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Whole Powder Pattern Modelling: Theory and Applications

  • P. Scardi
  • M. Leoni
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 68)

Abstract

In close analogy to the structural refinement provided by the Rietveld method, Whole Powder Pattern Modelling (WPPM) is proposed as a general technique for microstructure refinement. WPPM consists in a simultaneous modelling of all peak profiles in the diffraction pattern from (single or multi-phase) polycrystalline materials, without using arbitrary profile functions. The entire diffraction pattern is modelled directly in terms of physical parameters describing the main microstructural features influencing peak profile width, shape and position, also considering instrumental effects and background.

Keywords

Ball Milling Grain Boundary Milling Time Rietveld Method Pattern Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P. Scherrer: Nachr. Ges. Wiss. Göttingen 26, 98 (1918)Google Scholar
  2. 2.
    G.K. Williamson and W.H. Hall: Acta Metall. 1, 22 (1953)CrossRefGoogle Scholar
  3. 3.
    J.I. Langford: Accuracy in Powder Diffraction II. In: NIST Spec. Pub. No. 846. Ed. by E. Prince and J.K. Stalick. (US Dept of Commerce, Gaithersburg MA 1992) pp. 110–126 )Google Scholar
  4. 4.
    H.P. Klug and L.E. Alexander: X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials. 2nd edn. (Wiley, New York 1974)Google Scholar
  5. 5.
    B.E. Warren and B.L. Averbach: J. Appl. Phys. 21, 595 (1950);ADSCrossRefGoogle Scholar
  6. 5a.
    B.E. Warren and B.L. Averbach: J. Appl. Phys. 23, 497 (1952)ADSCrossRefGoogle Scholar
  7. 6.
    B.E. Warren: X-ray Diffraction (Addison-Wesley, Reading, MS 1969)Google Scholar
  8. 7.
    J.I. Langford and D. Louër: Rep. Prog. Phys. 59, 131 (1996)ADSCrossRefGoogle Scholar
  9. 8.
    Y.H. Dong and P. Scardi: J. Appl. Cryst. 33, 184 (2000)CrossRefGoogle Scholar
  10. 9.
    G.S. Pawley: J. Appl. Cryst. 14, 357 (1981)CrossRefGoogle Scholar
  11. 10.
    H. Toraya, in The Rietveld Method. Ed. by R.A. Young (Oxford University Press, Oxford 1993) pp. 254–275)Google Scholar
  12. 11.
    H.M. Rietveld: J. Appl. Cryst. 2, 65 (1969)CrossRefGoogle Scholar
  13. 12.
    R.A. Young (Ed:): The Rietveld Method. (Oxford University Press, Oxford 1993)Google Scholar
  14. 13.
    G. Caglioti, A. Paoletti and F.P. Ricci: Nucl. Instrum. Methods 35, 223 (1958)Google Scholar
  15. 14.
    J.I. Langford: J. Appl. Cryst. 11, 10 (1978)CrossRefGoogle Scholar
  16. 15.
    J.I. Langford, D. Louër, and P. Scardi: J. Appl. Cryst. 33, 964 (2000)CrossRefGoogle Scholar
  17. 16.
    P. Scardi, M. Leoni and Y.H. Dong: CPD Newsletter 24, 23 (2001)Google Scholar
  18. 17.
    P. Scardi and M. Leoni: Acta Cryst. A 58, 190 (2002)CrossRefGoogle Scholar
  19. 18.
    P. Scardi, M. Leoni and Y.H. Dong: Eur. Phys. J. B 18, 23 (2000)ADSCrossRefGoogle Scholar
  20. 19.
    P. Scardi, M. Leoni and Y.H. Dong; Mat. Sci. Forum. 378–381, 132 (2001)Google Scholar
  21. 20.
    J.G.M. van Berkum: Strain Fields in Crystalline Materials. (Technische Universiteit Delft, Delft, 1994)Google Scholar
  22. Ph.D. Thesis 21. A.J.C. Wilson: X-ray Optics, 2nd edn. (Methuen, London 1962)Google Scholar
  23. 22.
    A.R. Stokes and A.J.C. Wilson: Proc. Cambridge Phys. Soc. 38, 313 (1942)ADSCrossRefGoogle Scholar
  24. 23.
    A.R. Stokes and A.J.C. Wilson: Proc. Cambridge Phys. Soc. 41, 174 (1944)ADSCrossRefGoogle Scholar
  25. 24.
    E.F. Bertaut: C.R. Acad. Sci. Paris 228, 187, 492 (1949);Google Scholar
  26. 24a.
