Download - Powder Diffraction & Synchrotron Radiation
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •1
Powder Diffraction & Synchrotron Radiation
P. ScardiDepartment of Materials Engineering and Industrial Technologies
University of Trento
International Doctoral School in International Doctoral School in Materials Science & EngineeringMaterials Science & Engineering
About 15 new positions per year
University of Trento
Information and applications:
http://portale.unitn.it/drmse/
next deadline: September 14th
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •2
3
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
PRESENTATION OUTLINE
• Main applications of XRPD and RS-XRPD
PART I
• Some advantages and peculiaritiesof synchrotron radiation X-ray powderdiffraction (SR-XRPD)
PART II
• Diffraction from nanocrystalline andhighly deformed materials
4
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
single crystal100
110
020120220
powder(bulk polycrystalline)100
110
020120220
100
110
020120220
DIFFRACTION: SINGLE CRYSTAL AND POWDER
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •3
5
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
DIFFRACTION: SINGLE CRYSTAL AND POWDER
6
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
DEBYE-SCHERRER GEOMETRY
POWDER
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •4
7
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SRXRD POWDER GEOMETRY: A TYPICAL EXAMPLE
ID31 Goniometer andnine-crystal analyzer
X-r
ayde
tect
or
Parallel beam geometry at ID31 (ESRF)capillary holder / high temperature blower
8
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SRXRD POWDER GEOMETRY: A TYPICAL EXAMPLEParallel beam geometry of MCX (Elettra)
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •5
9
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SRXRD POWDER GEOMETRY: A TYPICAL EXAMPLEParallel beam geometry of MCX (Elettra)
10
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SRXRD POWDER GEOMETRY: A TYPICAL EXAMPLEParallel beam geometry of MCX (Elettra)
BEAMTIME APPLICATIONS:DEADLINE IS SEPTEMBER 15th
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •6
11
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
TYPICAL LAB GEOMETRY: BRAGG-BRENTANO (POWDER)
BULK orPOWDER
source
detector
20 40 60 80 100 120 1400
10002000
3000
4000
5000
6000
7000
Inte
nsity
(co
unts
)
2θ (degrees)
12
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
(why) do we need synchrotron radiation?
LAB vs SR XRD
… don’t use a cannonto kill a fly !
quoted by G. Artioli
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •7
13
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
1) High brillance, much better counting statistics / shorter data collectiontime (à fast kinetics, in situ studies)
40 60 80 100 120 140
10
100
1000
Inte
nsity
(co
unts
)
2θ (degrees) 10 2 0 30 40 50 60 70 80 9 0 100
10
100
Inte
nsity
(x10
3 cou
nts)
2θ (degrees)
SOME ADVANTAGES OF SRXRD
CuKα λ=0.15406 nm ESRF ID31 λ=0.0632 nmiron powder (ball milled)
14
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
2) With proper selection of optics, very narrow instrumental profile:increased resolution and accuracy in the measurement of peakposition, intensity and profile width/shape.
Lab instrument: ID31 @ESRF: FWHM≈0.05-0.1° FWHM≈0.003-0.004°
SOME ADVANTAGES OF SRXRD
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •8
15
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
3) Extending the accessible region of reciprocal space well beyond whattraditional lab instruments can make
λ1 λ2<λ1
SOME ADVANTAGES OF SRXRD
16
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
10 20 30 40 50 60 70 80 90 100
10
100 (110
)
(200
)
(2
11)
(220
)
(3
10)
(222
)
(3
21)
(400
)
(3
30),
(411
)(4
20)
(332
)
(4
22)
(431
), (5
10)
(521
)
(4
40)
(433
), (5
30)
(600
), (4
42)
(532
), (6
11)
(620
)
(5
41)
(622
)
(6
31)
(444
)
Inte
nsity
(x10
3 cou
nts)
2θ (degrees)
CuKα λ=0.15406 nm ESRF ID31 λ=0.0632 nm
SOME ADVANTAGES OF SRXRD
40 60 80 100 120 140
10
100
1000
Inte
nsity
(co
unts
)
2θ (degrees)
(110
)
(200
)
(211
)
(220
)
(310
)
(222
)
3) Extending the accessible region of reciprocal space well beyond whattraditional lab instruments can make
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •9
17
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
4) Tuning the energy according to adsorption edges. Resonant scattering, control of fluerescence emission and depth of analysis.
SOME ADVANTAGES OF SRXRD
4 6 8 10 12 14 16 18 200
200
400
600
µ/ρ
(cm
2 /g)
X-ray energy (keV)
Absorption edge of Fe
CuK
α
0
tI I e
µ ρρ
− =
18
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
X-RAY POWDER DIFFRACTION
• Crystal structure determination(Powder diffraction structure solution and refinement)
• Phase Identification – pure crystalline phases or mixtures(Search-Match procedures)
• Quantitative Phase Analysis (QPA)
• Crystalline domain size/shape and lattice defect analysis(Line Profile Analysis - LPA)
• Determination of residual stress field (Residual Stress Analysis)
• Amorphous phase analysis (radial distribution function)
most frequent applications
• Determination of preferred orientations (Texture Analysis)
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •10
19
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Structure solution of heptamethylene-1,7-bis(diphenylphosphane oxide)
Structural formulaPh2P(O)(CH2)7P(O)Ph2
B.M. Kariuki , P. Calcagno, K. D. M. Harris, D. Phi lp and R.L. Johnston, Angew. Chem. Int. Ed. 1999, 38, No. 6, 831-835.
