Diffraction from nanocrystalline...

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X-ray Diffraction

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Special thanks to: Luca Gelisio, Alberto Leonardi, Luca Rebuffi, Cristy L. Azanza Ricardo,Mirco D’Incau, Andrea Troian, Emmanuel Garnier, Mahmoud Abdellatief

• Basic aspects of x-ray crystallography and powder diffraction

• Diffraction from nanocrystalline materials

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P. Scardi – Diffraction from nanocrystalline materialsICTP School - Trieste, 04.04.2016 2

PRESENTATION OUTLINE

PART IIISelected case studies: highly deformed metals, and nanocrystalline catalyst

PART I Diffraction from nanocrystalline materials:why using synchrotron radiation?

PART IVTotal Scattering methods

PART II Reciprocal space vs direct space methods

Chapter XVIIIDiffraction from nanocrystalline materials

Paolo Scardi and Luca Gelisio


SYNCHROTRON RADIATION X-RAY DIFFRACTION main applications of (powder /polycrystalline material) diffraction

• Crystal structure determination: structure solution and refinement.

• Phase Identification (Search-Match procedures): pure crystalline phases or mixtures

• Quantitative Phase Analysis (QPA): crystalline and amorphous phases

• Line Profile Analysis (LPA): crystalline domain size/shape, lattice defect analysis – nanocrystalline materials

• X-ray Residual Stress Analysis (XRSA): measurement of strainfield / elastic behaviour

• Texture Analysis (TA): determination of preferred orientations

P. Scardi – Diffraction from nanocrystalline materialsICTP School - Trieste, 04.04.2016

20 30 40 50 600

2000

4000

6000

Inte

nsity

2θ (degrees)

4

powder(bulk polycrystalline)

100

110

020120220

100

110

020120220

DIFFRACTION PATTERN FROM A POLYCRYSTALLINE

sx [Å-1]

s y[Å

-1] s

s=Q/2π=2sinθ /λ

s

2θ


SYNCHROTRON RADIATION X-RAY DIFFRACTION from single-crystal to powder diffraction


SYNCHROTRON RADIATION X-RAY DIFFRACTION Powder diffraction ‘elective’ geometry: Debye-Scherrer (1918)

POWDER


SYNCHROTRON RADIATION X-RAY DIFFRACTION parallel beam, Debye Sherrer geometry of MCX (ELETTRA)


20 40 60 80 100 120 1400

2000

4000

6000

Inte

nsity

2θ (degrees)


powder(bulk polycrystalline)

100

110

020120220

100

110

020120220

nanocrystallinepowder

10 nm 20 40 60 80 100 120 1400

2000

4000

6000

Inte

nsity

2θ (degrees)

peaks from nanocrystals are broad: why using SR ???


SYNCHROTRON RADIATION X-RAY DIFFRACTION • high brillance: better counting statistics / shorter data

collection time / fast kinetics, in situ, in operando studies

40 60 80 100 120 140

10

100

1000

Inte

nsity

(co

unts

)

2θ (degrees) 10 20 30 40 50 60 70 80 90 100

10

100

Inte

nsity

(x10

3 cou

nts)

2θ (degrees)

counts · N° of peakstime

=1 =25.000

9-crystal analyzer: 1.500s ! (x100 counts)Lab instrument: ~80.000s

CuKα λ=0.15406 nm ESRF ID31 (now ID22) λ=0.0632 nmiron powder (ball milled)


SYNCHROTRON RADIATION X-RAY DIFFRACTION

40 60 80 100 120 140

10

100

1000

Inte

nsity

(co

unts

)

2θ (degrees)

counts · N° of peakstime

=1

Lab instrument: ~80.000s

CuKα λ=0.15406 nmiron powder (ball milled)

PSI MS-X04SA λ=0.072929 nm

Mythen detector: 100 s !! (x100 counts)

10 20 30 40 50 60 70 80 90 100 110

10

100

Inte

nsity

(x1

03 co

unts

)

2θ (degrees)

=350.000

• high brillance: better counting statistics / shorter data collection time / fast kinetics, in situ, in operando studies