    E.F. Bertaut: Acta Cryst. 3, 14 (1950)CrossRefGoogle Scholar
  27. 25.
    J.F. Nye: Physical Properties of Crystals: Their Representation by Tensors and Matrices. Reprint edn. (Oxford Univ. Press, Oxford 1987)Google Scholar
  28. 26.
    P. Scardi and M. Leoni: Acta Cryst. A 57, 604 (2001)Google Scholar
  29. 27.
    J.I. Langford and A.J.C. Wilson: J. Appl. Cryst. 11, 102 (1978)CrossRefGoogle Scholar
  30. 28.
    B.R. York: Advances in X-ray Analysis 41 544 (1999)Google Scholar
  31. 29.
    A.C. Vermeulen, R. Delhez, T.H. de Keijser, E.J. Mittemeijer: J. Appl. Phys. 77, 5026 (1995)ADSCrossRefGoogle Scholar
  32. 30.
    J.-D. Kamminga, L.J. Seijbel, R. Delhez: This volume, Chapter 12.Google Scholar
  33. 31.
    M.A. Krivoglaz and K.P. Ryaboshapka: Fizika Metall. 15, 18 (1963)Google Scholar
  34. 32.
    M. Wilkens: Phys. Stat. Sol. (a) 2, 359 (1970)ADSCrossRefGoogle Scholar
  35. 33.
    M. Wilkens: Fundamental Aspects of Dislocation Theory. Ed. by J.A. Simmons, R. de Wit, R. Bullough. Vol. II. Nat. Bur. Stand., (US) Spec. Publ. No. 317 (Washington, DC 1970) pp. 1195–1221 )Google Scholar
  36. 34.
    A.C. Nunes and D. Lin: J. Appl. Cryst. 28, 274 (1995)CrossRefGoogle Scholar
  37. 35.
    M. Leoni and P. Scardi: This volume, Chapter 16.Google Scholar
  38. 36.
    M.A. Krivoglaz, O.V. Martynenko and K.P. Ryaboshapka: Phys. Met. Metall. 55, 1 (1983)Google Scholar
  39. 37.
    J.-D. Kamminga and R. Delhez: J. Appl. Cryst. 33, 1122 (2000)CrossRefGoogle Scholar
  40. 38.
    I. Groma, T. Ungar and M. Wilkens: J. Appl. Cryst. 21, 47 (1988)CrossRefGoogle Scholar
  41. 39.
    P. Klimanek and R. Kuzel Jr.: J. Appl. Cryst. 21, 59 (1988)CrossRefGoogle Scholar
  42. 40.
    R. Kuzel Jr. and P. Klimanek: J. Appl. Cryst. 22, 299 (1989)CrossRefGoogle Scholar
  43. 41.
    M. Wilkens: Phys. stat. sol. (a) 104, K1 (1987)ADSCrossRefGoogle Scholar
  44. 42.
    N. Armstrong and P. Lynch. This volume, Chapter 10.Google Scholar
  45. 43.
    T. Ungar, I. Dragomir, A. Revesz and A. Borbely: J. Appl. Cryst. 32, 992 (1999)CrossRefGoogle Scholar
  46. 44.
    N.C. Popa: J. Appl. Cryst. 31, 176 (1998)ADSCrossRefGoogle Scholar
  47. 45.
    P.W. Stephens: J. Appl. Cryst. 32, 281 (1999)CrossRefGoogle Scholar
  48. 46.
    L. Velterop, R. Delhez, T.H. de Keijser, E.J. Mittemeijer and D. Reefman: J. Appl. Cryst. 33, 296 (2000)CrossRefGoogle Scholar
  49. 47.
    J.P. Cline, R.D. Deslattes, J.-L. Staudenmann, E.G. Kessler, L.T. Hudson, A. Henins and R.W. Cheary: Certificate SRM 640c.( NIST Gaithersburg, MD 2000)Google Scholar
  50. 48.
    J.P. Cline, R.D. Deslattes, J.-L. Staudenmann, E.G. Kessler, L.T. Hudson, A. Henins and R.W. Cheary: Certificate SRM 660a. (NIST Gaithersburg, MD 2000)Google Scholar
  51. 49.
    M. Leoni, P. Scardi, J.I. Langford: Powder Diffr. 13, 210 (1998)ADSCrossRefGoogle Scholar
  52. 50.
    P. Scardi and M. Leoni: J. Appl. Cryst. 32, 671 (1999)CrossRefGoogle Scholar
  53. 51.
    J.I. Langford: Prog. Cryst. Growth and Charact. 14, 185 (1987)CrossRefGoogle Scholar
  54. 52.
    R.W. Cheary and A.A. Coelho: J. Appl. Cryst. 25, 109 (1992)CrossRefGoogle Scholar
  55. 53.
    A.A. Kern and A.A. Coelho: A New Fundamental Parameters Approach in Profile Analysis of Powder Data. In: Proceedings of the international school on powder diffraction (ISPD’98), edited by S.P. SenGupta, Allied Publishers Ltd., New Delhi, 1998. pp. 144–151.Google Scholar
  56. 54.
    B.S. Garbow, K.E. Hillstrom and J.J. More: MINPACK Project. (Argonne National Laboratory, November 1996) http://www.netlib.org/minpackGoogle Scholar
  57. 55.
