Skip to main content

Information on Imperfections

  • Conference paper
  • First Online:
Book cover Uniting Electron Crystallography and Powder Diffraction

Abstract

Line Profile Analysis is the common name given to those methods allowing microstructure information to be extracted from the breadth and shape of the peaks in a diffraction pattern. A fast analysis is always possible via traditional techniques such as the Scherrer formula, Williamson-Hall plot and Warren-Averbach method, but at the expenses of the physical meaning of the result. A more sound alternative is offered by the Whole Powder Pattern Modelling, allowing physical information to be extracted from diffraction data in a self-consistent way.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Scherrer P (1918) Bestimmung der Grösse und der inneren Struktur von Kolloidteilchen mittels Röntgenstrahlen. Nachr Ges Wiss Goettingen Math-Phys Kl:98–100

    Google Scholar 

  2. Williamson GK, Hall WH (1953) X-ray line broadening from filed aluminium and wolfram. Acta Metall 1:22–31

    Article  Google Scholar 

  3. Warren BE, Averbach BL (1950) The effect of cold-work distortion on X-ray patterns. J Appl Phys 21:595–600

    Article  ADS  Google Scholar 

  4. Warren BE, Averbach BL (1952) The separation cold-work distortion and particle size broadening in X-ray patterns. J Appl Phys 23:497–512

    Article  ADS  Google Scholar 

  5. Warren BE (1969) X-ray diffraction. Addison-Wesley, Reading

    Google Scholar 

  6. Klug HP, Alexander LE (1974) X-ray diffraction procedures for polycrystalline and amorphous material. Wiley, New York

    Google Scholar 

  7. Langford JI, Louër D (1996) Powder diffraction. Rep Prog Phys 59:131–234

    Article  ADS  Google Scholar 

  8. Langford JI, Wilson AJC (1978) Scherrer after sixty years: a survey and some new results in the determination of crystallite size. J Appl Crystallogr 11:102–113

    Article  Google Scholar 

  9. Scardi P, Leoni M, Dong YH (2000) Whole diffraction pattern-fitting of polycrystalline fcc materials based on microstructure. Eur Phys J B 18:23–30

    Article  ADS  Google Scholar 

  10. Scardi P, Leoni M (2004) Whole powder pattern modelling: theory and application. In: Mittemeijer EJ, Scardi P (eds) Diffraction analysis of the microstructure of materials. Springer, Berlin, pp 51–91

    Google Scholar 

  11. Scardi P, Leoni M (2002) Whole powder pattern modelling. Acta Crystallogr A 58:190–200

    Article  Google Scholar 

  12. Snyder RL, Fiala J, Bunge HJ (eds) (1999) Microstructure analysis from diffraction. Oxford University Press, Oxford

    Google Scholar 

  13. Mittemeijer EJ, Scardi P (eds) (2004) Diffraction analysis of the microstructure of materials. Springer, Berlin

    Google Scholar 

  14. Guagliardi A, Masciocchi N (2010) Diffraction at the nanoscale. Nanocrystals, defective & amorphous materials. Insubria University Press, Como

    Google Scholar 

  15. Scardi P, Dinnebier R (eds) (2010) Extending the reach of powder diffraction modelling. Trans Tech Publications Ltd., Zurich

    Google Scholar 

  16. Bertaut EF (1949) X-ray study of the distribution of crystallite dimensions in a crystalline powder [in French]. CR Acad Sci Paris 228:492–494

    Google Scholar 

  17. Bertaut EF (1950) Raies de Debye-Scherreretrépartition des dimensions des domaines de Bragg dans les poudrespolycristallines. Acta Crystallogr 3:14–18

    Article  Google Scholar 

  18. Scardi P, Leoni M, Delhez R (2004) Line-broadening analysis using integral breadth methods: a critical review. J Appl Crystallogr 37:381–390

    Article  Google Scholar 

  19. Balzar D (1999) Voigt-function model in diffraction line-broadening analysis. In: Snyder RL, Fiala J, Bunge HJ (eds) Microstructure analysis from diffraction. Oxford University Press, Oxford