SYNCHROTRON RADIATION X-RAY DIFFRACTION • narrow instrumental profile: control of instrumental profile;

high resolution and accuracy in measuring peak position, intensity and profile width/shape

Lab instrument: ID31 @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°


SYNCHROTRON RADIATION X-RAY DIFFRACTION • extending the accessible region of reciprocal space well beyond

what traditional lab instruments can make

λ1 λ2<λ1



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

40 60 80 100 120 140

10

100

1000

Inte

nsity

(co

unts

)

2θ (degrees)

(110

)

(200

)

(211

)

(220

)

(310

)

(222

)

9-crystal analyzer: 1.500s ! (x100 counts): 28 peaks

Lab instrument: ~80.000s: 6 peaks

• extending the accessible region of reciprocal space well beyond what traditional lab instruments can make


SYNCHROTRON RADIATION X-RAY DIFFRACTION • extending the accessible region of reciprocal space well beyond

what traditional lab instruments can make: PDF analysis

High-pressure pair distribution function (PDF) measurement of nano Pt (50 nm) at 12.5 GPa in Methanol:Ethanol = 4:1.Focused X-ray beam, 66.054 keV, Brookhaven National Laboratory. Hong et al., Nat. Sci. Reports 6, 21434 (2016)



High-pressure pair distribution function (PDF) measurement of nano Pt (50 nm) at 12.5 GPa in Methanol:Ethanol = 4:1.Focused X-ray beam, 66.054 keV, Brookhaven National Laboratory. Hong et al., Nat. Sci. Reports 6, 21434 (2016)

• extending the accessible region of reciprocal space well beyond what traditional lab instruments can make: PDF analysis


SYNCHROTRON RADIATION X-RAY DIFFRACTION • tuning energy according to adsorption edges for, e.g.:

resonant scattering, in depth measurements (property gradients)

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

µρ

ρ

− =


10 20 30 40 50 60 70 80

103

104

105

Inte

nsity

(co

unts

)

2θ (degrees)

104

105

kapton

MCX beamline (Elettra), 15 keVNegligible absorption: µ=2.71 cm-1 à µR≈0.07

Special thanks to: M. Abdellatief

SYNCHROTRON RADIATION X-RAY DIFFRACTION • tuning energy according to adsorption edges for, e.g.:

resonant scattering, in depth measurements (property gradients); control fluorescence emission and absorption



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

10

100

1000

Inte

nsity

(co

unts

)

2θ (degrees)

10 20 30 40 50 60 70 80 90 10010

100

1000

Inte

nsity

(co

unts

x 1

00)

2θ (degrees)

10 20 30 40 50 60 70 80 90 100 110

100

1000

Inte

nsity

(co

unts

x 1

00)

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=0.072929nm). On the right: schematic of reciprocal space with extension of thelimiting 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 à extend Ewald sphere!• increase energy à high Q(=4πsinθ/λ) for PDF analysis• statistics /short time /kinetics / in situ / in operando• control absorption and instrumental effects


sx [Å-1]

s y[Å

-1]

19

DIFFRACTION FROM NANOCRYSTALLINE POWDER

( ) ( ) ( )2 2*m ni s r i s rsc m n

m n

I s f e f eπ π⋅ − ⋅∝ ∑ ∑ ( )2* mni s rm n

m nf f e π ⋅= ∑∑

( )( )

24sc

PD

I s dI s

sπ

Ω∝ ∫

2 sind s d dϑ ϑ φΩ =s=Q/2π=2sinθ /λ

orientational (or powder)

average

S

mrnr

mnr



( ) ( ) ( )2 2*m ni s r i s rsc m n

m n

I s f e f eπ π⋅ − ⋅∝ ∑ ∑ ( )2* mni s rm n

m nf f e π ⋅= ∑∑

sx [Å-1]

s y[Å

-1]

(1) sum, then average or

(2) average, then sum

( )( )2*

24

mni s rm n

m nPD

f f e dI s

s

π

π

⋅ Ω∝

∑∑∫

Traditional "reciprocal space" approach

Debye scattering equation, "direct space" Total scattering approach

s=Q/2π=2sinθ /λ 2 sind s d dϑ ϑ φΩ =

S

mrnr

mnr


( ) ( ) ( )2 2 22

2 2 2 2 2 2' ' '