    A.I. Salimon, A.M. Korsunsky, A.N. Ivanov: Mat. Sci. Eng. A271, 196 (1999)Google Scholar
  58. 56.
    R.Z. Valiev, R.K. Islamgaliev, I.V. Alexandrov: Prog. Mat. Sci. 45, 103 (2000)CrossRefGoogle Scholar
  59. 57.
    Y.H. Zhao, H.W. Sheng and K. Lu: Acta Mater. 49, 365 (2001)CrossRefGoogle Scholar
  60. 58.
    R.Z. Valiev, E.V. Kozlov, Y.F. Ivanov, J. Lian, A.A. Nazarov and B. Baudelet: Acta Metall. Mater. 42, 2467 (1994)CrossRefGoogle Scholar
  61. 59.
    R.K. Islamgaliev, F. Chmelik, R. Kuzel Jr.: Mat. Sci. Eng. A 237, 43 (1997)CrossRefGoogle Scholar
  62. 60.
    C.G. Granqvist and R.A. Buhrman: J. Appl. Phys. 47, 2200 (1976)ADSCrossRefGoogle Scholar
  63. 61.
    L.B. Kiss, J. Söderlund, G.A. Niklasson and C.G. Granqvist: Nanostr. Materials 12, 327 (1999)CrossRefGoogle Scholar
  64. 62.
    C.E. Krill and R. Birringer: Phil. Mag. 77, 621 (1998)Google Scholar
  65. 63.
    A.G. Every and A.K. McCurdy (Eds.): Landolt-Börnstein. Vol. 29 (Springer, Berlin Heidelberg New York 1992) p. 14Google Scholar
  66. 64.
    T. Ungar, H. Mughrabi, D. Rönnpagel and M. Wilkens: Acta Metall. 32, 333 (1984)CrossRefGoogle Scholar
  67. 65.
    H.J. Fecht, E. Hellstern, Z. Fu and W.L. Johnson: Metall. Trans. A 21, 2333 (1990)CrossRefGoogle Scholar
  68. 66.
    H.H. Tian and M. Atzmon: Acta Mater. 47, 1255 (1999)CrossRefGoogle Scholar
  69. 67.
    A.A. Nazarov, A.E. Romanov, R.Z. Valiev: Scripta Materialia 34, 729 (1996)CrossRefGoogle Scholar
  70. 68.
    J. Schiøtz, T. Rasmussen, K.W. Jacobsen and O.H. Nielsen: Phil. Mag. Lett. 74, 339 (1996)ADSCrossRefGoogle Scholar
  71. 69.
    J. Schiøtz, F.D. Di Tolla, K.W. Jacobsen: Nature 391, 561 (1998)ADSCrossRefGoogle Scholar
  72. 70.
    P.G. Sanders, A.B. Witney, J.R. Weertman, R.Z. Valiev, R.W. Siegel: Mat. Sci. Eng. A 204, 7 (1995)CrossRefGoogle Scholar
  73. 71.
    P. Chatterjee and S.P. Sen Gupta: Phil. Mag. A 81, 49 (2001)Google Scholar
  74. 72.
    X.D. Liu, H.Y. Zhang, K. Lu and Z.Q. Hu: J. Phys. Condens. Matter 6, L497 (1994)ADSCrossRefGoogle Scholar
  75. 73.
    International Center for Diffraction data: PDF card #4–850. (ICDD, Newtown Square, PA)Google Scholar
  76. 74.
    T. Ungar, J. Gubicza, G. Ribarik, and A. Borbely: J. Appl. Cryst. 34, 298 (2001)CrossRefGoogle Scholar
  77. 75.
    N.C. Popa: J. Appl. Cryst. 25, 611 (1992)CrossRefGoogle Scholar
  78. 76.
    M. Järvinen, in Defect and Microstructure Analysis by Diffraction. Ed. by R.L. Snyder, J. Fiala, H.J. Bunge. IUCr series (Oxford University Press, New York 1999) pp. 556–559Google Scholar
  79. 77.
    C.J. Howard and E.H. Kisi: J. Appl. Cryst. 32, 624 (1999)CrossRefGoogle Scholar
  80. 78.
    N.C. Popa: J. Appl. Cryst. 33, 103 (2000)CrossRefGoogle Scholar
  81. 79.
    D. Balzar and N.C. Popa. This volume, Chapter 5.Google Scholar
  82. 80.
    R. Hill, in The Rietveld Method. Ed. by R.A. Young (Oxford University Press, Oxford 1993) pp.61–101Google Scholar
  83. 81.
    I.C. Madsen, N.V.Y. Scarlett, L.M.D. Cranswick and T. Lwin: J. Appl. Cryst. 34, 409 (2001)CrossRefGoogle Scholar
  84. 82.
    P. Scardi and M. Leoni: (2004). In preparationGoogle Scholar
  85. 83.
    N. Amstrong, J.P. Cline, and W. Kelceff. This volume, Chapter 8; N. Armstrong, J.P. Cline, W. Kalceff, and J. Bonevich, in Proceedings of the 3rd Conference on Accuracy in Powder Diffraction. Ed. by J.P. Cline, J. Post and P. Scardi (NIST, Gaitherburg, MD 22.–25.4.2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • P. Scardi
  • M. Leoni

There are no affiliations available

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