[PPT] - X-ray Dif f ract ion Basic aspects of x- ray crystallography and PowerPoint Presentation

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X-ray Dif f ract ion

Paolo. Scardi@unitn. it

Special thanks to: Luca Gelisio, Alberto Leonardi, Luca Rebuf f i, Cristy L. Azanza Ricardo, Mirco D’I ncau, Andrea Troian, Emmanuel Garnier, Mahmoud Abdellatief

Basic aspects of x- ray crystallography and powder dif f raction
Dif f raction f rom nanocrystalline materials

SLIDE 2

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

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PRESENTATI ON OUTLI NE

PART I I I Select ed case st udies: highly def ormed met als, and nanocryst alline cat alyst PART I Dif f ract ion f rom nanocryst alline mat erials: why using synchrot ron radiat ion? PART I V Tot al Scat t ering met hods PART I I Reciprocal space vs direct space met hods

Chapter XVI I I

Dif f raction f rom nanocrystalline materials Paolo Scardi and Luca Gelisio

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P. Scardi – Dif f raction f rom nanocrystalline materials

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

main applicat ions of (powder / polycryst alline mat erial) dif f ract ion

Cryst al st ruct ure det erminat ion: st ruct ure solut ion and ref inement .
Phase I dent if icat ion (Search-Mat ch procedures): pure cryst alline

phases or mixt ures

Quant it at ive Phase Analysis (QPA): cryst alline and amorphous phases
Line Prof ile Analysis (LPA): cryst alline domain size/ shape, lat t ice

def ect analysis – nanocryst alline mat erials

X-ray Residual St ress Analysis (XRSA): measurement of st rain

f ield / elast ic behaviour

Text ure Analysis (TA): det erminat ion of pref erred orient at ions

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P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

20 30 40 50 60 2000 4000 6000

Intensity 2θ (degrees)

4

powder (bulk polycryst alline)

100 110 020 120 220 {100} {110} {020} {120} {220}

DI FFRACTI ON PATTERN FROM A POLYCRYSTALLI NE

sx [Å-1] sy [Å-1]

s

s=Q/2π=2sinθ /λ

s

2θ

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P. Scardi – Dif f raction f rom nanocrystalline materials

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

f rom single-cryst al t o powder dif f ract ion

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P. Scardi – Dif f raction f rom nanocrystalline materials

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

Powder dif f ract ion ‘elect ive’ geomet ry: Debye-Scherrer (1918)

POWDER

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P. Scardi – Dif f raction f rom nanocrystalline materials

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

parallel beam, Debye Sherrer geomet ry of MCX (ELETTRA)

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P. Scardi – Dif f raction f rom nanocrystalline materials

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20 40 60 80 100 120 140 2000 4000 6000

Intensity 2θ (degrees)

DI FFRACTI ON PATTERN FROM A POLYCRYSTALLI NE

powder (bulk polycryst alline)

100 110 020 120 220 {100} {110} {020} {120} {220}

nanocryst alline powder

10 nm

20 40 60 80 100 120 140 2000 4000 6000

Intensity 2θ (degrees)

peaks f rom nanocryst als are broad: why using SR ???

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P. Scardi – Dif f raction f rom nanocrystalline materials

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

high brillance: bet t er count ing st at ist ics / short er dat a

collect ion t ime / f ast kinet ics, in sit u, in operando st udies

40 60 80 100 120 140 10 100 1000

Intensity (counts) 2θ (degrees)

10 20 30 40 50 60 70 80 90 100 10 100

Intensity (x10

3 counts)

2θ (degrees)

count s · N° of peaks t ime

=1 =25. 000

9-cryst al analyzer: 1.500s ! (x100 count s) Lab inst rument : ~80.000s

CuKα λ=0.15406 nm ESRF I D31 (now I D22) λ=0.0632 nm iron powder (ball milled)

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P. Scardi – Dif f raction f rom nanocrystalline materials

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

40 60 80 100 120 140 10 100 1000

Intensity (counts) 2θ (degrees)

count s · N° of peaks t ime

=1

Lab inst rument : ~80.000s

CuKα λ=0.15406 nm iron powder (ball milled) PSI MS-X04SA λ=0.072929 nm

Myt hen det ect or: 100 s !! (x100 count s)

10 20 30 40 50 60 70 80 90 100 110 10 100

Intensity (x103 counts) 2θ (degrees)

=350. 000

high brillance: bet t er count ing st at ist ics / short er dat a

collect ion t ime / f ast kinet ics, in sit u, in operando st udies

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P. Scardi – Dif f raction f rom nanocrystalline materials