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

h k l

Nh Nk NlI F

h h k k l lπ π π

π π π

∞ ∞ ∞

=−∞ =−∞ =−∞

∝− − −∑ ∑ ∑

21

DIFFRACTION FROM NANOCRYSTALLINE POWDERTraditional "reciprocal space" approach (sum, then 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 0 1 2 3h a s s0

2

4

6

8

10

ytisnetnI

h’=-1( )2

2

sinsin ( )

Nhh

ππ

-3 -2 -1 0 1 2 3h as s0

2

4

6

8

10

ytisnetnI

h’=0

-3 -2 -1 0 1 2 3h as s0

2

4

6

8

10

ytisnetnI

h’=1

Inte

nsity

(a.u

.)

-3 -2 -1 0 1 2 3h

( )2

2

sinsin ( )

Nhh

ππ

( )2

2

sinsin ( )

Nhh

ππ

( )22

2

2

1sin ( )

( 1)

Nh

hdh

NI h N

π

πβ

∞

−∞ −= =

=

∫

Integral Breadth (β) of a (h00) peak:

1N

=1D

∝

Scherrer equation

D Na= a


( ) ( ) ( )2 2 22

2 2 2 2 2 2' ' '

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

h k l

Nh Nk NlI F

h h k k l lπ π π

π π π

∞ ∞ ∞

=−∞ =−∞ =−∞

∝− − −∑ ∑ ∑

22

DIFFRACTION FROM NANOCRYSTALLINE POWDERTraditional "reciprocal space" approach (sum, then 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 profilefunction

D Na= a

sx [Å-1]

s y[Å

-1]

s

( )( )

24sc

PD

I s dI s

sπ

Ω∝ ∫


small cubic / spherical fcc domains

( ) ( )2 ,PD sphereI s F s D∝ Φ


sx [Å-1]s y

[Å-1

]

s

D

sx [Å-1]

s y[Å

-1]

s

D

( ) ( )2 ,PD cubeI s F s D∝ Φ


4 5 6 7 8 9 100

200

400

600

800

1000

Inte

nsity

[a.u

.]

s [Å-1]4 5 6 7 8 9 10

0

200

400

600

800

1000

Inte

nsity

[a.u

.]s [Å-1]

24

( ) ( )2 ,PD sphereI s F s D∝ Φ



Na= a

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.61

10

100

1000

Inte

nsity

[a.u

.]

s [Å-1]

80.6 ÅD =100 ÅD =

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.61

10

100

1000

Inte

nsity

[a.u

.]

s [Å-1]

small cubic / spherical fcc domains


4 5 6 7 8 9 100

200

400

600

800

1000

Inte

nsity

[a.u

.]

s [Å-1]


Na= a80.6 ÅD =

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.61

10

100

1000

Inte

nsity

[a.u

.]

s [Å-1]

Microstructure: any deviation from perfect crystalline orderIDEAL vs REAL NANOCRYSTALS

[111][110]

[100]

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

Courtesy of A. Young & F. TsungBoston College,

2015


4 5 6 7 8 9 100

200

400

600

800

1000

Inte

nsity

[a.u

.]

s [Å-1]

26


Na= a80.6 ÅD =

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.61

10

100

1000

Inte

nsity

[a.u

.]

s [Å-1]


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. TsungBoston College,

2015


4 5 6 7 8 9 100

200

400

600

800

1000

Inte

nsity

[a.u

.]

s [Å-1]

27


Na= a80.6 ÅD =

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.61

10

100

1000

Inte

nsity

[a.u

.]

s [Å-1]


Surface relaxation in nanocrystals

a0

a0+∆aCeO2


4 5 6 7 8 9 100

200

400

600

800

1000

Inte

nsity

[a.u

.]

s [Å-1]

28


Na= a80.6 ÅD =

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.61

10

100

1000

Inte

nsity

[a.u

.]

s [Å-1]


Surface (A), near-surface (B), interior (C)

Surface reconstruction in anatase (TiO2) NCsBanfield & Zhang, Rev. Mineral. & Geochem. 44 (2001) 1