STRUCTURE SOLUTION: WHY POWDER ?
20
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Structure solution/refinement of a complex triclinic organic compound (C24H16O7)
STRUCTURE SOLUTION & REFINEMENT: SRXRD
K. D. Knudsen et al., Angew. Chem. Int. Ed., 37 (1998) 2340
• Narrow peak profiles• Large number of measurable peaks• Accurate peak position/intensity• X-ray energy tuning to adsorption edges
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •11
21
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Site occupancy in battery electrode material LaNi3.55Mn0.4Al0.3Co0.75)J.-M. Joubert et al., J. Appl. Cryst. 31 (1998) 327
• Narrow peak profiles• Large number of measurable peaks• Accurate peak position/intensity• X-ray energy tuning to adsorption edges
STRUCTURE SOLUTION & REFINEMENT: SRXRD
?????????
22
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Site occupancy in battery electrode material LaNi3.55Mn0.4Al0.3Co0.75)J.-M. Joubert et al., J. Appl. Cryst. 31 (1998) 327
STRUCTURE SOLUTION & REFINEMENT: SRXRD
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •12
23
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Site occupancy in battery electrode material LaNi3.55Mn0.4Al0.3Co0.75)J.-M. Joubert et al., J. Appl. Cryst. 31 (1998) 327
• Narrow peak profiles• Large number of measurable peaks• Accurate peak position/intensity• X-ray energy tuning to adsorption edges
STRUCTURE SOLUTION & REFINEMENT: SRXRD
24
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Solving Larger Molecular Crystal Structures from Powder Diffraction Data by Exploiting Anisotropic Thermal Expansion, M. Brunelli et al., Angew. Chem. Int. Ed. 42, 2029, (2003)
90 K
130 K
160 K
• Narrow peak profiles• Large number of measurable peaks• Accurate peak position/intensity• X-ray energy tuning to adsorption edges• Anisotropic thermal expansion
STRUCTURE SOLUTION & REFINEMENT: SRXRD
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •13
25
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
à in research & in industry (production, quality control and diagnostics)Each crystalline phase has its own pattern that can be used as a ‘fingerprint’
‘Fingerprints’ of unknown substances can be compared with those of known crystalline phases of a database à Search-Match procedures
PHASE IDENTIFICATION
26
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
ICDD datababes(International Centre for Diffraction Data – www.icdd.com)
PDF-2Peak pos/int
PDF-4
full structuralinformation
PHASE IDENTIFICATION
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •14
27
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Automatic search-match procedures based on peak position / intensity
PHASE IDENTIFICATION
28
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Intensity of i-th data-point in the pattern
, , ,ci j k j k j k j bij ky S I P yφ= ⋅ ⋅ +∑ ∑
Integrated Intensityk-th peak of j-th phase
∝ |F|2
Scale factorof j-th phase Profile function
Background term
THE RIETVELD METHOD
PreferredOrientation
F(hkl) = (1/V) Σj fj(S) e2πi(hxj + kyj + lzj)e-Bj sin2θ/λ2
From the lecture of G. Zanotti
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •15
29
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
In a polyphasic mixture: weight fraction xj of the phase j
j j jj
l l ll
S vx
S vρ
ρ=
∑
THE RIETVELD METHOD
, , ,ci j k j k j k j bij ky S I P yφ= ⋅ ⋅ +∑ ∑
Integrated Intensityk-th peak of j-th phase
∝ |F|2
Scale factorof j-th phase Profile function
Background termPreferredOrientation
à normalization condition (Σ phase fraction = 1)
Intensity of i-th data-point in the pattern
30
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Example: mixture of mineral phases in a ligand
RIETVELD-BASED QPA
2Th Degrees6560555045403530252015
Sqr
t(Cou
nts)
140130120110100908070605040302010
0-10-20-30
Lime CaCO3 26.28 %Dolomite CaMg(CO3)2 9.49 %Quartz 2.39 %Gypsum 0.69 %Bassanite 30.67 %Anhydrite 22.34 %Belite C2S 8.13 %
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •16
31
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Structural and electronic properties of noncubic fullerides A’40C60 (A’=Ba,Sr)
STRUCTURE SOLUTION IN MULTIPHASE SAMPLES
• Narrow peak profiles• Large number of measurable peaks• Accurate peak position/intensity• X-ray energy tuning to adsorption edges
C.M. Brown et al., Phys. Rev. Let. 83 (1999) 2258
ESRF BM161 λ=0.084884 nm
32
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Structural and electronic properties of noncubic fullerides A’40C60 (A’=Ba,Sr)
• Narrow peak profiles• Large number of measurable peaks• Accurate peak position/intensity• X-ray energy tuning to adsorption edges
C.M. Brown et al., Phys. Rev. Let. 83 (1999) 2258
STRUCTURE SOLUTION IN MULTIPHASE SAMPLES
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •17
33
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Crystalline structure
↓long-range order
AMORPHOUS PHASE ANALYSIS
Amorphous phase
↓short-range order
34
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Amorphous specimen of volume V (N atoms with scattering factor f, ):
AMORPHOUS PHASE ANALYSIS
( ) ( ) ( )20
11 4 2
2π ρ ρ π
π
≅ + −
∫V
I s Nf r r Sin sr drs
( ) ( ) ( )0 20
4 4 8 1 2I s
r r r s Sin sr dsNf
π ρ π ρ π π∞
≅ + −
∫By Fourier inversion:
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •18
35
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Structure of nanocrystalline materials using atomic Pair Distribution Function (PDF) analysis: study of LiMoS2.