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

narrow inst rument al prof ile: cont rol of inst rument al prof ile;

high resolut ion and accuracy in measuring peak posit ion, int ensit y and prof ile widt h/ shape Lab inst rument : I D31 @ESRF: FWHM≈0.05-0.1° FWHM≈0.003-0.004°

0.2
0.1

0.0 0.1 0.2

degrees

0.2
0.1

0.0 0.1 0.2

degrees

0. 05°
0. 05°

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P. Scardi – Dif f raction f rom nanocrystalline materials

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

ext ending t he accessible region of reciprocal space well beyond

what t radit ional lab inst rument s can make

λ1 λ2<λ1

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P. Scardi – Dif f raction f rom nanocrystalline materials

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

10 20 30 40 50 60 70 80 90 100 10 100 (110) (200) (211) (220) (310) (222) (321) (400) (330), (411) (420) (332) (422) (431), (510) (521) (440) (433), (530) (600), (442) (532), (611) (620) (541) (622) (631) (444)

Intensity (x10

3 counts)

2θ (degrees)

CuKα λ=0.15406 nm ESRF I D31 λ=0.0632 nm

40 60 80 100 120 140 10 100 1000

Intensity (counts) 2θ (degrees)

(110) (200) (211) (220) (310) (222)

9-cryst al analyzer: 1.500s ! (x100 count s) : 28 peaks Lab inst rument : ~80.000s : 6 peaks

ext ending t he accessible region of reciprocal space well beyond

what t radit ional lab inst rument s can make

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P. Scardi – Dif f raction f rom nanocrystalline materials

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

ext ending t he accessible region of reciprocal space well beyond

what t radit ional lab inst rument s can make: PDF analysis

High-pr essur e pair dist r ibut ion f unct ion (PDF) measur ement of nano Pt (50 nm) at 12.5 GPa in Met hanol:Et hanol = 4:1. Focused X-r ay beam, 66. 054 keV, Br ookhaven Nat ional Labor at ory. Hong et al., Nat . Sci. Repor t s 6, 21434 (2016)

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P. Scardi – Dif f raction f rom nanocrystalline materials

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

High-pr essur e pair dist r ibut ion f unct ion (PDF) measur ement of nano Pt (50 nm) at 12.5 GPa in Met hanol:Et hanol = 4:1. Focused X-r ay beam, 66. 054 keV, Br ookhaven Nat ional Labor at ory. Hong et al., Nat . Sci. Repor t s 6, 21434 (2016)

ext ending t he accessible region of reciprocal space well beyond

what t radit ional lab inst rument s can make: PDF analysis

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P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

t uning energy according t o adsorpt ion edges f or, e.g.:

resonant scat t ering, in dept h measurement s (propert y gradient s)

4 6 8 10 12 14 16 18 20 200 400 600

µ/ρ (cm2/g)

X-ray energy (keV) Absorption edge of Fe

CuKα

t

I I e

µ ρ ρ   −    

=

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P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

10 20 30 40 50 60 70 80

10

3

10

4

10

5

Intensity (counts) 2θ (degrees)

10

4

10

5

kapton

MCX beamline (Elet t ra), 15 keV Negligible absorpt ion: µ=2.71 cm-1 µR≈0.07 Special t hanks t o: M. Abdellat ief

SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

t uning energy according t o adsorpt ion edges f or, e.g.:

resonant scat t ering, in dept h measurement s (propert y gradient s); cont rol f luorescence emission and absorption

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P. Scardi – Dif f raction f rom nanocrystalline materials

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SYNCHROTRON RADI ATI ON X-RAY DI FFRACTI ON

30 40 50 60 70 80 90 100 110 120 130 140 150 10 100 1000

Intensity (counts) 2θ (degrees)

10 20 30 40 50 60 70 80 90 100 10 100 1000

Intensity (counts x 100) 2θ (degrees)

10 20 30 40 50 60 70 80 90 100 110 100 1000

Intensity (counts x 100) 2θ (degrees)

Powder diffraction and synchrotron radiation: visit the MCX beamline at ELETTRA (J.R. Plaisier)

Powder diffraction data from a ball milled Fe1.5%Mo powder collected (a) on a traditional laboratory instrument (Rigaku PMG-VH, Bragg- Brentano geometry) with CuKα radiation (λ=0.1540598 nm) and SR (Debye-Scherrer geometry): (b) ID31 (now ID22) at ESRF, Grenoble (F) (λ=0.0632 nm), and (c) MS-X04SA at PSI, Villigen (CH) (λ=0.072929 nm). On the right: schematic of reciprocal space with extension of the limiting sphere (radius 2/λ).

