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Crystallite size nanomaterials

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Crystallite size nanomaterials

  1. 1. Crystallite Size Analysis – NanomaterialsThis 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. 1
  2. 2. Note This presentation can be directly viewed using your browser. It can also be saved, and viewed, withMicrosoft® PowerPoint®. The authors have made additional comments in the notes section of this presentation, which canbe viewed within PowerPoint®, but is not visible using the browser. 2
  3. 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-LargeDr. Matteo Leoni (University of Trento), ICDD Regional Chair (Europe) September 19, 2008 3
  4. 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 4
  5. 5. Diffraction Pattern• Simulated digitized pattern 5
  6. 6. Profile Settings• pseudo-Voigt (pV)• Modified Thompson- Cox-Hastings pV• Gaussian• Lorentzian• Particle Size 6
  7. 7. Diffraction Pattern• Particle Size (Gamma distribution of diameters of spherical coherent-scattering domains) Particle Size Particle Size 7
  8. 8. Profile Settings• pseudo-Voigt (pV)• Modified Thompson- Cox-Hastings pV• Gaussian ? Given the variety of available• Lorentzian profile functions, why bother with a new one???• Particle Size  Answer: because the size distribution matters!!! 8
  9. 9. PIONEERS IN POWDER DIFFRACTION: PAUL SCHERRER The Scherrer formula [Gottinger Nachrichten 2 (1918) 98] ln 2 λ h – full width at half maximum h=2 × Λ – effective domain size π Λ cos θ λ θ – – wavelength Bragg anglePaul Scherrer (1890–1969) Cerium oxide powder from xerogel, 1 h @400°C β= ∫ I ( 2θ ) d 2θ I ( 2θB ) 9
  10. 10. EFFECTIVE SIZE AND GRAIN SIZE What is the meaning of L,the ‘effective size’ of the Scherrer formula? λ β ( 2θ ) = L cos θ D 5 nm L ≠ D 10
  11. 11. SCHERRER FORMULA AND SIZE DISTRIBUTION In most cases, crystalline domains have a distribution of sizes (and shapes). Distribution ‘moments’ M i = ∫ D i g ( D)dD <D> = M1  mean M2 - M12  varianceScherrer formula is still valid λ 1 M4β ( 2θ ) = → < L >V = < L >V cos θ Kβ M 3 Scherrer constant a shape factor, generally function of hkl (4/3 for spheres) 11
  12. 12. EFFECTS OF A SIZE DISTRIBUTION 1 M4 DL → < L >V = ≠ D Kβ M 3 5 nm Example: lognormal distributions of spheres, g(D) (mean µ , variance σ ) 12
  13. 13. EFFECTS OF A SIZE DISTRIBUTIONLognormal distribution of spheres: p ( D ) = exp  − ( ln D − µ ) 2 ) 2σ 2  Dσ 2π   D = 13.33 <L>V D = exp ( µ + σ 2 2 ) mean diameter < L >V = 3 4 exp ( µ + 7σ 2 2 ) ‘Scherrer’ size 13 P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
  14. 14. EFFECTS OF A SIZE DISTRIBUTIONLognormal distribution of spheres: p ( D ) = exp  − ( ln D − µ ) 2 ) 2σ 2  Dσ 2π   D = 13.33 <L>V D = 13.23 D = exp ( µ + σ 2 2 ) mean diameter < L >V = 3 4 exp ( µ + 7σ 2 2 ) ‘Scherrer’ size 14 P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
  15. 15. EFFECTS OF A SIZE DISTRIBUTIONLognormal distribution of spheres: p ( D ) = exp  − ( ln D − µ ) 2 ) 2σ 2  Dσ 2π   D = 13.33 <L>V D = 11.82 D = exp ( µ + σ 2 2 ) mean diameter < L >V = 3 4 exp ( µ + 7σ 2 2 ) ‘Scherrer’ size 15 P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
  16. 16. EFFECTS OF A SIZE DISTRIBUTIONLognormal distribution of spheres: p ( D ) = exp  − ( ln D − µ ) 2 ) 2σ 2  Dσ 2π   D = 13.33 <L>V D = 8.25 D = exp ( µ + σ 2 2 ) mean diameter < L >V = 3 4 exp ( µ + 7σ 2 2 ) ‘Scherrer’ size 16 P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
  17. 17. EFFECTS OF A SIZE DISTRIBUTIONLognormal distribution of spheres: p ( D ) = exp  − ( ln D − µ ) 2 ) 2σ 2  Dσ 2π   D = 13.33 <L>V D = 4.53 D = exp ( µ + σ 2 2 ) mean diameter < L >V = 3 4 exp ( µ + 7σ 2 2 ) ‘Scherrer’ size 17 P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
  18. 18. EFFECTS OF A SIZE DISTRIBUTIONLognormal distribution of spheres: p ( D ) = exp  − ( ln D − µ ) 2 ) 2σ 2  Dσ 2π   D = 13.33 <L>V D = 1.95 D = exp ( µ + σ 2 2 ) mean diameter < L >V = 3 4 exp ( µ + 7σ 2 2 ) ‘Scherrer’ size 18 P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
  19. 19. EFFECTS OF A SIZE DISTRIBUTIONLognormal distribution of spheres: p ( D ) = exp  − ( ln D − µ ) 2 ) 2σ 2  Dσ 2π   <L>V D = exp ( µ + σ 2 2 ) mean diameter < L >V = 3 4 exp ( µ + 7σ 2 2 ) ‘Scherrer’ size 19 P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
