Small Angle X-Ray Scattering From bulk to thin films

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1 Small Angle X-Ray Scattering From bulk to thin films Stephan V. Roth SAXS DESY summer school Hamburg,

The four-fold way > Main purpose and focus Appl. Phys. Lett. 104, 243107 (2014) Rev. Sci.

Sci. Instr. 84, 043901 (2013) Langmuir 29, 11260 (2013) J. Synchr, Rad.

2 The four-fold way > Main purpose and focus Appl. Phys. Lett. 104, (2014) Rev. Sci. Instr. 85, (2014) Nanoscale 5, 5053 (2013) J. Phys. Chem. Lett 4, 3170 (2013) Rev. Sci. Instr. 84, (2013) Langmuir 29, (2013) J. Synchr, Rad. 19, 647 (2012) Langmuir 28, 8230 (2012) Appl. Phys. Lett 88, (2006) Stephan V. Roth SAXS Lecture Page 2

3 Aim > To understand the structure property relation of materials on multiple length scales - q-resolution - Maximum q-value - Beam size - Real pieces & materials - Model systems - Nanotechnology GE-Gas-Turbine-Technology-Selectedfor-Pearl-GTL-Project-in-Qatar Courtesy: R. Gilles (TUM) Stephan V. Roth SAXS Lecture Page 3

4 Outline > SAXS Introduction > Instrumentation Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter. Eds: P. Lindner, Th. Zemb. North Holland Delta Series, Elsevier, Amsterdam (2002) ISBN: PETRA III > Bulk materials Transmission U/SAXS: Porous materials Ni-base superalloys Droplet drying > Thin films Grazing incidence SAXS : A Primer Nanostructuring by annealing Spray coating Sputter deposition Stephan V. Roth SAXS Lecture Page 4

5 Cross-section > Differential cross section Detector I Ω 2 I 0 k f L 2 k i Q d Ω Σ Ω 1 σ Ω V=Sample volume - k f k i sin > Scattering occurs due to density differences Stephan V. Roth SAXS Lecture Page 5

6 WAXS, SAXS, GISAXS Source: Streumethoden zur Untersuchung kondensierter Materie 1996; ISBN Limit Guinier Porod Bragg SAXS WAXS WAXS: Crystal structure d / resolution [Å] SAXS/GISAXS: density fluctuations, precipitates Log I q) q x d= =1nm =1µm =10µm qx R=1 Log q > R~particles radius > d~interatomic distance > SAXS: < 5 2 sin 1.54Å d R Stephan V. Roth SAXS Lecture Page 6

7 Scattering amplitude > Interference in far field ( r ), V, V P k f q 2 kf I 0, A( r ) A 0 e ikr ( r i )dv r i 2 k i 4 sin k f k 2 ˆ i e i > Phase difference: > Scattering amplitude: > Intensity: 0 Δ 3 = 2 Stephan V. Roth SAXS Lecture Page 7

8 Form factor and structure factor: Fourier transform p (r ) Single particle: Fourier transformation 3 Particle distribution function G(r) Electron density distribution 3 Scattering amplitudes of the whole arrangement ] 3 i Scattered Intensity = 2 r i Form factor Structure factor Stephan V. Roth SAXS Lecture Page 8

9 Two-phase model: Dilute systems > Only form of particle relevant > Matrix M, volume fraction Particles P, volume fraction (1- ) Electron density: M,P n M,P *f M,P f M,P : atomic form factor ( extension of the electron cloud, resonances) n M,P : number density of atoms > Consider as constant 2R 2R 2R >> R Stephan V. Roth SAXS Lecture Page 9

10 Two phase Model > Scattering amplitude: 3 = 3 3 Δ 3 3 > = 2 > Porod Invariant Q (Porod, 1982): Q 3 4 Φ 1 Φ Δ 2 > Only dependent on density contrast Stephan V. Roth SAXS Lecture Page 10

11 Two phase Model single particle approximation > Amplitude: Δ 3 > Intensity: = 2 > Closer look at I q for dilute systems: N P independent scatterers > Incoherent sum of intensities: ~ Δ R 2R Δ n P f P n M f M r n M f M = M n P f P = P Stephan V. Roth SAXS Lecture Page 11

12 Two phase Model single particle approximation > Amplitude: Δ 3 > Intensity: = 2 > Closer look at I q for dilute systems: N P independent scatterers > Incoherent sum of intensities: ~ Δ P( q) sin( qr) qr cos( qr) 3 3 ( qr) 2 - Form factor of a sphere of radius R - Isotropic scattering Stephan V. Roth SAXS Lecture Page 12

13 Colloid: homogeneous sphere of radius R P qr P qr qr qr Stephan V. Roth SAXS Lecture Page 13

14 Guinier radius > Q 0 > Homogenous sphere of radius R sin 3 3 ~ ~exp > Radius of gyration: replace homogenous sphere by shell of same moment of intertia: R g > > ~exp 1 general form of Guinier law [Guinier (1955)] > Independent of particle form Stephan V. Roth SAXS Lecture Page 14

R g 3/ 5 R 2nm Colloids domains Roth et al., Appl. Phys. Lett.