4 5 6 7 8 9 100

200

400

600

800

1000

Inte

nsity

[a.u

.]

s [Å-1]

29


Na= a80.6 ÅD =

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.61

10

100

1000

Inte

nsity

[a.u

.]

s [Å-1]


Ball-milled Fe-Mo alloyRebuffi et al., Nat. Sci. Reports 6 20712 (2016)

2 nm



Ø Instrumental factors: (g – profile component)

Ø Microstructure: (f – profile components)

h = g ⊗ f1 ⊗ f2 ⊗ f3 ⊗ …

Experimental peak profiles (h) can be represented as a convolution :


L

2θΒ

1L

∝

Instrumental factors (g – profile component)

Microstructure: (f – profile components)


2θΒ

2hkls ε∝ < >

⊗

h = g ⊗ f1 ⊗ f2

line broadening from instrument, domain size/shape and dislocations


Dislocation line broadening is markedly anisotropic, i.e., hkl dependent

*hkld *

hkld

dislocation visibility depends on the viewing direction

2θΒ

2hkls ε∝ < >

DOMAIN SIZE AND MICROSTRAIN BROADENING


*hkld

*hkld

‘invisible’

2θΒ

2hkls ε∝ < >

Dislocation line broadening is markedly anisotropic, i.e., hkl dependent

dislocation visibility depends on the viewing direction



2θΒ

2hkls ε∝ < >

L ⊗

2θΒ

1L

∝

Combined line broadening effect from domain size and dislocations

Instrumental factors (g – profile component)

Microstructure: (f – profile components)

h = g ⊗ f1 ⊗ f2 ⊗ f3 ⊗ f4 ⊗ …



gMost common line broadening sources


Anti-phase boundaries

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

*h k ld

ABC

AB

ABC

f1 ⊗

f2 ⊗

f3

⊗…

a0

a0+∆a

Grain surface relaxationGrain shape and size distribution

dislocations, disclinations

Stacking faults

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40 TEM WPPM

Freq

uenc

y


*hkld

ABC

AB

ABC

*h k ld

f1 ⊗

f2 ⊗

f3

⊗…

a0

Grain surface relaxationGrain shape and size distribution

dislocations, disclinations

Stacking faults

*hkld

2θ

*hkld

*hkld

*hkld

stoichiometry fluctuation


WHOLE POWDER PATTERN MODELLING

the Fourier Transform of I(s) is the product of the FTs of the single profile components

( ) ( ) 2e hkliL sLI s C dLπ ⋅∞

−∞

∝ ⋅ ∫

( ) ( ) ( )( ) ( ) ( ) ...IP S D F APBI s I s I s I s I s I s= ⊗ ⊗ ⊗ ⊗ ⊗

Diffraction profile as a convolution of (independent) effects:

P. Scardi, Chap. 13 in Powder Diffraction: Theory and Practice, R.E. Dinnebier & S.J.L. Billinge, eds. RSC, Cambridge, 2008

( ) ...IP S D F F APBi pV hkl hklhkl hkl hkl

iC A T A A A iB A= = ⋅ ⋅ ⋅ + ⋅ ⋅ ∏

instr. profile

microstrain / lattice defects/…domainsize/shape


Anti-Phase Domains: γ

( )( ) 2 2 2

2( ) expAPB

hklhkl

h k LA L

d h k lγ − + ⋅

= − + +

WPPM : HOW DOES IT WORK ??

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

⋅= − − +

=− ⋅ ⋅ ⋅ − − − +

AB

CA

BAB

C*hkld

*h k ld

Faulting: α (def.), β (twin)

*hkld

*h k ld

( )2 2 2 2 2 2

22 2 2hkl

h k k l l hC A B A B Hh k l

+ += + ⋅ = + ⋅

+ +

( ) ( ) ( ) ( )2 2 21 exp ln2 exp 2IPpV s sT L k L k Lπ σ π σ= − ⋅ − ⋅ + − ⋅ Instrumental profile

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

Mµ σ

σ−

=

⋅ − − −= ⋅ ⋅

∑

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40 TEM WPPM

Freq

uenc

y



Microstructural Parameters

DiffractionPattern

WHOLE POWDER PATTERN MODELLING - WPPMbased on physical models of the microstructure