    Google Scholar 

  20. Scardi P, Leoni M (2001) Diffraction line profiles from polydisperse crystalline systems. Acta Crystallogr A 57:604–613

    Article  Google Scholar 

  21. Ungár T, Gubicza J, Ribárik G, Borbély A (2001) A crystallite size distribution and dislocation structure determined by diffraction profile analysis: principles and practical application to cubic and hexagonal crystals. J Appl Crystallogr 34:298–310

    Article  Google Scholar 

  22. Ribárik G (2008) Modeling of diffraction patterns properties. PhD thesis, Eötvös University, Budapest

    Google Scholar 

  23. Scardi P, Dong YH, Leoni M (2001) Line profile analysis in the Rietveld method and whole-powder-pattern fitting. Mater Sci Forum 378–381:132–141

    Article  Google Scholar 

  24. Scardi P (2002) Profile modelling versus profile fitting in powder diffraction. Z Kristallogr 217:420–421

    Article  Google Scholar 

  25. Scardi P, Leoni M (2006) Line profile analysis: pattern modelling versus profile fitting. J Appl Crystallogr 39:24–31

    Article  Google Scholar 

  26. Leoni M, Scardi P (2004) Surface relaxation effects in nanocrystalline powders. In: Mittemeijer EJ, Scardi P, Mittemeijer EJ, Scardi P (eds) Diffraction analysis of the microstructure of materials. Springer, Berlin, pp 413–454

    Google Scholar 

  27. Leoni M (2004) Grain surface relaxation and grain interaction in powder diffraction. Mater Sci Forum 1–10:443–444

    Google Scholar 

  28. Scardi P, Leoni M (2005) Diffraction whole-pattern modelling for the study of anti-phase domains in Cu3Au. Acta Mater 53:5229–5239

    Article  Google Scholar 

  29. Leoni M, Scardi P (2004) Nanocrystalline domain size distributions from powder diffraction data. J Appl Crystallogr 37:629–634

    Article  Google Scholar 

  30. Armstrong N, Leoni M, Scardi P (2006) Some considerations concerning Wilkens’ theory of dislocation line-broadening. Z Kristallogr Suppl 23:81–86

    Article  Google Scholar 

  31. Leoni M, Confente T, Scardi P (2006) PM2K: a flexible program implementing whole powder pattern modelling. Z Kristallogr Suppl 23:249–254

    Article  Google Scholar 

  32. Scardi P, Leoni M, Faber J (2006) Diffraction line profile from a disperse system: a simple alternative to Voigtian profiles. Powder Diffr 21:270–277

    Article  ADS  Google Scholar 

  33. Leoni M, Martinez-Garcia J, Scardi P (2007) Dislocation effects in powder diffraction. J Appl Crystallogr 40:719–724

    Article  Google Scholar 

  34. Estevez-Rams E, Leoni M, Scardi P, Aragon-Fernandez B, Fuess H (2003) On the powder diffraction pattern of crystals with stacking faults. Phil Mag 83(36):4045–4057

    Article  ADS  Google Scholar 

  35. Martinez-Garcia J, Leoni M, Scardi P (2009) A general approach for determining the diffraction contrast factor of straight-line dislocations. Acta Crystallogr A 65:109–119

    Article  ADS  Google Scholar 

  36. Leoni M, Di Maggio R, Polizzi S, Scardi P (2004) An X-ray diffraction methodology for the microstructural analysis of nanocrystalline powders: application to cerium oxide. J Am Ceram Soc 87:1133–1140

    Article  Google Scholar 

  37. Scardi P (2005) Microstructure and lattice defects in highly deformed metals by X-ray diffraction whole powder pattern modelling. Z Metall 9:698–702

    Google Scholar 

  38. De Giudici G, Biddau R, D’Incau M, Leoni M, Scardi P (2005) Reactivity of nanocrystalline fluorite powders: defect density threshold. Geochimicaet Cosmochimica Acta 69(16):4073–4083