V. Petkov et al., Phys. Rev. B 65 (2002) 092105
PAIR DISTRIBUTION FUNCTION: USE OF SRXRD
( ) ( ) 0: 4π ρ ρ = − reduced PDF G r r r
36
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Structure of nanocrystalline materials using atomic Pair Distribution Function (PDF) analysis: study of LiMoS2.
V. Petkov et al., Phys. Rev. B 65 (2002) 092105
PAIR DISTRIBUTION FUNCTION: USE OF SRXRD
( ) ( ) 0: 4π ρ ρ = − reduced PDF G r r r
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •19
37
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
LINE PROFILE ANALYSIS: SRXRDXerogel obtained by vacuum-drying: broad diffraction lines of nanocrystalline fcc phase
10 20 30 40 50 60 70 80 90 100
0
10000
20000
30000
40000
50000
60000
70000
80000
Inte
nsity
(co
unts
)
2θ (degrees)
0 1 2 3 4 50.0
0.2
0.4
0.6
0.8
1.0<D>=2.25(10) nm
p(D
) (a
.u.)
D (nm)
P. Scardi & Leoni , ECS Transactions, 3(9) (2006) 125.
75 peaks
ESRF ID31 - glass capillary, λ=0.06325 nm
0.8 hour
38
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
QUESTIONS ??
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •20
39
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Scattering from a small crystal of Cu (fcc)SCATTERING FROM NANOCRYSTALS
( ) ( )* *2 2m ni d r i d rm n
m n
f e f eπ π⋅ − ⋅
= ∑ ∑
mr
nrO
*c m n
m n
I A A∝ ∑ ∑
2 *I A AA∝ =
One scattering centre (electron, atom, unit cell)0s λ
s λ*d
40
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
mr
nrO
( ) ( )* *2 2m ni d r i d ruc m n
m nI f e f e
π π⋅ − ⋅∝ ∑ ∑
SCATTERING FROM NANOCRYSTALSScattering from a unit cell of Cu (fcc)
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •21
41
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
mr
nrO
mn m nr r r= −
( ) ( )* *2 2m ni d r i d ruc m n
m nI f e f e
π π⋅ − ⋅∝ ∑ ∑
SCATTERING FROM NANOCRYSTALSScattering from two atoms in a Cu (fcc) unit cell
( )*2 mni d rm n
m nf f e
π ⋅= ∑∑
42
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
( ) ( )* *2 2m ni d r i d ruc m n
m nI f e f e
π π⋅ − ⋅∝ ∑ ∑
SCATTERING FROM NANOCRYSTALSScattering from two atoms in a Cu (fcc) unit cell
( )*2 mni d rm n
m nf f e
π ⋅= ∑∑
mnr
0s λ
s λ
*d0* 2 sins s
d θλ λ−
= =
2θ
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •22
43
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Two possible approaches
1. Reciprocal space approach(Laue – Wilson)
2. Direct space (or Real space) approach(Debye)
SCATTERING FROM A POWDER
44
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SCATTERING FROM NANOCRYSTALS
mnr
0s λ
s λ
*d
2θnn n nu a vr b w c= + +
( ) ( )* *2 2π π⋅ − ⋅∝ ∑ ∑m ni d r i d r
uc m nm n
I f e f e ( )2
2
1
π + +
=
= ∑ n n nN
i u h v k w ln
n
f e
0s s ha lcd kbλ
∗ ∗∗ ∗−= = + +
2F=
Two possible approaches - #1 reciprocal space1. Factorize the contribution from a
unit cell (|F|2 – F, structure factor )
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •23
45
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Then build the diffraction signalfor a small crystal (unit cell volume, Vuc)
SCATTERING FROM A POWDERTwo possible approaches - #1 reciprocal space
1. Factorize the contribution from aunit cell (|F|2 – F, structure factor )
( )2
2 2
1
n n nN
i u h v k w luc n
nI F f e π + +
=
∝ = ∑
(Interference function) à see ZANOTTI’s lecture
( ) ( ) ( )2 2 2 2
2 2 2 2
sin sin sinsin ( ) sin ( ) sin ( )sc
uc
F Nh Nk NlI
V h k lπ π ππ π π
∝ L=Na
a
( ) ( ) ( )2 2 2 2
2 2 2 2 2 2 2' ' '
sin sin sin( ') ( ') ( ')sc
h k luc
F Nh Nk NlI
V h h k k l lπ π π
π π π
∞ ∞ ∞
=−∞ =−∞ =−∞
∝− − −∑ ∑ ∑
46
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SCATTERING FROM A POWDERTwo possible approaches - #1 reciprocal space
1. Factorize the contribution from aunit cell (|F|2 – F, structure factor )
(Interference function)
( ) ( ) ( )2 2 2 2
2 2 2 2
sin sin sinsin ( ) sin ( ) sin ( )sc
uc
F Nh Nk NlI
V h k lπ π ππ π π
∝
( ) ( ) ( )2 2 2 2
2 2 2 2 2 2 2' ' '
sin sin sin( ') ( ') ( ')sc