P. Scardi & L. Gelisio, “Diffraction from nanocrystalline materials”, in

Synshrotron radiation, ed. S. Mobilio et al., Springer 2015. Chap. XVIII,.

increase energy

ext end Ewald sphere!

increase energy

high Q(=4πsinθ/ λ) f or PDF analysis

st at ist ics / short t ime / kinet ics / in sit u / in operando
cont rol absorpt ion and inst rument al ef f ect s

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P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

sx [Å-1] sy [Å-1]

19

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

( )

( ) ( )

2 2 *

m n

i s r i s r sc m n m n

I s f e f e

π π ⋅ − ⋅

∝∑

∑

( )

2 *

mn

i s r m n m n

f f e

π ⋅

= ∑∑

( ) ( )

2

4

sc PD

I s d I s s π Ω ∝ ∫

2 sin

d s d d ϑ ϑ φ Ω =

s=Q/2π=2sinθ /λ

rient at ional

(or powder) average

S

m

r

n

r

mn

r

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P. Scardi – Dif f raction f rom nanocrystalline materials

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DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

( )

( ) ( )

2 2 *

m n

i s r i s r sc m n m n

I s f e f e

π π ⋅ − ⋅

∝∑

∑

( )

2 *

mn

i s r m n m n

f f e

π ⋅

= ∑∑

sx [Å-1] sy [Å-1]

(1) sum, t hen average

r

(2) average, t hen sum

( )

2 * 2

4

mn

i s r m n m n PD

f f e d I s s

π

⋅

Ω ∝ ∑∑

∫

Tradit ional "reciprocal space" approach Debye scat t ering equat ion, "direct space" Tot al scat t ering approach

s=Q/2π=2sinθ /λ

2 sin

d s d d ϑ ϑ φ Ω =

S

m

r

n

r

mn

r

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P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

( ) ( ) ( )

2 2 2 2 2 2 2 2 2 2 ' ' '

sin sin sin ( ') ( ') ( ')

sc h k l

Nh Nk Nl I F h h k k l l π π π π π π

∞ ∞ ∞ =−∞ =−∞ =−∞

∝ − − −

∑ ∑ ∑

21

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

Tradit ional "reciprocal space" approach (sum, t hen average)

1. Factorize the contribution of a unit cell

(|F|2 – F, structure factor )

2. Build the diffraction signal as interference between unit cells
3
2
1

1 2 3 h a s  s0    2 4 6 8 10 y t i s n e t n I

h’=-1

( )

2 2

sin sin ( ) Nh h π π

3
2
1

1 2 3 h as  s0    2 4 6 8 10 y t i s n e t n I

h’=0

3
2
1

1 2 3 h as  s0    2 4 6 8 10 y t i s n e t n I

h’=1

Intensity (a.u.)

3 -2 -1 0 1 2 3

h

( )

2 2

sin sin ( ) Nh h π π

( )

2 2

sin sin ( ) Nh h π π

( )

2 2

1

sin ( ) ( 1)

Nh

h

dh N I h N

π

β

∞ −∞

−

= = =

∫

I nt egral Breadt h (β) of a (h00) peak:

1 N = 1 D ∝

Scherrer equat ion

D Na = a

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P. Scardi – Dif f raction f rom nanocrystalline materials

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( ) ( ) ( )

2 2 2 2 2 2 2 2 2 2 ' ' '

sin sin sin ( ') ( ') ( ')

sc h k l

Nh Nk Nl I F h h k k l l π π π π π π

∞ ∞ ∞ =−∞ =−∞ =−∞

∝ − − −

∑ ∑ ∑

22

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

Tradit ional "reciprocal space" approach (sum, t hen average)

1. Factorize the contribution of a unit cell

(|F|2 – F, structure factor )

2. Build the diffraction signal as interference between unit cells
3. Integrate over the powder diffraction sphere (orientational average)

( ) ( )

2

, I q F q D ∝ Φ

line prof ile f unct ion

D Na = a

sx [Å-1] sy [Å-1] s

( ) ( )

2

4

sc PD

I s d I s s π Ω ∝ ∫

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P. Scardi – Dif f raction f rom nanocrystalline materials

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small cubic / spherical f cc domains

( ) ( )