    Article  ADS  Google Scholar 

  39. Scardi P, Leoni M, Lamas DG, Cabanillas ED (2005) Grain size distribution of nanocrystalline systems. Powder Diffr 20(4):353–358

    Article  ADS  Google Scholar 

  40. Leoni M, De Giudici G, Biddau R, D’Incau M, Scardi P (2006) Analysis of polydisperse ball-milled fluorite powders using a full pattern technique. Z Kristallogr Suppl 23:111–116

    Article  Google Scholar 

  41. Scardi P, Leoni M, D’Incau M (2007) Whole powder pattern modelling of cubic metal powders deformed by high energy milling. Z Kristallogr 222:129–135

    Article  Google Scholar 

  42. Scardi P, Leoni M, Straffelini G, GiudiciG D (2007) Microstructure of Cu-Be alloy triboxidative wear debris. Acta Mater 55:2531–2538

    Article  Google Scholar 

  43. Scardi P, D’Incau M, Leoni M (2007) Full pattern methods for the analysis of plastically deformed materials. Solid State Phenom 130:27–32

    Article  Google Scholar 

  44. D’Incau M, Leoni M, Scardi P (2007) High energy grinding of FeMo powders. J Mater Res 22:1744–1753

    Article  ADS  Google Scholar 

  45. Pesenti H, Leoni M, Scardi P (2008) XRD line profile analysis of calcite powders produced by 318 high energy milling. Z Kristallogr Suppl 27:143–150

    Article  Google Scholar 

  46. Ungár T (2004) Microstructure parameters from X-ray diffraction peak broadening. Scripta Mater 51:777–781

    Article  Google Scholar 

  47. Ribárik G, Gubicza J, Ungár T (2004) Correlation between strength and microstructure of ball-milled Al–Mg alloys determined by X-ray diffraction. Mater Sci Eng A 387–389:343–347

    Google Scholar 

  48. Balogh L, Ribárik G, Ungár T (2006) Stacking faults and twin boundaries in fcc crystals determined by X-ray diffraction profile analysis. J Appl Phys 100:023512

    Article  ADS  Google Scholar 

  49. Pawley GS (1981) Unit-cell refinement from powder diffraction scans. J Appl Crystallogr 14:357–361

    Article  Google Scholar 

  50. Rietveld HM (1967) Line profiles of neutron powder-diffraction peaks for structure refinement. Acta Crystallogr 22:151–152

    Article  Google Scholar 

  51. Rietveld HM (1969) A profile refinement method for nuclear and magnetic structures. J Appl Crystallogr 2:65–71

    Article  Google Scholar 

  52. Young RA (ed) (1993) The Rietveld method. Oxford University Press, Oxford

    Google Scholar 

  53. Leineweber A, Mittemeijer EJ (2004) Diffraction line broadening due to lattice-parameter variations caused by a spatially varying scalar variable: its orientation dependence caused by locally varying nitrogen content in \( \varepsilon \)-FeN0.433. J Appl Crystallogr 37:123–135

    Article  Google Scholar 

  54. van Berkum JGM (1994) Strain fields in crystalline materials. PhD thesis, Technische Universiteit Delft, Delft, The Netherlands

    Google Scholar 

  55. Leoni M, Gualtieri A, Roveri N (2004) Simultaneous refinement of structure and microstructure of layered materials. J Appl Crystallogr 37:166–173

    Article  Google Scholar 

Download references

Acknowledgments

The author wishes to thank Prof. P. Scardi for continuous support, critical reading and useful discussions. The PM2K software implementing the WPPM method and the DIFFaX+ code for the analysis of systems with heavy faulting are both available on request from the author. A free license is granted for academic and non-profit use.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Matteo Leoni .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Leoni, M. (2012). Information on Imperfections. In: Kolb, U., Shankland, K., Meshi, L., Avilov, A., David, W. (eds) Uniting Electron Crystallography and Powder Diffraction. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5580-2_16

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-5580-2_16

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-5579-6

  • Online ISBN: 978-94-007-5580-2

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics