JOM

, Volume 63, Issue 7, pp 61–70 | Cite as

X-ray line profile analysis—An ideal tool to quantify structural parameters of nanomaterials

  • Michael B. Kerber
  • Michael J. Zehetbauer
  • Erhard Schafler
  • Florian C. Spieckermann
  • Sigrid Bernstorff
  • Tamas Ungar
Advanced Materials Analysis, Part II Research Summary

Abstract

For a long time the shift and broadening of Bragg profiles have been used to evaluate internal stresses and coherent domain sizes, i.e. the smallest crystalline region without lattice defects. Modern technology provides both enhanced detector resolution and high brilliance x-ray sources thus allowing measurements of x-ray peaks with a high resolution in space and time. In parallel to the hardware, also diffraction theories have been substantially improved so that the shape of Bragg profiles can be quantitatively evaluated not only in terms of the crystallite size and its distribution, but also in terms of the density, type and arrangement of dislocations, twins and stacking faults. Thus state-of-the-art x-ray line profile analysis enables the thorough characterization especially of nanostructured materials which also contain lattice defects. The method can be used also to prove the existence of dislocations in crystalline materials. Examples of nanostructured metals, polymers and even molecular crystals like fullerenes are given.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B.E. Warren, X-ray Diffraction (New York: Dover, 1990.Google Scholar
  2. 2.
    B.E. Warren and B.L. Averbach, J. Appl. Phys., 21 (1950), p. 595.CrossRefGoogle Scholar
  3. 3.
    M.A. Krivoglaz, X-ray and Neutron Diffraction in Nonideal Crystals (New York: Springer, 1996).Google Scholar
  4. 4.
    T. Ungár, L. Balogh, and G. Ribárik, Metall. Mat. Trans. A, 41 (2009), pp. 1202–1209.CrossRefGoogle Scholar
  5. 5.
    M. Zehetbauer, T. Ungár, R. Kral, A. Borbely, E. Schafler, B. Ortner, H. Amenitsch, and S. Bernstorff, Acta Mater., 47 (1999), p. 1053.CrossRefGoogle Scholar
  6. 6.
    M. Zehetbauer, E. Schafler, and T. Ungár, Z. Metallk., 96 (2005), p. 1044.Google Scholar
  7. 7.
    T. Ungár, A. Revesz, and A. Borbely, J. Appl. Cryst., 31 (1998), p. 554.CrossRefGoogle Scholar
  8. 8.
    T. Ungár, S. Ott, P. G. Sanders, A. Borbely, and J.R. Weertman, Acta Mater., 46 (1998), p. 3693.CrossRefGoogle Scholar
  9. 9.
    I. Groma, T. Ungár, and M. Wilkens, J. Appl. Cryst., 21 (1988), pp. 47–53.CrossRefGoogle Scholar
  10. 10.
    E. Schafler, K. Simon, S. Bernstorff, P. Hanak, G. Tichy, T. Ungár, and M. Zehetbauer, Acta Mater., 53 (2005), p. 315.CrossRefGoogle Scholar
  11. 11.
    T. Ungár, I. Groma, and M. Wilkens, J. Appl. Cryst., 22 (1989), pp. 26–34.CrossRefGoogle Scholar
  12. 12.
    P. Scardi, ch. 13 in Powder Diffraction: Theory and Practice, ed. R. Dinnebier and S.J.L. Billinger (Cambridge, U.K.: Royal Society of Chemistry, 2008), p. 376.CrossRefGoogle Scholar