h k luc
F Nh Nk NlI
V h h k k l lπ π π
π π π
∞ ∞ ∞
=−∞ =−∞ =−∞
∝− − −∑ ∑ ∑
010 110 210
000 100 200
010 110 210
2θ
0ν λ
ν λ
Inte
nsity
h = 2h = 10
Then build the diffraction signalfor a small crystal (unit cell volume, Vuc)
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •24
47
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SCATTERING FROM A POWDER
(Interference function)
( ) ( ) ( )2 2 2 2
2 2 2 2 2 2 2' ' '
sin sin sin( ') ( ') ( ')sc
h k luc
F Nh Nk NlI
V h h k k l lπ π π
π π π
∞ ∞ ∞
=−∞ =−∞ =−∞
∝− − −∑ ∑ ∑
010 110 210
000 100 200
010 110 210
2θ
0ν λ
ν λ
( )2100
2 2
sin( 1)
ππ
∝−scNh
Ih
Example:(100) point
Inte
nsity
h = 2h = 10
Two possible approaches - #1 reciprocal space1. Factorize the contribution from a
unit cell (|F|2 – F, structure factor )
Then build the diffraction signalfor a small crystal (unit cell volume, Vuc)
48
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
-2 -1 0 1 2
-2
-1
0
1
2
2 λ
Powder Diffractionsphere
NANOCRYSTAL à POWDERTwo possible approaches - #1 reciprocal space
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •25
49
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
-2 -1 0 1 2
-2
-1
0
1
2
2 λ
NANOCRYSTAL à POWDERTwo possible approaches - #1 reciprocal space
50
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Example: (001) peak, powder made of cubic crystallites, cube edge L
001
002
0s sθ θ
*001d
h - [100]
k - [010]
( ) ( ) ( ) ( )
2 2 2 22 2
2 2 2 2
sin ( ) sin ( ) sin ( ) sin ( )Nh Nk Nl NlI F dh dk Fh k l lπ π π π
π π π π∝ ⋅ →∫∫
1=l
l
I(l)
l - [001]
NANOCRYSTAL à POWDER
( )2
2sin ( )1
(0)
π
π
∞
−∞ =∫
Nl
ldl
I N
L=Na
a
Two possible approaches - #1 reciprocal space
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •26
51
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SCATTERING FROM A POWDERTwo possible approaches - #1 reciprocal space
1. Factorize the contribution from aunit cell (|F|2 – F, structure factor )
Then build the diffractionsignal for a small crystal,
and integrate over thepowder diffractionsphere for calculatingthe signal from alldomains in the powder
100
110
020120220
100
110
020120220
( )2 * ,PDI F d D∝ ΦL
standard Powder Diffraction approach
( ) ( ) ( )2 2 2
2 2 2
sin sin sinsin ( ) sin ( ) sin ( )
π π ππ π πNh Nk Nlh k l
52
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SCATTERING FROM NANOCRYSTALS
mr
nrO
mn m nr r r= −
( ) ( )* *2 2m ni d r i d ruc m n
m nI f e f e
π π⋅ − ⋅∝ ∑ ∑ ( )*2 mni d r
m nm n
f f eπ ⋅
= ∑∑
Two possible approaches - #2 real space2. Average over all possible orientations of
rmn in space
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •27
53
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
( ) ( )* *2 2π π⋅ − ⋅∝ ∑ ∑m ni d r i d r
sc m nm n
I f e f e
SCATTERING FROM NANOCRYSTALS
( )*2 mni d rm n
m nf f e
π ⋅= ∑∑
0* 2sins sd θ
λ λ−
= =0s λ
s λ
*d
2θmnr
** cosmn mnd d rr φ= ⋅
φ
Two possible approaches - #2 real space2. Average over all possible orientations of rmn in space
54
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
mnr
0s λ
s λ
*d
( )*2 mni d rD m n
m n
I f f eπ ⋅
∝ ∑∑ ( )*
*
sin 22
mnm n
m n mn
d rf f
d rπ
π= ∑∑
Two possible approaches - #2 real space
2. Average over all possible cosφ values:rmn is allowed to take all possibleorientations in space
SCATTERING FROM A POWDER
* cosmmn nd rd r φ= ⋅
φ
Debye formula
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •28
55
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Debye formula for one (fcc) unit cell
*
*
sin 22
mnD m n
m n mn
d rI f f
d rπ
π= ∑∑
( ) ( ) ( ) ( )72sin 2 48sin 3 2 24sin 2 8sin 330sin142 3 2 2 3D
ka ka ka kakaIkaka ka ka ka
= + + + + +
0mnr =
a
2a a 3 2a 2a 3a
14 72 30 48 24 8
SCATTERING FROM A NANOCRYSTAL POWDER
56
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
0 10 20 30 40 50 60 700
5
10
15
20
25
30
35
11
12
00
22
0
31
12
22
40
0
33
14
20
42
2
33
35
11
44
0
Inte
nsity
(a.u
.)