2

,

PD sphere

I s F s D ∝ Φ

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

sx [Å-1] sy [Å-1]

s

D

sx [Å-1] sy [Å-1]

s

D

( ) ( )

2

,

PD cube

I s F s D ∝ Φ

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P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

4 5 6 7 8 9 10 200 400 600 800 1000

Intensity [a.u.] s [Å

1]

4 5 6 7 8 9 10 200 400 600 800 1000

Intensity [a.u.] s [Å

1]

24

( ) ( )

2

,

PD sphere

I s F s D ∝ Φ

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

( ) ( )

2

,

PD cube

I s F s D ∝ Φ

Na = a

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 1 10 100 1000

Intensity [a.u.] s [Å

1]

80.6 Å D = 100 Å D =

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 1 10 100 1000

Intensity [a.u.] s [Å

1]

small cubic / spherical f cc domains

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P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

4 5 6 7 8 9 10 200 400 600 800 1000

Intensity [a.u.] s [Å

1]

( ) ( )

2

,

PD cube

I s F s D ∝ Φ

Na = a 80.6 Å D =

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 1 10 100 1000

Intensity [a.u.] s [Å

1]

Microst ruct ure: any deviat ion f rom perf ect cryst alline order

I DEAL vs REAL NANOCRYSTALS

[111] [110] [100]

Pd nanocrystals

Solla-Gullon et al., J. Appl. Cryst. 48 (2015) 1534

Courtesy of A. Young & F. Tsung Boston College, 2015

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P. Scardi – Dif f raction f rom nanocrystalline materials

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4 5 6 7 8 9 10 200 400 600 800 1000

Intensity [a.u.] s [Å

1]

26

( ) ( )

2

,

PD cube

I s F s D ∝ Φ

Na = a 80.6 Å D =

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 1 10 100 1000

Intensity [a.u.] s [Å

1]

Microst ruct ure: any deviat ion f rom perf ect cryst alline order

I DEAL vs REAL NANOCRYSTALS

Scardi et al., Phys.Rev. B 91 (2015) 155414

[111] [110] [100]

Pd nanocrystals

Solla-Gullon et al., J. Appl. Cryst. 48 (2015). In press.

Courtesy of A. Young & F. Tsung Boston College, 2015

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P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

4 5 6 7 8 9 10 200 400 600 800 1000

Intensity [a.u.] s [Å

1]

27

( ) ( )

2

,

PD cube

I s F s D ∝ Φ

Na = a 80.6 Å D =

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 1 10 100 1000

Intensity [a.u.] s [Å

1]

Microst ruct ure: any deviat ion f rom perf ect cryst alline order

I DEAL vs REAL NANOCRYSTALS

Surface relaxation in nanocrystals

a0 a0+∆a CeO2

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P. Scardi – Dif f raction f rom nanocrystalline materials

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4 5 6 7 8 9 10 200 400 600 800 1000

Intensity [a.u.] s [Å

1]

28

( ) ( )

2

,

PD cube

I s F s D ∝ Φ

Na = a 80.6 Å D =

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 1 10 100 1000

Intensity [a.u.] s [Å

1]

Microst ruct ure: any deviat ion f rom perf ect cryst alline order

I DEAL vs REAL NANOCRYSTALS

Surface (A), near-surface (B), interior (C) Surface reconstruction in anatase (TiO2) NCs

Banfield & Zhang, Rev. Mineral. & Geochem. 44 (2001) 1

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P. Scardi – Dif f raction f rom nanocrystalline materials

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4 5 6 7 8 9 10 200 400 600 800 1000

Intensity [a.u.] s [Å

1]

29

( ) ( )

2

,

PD cube

I s F s D ∝ Φ

Na = a 80.6 Å D =

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 1 10 100 1000

Intensity [a.u.] s [Å

1]

Microst ruct ure: any deviat ion f rom perf ect cryst alline order

I DEAL vs REAL NANOCRYSTALS

Ball-milled Fe-Mo alloy

Rebuffi et al., Nat. Sci. Reports 6 20712 (2016)

2 nm

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P. Scardi – Dif f raction f rom nanocrystalline materials

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DI FFRACTI ON PATTERN FROM A POLYCRYSTALLI NE

I nst rument al f act ors: (g – prof ile component )
Microst ruct ure:

(f – prof ile component s)

h = g ⊗ f 1 ⊗ f 2 ⊗ f 3 ⊗ …

Experiment al peak prof iles (h) can be represent ed as a convolut ion :

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P. Scardi – Dif f raction f rom nanocrystalline materials