( ) ( ) 2e hkliL sLI s C dLπ ⋅∞

−∞

∝ ⋅ ∫

P. Scardi, Chap. 13 in Powder Diffraction: Theory and Practice, R.E. Dinnebier & S.J.L. Billinge, eds. RSC, Cambridge, 2008

( ) ...IP S D F F APBi pV hkl hklhkl hkl hkl

iC A T A A A iB A= = ⋅ ⋅ ⋅ + ⋅ ⋅ ∏

instr. profile

microstrain / lattice defects/…domainsize/shape

Direct modelling of diffraction profiles in terms of relatively fewmicrostructural parameters: µ, σ - ρ, Re - α, β - γ …


10 20 30 40 50 60 70 80 90 100

0

50

100

150

200

250

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)

Ball milled Fe-1.5%Mo

20 µm

ESRF – ID31 λ=0.0632 nm

“identical” Pd nanoparticles

5 nm

WPPM APPLICATIONS: TWO TYPICAL CASES OF STUDY

MCX - ELETTRAλ=0.082666 nm


NANOCRYSTALLINE Fe-1.5%Mo POWDER Planetary ball milling - production of nanocrystalline Fe-1.5%Mo

Ω

ω

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

2 nm


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


SIZE AND MICROSTRAIN PROFILE COMPONENTS

20 30 40 50 60 70 80 901000

10000

100000

Inte

nsity

(cou

nts)

2θ (degrees)

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



20 30 40 50 60 70 80 900

20000

40000

60000

80000

100000

120000

140000

160000

Inte

nsity

(cou

nts)

2θ (degrees)


16 17 18 19 200

40000

80000

120000

160000

200000

Inte

nsity

(cou

nts)

2θ (degrees)

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

72 73 74 75 760

1000

2000

3000

4000

5000

Inte

nsity

(cou

nts)

2θ (degrees)


38 39 40 41 42 430

5000

10000

15000

20000

Inte

nsity

(cou

nts)

2θ (degrees)




20 30 40 50 60 70 80 900

20000

40000

60000

80000

100000

120000

140000

160000

Inte

nsity

(cou

nts)

2θ (degrees)


4 6 8 10 12 14 16 18 20 22 240,00,10,20,30,40,50,60,70,80,91,0

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

totalstrain

size

β (n

m-1

)

s (nm-1)

IPF


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

0

50

100

150

200

250

Inte

nsity

(x10

3 cou

nts)

2θ (degrees)

(b)



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

)


0 20 40 60 80 100 120 140 1600.00

0.02

0.04

0.06

0.08

0.10 0 h 2 h 16 h 32 h 64 h 128 h

Dom

ain

size

dis

tribu

tion,

g(D

)

D (nm)

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)D

islo

catio

n de

nsity

, ρ (

x1016

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


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


[111][110]

[100]

Pdnanocrystals

CHALLENGES IN NANOTECHNOLOGYProduction of “identical” nanoparticles. Nanocrystal size and shape:

X-ray Powder Diffraction and Transmission Electron Microscopy (TEM)

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


(i) some cubes don’t lie on faces, (ii) truncated edges and corners

0 5 10 15 20 25 30 35 40 45 50 55 600

50

100

150

200

250

300 #1 #2 #3 Total (768 np)

frequ

ency

edge length (nm)



10 20 30 40 50 60 70 80

103

104

105

Inte

nsity

(co

unts

)

2θ (degrees)

104

105

kapton

MCX beamline (Elettra Sincrotrone Trieste, Trieste)Debye-Scherrer geometry , 15 keV, Ø 0.5 mm kapton capillary

Ø Narrow instrumental profiles Ø Good counting statistics

Special thanks to: M. Abdellatief, L. Rebuffi, J. Plaisier, A. Lausi





20 40 60 800.0

0.2

0.4

0.6

0.8

1.0

A(θ,

R,µ

)

2θ (degrees)

