Crystallite Size Analysis

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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.

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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.

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ICDD PDF-4 2008 EPDIC Workshop 3
Featuring ICDD PDF-4/DDView 2008Applications
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
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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

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Diffraction Pattern

• Simulated digitized pattern

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Profile Settings

• pseudo-Voigt (pV)
• Modified Thompson-Cox-Hastings pV
• Gaussian
• Lorentzian
• Particle Size

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Diffraction Pattern

• Particle Size (Gamma distribution of diameters of
  spherical coherent-scattering domains)

Particle Size
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Profile Settings

• 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!!!
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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 (18901969)
Cerium oxide powder from xerogel, 1 h _at_400C
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EFFECTIVE SIZE AND GRAIN SIZE
What is the meaning of L, the effective size
of the Scherrer formula?
?
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SCHERRER FORMULA AND SIZE DISTRIBUTION
In most cases, crystalline domains have a
distribution of sizes (and shapes).
ltDgt M1 ? meanM2 - M12 ? variance
Scherrer formula is still valid
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EFFECTS OF A SIZE DISTRIBUTION
Example lognormal distributions of spheres, g(D)
(mean m, variance s)
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EFFECTS OF A SIZE DISTRIBUTION
Lognormal distribution of spheres
P. Scardi, Size-Strain V (Garmisch (D) Sept.
2007). Z. Kristallogr. 2008. In press
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EFFECTS OF A SIZE DISTRIBUTION
Lognormal distribution of spheres
P. Scardi, Size-Strain V (Garmisch (D) Sept.
2007). Z. Kristallogr. 2008. In press
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EFFECTS OF A SIZE DISTRIBUTION
Lognormal distribution of spheres
P. Scardi, Size-Strain V (Garmisch (D) Sept.
2007). Z. Kristallogr. 2008. In press
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EFFECTS OF A SIZE DISTRIBUTION
Lognormal distribution of spheres
P. Scardi, Size-Strain V (Garmisch (D) Sept.
2007). Z. Kristallogr. 2008. In press
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EFFECTS OF A SIZE DISTRIBUTION
Lognormal distribution of spheres
P. Scardi, Size-Strain V (Garmisch (D) Sept.
2007). Z. Kristallogr. 2008. In press
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EFFECTS OF A SIZE DISTRIBUTION
Lognormal distribution of spheres
P. Scardi, Size-Strain V (Garmisch (D) Sept.
2007). Z. Kristallogr. 2008. In press
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EFFECTS OF A SIZE DISTRIBUTION
Lognormal distribution of spheres
P. Scardi, Size-Strain V (Garmisch (D) Sept.
2007). Z. Kristallogr. 2008. In press
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EFFECTS OF A SIZE DISTRIBUTION
Lognormal distribution of spheres
P. Scardi, Size-Strain V (Garmisch (D) Sept.
2007). Z. Kristallogr. 2008. In press
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EFFECT OF A BIMODAL SIZE DISTRIBUTION
If the size distribution is multimodal, a single
(mean size) number is of little use, and
possibly misleading!!
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Profile Settings

• 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!!!
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Particle size option in DDView
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Particle size option in DDView
M. Leoni P. Scardi, Nanocrystalline domain
size distributions from powder diffraction data,
J. Appl. Cryst. 37 (2004) 629
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Particle size option in DDView
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Particle size option in DDView
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Particle size option in DDView
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Particle size option in DDView
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Particle size option in DDView
PDF 04-001-2097 cerium oxide
PDF 04-001-2097 cerium oxide
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Particle size option in DDView
PDF 04-001-2097 cerium oxide
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Particle size option in DDView
PDF 04-001-2097 cerium oxide
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Particle size option in DDView
PDF 04-001-2097 cerium oxide
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Particle size option in DDView
PDF 04-001-2097 cerium oxide
M. Leoni P. Scardi, Nanocrystalline domain
size distributions from powder diffraction data,
J. Appl. Cryst. 37 (2004) 629
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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)
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Particle size option in DDView
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Particle size option in DDView
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Particle size option in DDView
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Particle size option in DDView
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Particle size option in DDView
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Particle size option in DDView
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Particle size option in DDView
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Particle size option in DDView
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Particle size option in DDView
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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,
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_at_unitn.it)
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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 [phone]