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Critical evaluation of the Lotgering degree of orientation texture indicator

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Abstract

Preferred orientation in textured ceramics is often assessed by comparing the relative intensities of x-ray diffraction reflections to those of a randomly oriented ceramic using the Lotgering degree of orientation (f). However, this paper provides evidence that indiscriminate assessments of f can be misleading. Using measured intensities of a modestly textured tape cast bismuth titanate (Na0.5Bi4.5Ti4O15) ceramic, calculated f values vary from 7.4 to 73.2% depending on the reflections included in the calculation. The texture is also quantified by calculating the orientation distribution function (ODF) using measured pole figures. A model is then presented that demonstrates f is nonlinear with the multiple of preferred (00l)-orientations, the standard unit of the 00l pole figure.

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References

  1. B. Jaffe, W.R. Cook, Jr., and H. Jaffe: Piezoelectric Ceramics (Academic Press Limited, India, 1971).

    Google Scholar 

  2. T.R. Shrout, R. Eitel, and C. Randall: In Piezoelectric Materials in Devices, edited by N. Setter (Setter, Lausanne, 2002), p. 413.

  3. K. Sakata, T. Takenaka, and K. Shoji: Hot-forged ferroelectric ceramics of some bismuth compounds with layer structure. Ferroelectrics 22, 825 (1978).

    Article  CAS  Google Scholar 

  4. T. Takenaka and K. Sakata: Grain orientation and electrical properties of hot-forged Bi4Ti3O12 ceramics. Jpn. J. Appl. Phys. 19, 31 (1980).

    Article  CAS  Google Scholar 

  5. T. Takenaka, K. Sakata, and K. Toda: Piezoelectric properties of bismuth layer-structured ferroelectric Na0.5Bi4.5Ti4O15 ceramic. Jpn. J. Appl. Phys. 24-2, 730 (1985).

    Article  Google Scholar 

  6. T. Takenaka and K. Sakata: Grain-oriented and Mn-doped (NaBi)(1−x)/2CaxBi4Ti4O15 ceramics for piezo- and pyrosensor materials. Sens. Mater. 1, 35 (1988).

    Google Scholar 

  7. M.V. Gelfuso, D. Thomazini, and J.A. Eiras: Synthesis and structural, ferroelectric, and piezoelectric properties of SrBi4Ti4O15 ceramics. J. Am. Ceram. Soc. 82, 2368 (1999).

    Article  CAS  Google Scholar 

  8. J.S. Patwardhan and M.N. Rahaman: Compositional effects on densification and microstructural evolution of bismuth titanate. J. Mater. Sci. 39, 133 (2004).

    Article  CAS  Google Scholar 

  9. S. Swartz, W.A. Schulze, and J.V. Biggers: Fabrication and electrical properties of grain oriented Bi4Ti3O12 ceramics. Ferroelectrics 38, 765 (1981).

    Article  CAS  Google Scholar 

  10. H. Watanabe, T. Kimura, and T. Yamaguchi: Particle orientation during tape casting in the fabrication of grain-oriented bismuth titanate. J. Am. Ceram. Soc. 72, 289 (1989).

    Article  CAS  Google Scholar 

  11. H. Watanabe, T. Kimura, and T. Yamaguchi: Sintering of platelike bismuth titanate powder compacts with preferred orientation. J. Am. Ceram. Soc. 74, 139 (1991).

    Article  CAS  Google Scholar 

  12. J.A. Horn, S.C. Zhang, U. Selvaraj, G.L. Messing, and S. Trolier- McKinstry: Templated grain growth of textured bismuth titanate. J. Am. Ceram. Soc. 82, 921 (1999).

    Article  CAS  Google Scholar 

  13. T. Takeuchi, T. Tani, and Y. Saito: Piezoelectric properties of bismuth layer-structured ferroelectric ceramics with a preferred orientation processed by the reactive templated grain growth method. Jpn. J. Appl. Phys. 38, 5553 (1999).

    Article  CAS  Google Scholar 

  14. S-H. Hong, S. Trolier-McKinstry, and G.L. Messing: Dielectric and electromechanical properties of textured bismuth titanate ceramics. J. Am. Ceram. Soc. 83, 113 (2000).

    Article  CAS  Google Scholar 

  15. T. Takeuchi, T. Tani, and Y. Saito: Unidirectionally textured CaBi4Ti4O15 ceramics by the reactive templated grain growth with an extrusion. Jpn. J. Appl. Phys. 39, 5577 (2000).

    Article  CAS  Google Scholar 

  16. H-J. Bunge: Texture Analysis in Materials Science: Mathematical Methods (Butterworths, Boston, 1982).

    Google Scholar 

  17. U.F. Kocks, C.N. Tomé, and H-R. Wenk: Texture and Anisotropy (Cambridge University Press, Cambridge, U.K., 2000).

    Google Scholar 

  18. G. Senthill Murugan and K.B.R. Varma: Microstructural, dielectric, pyroelectric, and ferroelectric studies of partially grainoriented SrBi2Ta2O9 ceramics. J. Electroceram. 8, 37 (2002).

    Article  Google Scholar 

  19. B.H. Venkataraman and K.B.R. Varma: Grain orientation and anisotropy in the physical properties of SrBi2(Nb1−xVx)2O9 (0 x 0.3) ceramics. J. Mater. Sci. 38, 4895 (2003).

    Article  CAS  Google Scholar 

  20. F.K. Lotgering: Topotactical reactions with ferromagnetic oxides having hexagonal crystal structures–I. J. Inorg. Nucl. Chem. 9, 113 (1959).

