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

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

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X-ray Dif f ract ion Basic aspects of x- ray crystallography and powder dif f raction Dif f raction f rom nanocrystalline materials Paolo. Scardi@unitn. it Special thanks to: Luca Gelisio, Alberto Leonardi, Luca Rebuf f i, Cristy

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SLIDE 1

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
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SLIDE 2
  • P. Scardi – Dif f raction f rom nanocrystalline materials

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FROM SI NGLE CRYSTAL TO POWDER DI FFRACTI ON

( ) ( )

2

4

sc PD

I s d I s s π Ω ∝ ∫

( )

2

F I s =

perf ect (inf init e) cryst al

D

( )

( )

2 *

mn

i S r sc m n m n

I s f f e

π ⋅

∝∑∑ ( ) ( ) ( ) ( )

{ }

( ) ( ) ( ) ...

IP S D F APB C GRS

I s I s I s I s I s I s I s ⊗ ⊗ ⊗ ⊗ ⊗ ⊗

  • 1. Tradit ional reciprocal space approach : sum & average
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SLIDE 3
  • P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

Debye formula (Direct Space)

L real nanocryst als are complex obj ect s

DI FFRACTI ON FROM NANOCRYSTALLI NE MATERI ALS

CdS-CdSe OCTAPODS

non-cryst allographic (e.g. mult iply t winned) nanopart icles, 2D and highly disordered layer syst ems:

  • t ranslat ional symmet ry: not verif ied
  • large st rain / misf it – complex local at omic arrangement
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  • P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

DI FFRACTI ON FROM NANOCRYSTALLI NE MATERI ALS

( )

( )

2 2 2

4

mn

i s r m n PD

f e d I s s

π

π

⋅

Ω =

∑∑ ∫

  • 2. Direct (real) space approach : average & sum

rmn rmn

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SLIDE 5
  • P. Scardi – Dif f raction f rom nanocrystalline materials

I CTP School - Trieste, 04. 04. 2016

DI FFRACTI ON FROM NANOCRYSTALLI NE MATERI ALS

( )

( )

2 2 2

4

mn

i s r m n PD

f e d I s s

π

π

⋅

Ω =

∑∑∫

( ) ( )

2

sin 2 2

mn PD m n mn

sr I s f sr π π =

∑∑

( )

( )

2 2 cos 2 2

sin 2 1 2 sin 4 2

mn mn

i s r isr mn mn mn mn

sr e e r d r sr

π π π φ

π π φ φ π π

⋅

= =

∫

Debye Scat t ering Equat ion (DSE)

rmn

  • 2. Direct (real) space approach : average & sum

rmn rmn

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  • P. Scardi – Dif f raction f rom nanocrystalline materials

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66

( )

2

sin 2 ( ) 2

mn PD m n mn

sr I s f sr π π =

∑∑

DSE APPLI CATI ON TO NON-CRYSTALLOGRAPHI C NPs

Debye Scat t ering Equat ion (DSE)

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  • P. Scardi – Dif f raction f rom nanocrystalline materials

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67

( )

2

sin 2 ( ) 2

mn PD m n mn

sr I s f sr π π =

∑∑

DSE APPLI CATI ON TO GRAPHENE AND RELATED MATERI ALS

Debye Scat t ering Equat ion (DSE)

  • L. Gelisio et al., J . Appl. Cryst . 43 (2014) 647
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  • P. Scardi – Dif f raction f rom nanocrystalline materials

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68

( )

2

sin 2 ( ) 2

mn PD m n mn

sr I s f sr π π =

∑∑

DSE APPLI CATI ON TO GRAPHENE AND RELATED MATERI ALS

Debye Scat t ering Equat ion (DSE)

Carbon nanot ubes

  • L. Gelisio, PhD Thesis, Univ. of Trent o, 2014
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  • P. Scardi – Dif f raction f rom nanocrystalline materials

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1 2 3 4 5 2000 4000 6000 8000 10000 12000 14000 16000

0.00.1 4.4 4.6 4.8 5.0 5.2 100 200 300 600 700 800

Bn rn (nm)

Bmn rmn (nm) (a)

69

( ) ( )

2 2

sin 2 sin 2 ( ) 2 2

mn mn PD mn m n mn mn mn

sr sr I s f f B sr sr π π π π = ≡

∑∑ ∑

DSE CALCULATI ON BY ATOMI C DI STANCE HI STOGRAM

Debye Scat t ering Equat ion (DSE)

Atomic distance histogram (B

mn) f or a cubic cr yst al wit h 8x8x8 sc unit cells (a) and cor r esponding powder pat t er n accor ding t o

I PD(s), wit h f =1, unit cell par amet er , a0=0.361 nm (b).