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L

2θΒ

1 L ∝

I nstrumental f actors (g – prof ile component) Microstructure: (f – prof ile components)

DI FFRACTI ON PATTERN FROM A POLYCRYSTALLI NE

2θΒ

2 hkl

s ε ∝ < >

⊗

h = g ⊗ f 1 ⊗ f 2

line broadening f rom inst rument , domain size/ shape and dislocat ions

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P. Scardi – Dif f raction f rom nanocrystalline materials

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Dislocat ion line broadening is markedly anisot ropic, i.e., hkl dependent

* hkl

d

* hkl

d

dislocat ion visibilit y depends on t he viewing direct ion

2θΒ

2 hkl

s ε ∝ < >

DOMAI N SI ZE AND MI CROSTRAI N BROADENI NG

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P. Scardi – Dif f raction f rom nanocrystalline materials

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33 * hkl

d

* hkl

d

‘invisible’

2θΒ

2 hkl

s ε ∝ < > Dislocat ion line broadening is markedly anisot ropic, i.e., hkl dependent dislocat ion visibilit y depends on t he viewing direct ion

DOMAI N SI ZE AND MI CROSTRAI N BROADENI NG

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P. Scardi – Dif f raction f rom nanocrystalline materials

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2θΒ

2 hkl

s ε ∝ < >

L

⊗

2θΒ

1 L ∝

Combined line broadening ef f ect f rom domain size and dislocat ions

I nstrumental f actors (g – prof ile component) Microstructure: (f – prof ile components)

h = g ⊗ f 1 ⊗ f 2 ⊗ f 3 ⊗ f 4 ⊗ … DOMAI N SI ZE AND MI CROSTRAI N BROADENI NG

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g

Most common line broadening sources

DI FFRACTI ON PATTERN FROM A POLYCRYSTALLI NE

Ant i-phase boundar ies

2 4 6 8 10 12 5 10 15 20 25 30 35 40

TEM WPPM Fr equency Grain diamet er (nm)

5 nm

* hkl

d

* hkl

d

AB CAB AB C

f 1 ⊗ f 2 ⊗ f 3 ⊗ …

a0 a0+∆a

Gr ain sur f ace r elaxat ion Gr ain shape and size dist r ibut ion dislocat ions, disclinat ions St acking f ault s

2 4 6 8 10 12 5 10 15 20 25 30 35 40

TEM WPPM Fr equency Grain diamet er (nm)

5 nm

* hkl

d

AB CAB AB C

* hkl

d

f 1 ⊗ f 2 ⊗ f 3 ⊗ …

a0

Gr ain sur f ace r elaxat ion Gr ain shape and size dist r ibut ion dislocat ions, disclinat ions St acking f ault s

* hkl

d

2θ

* hkl

d

* hkl d * hkl d

st oichiomet r y f luct uat ion

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P. Scardi – Dif f raction f rom nanocrystalline materials

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WHOLE POWDER PATTERN MODELLI NG

t he Fourier Transf orm of I (s) is t he product of t he FTs of t he single prof ile component s

( )

2

e

hkl

iL s

L

I s C dL

π ⋅

∞ −∞

∝ ⋅ ∫

( ) ( ) ( )

( ) ( ) ( ) ...

IP S D F APB

I s I s I s I s I s I s = ⊗ ⊗ ⊗ ⊗ ⊗

Dif f ract ion prof ile as a convolut ion of (independent ) ef f ect s:

P. Scar di, Chap. 13 in Powder Dif f r act ion: Theor y and Pr act ice, R.E. Dinnebier & S.J .L. Billinge, eds. RSC, Cambr idge, 2008

{ } { } { }

( ) ...

IP S D F F APB i pV hkl hkl hkl hkl hkl i

C A T A A A iB A = = ⋅ ⋅ ⋅ + ⋅ ⋅

∏

inst r. prof ile microst rain / lat t ice def ect s/ … domain size/ shape

SLIDE 37

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

37

Ant i-Phase Domains: γ

( )

{ } 2 2 2

2 ( ) exp

APB hkl hkl

h k L A L d h k l γ   − + ⋅ = −   + +    

WPPM : HOW DOES I T WORK ??