  13. 13.
    L. Balogh, T. Ungár, Y. Zhao, Y. Zhu, Z. Horita, C. Xu, and T. Langdon, Acta Mater., 56 (2008), pp. 809–820.CrossRefGoogle Scholar
  14. 14.
    T. Ungár, E. Schafler, P. Hanak, S. Bernstorff, and M. Zehetbauer, Mater. Sci. Eng. A, 462 (2007), p. 398.CrossRefGoogle Scholar
  15. 15.
    T. Ungár, E. Schafler, P. Hanak, S. Bernstorff, and M. Zehetbauer, Z. Metallk., 96 (2005), p. 578.Google Scholar
  16. 16.
    M.B. Kerber, E. Schafler, A.K. Wieczorek, G. Ribarik, S. Bernstorff, T. Ungar, and M.J. Zehetbauer, Int. J. Mater. Res., 100 (2009), pp. 770–774.Google Scholar
  17. 17.
    R. Asaro, P. Krysl, and B. Kad, Phil. Mag. Lett., 83 (2003), pp. 733–743.CrossRefGoogle Scholar
  18. 18.
    M. Chen, E. Ma, K. Hemker, H. Sheng, Y. Wang, and X. Cheng, Science, 300 (2003), pp. 1275–1277.CrossRefGoogle Scholar
  19. 19.
    X. Liao, J. Huang, Y. Zhu, F. Zhou, and E. Lavernia, Phil. Mag., 83 (2003), pp. 3065–3075.CrossRefGoogle Scholar
  20. 20.
    X. Liao, Y. Zhao, S. Srinivasan, Y. Zhu, R. Valiev, and D. Gunderov, Appl. Phys. Lett., 84 (2004), pp. 592–594.CrossRefGoogle Scholar
  21. 21.
    X. Liao, Y. Zhao, Y. Zhu, R. Valiev, and D. Gunderov, J. Appl. Phys., 96 (2004), pp. 636–640.CrossRefGoogle Scholar
  22. 22.
    X. Liao, F. Zhou, E. Lavernia, D. He, and Y. Zhu, Appl. Phys. Lett., 83 (2003), pp. 5062–5064.CrossRefGoogle Scholar
  23. 23.
    M. Meyers, O. Vöhringer, and V. Lubarda, Acta Mater., 49 (2001), pp. 4025–4039.CrossRefGoogle Scholar
  24. 24.
    R. Valiev, E. Kozlov, Y. Ivanov, J. Lian, A. Nazarov, and B. Baudelet, Acta Metall. Mater., 42 (1994), pp. 2467–2475.CrossRefGoogle Scholar
  25. 25.
    H. Van Swygenhoven, P. Derlet, and A. Froseth, Nature Mater., 3 (2004), pp. 399–403.CrossRefGoogle Scholar
  26. 26.
    Y. Zhu, X. Liao, S. Srinivasan, and E. Lavernia, J. Appl. Phys., 98 (2005), pp. 1–8.Google Scholar
  27. 27.
    Y. Zhu, X. Liao, S. Srinivasan, Y. Zhao, M. Baskes, F. Zhou, and E. Lavernia, Appl. Phys. Lett., 85 (2004), pp. 5049–5051.CrossRefGoogle Scholar
  28. 28.
    G. Ribárik, T. Ungár, and J. Gubicza, J. Appl. Cryst., 34 (2001), p. 669.CrossRefGoogle Scholar
  29. 29.
    I. Groma, and F. Székely, J. Appl. Cryst., 33 (2000), pp. 1329–1334.CrossRefGoogle Scholar
  30. 30.
    P. Scherrer, Göttinger Nachrichten, 2 (1918), p. 98.Google Scholar
  31. 31.
    A. Patterson, Phys. Rev., 56 (1939), p. 978.CrossRefGoogle Scholar
  32. 32.
    G. Ribárik, J. Gubicza, and T. Ungár, Mater. Sci. Eng. A, 387–389 (2004), p. 343.Google Scholar
  33. 33.
    P. Scardi and M. Leoni, Acta Crystallogr. A, 58 (2002), pp. 190–200.CrossRefGoogle Scholar
  34. 34.
    P. Scardi, M. Leoni, D. Lamas, and E. Cabanillas, Powder Diffr., 20 (2005), p. 353.CrossRefGoogle Scholar
