A.M. Abakumov, D.D. Zaytsev, Yu.D. Tretyakov, N.R. Khasanova, G. Van Tendeloo and M. Jansen: “Synthesis and crystal structure of Sr2ScBiO6”, J. Solid State Chem., Vol. 162(1), (2001), pp. 142–147.

    Article  CAS  Google Scholar 

  26. H.W. Eng: The crystal and electronic structures of oxides containing d 0 transition metals in octahedral coordination, ‘Thesis (PhD), The Ohio State University, 2003.

  27. Y. Teraoka, M.-D. Wei and S. Kagawa: “Double perovskites containing hexavalent molybdenum and tungsten: synthesis, structural investigation and proposal of fitness factor to discriminate the crystal symmetry”, J. Mater. Chem., Vol. 8(11), (1998), pp. 2323–2325.

    Article  CAS  Google Scholar 

  28. M.J. Martínez-Lope, J.A. Alonso, M.T. Casais and M.T. Fernández-Díaz: “Preparation, crystal and magnetic structure of the double perovskites Ba2CoBO6 (B=Mo, W)”, Europian J. Inorg. Chem., Vol. 2002(9), (2002), pp. 2463–2469.

    Article  Google Scholar 

  29. A.K. Azad, S.-G. Eriksson, S.A. Ivanov, R. Mathieu, P. Svedlindh, J. Eriksen and H. Rundlöf: “Synthesis, structural and magnetic characterisation of the double perovskite A2MnMoO6 (A=Ba, Sr)”, J. Alloys and Comp., Vol. 364(1–2), (2004), pp. 77–82.

    Article  CAS  Google Scholar 

  30. C.M. Lapa, Y.P. Yadava, R.A. Sanguinetti Ferreira, J. Albino Aguiar, C.L. Da Silva, D.P.F. De Souza: “Production, sintering and microstructural characteristics of Ba2NiWO6 complex perovskite oxide ceramics”, Acta Microscopica, Vol. 12 Supplement C, (2003) (XIX Congress of the Brazilian Society for Microscopy and Microanalysis), pp. 77–78.

  31. S.-O. Lee, T.Y. Cho and S.-H. Byeon: “Magnetic propertiy of oxide with the perovskite structure, A2Fe(III)BO6 (A=Ca, Sr, Ba and B=Sb, Bi)”, Bull. Korean Chem. Soc., Vol. 18(1), (1997), pp. 91–97.

    CAS  Google Scholar 

  32. G. Baldinozzi, Ph. Scian, M. Pinot and D. Grebille: “Crystal structure of the antiferroelectric perovskite Pb2MgWO6”, Acta Cryst. B, Vol. 51, (1995), pp. 668–673.

    Article  Google Scholar 

  33. V. Primo-Martín and M. Jansen: “Synthesis, Structure, and Physical Properties of Cobalt Perovskites: Sr3CoSb2O9 and Sr2CoSbO6-δ”, J. Solid State Chem., Vol. 157, (2001), pp. 76–85.

    Article  Google Scholar 

  34. R.D. Shannon: “Revised effective ionic radii in halides and chalcogenides”, Acta Cryst. A, Vol. 32, (1976), pp. 751–767.

    Article  Google Scholar 

  35. D.R. Lide: Handbook of Chemistry and Physics, CRC Press/Chapman and Hall, Boca Raton, FL/London, 2002.

    Google Scholar 

  36. STATGRAPHICS PLUS, VER, 3.0, Statistical Graphics Package, Educational Institution edition, Statistical Graphics, 1994–1997.

  37. A. Bos, M. Bos and W.E. van der Linden: “Artificial neural networks as a tool for soft-modelling in quantitative analytical chemistry: the prediction of the water content of cheese”, Anal. Chim. Acta, Vol. 256, (1992), pp. 133–144.

    Article  CAS  Google Scholar 

  38. J. Zupan and J. Gasteiger: Neural Networks in Chemistry and Drug Design, WCH, Weinhaim, 1999.

    Google Scholar 

  39. D. Nguyen and B. Widrow: “Inproving the learning speed of 2-layer neural network by choosing initial values of the aspative weights”, IEEE Proc. 1st Int. Joint. Conf. Neural Networks, Vol. 3, (1990), pp. 21–26.

    Google Scholar 

  40. J.J. Moré: “The Levenberg-Marquardt Algorithm: Implementation and Theory”, In: G.A. Watson (Ed.): Numerical Analysis, Lecture Notes in Mathematics 630, Springer Verlag, 1977, pp. 105–116.

  41. MATLAB 6.0, Mathworks, 1984–2000.

  42. I. Kuzmanovski, M. Trpkovska, B. Šoptrajanov and V. Stefov: “Détermination of the composition of human urinary calculi composed of whewellite, weddellite and carbonate apatite using artificial neural nentworks”, Anal. Chim. Acta, Vol. 491, (2003), pp. 211–218.

    Article  CAS  Google Scholar 

  43. I. Kuzmanovski, M. Ristova, B. Šoptrajanov, V. Stefov and V. Popovski: “Determination of the composition of sialoliths composed of carbonate apatite and albumin using artificial neural networks”, Talanta, Vol. 62, (2004), pp. 813–817.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Chemistry, Faculty of Natural Sciences and Mathematics, University “Sv. Kiril i Metodij”, PO Box 162, 1001, Skopje, Republic of Macedonia

    Sandra Dimitrovska, Slobotka Aleksovska & Igor Kuzmanovski

Authors
  1. Sandra Dimitrovska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Slobotka Aleksovska
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Igor Kuzmanovski
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Dimitrovska, S., Aleksovska, S. & Kuzmanovski, I. Prediction of the unit cell edge length of cubic A 2+2 BB′O6 perovskites by multiple linear regression and artificial neural networks. cent.eur.j.chem. 3, 198–215 (2005). https://doi.org/10.2478/BF02476250

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.2478/BF02476250

Keywords

Search

Navigation