  • P. Scar di & L. Gelisio, “Dif f r act ion f r om nanocr yst alline mat er ials”, Chapt er XVI I I in Synchr ot ron Radiat ion, ed. S. Mobilio et al.

Spr inger 2015.

20 40 60 80 100 120 140 160 1 2 3 4 5 6 7 8

100 110 111 200 210 211 220 221 300/ 310 311 222 320 321 400 410 322 330/ 411 331 420 421 2 4 6 8 10 12 14 16 18 20 0.01 0.1 1 10 100 1000

Intensity 2θ (degrees)

Intensity 2θ (degrees)

(b)

I n the coming months, look f or a special issue of Acta Crystallographyca A, edited by Billinge, Cervellino, Neder & Scardi Total Scattering methods – the 100 Years of the Debye Scattering Equation (DSE2015 conf erence, Cavalese (I ) June 2015)

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  • P. Scardi – Dif f raction f rom nanocrystalline materials

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PAI R DI STRI BUTI ON FUNCTI ON (PDF)

Zernike & Prins (1927): f or amorphous specimens, volume V, N at oms, t he radial dist ribut ion f unct ion (RDF) is:

( ) ( ) ( )

2 2 2

4 4 8 1 2 I s r r r r s Sin sr ds Nf π ρ π ρ π π

∞ 

 ≅ + −    

∫

( )

RDF r =

int ensit y in absolut e unit s:

( )

2 2

I s N f f   −    

( )

a d c c − −   → =    

2

f

( ) ( )

i M Compton

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  • P. Scardi – Dif f raction f rom nanocrystalline materials

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PDF AND SYNCHROTRON RADI ATI ON

SR is mandat ory t o improve resolut ion!

  • S. J . L. Billinge, Z. Krist allogr. 219 (2004) 117

1950 1999

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SLIDE 12
  • P. Scardi – Dif f raction f rom nanocrystalline materials

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PAI R DI STRI BUTI ON FUNCTI ON (PDF)

( ) ( )

2 1 1 2 s S s Sin sr ds r π ρ

∞

= + −    

∫

( ) ( )

4 G r r r π ρ ρ = −    

( ) ( )

2

4 RDF r r r π ρ =

reduced radial dist ribut ion f unct ion radial dist ribut ion f unct ion

( ) ( )

g r r ρ ρ =

pair dist ribut ion f unct ion - PDF

( ) ( )

2

I s S s Nf =

  • S. J . L. Billinge, Z. Krist allogr. 219 (2004) 117
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  • P. Scardi – Dif f raction f rom nanocrystalline materials

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PDF AND SYNCHROTRON RADI ATI ON

SR is mandat ory t o improve resolut ion!

  • Court esy of R. Neder
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SLIDE 14
  • P. Scardi – Dif f raction f rom nanocrystalline materials

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PDF OF NANOPARTI CLE SYSTEMS

  • Court esy of R. Neder

Ef f ect of f init e size and shape

  • f t he nanopart icle
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SLIDE 15
  • P. Scardi – Dif f raction f rom nanocrystalline materials

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PDF OF NANOPARTI CLE SYSTEMS

  • Court esy of R. Neder

I ndicat ion of st acking f ault s

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SLIDE 16
  • P. Scardi – Dif f raction f rom nanocrystalline materials

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PDF ANALYSI S OF NANOPARTI CLE SYSTEMS

  • Court esy of R. Neder

Au nanopart icle + ligand

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SLIDE 17
  • P. Scardi – Dif f raction f rom nanocrystalline materials

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  • Court esy of R. Neder

PDF ANALYSI S OF NANOPARTI CLE SYSTEMS

Au nanopart icle + ligand

Bottom-up modelling DISCUS DIFFEV

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  • P. Scardi – Dif f raction f rom nanocrystalline materials

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TOTAL SCATTERI NG TECHNI QUES

  • K. Page et al., J .Appl.Cr yst . 44 (2011) 327

PDF approach Debye Scat t ering Equat ion

  • P. Scar di et al., Phys. Rev. B91 (2015) 155414
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SLIDE 19
  • P. Scardi – Dif f raction f rom nanocrystalline materials

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TOTAL SCATTERI NG TECHNI QUES

  • K. Page et al., J .Appl.Cr yst . 44 (2011) 327

PDF approach Debye Scat t ering Equat ion

  • P. Scar di & L. Gelisio, Nat . Sci. Repor t s 6, 22221 (2016)
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SLIDE 20
  • P. Scardi – Dif f raction f rom nanocrystalline materials

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DI FFRACTI ON FROM NANOCRYSTALLI NE MATERI ALS

( ) ( )

2

4

sc PD

I s d I s s π Ω ∝ ∫

( ) ( ) ( ) ( )

{ }

2

( ) ( ) ( ) ...