    Article  CAS  Google Scholar 

  21. J.L. Jones: Ph.D. Thesis, Purdue University (2004).

    Google Scholar 

  22. JCPDS—International Centre for Diffraction Data: Newtown Square, PA (1998).

  23. B. Aurivillius: Mixed oxides with layer lattices III. Structure of BaBi4Ti4O15. Ark. Kemi 2, 519 (1950).

    CAS  Google Scholar 

  24. B. Aurivillius: The structure of Bi2NbO5F and isomorphous compounds. Ark. Kemi 5, 39 (1952).

    CAS  Google Scholar 

  25. B. Aurivillius: Mixed bismuth oxides with layer lattices I. The structure type of CaNb2Bi2O9. Ark. Kemi 1, 463 (1949).

    CAS  Google Scholar 

  26. R.E. Newnham: Cation ordering in Na0.5Bi4.5Ti4O15. Mater. Res. Bull. 2, 1041 (1967).

    Article  CAS  Google Scholar 

  27. H.M. Rietveld: A profile refinement method for nuclear and magnetic structures. J. Appl. Crystallogr. 2, 65 (1969).

    Article  CAS  Google Scholar 

  28. A. Castro, P. Millán, and M.J. Martínez-Lope: Substitutions for Bi3+ into (Bi2O2)2+ layers of the Aurivillius (Bi2O2)(An−1BnO3n+1) oxides. Solid State Ionics 63–65, 897 (1993).

    Article  Google Scholar 

  29. A. Ramirez, P. Millán, A. Castro, and J.B. Torrance: Compensated doping between layers in Aurivillius oxides. Eur. J. Solid State Inorg. Chem. 31, 173 (1994).

    CAS  Google Scholar 

  30. S.M. Blake, M.J. Falconer, M. McCreedy, and P. Lightfoot: Cation disorder in ferroelectric Aurivillius phases of the type Bi2ANb2O9 (A = Ba, Sr, Ca). J. Mater. Chem. 7, 1609 (1997).

    Article  CAS  Google Scholar 

  31. Ismunandar and B.J. Kennedy: Effect of temperature on cation disorder in ABiNb2O9 (A = Sr, Ba). J. Mater. Chem. 9, 541 (1999).

    Article  CAS  Google Scholar 

  32. R. Macquart, B.J. Kennedy, and Y. Shimakawa: Cation disorder in the ferroelectric oxeds ABi2Ta2O9, A = Ca, Sr, Ba. J. Solid State Chem. 160, 174 (2001).

    Article  CAS  Google Scholar 

  33. Ch. Muller, F. Jacob, Y. Gagou, and E. Elkaïm: Cationic disorder, microstructure and dielectric response of ferroelectric SBT ceramics. J. Appl. Crystallogr. 36, 880 (2003).

    Article  Google Scholar 

  34. C.H. Hervoches and P. Lightfoot: Cation disorder in three-layer Aurivillius phases: Structural studies of Bi2−xSr2+xTi1−xNb2+xO12 (0 < x < 0.8) and Bi4−xLaxTi3O12 (x = 1 and 2). J. Solid State Chem. 153, 66 (2000).

    Article  CAS  Google Scholar 

  35. C.H. Hervoches, A. Snedden, R. Riggs, S.H. Kilcoyne, P. Manuel, and P. Lightfoot: Structural behavior of the four-layer Aurivillius-phase ferroelectrics SrBi4Ti4O15 and Bi5Ti3FeO15. J. Solid State Chem. 164, 280 (2002).

    Article  CAS  Google Scholar 

  36. S. Borg, G. Svensson, and J-O. Bovin: Structure study of Bi2.5Na0.5Ta2O9 and Bi2.5Nam−1.5NbmO3m+3 (m = 2-4) by neutron powder diffraction and electron microscopy. J. Solid State Chem. 167, 86 (2002).

    Article  CAS  Google Scholar 

  37. L. Lutterotti, S. Matthies, and H-R. Wenk: MAUD (materials analysis using diffraction): A user friendly java program for Rietveld texture analysis and more, edited by Jerzy A. Szpunar. Proc. Int. Conf. Textures Mater. (National Research Council of Canada, Ontario, Canada), 1, 1599 (1999).

  38. I. Radosavljevic, J.S.O. Evans, and A.W. Sleight: Synthesis and structure of pyrochlore-type bismuth titanate. J. Solid State Chem. 136, 63 (1998).

    Article  CAS  Google Scholar 

  39. W.A. Dollase: Correction of intensities for preferred orientation in powder diffractometry: Application of the March model. J. Appl. Crystallogr. 19, 267 (1986).

    Article  CAS  Google Scholar 

  40. K. Pawlik, J. Pospiech, and K. Lücke: The ODF approximation from pole figures with the aid of the ADC method. Textures Microstruct. 14-18, 25 (1991).

    Article  Google Scholar 

  41. C. Duran, S. Trolier-McKinstry, and G.L. Messing: Dielectric and piezoelectric properties of textured Sr0.53Ba0.47Nb2O6 ceramics prepared by templated grain growth. J. Mater. Res. 18, 228 (2003).

    Article  CAS  Google Scholar 

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Jones, J.L., Slamovich, E.B. & Bowman, K.J. Critical evaluation of the Lotgering degree of orientation texture indicator. Journal of Materials Research 19, 3414–3422 (2004). https://doi.org/10.1557/JMR.2004.0440

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