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 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 –F–Fixed Slit Intensity –V–Variable Slit Intensity –I–Integrated Intensity –N–New: Footnotes for d-Spacings (*) Options –2–2D/3D Structure –B–Bond Distances/Angles –E–Electron Patterns –N–New: PD3 Pattern –D–Diffraction Pattern

5 Diffraction Pattern Simulated digitized pattern

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

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

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

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

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

11 SCHERRER FORMULA AND SIZE DISTRIBUTION In most cases, crystalline domains have a distribution of sizes (and shapes). Scherrer constant a shape factor, generally function of hkl (4/3 for spheres) = M 1  mean M 2 - M 1 2  variance Distribution ‘moments’ Scherrer formula is still valid

12 EFFECTS OF A SIZE DISTRIBUTION Example: lognormal distributions of spheres, g(D) (mean , variance  ) 5 nm D

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

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

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

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

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

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

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

20 Lognormal distribution of spheres : mean diameter ‘Scherrer’ size EFFECTS OF A SIZE DISTRIBUTION P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr 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 pseudo-Voigt (pV) Modified Thompson- Cox-Hastings pV Gaussian Lorentzian Particle Size ? Given the variety of available profile functions, why bother with a new one???  Answer: because the size distribution matters!!! Profile Settings

23 “Particle size” option in DDView+  s s=2sin  /  Gamma distribution  : mean  variance  : mean  variance

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 PDF cerium oxide “Particle size” option in DDView+ PDF cerium oxide

30 “Particle size” option in DDView+ PDF cerium oxide

31 “Particle size” option in DDView+ PDF cerium oxide

32 “Particle size” option in DDView+ PDF cerium oxide

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

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

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