  20. 20. EFFECTS OF A SIZE DISTRIBUTIONLognormal distribution of spheres: p ( D ) = exp  − ( ln D − µ ) 2 ) 2σ 2  Dσ 2π   D = exp ( µ + σ 2 2 ) mean diameter < L >V = 3 4 exp ( µ + 7σ 2 2 ) ‘Scherrer’ size 20 P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
  21. 21. EFFECT OF A BIMODAL SIZE DISTRIBUTION If the size distribution is multimodal, a single (“meansize”) number is of little use, and possibly misleading!! 21
  22. 22. Profile Settings• pseudo-Voigt (pV)• Modified Thompson- Cox-Hastings pV• Gaussian• Lorentzian ? Given the variety of available profile functions, why bother• Particle Size with a new one???  Answer: because the size distribution matters!!! 22
  23. 23. “Particle size” option in DDView+ µ: mean σ: varianceGamma distribution ψ=πµs s=2sinθ/λµ: mean σ: variance 23
  24. 24. “Particle size” option in DDView+ M. Leoni & P. Scardi, “Nanocrystalline domain size distributions 24 from powder diffraction data”, J. Appl. Cryst. 37 (2004) 629
  25. 25. “Particle size” option in DDView+ 25
  26. 26. “Particle size” option in DDView+ 26
  27. 27. “Particle size” option in DDView+ 27
  28. 28. “Particle size” option in DDView+ 28
  29. 29. “Particle size” option in DDView+ PDF 04-001-2097 cerium oxide PDF 04-001-2097 cerium oxide 29
  30. 30. “Particle size” option in DDView+ PDF 04-001-2097 cerium oxide 30
  31. 31. “Particle size” option in DDView+ PDF 04-001-2097 cerium oxide 31
  32. 32. “Particle size” option in DDView+ PDF 04-001-2097 cerium oxide 32
  33. 33. “Particle size” option in DDView+ PDF 04-001-2097 cerium oxide TEM: 4.5 nm XRD/WPPM:4.4nm M. Leoni & P. Scardi, “Nanocrystalline domain size distributions 33 from powder diffraction data”, J. Appl. Cryst. 37 (2004) 629
  34. 34. “Particle size” option in DDView+ Validating the procedure Diffraction pattern of Au generated by Debye equation 14000 1.0 Lognormal distribution of spherical domains (m=1.2, s=0.15) <D>=3.36 nm 12000 0.8 Frequency (a.u.) 10000 Intensity (a.u.) 0.6 8000 0.4 0.2 6000 0.0 4000 0 1 2 3 4 5 6 7 8 9 Spherical domain size (nm) 2000 0 20 30 40 50 60 70 80 90 100 2theta (deg) 34K. Beyerlein, A. Cervellino, M. Leoni, R.L. Snyder & P. Scardi. EPDIC-11 (Warsaw (PL) Sept. 2008)
  35. 35. “Particle size” option in DDView+ 35
  36. 36. “Particle size” option in DDView+ 36
  37. 37. “Particle size” option in DDView+ 37
  38. 38. “Particle size” option in DDView+ 1.0 Lognormal (m=1.2, s=0.15) <D>=3.36 nm DDView+ Gamma (m=3.36, s=50) <D>=3.36 nm 0.8 Frequency (a.u.) 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 Spherical domain size (nm) 38
  39. 39. “Particle size” option in DDView+ 1.0 Lognormal (m=1.2, s=0.15) <D>=3.36 nm DDView+ Gamma (m=4.0, s=50) <D>=4.0 nm 0.8 Frequency (a.u.) 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 Spherical domain size (nm) 39
  40. 40. “Particle size” option in DDView+ 1.0 Lognormal (m=1.2, s=0.15) <D>=3.36 nm DDView+ Gamma (m=5.0, s=50) <D>=5.0 nm 0.8 Frequency (a.u.) 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 Spherical domain size (nm) 40
  41. 41. “Particle size” option in DDView+ 1.2 Lognormal (m=1.2, s=0.15) <D>=3.36 nm DDView+ Gamma (m=3.0, s=50) <D>=3.0 nm 1.0 Frequency (a.u.) 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 Spherical domain size (nm) 41
  42. 42. “Particle size” option in DDView+ 1.6 Lognormal (m=1.2, s=0.15) <D>=3.36 nm 1.4 DDView+ Gamma (m=2.0, s=50) <D>=2.0 nm 1.2 Frequency (a.u.) 1.0 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 Spherical domain size (nm) 42
  43. 43. “Particle size” option in DDView+ 1.0 Lognormal (m=1.2, s=0.15) <D>=3.36 nm DDView+ Gamma (m=3.36, s=50) <D>=3.36 nm 0.8 Frequency (a.u.) 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 Spherical domain size (nm) 43
  44. 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 for estimating domain size, especiallyin nano materials where the line width/shape isdominated 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) 44
  45. 45. Thank you for viewing ourtutorial. Additional tutorials areavailable 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 45

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