2θ (degrees)
Scattering from (random oriented) Cu unit cells . Mo Kα (0.07093 nm)
( ) ( ) ( ) ( )72sin 2 48sin 3 2 24sin 2 8sin 330sin142 3 2 2 3D
ka ka ka kakaIkaka ka ka ka
= + + + + +
Cu bars: multiplicity
SCATTERING FROM A NANOCRYSTAL POWDER
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •29
57
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
0 10 20 30 40 50 60 700
20
40
60
80
100
120
1401
11
20
0
22
0
31
12
22
40
0
33
14
20
42
2
33
3,5
11
44
0
Inte
nsity
(a.
u.)
2θ (degrees)
Scattering from (random oriented) Cu unit cells . Mo Kα (0.07093 nm)2 2
*dk uDI LP e−
⋅ ⋅
Cu bars: ICSD #46699
SCATTERING FROM A NANOCRYSTAL POWDER
58
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Scattering from bcc-Fe cubic crystals . Cu Kα (0.15406 nm)
SCATTERING FROM A NANOCRYSTAL POWDER
0 20 40 60 80 100 120 140 1600
20k
40k
60k
80k
100k
120k
(222)
(311)
(220)
(211)
(200)
Inte
nsity
2θ (degrees)
(110)
0 20 40 60 80 100 120 140 1600
500
1000
1500
2000
(222)
(311)
(220)
(211)
(200)
Inte
nsity
2θ (degrees)
(110)
5x5x5 15x15x15
3x3x31x1x1
0 20 40 60 80 100 120 140 1600
100
200
300
400
(222)
(311)
(220)
(211)
(200)
Inte
nsity
2θ (degrees)
(110)
0 20 40 60 80 100 120 140 1600
5
10
15
20
(222)
(311)
(220)
(211)
(200)
Inte
nsity
2θ (degrees)
(110)
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •30
59
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Scattering from bcc-Fe cubic crystals . Cu Kα (0.15406 nm)
SCATTERING FROM A NANOCRYSTAL POWDER
0 20 40 60 80 100 120 140 1600
20k
40k
60k
80k
100k
120k
(222)
(311)
(220)
(211)
(200)
Inte
nsity
2θ (degrees)
(110)15x15x15
7471 atoms
60
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Scattering from bcc-Fe cubic crystals . Cu Kα (0.15406 nm)
SCATTERING FROM A NANOCRYSTAL POWDER
0 2 4 6 8 10 12 140
100k
200k
300k
400k
500k
Inte
nsity
2θ (degrees)
15x15x157471 atoms
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •31
61
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Scattering from bcc-Fe cubic crystals . Cu Kα (0.15406 nm)
SCATTERING FROM A NANOCRYSTAL POWDER
0 2 4 6 8 10 12 14100
1k
10k
100k
1M
10M
100MIn
tens
ity
2θ (degrees)
15x15x157471 atoms
I(0) = 55.815.841 = 74712
62
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SCATTERING FROM A NANOCRYSTAL POWDER
Twinned spherical domains (fcc, 28897 Au atoms, nominal size 9.8 nm)
0 20 40 60 80 100 120 140 160105
106
107
108
109
1010
1011
1012
Inte
nsity
2θ (degrees)
K. Beyerlein, Univ. of Trento
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •32
63
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
The Debye formula approach can be extended to a distribution of nanocrystals, also including a radial, homogeneous strain
POWDER DIFFRACTION LINE PROFILE ANALYSIS
C - cubooctahedron
I - icosahedron
D - decahedron
A. Cervellino et al., J. Appl. Cryst. 36 (2003) 1148
64
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SCATTERING FROM A NANOCRYSTAL POWDER
graphene(sp2 carbon single-layer)
L. Gelisio, Univ. of Trento
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •33
65
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SCATTERING FROM A NANOCRYSTAL POWDER
Carbon nanotubes
L. Gelisio, Univ. of Trento
66
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
SCATTERING FROM A NANOCRYSTAL POWDER
20 40 60 80 100 120 140 1600
1x106
2x106
3x106
4x106
Inte
nsity
(a.
u.)
2θ (degrees)
cluster of nanocrystalline grains: 7.6 million atomsatomistic simulations – molecular dynamics
A. Leonardi , Univ. of Trento
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •34
67
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
QUESTIONS ??