Dislocat ion (st rain) ef f ect : ρ, Re, (C

hkl)

{ }

( )

2

2 * 2 * { }

1 ( ) exp 2

D hkl hkl e hkl

A L b C d L f L R π ρ   = − ⋅    

( )

{ }

( )

* 2

2 1 2 2 2

1 2

( ) 1 3 2 3 ( ) 3 6 12 12

hkl

L
F

hkl F

hkl

L

L

Ld h

A L L L B L L L

σ

α β α σ β β α β α

⋅

= − − + =− ⋅ ⋅ ⋅ − − − +

AB CAB AB C

* hkl

d

* hkl

d

Fault ing: α (def .), β (t win)

* hkl

d

* hkl

d

( )

2 2 2 2 2 2 2 2 2 2 hkl

h k k l l h C A B A B H h k l + + = + ⋅ = + ⋅ + +

( ) ( )

( )

2 2 2

1 exp ln2 exp 2

IP pV s s

T L k L k L π σ π σ = − ⋅ − ⋅ + − ⋅

I nst rument al prof ile

Domain size ef f ect : µ, σ

( )

2 3 ,3 ,3

ln (3 ) ( ) 2 2

c l n S c n n n l

L K n M A L H Erfc L M µ σ σ

− =

  ⋅ − − − = ⋅ ⋅      

∑

2 4 6 8 10 12 5 10 15 20 25 30 35 40

TEM WPPM Frequency Grain diamet er (nm)

5 nm

SLIDE 38

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

38

Microst ruct ural Paramet ers Dif f ract ion Pat t ern

WHOLE POWDER PATTERN MODELLI NG - WPPM

based on physical models of t he microst ruct ure

( )

2

e

hkl

iL s

L

I s C dL

π ⋅

∞ −∞

∝ ⋅ ∫

P. Scar di, Chap. 13 in Powder Dif f r act ion: Theor y and Pr act ice, R.E. Dinnebier & S.J .L. Billinge, eds. RSC, Cambr idge, 2008

{ } { } { }

( ) ...

IP S D F F APB i pV hkl hkl hkl hkl hkl i

C A T A A A iB A = = ⋅ ⋅ ⋅ + ⋅ ⋅

∏

inst r. prof ile microst rain / lat t ice def ect s/ … domain size/ shape

Direct modelling of dif f ract ion prof iles in t erms of relat ively f ew microst ruct ural paramet ers: µ, σ - ρ, Re - α, β - γ …

SLIDE 39

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

39

10 20 30 40 50 60 70 80 90 100 50 100 150 200 250

Intensity (x10

3 counts)

2θ (degrees)

10 20 30 40 50 60 70 80 90 100 10 100

Intensity (x103 counts) 2θ (degrees)

Ball milled Fe-1.5%Mo

20 µm ESRF – I D31 λ=0.0632 nm

“ident ical” Pd nanopart icles

5 nm

WPPM APPLI CATI ONS: TWO TYPI CAL CASES OF STUDY

MCX - ELETTRA λ=0.082666 nm

SLIDE 40

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

40

NANOCRYSTALLI NE Fe-1.5%Mo POWDER

Planet ary ball milling - product ion of nanocryst alline Fe-1.5%Mo

Ω ω

Rebuffi et al., Nat. Sci. Reports 6 20712 (2016)

2 nm

SLIDE 41

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

41

10 20 30 40 50 60 70 80 90 100 50 100 150 200 250

Intensity (x10

3 counts)

2θ (degrees) (b)

10 20 30 40 50 60 70 80 90 100 10 100

Intensity (x10

3 counts)

96 hours

Ball milled Fe1.5Mo (Frit sch P4) – dat a collect ed at ESRF – I D31 λ=0.0632 nm

NANOCRYSTALLI NE Fe-1.5%Mo POWDER

SLIDE 42

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

42

SI ZE AND MI CROSTRAI N PROFI LE COMPONENTS

20 30 40 50 60 70 80 90 1000 10000 100000

Intensity (counts) 2θ (degrees)

"Size" - profile component "Strain" - profile component

SLIDE 43

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

43

SI ZE AND MI CROSTRAI N PROFI LE COMPONENTS

20 30 40 50 60 70 80 90 20000 40000 60000 80000 100000 120000 140000 160000

Intensity (counts) 2θ (degrees)

"Size" - profile component "Strain" - profile component

16 17 18 19 20 40000 80000 120000 160000 200000

Intensity (counts) 2θ (degrees)

"Size" - profile component "Strain" - profile component Instrumental profile component

72 73 74 75 76 1000 2000 3000 4000 5000

Intensity (counts) 2θ (degrees)

"Size" - profile component "Strain" - profile component Instrumental profile component

38 39 40 41 42 43 5000 10000 15000 20000

Intensity (counts) 2θ (degrees)