  35. 35.
    P. Scardi, M. Leoni, and J. Faber, Powder Diffr., 21 (2006), pp. 270–277.CrossRefGoogle Scholar
  36. 36.
    B. E. Warren, J. Appl. Phys., 32 (1961), pp. 2428–2431.CrossRefGoogle Scholar
  37. 37.
    L. Balogh, G. Ribárik, and T. Ungár, J. Appl. Phys., 100 (2006), p. 023512.CrossRefGoogle Scholar
  38. 38.
    L. Balogh, G. Tichy, and T. Ungár, J. Appl. Cryst., 42 (2009), pp. 580–591.CrossRefGoogle Scholar
  39. 39.
    E. Estevez-Rams, A. Penton Madrigal, P. Scardi, and M. Leoni, Z. Krist Suppl., 1 (2007), pp. 99–104.CrossRefGoogle Scholar
  40. 40.
    P. Scardi and M. Leoni, J. Appl. Cryst., 32 (1999), pp. 671–682.CrossRefGoogle Scholar
  41. 41.
    P. Scardi, M. Leoni, and M. D’Incau, Z. Krist., 222 (2007), pp. 129–135.CrossRefGoogle Scholar
  42. 42.
    H. Mughrabi, Acta Metal., 31 (1983), pp. 1367–1379.CrossRefGoogle Scholar
  43. 43.
    H. Mughrabi, T. Ungár, W. Kienle, and M. Wilkens, Phil. Mag. A, 53 (1986), pp. 793–813.CrossRefGoogle Scholar
  44. 44.
    T. Ungár, H. Mughrabi, M. Wilkens, and A. Hilscher, Phil. Mag. A, 64 (1991), pp. 495–496.CrossRefGoogle Scholar
  45. 45.
    E. Schafler, K. Simon, S. Bernstorff, P. Hanak, G. Tichy, T. Ungár, and M. Zehetbauer, Acta Mater., 53 (2005), pp. 315–322.CrossRefGoogle Scholar
  46. 46.
    E. Schafler, A. Dubravina, B. Mingler, H. Karnthaler, and M. Zehetbauer, Mater. Sci. Forum, 503–504 (2006), pp. 51–56.CrossRefGoogle Scholar
  47. 47.
    E. Schafler, M. Zehetbauer, A. Borbely, and T. Ungár, Mater. Sci. Eng., A234–236 (1997), pp. 445–448.Google Scholar
  48. 48.
    M. Leoni, M. Ortolani, M. Bertoldi, V. Sglavo, and P. Scardi, J. Am. Ceram. Soc., 91 (2008), pp. 1218–1225.CrossRefGoogle Scholar
  49. 49.
    G. Bolelli, L. Lusvarghi, T. Varis, E. Turunen, M. Leoni, P. Scardi, C. Azanza-Ricardo, and M. Barletta, Surf. Coat. Tech., 202 (2008), pp. 4810–4819.CrossRefGoogle Scholar
  50. 50.
    M. Ortolani, M. Leoni, P. Scardi, and M. Golshan, Z. Krist Suppl., 1 (2007), pp. 91–96.CrossRefGoogle Scholar
  51. 51.
    A. Molinari, S. Libardi, M. Leoni, and P. Scardi, Acta Mat., 58 (2010), pp. 963–966.CrossRefGoogle Scholar
  52. 52.
    P. Scardi and M. Leoni, Acta Mat., 53 (2005), pp. 5229–5239.CrossRefGoogle Scholar
  53. 53.
    G. Ribárik, N. Audebrand, H. Palancher, T. Ungár, and D. Louër, J. Appl. Cryst., 38 (2005), pp. 912–926.CrossRefGoogle Scholar
  54. 54.
    P. Scardi and M. Leoni, J. Appl. Cryst., 39 (2006), pp. 24–31.CrossRefGoogle Scholar
  55. 55.
    E. Korznikova, E. Schafler, G. Steiner, and M. Zehetbauer, Ultrafine Grained Materials IV, ed. Y.T. Zhu et al. (Warrendale, PA: TMS, 2006), p. 97.Google Scholar
  56. 56.
    D. Setman, E. Schafler, E. Korznikova, and M. Zehetbauer, Mater. Sci. Eng., A493 (2008), pp. 116–122.Google Scholar
  57. 57.
