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Crystallite Size Analysis – Nanomaterials

Crystallite Size Analysis – Nanomaterials. This tutorial was created from a presentation by Professor Paolo Scardi and Dr. Mateo Leone from the University of Trento, Italy. The presentation was given at an ICDD workshop held during the

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Crystallite Size Analysis – Nanomaterials

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  1. Crystallite Size Analysis –Nanomaterials This tutorial was created from a presentation by Professor Paolo Scardi and Dr. Mateo Leone from the University of Trento, Italy. The presentation was given at an ICDD workshop held during the 2008 EPDIC-11 Meeting in Warsaw, Poland. Professor Paolo Scardi is shown above on the right. The tutorial includes the theory and examples of the particle size algorithm and display features that are embedded in PDF-4+! It also demonstrates how this simulation can be used for the study of nanomaterials. The ICDD is grateful to both Paolo and Mateo as well as the University of Trento for allowing the ICDD to use their data for this tutorial.

  2. Note This presentation can be directly viewed using your browser. It can also be saved, and viewed, with Microsoft® PowerPoint®. The authors have made additional comments in the notes section of this presentation, which can be viewed within PowerPoint®, but is not visible using the browser.

  3. ICDD PDF-4+ 2008 EPDIC Workshop 3 Featuring: ICDD PDF-4+/DDView+ 2008:Applications to Nanomaterials Prof. Paolo Scardi (University of Trento), ICDD Director-at-Large Dr. Matteo Leoni (University of Trento), ICDD Regional Chair (Europe) September 19, 2008

  4. PDF Card • Contains Diffraction Data of Material • Multiple d-Spacing Sets • Fixed Slit Intensity • Variable Slit Intensity • Integrated Intensity • New: Footnotes for d-Spacings (*) • Options • 2D/3D Structure • Bond Distances/Angles • Electron Patterns • New: PD3 Pattern • Diffraction Pattern

  5. Diffraction Pattern Simulated digitized pattern

  6. Profile Settings pseudo-Voigt (pV) Modified Thompson-Cox-Hastings pV Gaussian Lorentzian Particle Size

  7. Diffraction Pattern Particle Size Particle Size (Gamma distribution of diameters of spherical coherent-scattering domains)

  8. Profile Settings • Given the variety of available profile functions, why bother with a new one??? Answer: because the size distribution matters!!! pseudo-Voigt (pV) Modified Thompson-Cox-Hastings pV Gaussian Lorentzian Particle Size

  9. PIONEERS IN POWDER DIFFRACTION: PAUL SCHERRER The Scherrer formula [Gottinger Nachrichten 2 (1918) 98] • h – full width at half maximum • L – effective domain size • – wavelength q– Bragg angle Paul Scherrer (1890–1969) Cerium oxide powder from xerogel, 1 h @400°C

  10. EFFECTIVE SIZE AND GRAIN SIZE D 5 nm L D What is the meaning of L, the ‘effective size’ of the Scherrer formula? ≠

  11. SCHERRER FORMULA AND SIZE DISTRIBUTION Distribution ‘moments’ Scherrer constanta shape factor, generally function of hkl (4/3 for spheres) In most cases, crystalline domains have a distribution of sizes (and shapes). <D> = M1 meanM2 - M12  variance Scherrer formula is still valid

  12. D 5 nm EFFECTS OF A SIZE DISTRIBUTION Example: lognormal distributions of spheres, g(D) (meanm, variances)

  13. <L>V mean diameter ‘Scherrer’ size EFFECTS OF A SIZE DISTRIBUTION Lognormal distribution of spheres: P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press

  14. <L>V mean diameter ‘Scherrer’ size EFFECTS OF A SIZE DISTRIBUTION Lognormal distribution of spheres: P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press

  15. <L>V mean diameter ‘Scherrer’ size EFFECTS OF A SIZE DISTRIBUTION Lognormal distribution of spheres: P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press

  16. <L>V mean diameter ‘Scherrer’ size EFFECTS OF A SIZE DISTRIBUTION Lognormal distribution of spheres: P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press

  17. <L>V mean diameter ‘Scherrer’ size EFFECTS OF A SIZE DISTRIBUTION Lognormal distribution of spheres: P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press

  18. <L>V mean diameter ‘Scherrer’ size EFFECTS OF A SIZE DISTRIBUTION Lognormal distribution of spheres: P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press

  19. <L>V mean diameter ‘Scherrer’ size EFFECTS OF A SIZE DISTRIBUTION Lognormal distribution of spheres: P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press

  20. mean diameter ‘Scherrer’ size EFFECTS OF A SIZE DISTRIBUTION Lognormal distribution of spheres: P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press

  21. EFFECT OF A BIMODAL SIZE DISTRIBUTION If the size distribution is multimodal, a single (“mean size”) number is of little use, and possibly misleading!!

  22. Profile Settings • Given the variety of available profile functions, why bother with a new one??? Answer: because the size distribution matters!!! pseudo-Voigt (pV) Modified Thompson-Cox-Hastings pV Gaussian Lorentzian Particle Size

  23. “Particle size” option in DDView+ • m: mean • s: variance • Gamma distribution • m: means: variance y=pms s=2sinq/l

  24. “Particle size” option in DDView+ M. Leoni & P. Scardi, “Nanocrystalline domain size distributions from powder diffraction data”, J. Appl. Cryst. 37 (2004) 629

  25. “Particle size” option in DDView+

  26. “Particle size” option in DDView+

  27. “Particle size” option in DDView+

  28. “Particle size” option in DDView+

  29. “Particle size” option in DDView+ PDF 04-001-2097 cerium oxide PDF 04-001-2097 cerium oxide

  30. “Particle size” option in DDView+ PDF 04-001-2097 cerium oxide

  31. “Particle size” option in DDView+ PDF 04-001-2097 cerium oxide

  32. “Particle size” option in DDView+ PDF 04-001-2097 cerium oxide

  33. “Particle size” option in DDView+ TEM: 4.5 nm XRD/WPPM:4.4nm PDF 04-001-2097 cerium oxide M. Leoni & P. Scardi, “Nanocrystalline domain size distributions from powder diffraction data”, J. Appl. Cryst. 37 (2004) 629

  34. “Particle size” option in DDView+ Validating the procedure K. Beyerlein, A. Cervellino, M. Leoni, R.L. Snyder & P. Scardi. EPDIC-11 (Warsaw (PL) Sept. 2008)

  35. “Particle size” option in DDView+

  36. “Particle size” option in DDView+

  37. “Particle size” option in DDView+

  38. “Particle size” option in DDView+

  39. “Particle size” option in DDView+

  40. “Particle size” option in DDView+

  41. “Particle size” option in DDView+

  42. “Particle size” option in DDView+

  43. “Particle size” option in DDView+

  44. “Particle size” option in DDView+ CAVEAT! • DDView+ “Particle size” is NOT a profile fitting! • NO other sources of line broadening (e.g., instrumental profile, dislocations, etc.) are considered! • Gamma distribution is flexible and handy, but in some cases it MIGHT NOT work! Domains might not be • spherical! Use this feature only forestimating domain size, especially in nano materials where the line width/shape is dominated by the size effects. In all other cases, use a Line Profile Analysis software, e.g., PM2K, based on the WPPM algorithm (Paolo.Scardi@unitn.it)

  45. Thank you for viewing our tutorial. Additional tutorials are available at the ICDD web site (www.icdd.com). International Centre for Diffraction Data 12 Campus Boulevard Newtown Square, PA 19073 Phone: 610.325.9814 Fax: 610.325.9823

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