"Size" - profile component "Strain" - profile component Instrumental profile component

SLIDE 44

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

44

SI ZE AND MI CROSTRAI N PROFI LE COMPONENTS

20 30 40 50 60 70 80 90 20000 40000 60000 80000 100000 120000 140000 160000

Intensity (counts) 2θ (degrees)

"Size" - profile component "Strain" - profile component

4 6 8 10 12 14 16 18 20 22 24 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

110 200 211 220 310 222 321 400 411 420 332 422 431 521 440 530 442 532 620 541 622 631 444 600 611

total strain size

β (nm-1)

s (nm

1)

IPF

SLIDE 45

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

45

10 20 30 40 50 60 70 80 90 100 50 100 150 200 250

Intensity (x10

3 counts)

2θ (degrees) (b)

Ball milled Fe1.5Mo (Frit sch P4) – dat a collect ed at ESRF – I D31 λ=0.0632 nm

NANOCRYSTALLI NE Fe-1.5%Mo POWDER

SLIDE 46

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

46

10 20 30 40 50 60 70 80 90 100 50 100 150 200 250

Intensity (x10

3 counts)

2θ (degrees) (b)

Ball milled Fe1.5Mo (Frit sch P4) – dat a collect ed at ESRF – I D31 λ=0.0632 nm

NANOCRYSTALLI NE Fe-1.5%Mo POWDER

20 40 60 80 100 120 140 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5

Ball milling time (h) Dislocation density, ρ (x10

16 m

2)

20 40 60 80 100 120 140 160

Mean domain size, D (nm)

SLIDE 47

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

47

20 40 60 80 100 120 140 160 0.00 0.02 0.04 0.06 0.08 0.10

0 h 2 h 16 h 32 h 64 h 128 h

Domain size distribution, g(D)

D (nm)

20 40 60 80 100 120 140 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Ball milling time (h) Dislocation density, ρ (x1016 m-2)

20 40 60 80 100 120 140 160

Mean domain size, D (nm)

Ball milled Fe1.5Mo (Frit sch P4) – dat a collect ed at ESRF – I D31 λ=0.0632 nm I n addit ion t o mean values, WPPM provides t he size dist ribut ion

NANOCRYSTALLI NE Fe-1.5%Mo POWDER

Rebuffi et al., Nat. Sci. Reports 6 20712 (2016) - open access – and references therein

SLIDE 48

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

48

[111] [110] [100]

Pd nanocrystals

CHALLENGES I N NANOTECHNOLOGY

Product ion of “ident ical” nanopart icles. Nanocryst al size and shape: X-ray Powder Dif f ract ion and Transmission Elect ron Microscopy (TEM)

Solla Gullon et al. , J. Appl. Cryst. 48 (2015) 1534

SLIDE 49

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016 (i) some cubes don’t lie on faces, (ii) truncated edges and corners

5 10 15 20 25 30 35 40 45 50 55 60 50 100 150 200 250 300

#1 #2 #3 Total (768 np)

frequency edge length (nm)

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

SLIDE 50

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

10 20 30 40 50 60 70 80

10

3

10

4

10

5

Intensity (counts) 2θ (degrees)

10

4

10

5

kapton

MCX beamline (Elet t ra Sincrot rone Triest e, Triest e) Debye-Scherrer geomet ry , 15 keV, Ø 0.5 mm kapt on capillary

Narrow inst rument al prof iles
Good count ing st at ist ics

Special t hanks t o: M. Abdellat ief , L. Rebuf f i, J . Plaisier, A. Lausi

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

SLIDE 51

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

MCX beamline (Elet t ra Sincrot rone Triest e, Triest e) Debye-Scherrer geomet ry , 15 keV, Ø 0.5 mm kapt on capillary

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

20 40 60 80 0.0 0.2 0.4 0.6 0.8 1.0

A(θ,R,µ) 2θ (degrees)

( ) ( ) ( )

{ }

( )

2 2 2 2 2 2 2 2 0 0

1 , , exp sin sin cosh 2 sin sin

R

A R R r R r r rdrd R

π

θ µ µ θ ϕ θ ϕ µ θ ϕ ϕ π   = − − + + − −  

∫ ∫

Negligible absorpt ion: µ=2.71 cm-1 µR≈0.07

SLIDE 52

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

MCX beamline (Elet t ra Sincrot rone Triest e, Triest e) Debye-Scherrer geomet ry , 15 keV, Ø 0.5 mm kapt on capillary