( ) ( ) ( ) ( )2

2 2 2 2 2 22

0 0

1, , exp sin sin cosh 2 sin sinR

A R R r R r r rdrdR

π

θ µ µ θ ϕ θ ϕ µ θ ϕ ϕπ

= − − + + − − ∫ ∫

Ø Negligible absorption: µ=2.71 cm-1 à µR≈0.07




Ø Carefully reproducible / controlled signal from the capillary

10 20 30 40 50 60 70 80

103

104

105

Inte

nsity

(co

unts

)

2θ (degrees)

104

105

kapton




Ø Carefully reproducible / controlled signal from the capillary

10 20 30 40 50 60 70 800

2000

4000

6000

8000

10000

12000

Inte

nsity

2θ (degrees)

10 20 30 40 50 60 70 800

2000

4000

6000

8000

10000

12000

Inte

nsity

2θ (degrees)


10 20 30 40 50 60 70 80

0

1x105

2x105

3x105

4x105

5x105In

tens

ity (c

ount

s)

2θ (degrees)

10 20 30 40 50 60 70 800

1x104

2x104

Inte

nsity

(cou

nts)

2θ (degrees)

TDS

Whole Powder Pattern Modelling (WPPM)


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


10 20 30 40 50 60 70 80

0

1x105

2x105

3x105

4x105

5x105

Inte

nsity

(cou

nts)

2θ (degrees)

Whole Powder Pattern Modelling (WPPM)

10 20 30 40 50 60 70 80

104

105

Inte

nsity

(cou

nts)

2θ (degrees)



lognormal distribution of cubes vs spheres: shape matters !


10 20 30 40 50 60 70 80

0

1x105

2x105

3x105

4x105

5x105

Inte

nsity

(cou

nts)

2θ (degrees)19 20 21 22 23 24 25 26

0

1x105

2x105

3x105

4x105

5x105

Inte

nsity

(cou

nts)

2θ (degrees)

10 20 30 40 50 60 70 80

0

1x105

2x105

3x105

4x105

5x105

Inte

nsity

(cou

nts)

2θ (degrees)19 20 21 22 23 24 25 26

0

1x105

2x105

3x105

4x105

5x105

Inte

nsity

(cou

nts)

2θ (degrees)


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

111

110

100

Surfa

ce a

rea

fract

ion

truncation

111

0.66

0.32

0.02

10 20 30 40 50 60 70 80

0

1x105

2x105

3x105

4x105

5x105

Inte

nsity

(cou

nts)

2θ (degrees)

0 5 10 15 20 25 30 35 40 45 50 55 600

50

100

150

200

250

300

TEM histogram

frequ

ency

edge length (nm)

XRD-WPPM

WPPM : truncated cubic Pd nanocrystal[111][110]

[100]

10% 90%



0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

111

110

100

Surfa

ce a

rea

fract

ion

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 Potential Deposition (UPD)

0 5 10 15 20 25 30 35 40 45 50 55 600

50

100

150

200

250

300

TEM histogram

frequ

ency

edge length (nm)

XRD-WPPM

WPPM : truncated cubic Pd nanocrystal

10 20 30 40 50 60 70 80

0

1x105

2x105

3x105

4x105

5x105

Inte

nsity

(cou

nts)

2θ (degrees)

DIFFRACTION & Cu-UPD

P. Scardi – Diffraction from nanocrystalline materialsICTP School - Trieste, 04.04.201610% 90%

(100) area: 64 %(110) area: 28%(111) area: 8%

(100) area ≈ 55-60 %

(111)

(100)

(110)

Cu Under Potential Deposition (UPD)

10 20 30 40 50 60 70 80

0

1x105

2x105

3x105

4x105

5x105

Inte

nsity

(cou

nts)

2θ (degrees)

0 5 10 15 20 25 30 35 40 45 50 55 600

50

100

150

200

250

300

TEM histogram

frequ

ency

edge length (nm)

XRD-WPPM

WPPM : truncated cubic Pd nanocrystal

≈3 steps perh00 face

DIFFRACTION, Cu-UPD, HRTEM


WPPM SOFTWARE: X-DREAM EPDIC15 Bari June 2016

Ø Open sourceØ Multi -platform, -thread, -programming language basedØ Specifically designed to support learning and education

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