    D. Setman, M. Kerber, E. Schafler, and M. Zehetbauer, Metall. Mater. Trans., A41 (2009), pp. 1–6.Google Scholar
  58. 58.
    A.R. Stokes, Proc. Phys. Soc., 61 (1948), p. 382.CrossRefGoogle Scholar
  59. 59.
    E.F. Bertaut, Acta Cryst., 3 (1950), pp. 14–18.CrossRefGoogle Scholar
  60. 60.
    A. Guinier, X-ray Diffraction (Cranbury, NJ: Freeman, 1963).Google Scholar
  61. 61.
    C.E. Krill and R. Birringer, Phil. Mag., A77 (1998), p. 621.Google Scholar
  62. 62.
    J. Gubicza, J. Szépvölgyi, I. Mohai, G. Ribárik, and T. Ungár, J. Mater. Sci., 35 (2000), pp. 3711–3717.CrossRefGoogle Scholar
  63. 63.
    J.I. Langford, D. Louër, and P. Scardi, J. Appl. Cryst., 33 (2000), pp. 964–974.CrossRefGoogle Scholar
  64. 64.
    M. Wilkens, Phys. Stat. Sol. A, 2 (1970), pp. 359–370.CrossRefGoogle Scholar
  65. 65.
    M. Wilkens, Fundamental Aspects of Dislocation Theory, volume II., Nat. Bur. Stand. (US) Spec. Publ. No. 317, ed. J.A. Simmons, R.D. It, and R. Bullough (Washington, D.C.: NBS, 1970), p. 1195.Google Scholar
  66. 66.
    M. Wilkens, Phys. Stat. Sol. A, 104 (1987), p. K1.CrossRefGoogle Scholar
  67. 67.
    M. Wilkens, Krist. Tech., 11 (1976), p. 1159.CrossRefGoogle Scholar
  68. 68.
    P. Klimanek and R. Kuzel, J. Appl. Cryst., 21 (1988), pp. 59–66.CrossRefGoogle Scholar
  69. 69.
    J. Martinez-Garcia, M. Leoni, and P. Scardi, Acta Cryst. A, 65 (2009), pp. 109–119.CrossRefGoogle Scholar
  70. 70.
    T. Ungár, I. Dragomir, A. Revesz, and A. Borbely, J. Appl. Cryst., 32 (1999), p. 992.CrossRefGoogle Scholar
  71. 71.
    I. Dragomir and T. Ungár, J. Appl. Cryst., 35 (2002), p. 556.CrossRefGoogle Scholar
  72. 72.
    N. Armstrong, M. Leoni, and P. Scardi, Z. Krist., 1 (2006), pp. 81–86.Google Scholar
  73. 73.
    E. Tothkadar, I. Bakonyi, L. Pogany, and A. Cziraki, Surf. Coat. Tech., 88 (1997), pp. 57–65.CrossRefGoogle Scholar
  74. 74.
    I. Noyan, Residual Stress: Measurement by Diffraction and Interpretation (New York: Springer, 1987).Google Scholar
  75. 75.
    T. Ungár and A. Borbely, Appl. Phys. Lett., 69 (1996), p. 3173.CrossRefGoogle Scholar
  76. 76.
    G. K. Williamson and W.H. Hall, Acta Metall., 1 (1953), p. 22.CrossRefGoogle Scholar
  77. 77.
    T. Ungár, J. Gubicza, G. Ribárik, and A. Borbély, J. Appl. Cryst., 34 (2001), pp. 298–310.CrossRefGoogle Scholar
  78. 78.
    P. Scardi, M. Leoni, and M. D’Incau, Diffus. Defect Data, Pt. B,130 (2007), pp. 27–32.Google Scholar
  79. 79.
    I. Groma, Phys. Rev. B, 57 (1998), pp. 7535–7542.CrossRefGoogle Scholar
  80. 80.
    A. Borbely and I. Groma, Appl. Phys. Lett., 79 (2001), p. 1772.CrossRefGoogle Scholar
  81. 81.
    F. Székely, I. Groma, and J. Lendvai, Scripta Mater., 45 (2001), pp. 55–60.CrossRefGoogle Scholar
  82. 82.
    H. Wilhelm, A. Paris, E. Schafler, S. Bernstorff, J. Bonarski, T. Ungar, and M. Zehetbauer, Mater. Sci. Eng. A, 387–389 (2004), pp. 1018–1022.Google Scholar