68
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Two possible approaches
1. Reciprocal space approach(Laue – Wilson)
2. Direct space (or Real space) approach(Debye)
SCATTERING FROM A POWDER
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •35
69
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
CRYSTAL, NANOCRYSTAL AND POWDER: SIZE EFFECT
LARGE crystal
100
110
020120220
NANOcrystal
5 nm
NANOcrystal
POWDER 10 nm
70
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
-2 -1 0 1 2
-2
-1
0
1
2
NANOCRYSTAL à POWDER
2 λ
Ewald sphere
0s λ
s λ2θ
d ∗
Powder Diffractionsphere
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •36
71
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
-2 -1 0 1 2
-2
-1
0
1
2
2 λ
NANOCRYSTAL à POWDER
72
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Powder made of simple-shape crystallites(one param., convex solids: sphere, cube, tetrahedron, octahedron,…)
( )* Kd
Dββ =
DIFFRACTION FROM A POLYCRYSTALLINE MATERIAL
Kβ , Scherrer constant, changes with crystallite shapes and (hkl)
Paul Scherrer (1890–1969)
Scherrer formula (1918)
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •37
73
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Powder made of simple-shape crystallites(one param., convex solids: sphere, cube, tetrahedron, octahedron,…)
DIFFRACTION FROM A POLYCRYSTALLINE MATERIAL
Kβ , Scherrer constant, changes with crystallite shapes and (hkl). For a sphere:
( )* Kd
Dββ =
Paul Scherrer (1890–1969)
Scherrer formula (1918)
43
Kβ =
74
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
TRADITIONAL LPA: INTEGRAL BREADTH METHODS
( )* Kd
Dββ =( )2
cosK
Dβ λ
β θθ
=
Scherrer formula2θ space recipr. space
Profile information can be represented by the Integral Breadth β, (peak area / peak maximum). Assuming domain size effects only:
20 40 60 80 100 120 1400
1000
2000
3000
4000
5000
6000
7000
Inte
nsity
(co
unts
)
2θ (degrees)
20 30 40 50 600
1000
2000
3000
4000
5000
6000
7000
Inte
nsity
(co
unts
)
2θ (degrees)
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •38
75
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
CAVEAT #1 – what is the true result of the Scherrer formula ?
DIFFRACTION FROM A POLYCRYSTALLINE MATERIAL
The integral breadth still provides a valid mean size value, but:
( )* 3
4V
K Md KD M
βββ = =
< >where M3, M4 are 3rd and 4th moments of g(D) ( )( )i
iM D g D dD= ∫
M1à meanM2 - M1
2 à variance
For a DISTRIBUTION of crystallitesg(D)
D
76
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
( )*2 2 iLd LcI F e π ε∝
b
ac
a
L=n·a
undistorted
b
ac
a
L=n·a
dL
distorted
Quite complex: unit cells at distance L=na can be displaced and rotated.Neglecting rotation and considering an average strain dL Lε =
MICROSTRAIN EFFECT IN POWDER DIFFRACTION
CAVEAT #2 – what is the effect of lattice distortions ?
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •39
77
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Considering both domain size and lattice distortion (microstrain) effects
( ) ( )* 2 cosdβ β θ θ λ = ⋅
INTEGRAL BREADTH METHODS
( ) 1 / 222 2 tancosV
KD
β λβ θ ε θ
θ≈ +
< >
(as a first order approximation):
78
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
( )* *2V
Kd e d
Dββ = + ⋅
< >
Considering both domain size and lattice distortion (microstrain) effects
( ) ( )* 2 cosdβ β θ θ λ = ⋅
in a β(d*) vs. d* plot, intercept and slope of linear regression are related, respectively, to <D>V and e
INTEGRAL BREADTH METHODS
0 2 4 6 8 10 120,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
β(d*
) (n
m-1)
d * (nm -1) [ =2sinθ/λ ]
Williamson-Hall (WH) plot
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •40
79
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Peak profiles invariably overlap in powder patterns. This can make it difficult to extract profile information directly from observed data
INTEGRAL BREADTH METHODS
20 40 60 80 100 120 1400
1000
2000
3000
4000
5000
6000
7000
Inte
nsity
(co
unts
)
2θ (degrees)
20 40 60 80 100 120 140
100
1000
10000
111
200
220
311
222
400
331
420
422
511/
333
440
531
600/
442
620
533
622
Inte
nsity
(co
unts
)
2θ (degrees)
80
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
… a step forward
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •41
81
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
20 40 60 80 100 120 1400
1000200030004000500060007000 Sol-gel cerium oxide powder, 1h @ 400°C
Inte
nsity
(co
unts
)
2θ (degrees)
Microstructural Parameters
DiffractionPattern
WPPMPhysical Model
WPPM is based on a direct modelling of the experimental pattern, based on physical models of the microstructure and lattice defects:
WHOLE POWDER PATTERN MODELLING
20 40 60 80 100 120 140
01000200030004000500060007000
Nanocrystalline cerium oxidefrom xerogel, 1h @ 400°C
Inte
nsity
(co
unts
)
2θ (degrees)M. Leoni, R. Di Maggio, S. Polizzi & P. Scardi, J. Am. Ceram. Soc. 87 (2004) 1133.
P.Scardi & M. Leoni, Acta Cryst. A 57 (2001) 604. P.Scardi & M. Leoni, Acta Cryst. A 58 (2002) 190
82
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
0 2 4 6 8 10 120
5
10
15
20
25
30
35
40 TEM WPPM
Freq
uenc
y
Grain diameter (nm)
5 nm
*hkld
*hk ld
ABC
AB
AB
C
*hkld
*hk ld
(…)
WHOLE POWDER PATTERN MODELLING
20 40 60 80 100 120 1400
1000200030004000500060007000 Sol-gel cerium oxide powder, 1h @ 400°C
Inte
nsity
(co
unts
)
2θ (degrees)20 40 60 80 100 120 140
01000200030004000500060007000
Nanocrystalline cerium oxidefrom xerogel, 1h @ 400°C
Inte
nsity
(co
unts
)
2θ (degrees)M. Leoni, R. Di Maggio, S. Polizzi & P. Scardi, J. Am. Ceram. Soc. 87 (2004) 1133.
