1 crystallite size analysis – nanomaterials this tutorial was created from a presentation by...
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Crystallite Size Analysis –Nanomaterials
This tutorial was created from a presentation by Professor Paolo Scardi and Dr. Mateo Leone fromthe University of Trento, Italy. The presentation was given at an ICDD workshop held during the2008 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 ofnanomaterials.
The ICDD is grateful to both Paolo and Mateo as well as the University of Trento for allowing theICDD to use their data for this tutorial.
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Note
This presentation can be directly viewedusing your browser.
It can also be saved, and viewed, withMicrosoft® PowerPoint®. The authors have
made additional comments in the notessection of this presentation, which can
be viewed within PowerPoint®, but is notvisible using the browser.
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ICDD PDF-4+ 2008ICDD PDF-4+ 2008EPDIC Workshop 3EPDIC Workshop 3
Featuring:Featuring:ICDD PDF-4+/DDView+ 2008:ICDD PDF-4+/DDView+ 2008:
Applications to NanomaterialsApplications 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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• pseudo-Voigt (pV)• Modified Thompson-
Cox-Hastings pV• Gaussian• Lorentzian• Particle Size
Profile Settings
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• Particle Size (Gamma distribution of diameters of spherical coherent-scattering domains)
Particle SizeParticle Size
Diffraction Pattern
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• 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
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PIONEERS IN POWDER DIFFRACTION: PAUL SCHERRER
2 2
2 B
I d
I
The Scherrer formula [Gottinger Nachrichten 2 (1918) 98]
ln 22
cosh
h – full width at half maximum – effective domain size – wavelength – Bragg angle
Cerium oxide powder from xerogel, 1 h @400°C
Paul Scherrer (1890–1969)
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EFFECTIVE SIZE AND GRAIN SIZE
What is the meaning of L, the ‘effective size’ of the Scherrer formula?
2cosL
L ≠ D
5 nm
D
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SCHERRER FORMULA AND SIZE DISTRIBUTION
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3
1V
ML
K M
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)
<D> = M1 meanM2 - M1
2 variance
2cosVL
( )iiM D g D dD
Distribution ‘moments’
Scherrer formula is still valid
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4
3
1V
ML L
K MD
EFFECTS OF A SIZE DISTRIBUTION
Example: lognormal distributions of spheres, g(D) (mean , variance )
5 nm
D
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<L>V
13.33D
Lognormal distribution of spheres: 2 2exp ln ) 2 2p D D D
2 2D exp
23 4 7 2VL exp mean diameter
‘Scherrer’ size
EFFECTS OF A SIZE DISTRIBUTION
P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
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13.33D
13.23D <L>V
2 2exp ln ) 2 2p D D D Lognormal distribution of spheres:
2 2D exp
23 4 7 2VL exp mean diameter
‘Scherrer’ size
EFFECTS OF A SIZE DISTRIBUTION
P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
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13.33D
11.82D
<L>V
2 2exp ln ) 2 2p D D D Lognormal distribution of spheres:
2 2D exp
23 4 7 2VL exp mean diameter
‘Scherrer’ size
EFFECTS OF A SIZE DISTRIBUTION
P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
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13.33D
8.25D <L>V
2 2exp ln ) 2 2p D D D Lognormal distribution of spheres:
2 2D exp
23 4 7 2VL exp mean diameter
‘Scherrer’ size
EFFECTS OF A SIZE DISTRIBUTION
P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
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13.33D
4.53D <L>V
2 2exp ln ) 2 2p D D D Lognormal distribution of spheres:
2 2D exp
23 4 7 2VL exp mean diameter
‘Scherrer’ size
EFFECTS OF A SIZE DISTRIBUTION
P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
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13.33D
1.95D <L>V
2 2exp ln ) 2 2p D D D Lognormal distribution of spheres:
2 2D exp
23 4 7 2VL exp mean diameter
‘Scherrer’ size
EFFECTS OF A SIZE DISTRIBUTION
P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
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<L>V
2 2exp ln ) 2 2p D D D Lognormal distribution of spheres:
2 2D exp
23 4 7 2VL exp mean diameter
‘Scherrer’ size
EFFECTS OF A SIZE DISTRIBUTION
P. Scardi, Size-Strain V (Garmisch (D) Sept. 2007). Z. Kristallogr. 2008. In press
20
2 2exp ln ) 2 2p D D D Lognormal distribution of spheres:
2 2D exp
23 4 7 2VL exp mean diameter
‘Scherrer’ size
EFFECTS OF A SIZE DISTRIBUTION
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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• 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
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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+
TEM: 4.5 nmXRD/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
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Validating the procedure
“Particle size” option in DDView+
20 30 40 50 60 70 80 90 1000
2000
4000
6000
8000
10000
12000
14000
Inte
nsi
ty
(a.u
.)
2theta (deg)
Diffraction pattern of Au generated by Debye equation
0 1 2 3 4 5 6 7 8 9
0.0
0.2
0.4
0.6
0.8
1.0
Fre
qu
ency
(a
.u.)
Spherical domain size (nm)
Lognormal distribution of spherical domains (m=1.2, s=0.15) <D>=3.36 nm
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+
0 1 2 3 4 5 6 7 8 9
0.0
0.2
0.4
0.6
0.8
1.0
Fre
qu
ency
(a
.u.)
Spherical domain size (nm)
Lognormal (m=1.2, s=0.15) <D>=3.36 nm DDView+ Gamma (m=3.36, s=50) <D>=3.36 nm
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0 1 2 3 4 5 6 7 8 9
0.0
0.2
0.4
0.6
0.8
1.0
Fre
qu
ency
(a
.u.)
Spherical domain size (nm)
Lognormal (m=1.2, s=0.15) <D>=3.36 nm DDView+ Gamma (m=4.0, s=50) <D>=4.0 nm
“Particle size” option in DDView+
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0 1 2 3 4 5 6 7 8 9
0.0
0.2
0.4
0.6
0.8
1.0
Fre
qu
ency
(a
.u.)
Spherical domain size (nm)
Lognormal (m=1.2, s=0.15) <D>=3.36 nm DDView+ Gamma (m=5.0, s=50) <D>=5.0 nm
“Particle size” option in DDView+
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0 1 2 3 4 5 6 7 8 90.0
0.2
0.4
0.6
0.8
1.0
1.2
Fre
qu
ency
(a
.u.)
Spherical domain size (nm)
Lognormal (m=1.2, s=0.15) <D>=3.36 nm DDView+ Gamma (m=3.0, s=50) <D>=3.0 nm
“Particle size” option in DDView+
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0 1 2 3 4 5 6 7 8 90.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Fre
qu
ency
(a
.u.)
Spherical domain size (nm)
Lognormal (m=1.2, s=0.15) <D>=3.36 nm DDView+ Gamma (m=2.0, s=50) <D>=2.0 nm
“Particle size” option in DDView+
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“Particle size” option in DDView+
0 1 2 3 4 5 6 7 8 9
0.0
0.2
0.4
0.6
0.8
1.0
Fre
qu
ency
(a
.u.)
Spherical domain size (nm)
Lognormal (m=1.2, s=0.15) <D>=3.36 nm DDView+ Gamma (m=3.36, s=50) <D>=3.36 nm
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“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 (Paolo.Scardi@unitn.it)
CAVEAT!CAVEAT!
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International Centre for Diffraction Data
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Phone: 610.325.9814
Fax: 610.325.9823
Thank you for viewing our tutorial. Additional tutorials are available at the ICDD web site (
www.icdd.com).
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