IP S D F APB C GRS

F I s I s I s I s I s I s I s = ⊗ ⊗ ⊗ ⊗ ⊗ ⊗

  • 1. Tradit ional reciprocal space approach : sum & average

( ) ( )

2

sin 2 2

mn PD m n mn

sr I s f sr π π =

∑∑

Direct (real) space approach: average & sum Debye Scat t ering Equat ion (DSE)

  • 2. Tot al Scat t ering met hods

( ) ( ) ( ) ( )

2

1 1 1 2 r g r Q S Q Sin Qr dQ r ρ ρ π ρ

∞

= = + −    

∫

Pair Dist ribut ion Funct ion (PDF)

( ) ( ) ( )

2

1 1 4 2 2

V

I s N f r r Sin sr dr s π ρ ρ π π   = + −        

∫

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SLIDE 21
  • P. Scardi – Dif f raction f rom nanocrystalline materials

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DI FFRACTI ON FROM NANOCRYSTALLI NE MATERI ALS

relaxed (energy minimization) geometrical

  • L. Gelisio, K.R. Beyerlein & P. Scardi, Thin Solid Films (2012). In press.

Debye Scat t ering Equat ion

( )

2

sin 2 ( ) 2

mn PD m n mn

sr I s f sr π π =

∑∑

  • t oward an int egrat ion bet ween at omist ic modelling and dif f ract ion analysis:

real st ruct ure of nanopart icle syst ems

Current research / f ut ure t rends

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SLIDE 22
  • P. Scardi – Dif f raction f rom nanocrystalline materials

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82

  • t oward an int egrat ion bet ween at omist ic modelling and dif f ract ion analysis:

plast ically def ormed nanocryst alline syst ems; grain boundary, line and planar def ect s

10 20 30 40 50 60 70 80 90 100 0,0 0,5 1,0 1,5 2,0 2,5

Intensity (a.u.) 2θ (degrees)

10 20 30 40 50 60 70 80 90 100 0.01 0.1 1

Intensity (a.u.) 2θ (degrees)

DI FFRACTI ON FROM NANOCRYSTALLI NE MATERI ALS

Current research / f ut ure t rends

20 30 40 50 60 70 80 90 100 110 120 5000 10000 15000 20000

20 30 40 50 60 70 80 90 100 110 120 1 10 100 1000 10000

Intensity Q = 4πsinθ/λ (nm

  • 1)

20 30 40 50 60 70 80 90 100 110 120

  • 1000

1000 Residual

Intensity Q = 4πsinθ/λ (nm

  • 1)
  • A. Leonar di & P. Scar di, Met . Mat .Tr ans A (2015). I n pr ess
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  • P. Scardi – Dif f raction f rom nanocrystalline materials

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GENERAL REFERENCES

B.E. Warren, X-ray Dif f ract ion, Addison-Wesley, Reading, MA, 1969.

  • A. Guinier, X-ray Dif f ract ion, Freeman & Co, S. Francisco, 1963.

A.J .C. Wilson, X-ray Opt ics, 2nd ed., Met huen & Co, London, 1962. H.P. Klug & L.E. Alexander, X-ray Dif f ract ion procedures, Wiley, New York, 1974. B.D. Cullit y, Element s of X-ray Dif f ract ion, Addison-Wesley, Reading Ma, 1978.

Powder Dif f ract ion: Theory and Pract ice R.E. Dinnebier & S.J .L. Billinge, edit ors. Cambridge: Royal Societ y of Chemist ry, 2008.

  • P. Scardi, Chapt er 13 on Line Prof ile Analysis:
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  • P. Scardi – Dif f raction f rom nanocrystalline materials

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REFERENCES - Paolo.Scardi@unit n.it

Ext ending t he Reach of Powder Dif f ract ion Modelling by User Def ined Macros

  • P. Scardi & R. E. Dinnebier, edit ors

A special issue of Mat erials Science Forum, 2010. Dif f ract ion Analysis of Mat erials Microst ruct ure E.J . Mit t emeij er & P. Scardi, edit ors. Berlin: Springer-Verlag, 2004. Synchrot ron Radiat ion. Basics, Met hods and Applicat ions

  • S. Mobilio, F. Boscherini, C. Meneghini, edit ors.

Springer-Verlag, 2015

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  • P. Scardi – Dif f raction f rom nanocrystalline materials

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REFERENCES - Paolo.Scardi@unit n.it

St at e-of -t he-art Line Prof ile Analysis based on Whole Powder Pat t ern Modelling The Debye Scat t ering Equat ion f or st udying st at ic and dynamic disorder in nanocryst als

doi: 10.1038/srep20712 (2016) doi: 10.1038/srep22221 (2016)

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SLIDE 26

X-ray Dif f ract ion

  • Paolo. Scardi@unitn. it

per aspera ad ast ra