P.Scardi & M. Leoni, Acta Cryst. A 57 (2001) 604. P.Scardi & M. Leoni, Acta Cryst. A 58 (2002) 190
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •42
83
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Microstructural Parameters
DiffractionPattern
WPPMPhysical Model
WPPM is based on a direct modelling of the experimental pattern, based on physical models of the microstructure and lattice defects:
WHOLE POWDER PATTERN MODELLING
How does it work ??
84
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
DIFFRACTION LINE PROFILE: CONVOLUTION OF EFFECTS
So far we consider that different effects affecting the line profile simply ‘add’, i.e., the peak width is the sum of different components.
According to the Williamson-Hall formula,
( )* *2ββ = + ⋅< >V
Kd e d
D
‘size’ ‘strain’
Actually, this is not the general case …
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •43
85
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
DIFFRACTION LINE PROFILE: CONVOLUTION OF EFFECTS
A diffraction peak is a convolution ( ) of profile components produced by different sources: instrumental profile (IP), domain size (S), microstrain (D), faulting (F), anti-phase domain boundaries (APB), stoichiometry fluctuations (C), grain surface relaxation (GSR), etc.
⊗
( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ...IP S D F APB C GRSI s I s I s I s I s I s I s I s= ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
h = g ⊗ f
What is the difference between convolution and sum of effects ??
86
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
DIFFRACTION LINE PROFILE: CONVOLUTION OF EFFECTS
What is the difference between convolution and sum of effects ??
2θ 2θ2θ
⊗
g profile, slit (box) function; f profile, bell-shape function (e.g. gaussian)
( ) ( ) ( )= ⊗IP SI s I s I sExample: let’s just consider instrument (IP) and domain size (S):
( ) ( )( )= −∫ IP SI s I t I s t dt
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •44
87
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
DIFFRACTION LINE PROFILE: CONVOLUTION OF EFFECTS
h fg= ⊗
2θ
2θ
2θ
2θ
2θ
2θ
2θ
2θ
2θ
2θ
88
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
DIFFRACTION LINE PROFILE: CONVOLUTION OF EFFECTS
A diffraction peak is a convolution ( ) of profile components produced by different sources: instrumental profile (IP), domain size (S), microstrain (D), faulting (F), anti-phase domain boundaries (APB), stoichiometry fluctuations (C), grain surface relaxation (GSR), etc.
⊗
( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ...IP S D F APB C GRSI s I s I s I s I s I s I s I s= ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
h = g ⊗ f
the Fourier Transform of I(s) is the product of the FTs of the single profile components
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •45
89
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
the Fourier Transform of I(s) is the product of the FTs of the single profile components
( ) ( ) 2e hkliL sLI s C d Lπ ⋅∞
− ∞
∝ ⋅ ∫
( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ...IP S D F APB C GRSI s I s I s I s I s I s I s I s= ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
The diffraction profile results from a convolution of effects:
WPPM : HOW DOES IT WORK ??
P. Scardi & M. Leoni J. Appl. Cryst. 39 (2006) 24 - P. Scardi & M. Leoni, Acta Cryst. A58 (2002) 190
( ) ...IP S D F F APBi pV hkl hklhkl hkl hkl
i
C A T A A A iB A= = ⋅ ⋅ ⋅ + ⋅ ⋅ ∏instr. profile lattice defects / straindomain
size/shape
90
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
( ) ( ) ( ) ( )2 2 21 exp ln2 exp 2IPpV s sT L k L k Lπ σ π σ= − ⋅ − ⋅ + − ⋅ Instrumental profile
Ai(L) EXPRESSIONS (ANALYTICAL OR NUMERICAL FORM)
Domain size effect: µ, σ
( ) 23,3
0 ,3
ln (3 )( )
22
cl nS c n
nn l
L K n MA L H Erfc L
M
µ σ
σ−
=
⋅ − − − = ⋅ ⋅
∑
Dislocation (strain) effect: ρ, Re,(Chkl)
( )22 * 2 *
1( ) exp2
Dhklhkl ehklA L b C d L f L Rπ ρ = − ⋅
( )
( )
*22
1 22 2
12( ) 1 3 2 3
( ) 3 6 12 12
hkl
o
oLo
oFhkl
F ohkl L
o
LLdhA L
LLB LL L
σα β α
σ β β α β α
⋅= − − +
= − ⋅ ⋅ ⋅ − − − +
Anti-Phase Domains: γ
( )( ) 2 2 2
2( ) expAPB
hklhkl
h k LA L
d h k lγ − + ⋅
= −+ +
ABC
AB
ABC
*hkld
*hk ldFaulting: α (def.), β (twin)
*hkld
*hk ld
0 2 4 6 8 10 120
5
10
15
20
25
30
35
40 TEM WPPM
Fre
quen
cy
Grai n d iame te r (nm)5 nm
( )2 2 2 2 2 2
22 2 2hkl
h k k l l hC A B A B Hh k l
+ += + ⋅ = + ⋅
+ +
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •46
91
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
WPPM APPLICATIONS
TWO EXAMPLES
WHOLE POWDER PATTERN MODELLING
92
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
10 20 30 40 50 60 70 80 90 100
0
10000
20000
30000
40000
50000
60000
70000
80000
10 15 20 25 3 0 35
10000
20000
30000
40000
50000
60000
70000
80000
Inte
nsity
(co
unts
)
2θ (degrees)
Inte
nsity
(co
unts
)
2θ (degrees)
Xerogel obtained by vacuum-drying: broad diffraction lines of nanocrystalline fcc phaseESRF ID31 - glass capillary, λ=0.6325 nm
WPPM APPLICATIONS: NANOCRYSTALLINE CERIA
P. Scardi, M. Leoni, ECS Transactions, 3 (2006) 125
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •47
93
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
WPPM APPLICATIONS: NANOCRYSTALLINE CERIAXerogel obtained by vacuum-drying: broad diffraction lines of nanocrystalline fcc phase
10 20 30 40 50 60 70 80 90 100
0
10000
20000
30000
40000
50000
60000
70000
80000
Inte
nsity
(co
unts
)
2θ (degrees)
0 1 2 3 4 50.0
0.2
0.4
0.6
0.8
1.0<D>=2.25(10) nm
p(D
) (a
.u.)