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

Caref ully reproducible / cont rolled signal f rom t he capillary

10 20 30 40 50 60 70 80

10

3

10

4

10

5

Intensity (counts) 2θ (degrees)

10

4

10

5

kapton

SLIDE 53

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

MCX beamline (Elet t ra Sincrot rone Triest e, Triest e) Debye-Scherrer geomet ry , 15 keV, Ø 0.5 mm kapt on capillary

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

Caref ully reproducible / cont rolled signal f rom t he capillary

10 20 30 40 50 60 70 80 2000 4000 6000 8000 10000 12000

Intensity 2θ (degrees)

10 20 30 40 50 60 70 80 2000 4000 6000 8000 10000 12000

Intensity 2θ (degrees)

SLIDE 54

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

10 20 30 40 50 60 70 80 1x10

5

2x10

5

3x10

5

4x10

5

5x10

5

Intensity (counts) 2θ (degrees)

10 20 30 40 50 60 70 80 1x10

4

2x10

4

Intensity (counts) 2θ (degrees)

TDS

Whole Powder Pat t ern Modelling (WPPM)

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

Beyerlein et al. , Acta Cryst. A68 (2012) 382

SLIDE 55

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

10 20 30 40 50 60 70 80 1x10

5

2x10

5

3x10

5

4x10

5

5x10

5

Intensity (counts) 2θ (degrees)

Whole Powder Pat t ern Modelling (WPPM)

10 20 30 40 50 60 70 80 10

4

10

5

Intensity (counts) 2θ (degrees)

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

SLIDE 56

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

lognormal dist ribut ion of cubes vs spheres: shape mat t ers !

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

10 20 30 40 50 60 70 80 1x10

5

2x10

5

3x10

5

4x10

5

5x10

5

Intensity (counts) 2θ (degrees)

19 20 21 22 23 24 25 26 1x10

5

2x10

5

3x10

5

4x10

5

5x10

5

Intensity (counts) 2θ (degrees)

10 20 30 40 50 60 70 80 1x10

5

2x10

5

3x10

5

4x10

5

5x10

5

Intensity (counts) 2θ (degrees)

19 20 21 22 23 24 25 26 1x10

5

2x10

5

3x10

5

4x10

5

5x10

5

Intensity (counts) 2θ (degrees)

SLIDE 57

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

111 110 100 Surface area fraction truncation 111

0.66 0.32 0.02 10 20 30 40 50 60 70 80 1x10

5

2x10

5

3x10

5

4x10

5

5x10

5

Intensity (counts) 2θ (degrees)

5 10 15 20 25 30 35 40 45 50 55 60 50 100 150 200 250 300

TEM histogram

frequency edge length (nm)

XRD-WPPM

WPPM : t runcat ed cubic Pd nanocryst al

[111] [110] [100]

10% 90%

DI FFRACTI ON FROM NANOCRYSTALLI NE POWDER

SLIDE 58

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

111 110 100 Surface area fraction truncation 111

0.66 0.32 0.02

10% 90% (100) area: 64 % (110) area: 28% (111) area: 8% (100) area ≈ 55-60 %

(111) (100) (110)

Cu Under Pot ent ial Deposit ion (UPD)

5 10 15 20 25 30 35 40 45 50 55 60 50 100 150 200 250 300

TEM histogram

frequency edge length (nm)

XRD-WPPM

WPPM : t runcat ed cubic Pd nanocryst al

10 20 30 40 50 60 70 80 1x10

5

2x10

5

3x10

5

4x10

5

5x10

5

Intensity (counts) 2θ (degrees)

DI FFRACTI ON & Cu-UPD

SLIDE 59

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

10% 90% (100) area: 64 % (110) area: 28% (111) area: 8% (100) area ≈ 55-60 %

(111) (100) (110)

Cu Under Pot ent ial Deposit ion (UPD)

10 20 30 40 50 60 70 80 1x10

5

2x10

5

3x10

5

4x10

5

5x10

5

Intensity (counts) 2θ (degrees)

5 10 15 20 25 30 35 40 45 50 55 60 50 100 150 200 250 300

TEM histogram

frequency edge length (nm) XRD-WPPM

WPPM : truncated cubic Pd nanocrystal

≈3 steps per h00 f ace

DI FFRACTI ON, Cu-UPD, HRTEM

SLIDE 60

P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

60

WPPM SOFTWARE: X- DREAM EPDI C15 Bari J une 2016

Open source
Mult i -plat f orm, -t hread, -programming language based
Specif ically designed t o support learning and educat ion