  83. 83.
    F. Spieckermann, H. Wilhelm, E. Schafler, M. Kerber, S. Bernstorff, and M. Zehetbauer, J. Phys.: Conf. Ser. 240 (2010), p. 012146.Google Scholar
  84. 84.
    K. Yamada, M. Hikosaka, A. Toda, S. Yamazaki, and K. Tagashira, Macromolecules, 36 (2003a), pp. 4790–4801.CrossRefGoogle Scholar
  85. 85.
    K. Yamada, M. Hikosaka, A. Toda, S. Yamazaki, and K. Tagashira, Macromolecules, 36 (2003b), pp. 4802–4812.CrossRefGoogle Scholar
  86. 86.
    B. Crist and F.M. Mirabella, Polym. Sci. Ser. A Polym. Phys., 37 (1999), pp. 3131–3140.Google Scholar
  87. 87.
    F. Spieckermann, H. Wilhelm, M. Kerber, E. Schafler, G. Polt, S. Bernstorff, F. Addiego, and M. Zehetbauer, Polymer, 51 (2010), pp. 4195–4199.CrossRefGoogle Scholar
  88. 88.
    J.D. Hoffman and R.L. Miller, Polymer, 38 (1997), pp. 3151–3212.CrossRefGoogle Scholar
  89. 89.
    R. Séguéla, J. Polymer Science:Part B: Polymer Physics, 40 (2002), pp. 593–601.CrossRefGoogle Scholar
  90. 90.
    G. Fischer, J.E. Bendele, R. Dinnebier, P.W. Stephens, C.L. Lin, N. Bykovetz, and Q. Zhu, J. Phys. Chem. Solids, 56 (1995), p. 1445.CrossRefGoogle Scholar
  91. 91.
    S. Muto, G. van Tendeloo, and S. Amelinckx, Phil. Mag. B, 67 (1993), p. 443.CrossRefGoogle Scholar
  92. 92.
    B. Bonarski, B. Mikulowski, E. Schafler, C. Holzleithner, and M. Zehetbauer, Arch. Metall. Mater., 53 (2008), pp. 117–123.Google Scholar
  93. 93.
    C. Mangler, “Transmission Electron Microscopy Studies of Nanocrystalline FeAl Produced by High Pressure Torsion” (Ph.D. thesis, University of Vienna, Austria, 2009).Google Scholar
  94. 94.
    M. Kerber, E. Schafler, P. Hanak, G. Ribárik, S. Bernstorff, T. Ungár, and M. Zehetbauer, Z. Krist. Suppl., 23 (2006), p. 105.CrossRefGoogle Scholar
  95. 95.
    A. Dubravina, M. Zehetbauer, E. Schafler, and I. Alexandrov, Mater. Sci. Eng., 387–389 (2004), pp. 817–821.Google Scholar
  96. 96.
    M. Zehetbauer and D. Trattner, Mater. Sci. Eng. A, 89 (1987), p. 93.CrossRefGoogle Scholar
  97. 97.
    E. Schafler, Scripta Mater., 62(6) (2010), pp. 423–426.CrossRefGoogle Scholar
  98. 98.
    A. Vorhauer and R. Pippan, Scripta Mater., 51 (2004), p. 921.CrossRefGoogle Scholar
  99. 99.
    T. Ungár, L. Li, G. Tichy, W. Pantleon, H. Choo, and P. Liaw, Scripta Mater., 64 (2011), pp. 876–879.CrossRefGoogle Scholar

Copyright information

© TMS 2011

Authors and Affiliations

  • Michael B. Kerber
    • 1
  • Michael J. Zehetbauer
    • 1
  • Erhard Schafler
    • 1
  • Florian C. Spieckermann
    • 1
  • Sigrid Bernstorff
    • 2
  • Tamas Ungar
    • 3
  1. 1.Research Group Physics of Nanostructured Materials, Faculty of PhysicsUniversity of ViennaWienAustria
  2. 2.Sincrotrone TriesteBasovizzaItaly
  3. 3.Department of Materials PhysicsEötvös University BudapestBudapestHungary

Personalised recommendations