D (nm)
ESRF ID31 - glass capillary, λ=0.6325 nm
P. Scardi, M. Leoni, ECS Transactions, 3 (2006) 125
94
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
NANOCRYSTALLINE Fe-1.5%Mo POWDER Planetary ball milling - production of nanocrystalline Fe-1.5%Mo
Ωω
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •48
95
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
10 20 30 40 50 60 70 80 90 100
0
50
100
150
200
250
300
350
400
450
Inte
nsity
(x10
3 cou
nts)
2θ (degrees)
10 20 30 40 50 60 70 80 90 100
10
100
Inte
nsity
(x10
3 cou
nts)
2θ (degrees)
2 hours
Ball milled Fe1.5Mo (Fritsch P4) – data collected at ESRF – ID31 λ=0.0632 nm
NANOCRYSTALLINE Fe-1.5%Mo POWDER
M. D’Incau, M. Leoni & P. Scardi, J. Mat. Research, 22 (2007) 1744
96
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
10 20 30 40 50 60 70 80 90 100
0
50
100
150
200
250
Inte
nsity
(x10
3 cou
nts)
2θ (degrees)
(b)
10 20 30 40 50 60 70 80 90 100
10
100
Inte
nsity
(x10
3 cou
nts)
96 hours
Ball milled Fe1.5Mo (Fritsch P4) – data collected at ESRF – ID31 λ=0.0632 nm
NANOCRYSTALLINE Fe-1.5%Mo POWDER
M. D’Incau, M. Leoni & P. Scardi, J. Mat. Research, 22 (2007) 1744
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •49
97
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
10 20 30 40 50 60 70 80 90 100
0
50
100
150
200
250
In
tens
ity (x
103 c
ount
s)
2θ (degrees)
(b)
Ball milled Fe1.5Mo (Fritsch P4) – data collected at ESRF – ID31 λ=0.0632 nm
NANOCRYSTALLINE Fe-1.5%Mo POWDER
0 20 40 60 80 100 120 1400,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
Ball milling time (h)
Dis
loca
tion
dens
ity, ρ
(x1
016 m
-2)
0
20
40
60
80
100
120
140
160M
ean domain size, D
(nm)
M. D’Incau, M. Leoni & P. Scardi, J. Mat. Research, 22 (2007) 1744
98
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 00 .0 0
0 .0 2
0 .0 4
0 .0 6
0 .0 8
0 .1 0 0 h 2 h 16 h 32 h 64 h 128 h
Dom
ain
size
dis
tribu
tion,
g(D
)
D (n m )
0 20 40 60 80 100 120 1400.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Ball milling time (h)
Dis
loca
tion
dens
ity, ρ
(x1
016 m
-2)
0
20
40
60
80
100
120
140
160
Mean dom
ain size, D (nm
)
Ball milled Fe1.5Mo (Fritsch P4) – data collected at ESRF – ID31 λ=0.0632 nmIn addition to mean values, WPPM provides the size distribution
M. D’Incau, M. Leoni & P. Scardi, J. Mat. Research, 22 (2007) 1744
NANOCRYSTALLINE Fe-1.5%Mo POWDER
•Prof. Paolo Scardi, Università di Trento
•Diffrazione da Materiali Policristallini •50
99
P. Scardi – Powder Diffraction & Synchrotron RadiationX SILS School - Duino, 11.09.2009
Diffraction Analysis of Materials MicrostructureE.J. Mittemeijer & P. Scardi, editors.Berlin: Springer-Verlag, 2004.
Powder Diffraction: Theory and PracticeR.E. Dinnebier & S.J.L. Billinge, editors.Cambridge: RSC Publishing, 2008. Cap. XIII, p.376