15 Guinier Approximation I(q) qr lim I( q) q 0 2 V 2 exp( q 2 R 2 g 3 ) Radius of Gyration R g Monodisperse spheres of radius R: R g 3/ 5 R 2nm Colloids domains Roth et al., Appl. Phys. Lett. 91, (2007) Stephan V. Roth SAXS Lecture Page 15

16 Porod s Law I qr log I [a.u.] SAXS q^-4 q^-4 USAX qr log q [nm-1] qr R>1µm R~18nm > Depends only on Surface and particle Volume > No shape dependance Stephan V. Roth SAXS Lecture Page 16

The structure factor many particles, close distance > Real systems: not dilute, many particles > Generalisation of Bragg s Law in crystallography: I q c P q S q Form factor Structure factor 2R

17 The structure factor many particles, close distance > Real systems: not dilute, many particles > Generalisation of Bragg s Law in crystallography: I q c P q S q Form factor Structure factor 2R Interference due to assembly of particles D max, > Periodic ordering with periodicity d, in the electron density : > I q shows a corresponding maximum at q 2 /(D max, ) Smearing Lode (1998) Roth et al., J. Appl. Cryst. 36, 684 (2003) Distance of particles Stephan V. Roth SAXS Lecture Page 17

18 The structure factor many particles, close distance > Real systems: not dilute, many particles > Generalisation of Bragg s Law in crystallography: I q c P q S q > Examples: R=5nm, D max =100nm, 25nm, D/D max =25% I q Low P q, S q 1 High S q P q q nm 1 q nm 1 Stephan V. Roth SAXS Lecture Page 18

Shift in maximum: Decreasing distance Hu et al.

19 Colloidal systems > Latex spheres in water I q c P q S q Low High P q, S q 1 S q P q > Gaussian distribution of particle sizes > Shift in maximum: Decreasing distance Hu et al., Macromolecules, 41, 5073 (2008) q [nm -1 ] Stephan V. Roth SAXS Lecture Page 19

20 Illustration > USAXS at photonic crystals > USAXS in highly concentrated colloidal suspensions Beamstop 270 nm onic_table.html Stephan V. Roth SAXS Lecture Page 20

21 Outline > SAXS Introduction > Instrumentation PETRA III > Bulk materials Transmission U/SAXS: Porous materials Ni-base superalloys Droplet drying > Thin films Grazing incidence SAXS : A Primer Nanostructuring by annealing Spray coating Sputter deposition Stephan V. Roth SAXS Lecture Page 21

22 SAXS collimation and scattering geometry Detector Collimating Slit 2 Collimating Slit 1 bs min L SD Sample L SD determines resolution min =bs / (2 L SD ) Use Bragg s law: d max = min Stephan V. Roth SAXS Lecture Page 22

4m Det 42x20µm 2 > Nanofocus end station: 32x23µm 2 <1.5x1.5µm 2 500x500nm 2 Krywka, SVR et al., J. of Appl. Cryst.

23 Layout Different µfocussing schemes > Flexible choice of beam size and divergence > Fixed focal spot position and size E=13keV 22x12µm 2 E=15keV 24x17µm 2 > Full user operation within design values! CRL System 1 CRL System 2 ~5x10 11 Ph/sec 76.7m 85m 81.7m 86.4m Det 42x20µm 2 > Nanofocus end station: 32x23µm 2 <1.5x1.5µm 2 500x500nm 2 Krywka, SVR et al., J. of Appl. Cryst. 45, 85 (2012) 22x12µm 2 8x8µm 2 <2x2µm 2 Roth et al., J. Phys.: Cond. Matter 23, (2011) Buffet, SVR et al., J. Synchr. Rad., 19, 647 (2012) Stephan V. Roth SAXS Lecture Page 23

24 Rapid Change (GI)SAXS / (GI)WAXS 2012 > Adjust scattering angles dω q-ranges > 5cm<D SD <8.6m > Highly flexible > Separate WAXS device Stephan V. Roth SAXS Lecture Page 24

25 µusaxs focus > Beam size: 32x23µm 2 > SDD=8470mm > N 2 =12 > PS particles: 400nm Dried on glass slide t acq =1s background corrected Stephan V. Roth SAXS Lecture Page 25

26 Outline > SAXS Introduction > Instrumentation PETRA III > Bulk materials Transmission U/SAXS: Porous materials Ni-base superalloys Droplet drying > Thin films Grazing incidence SAXS : A Primer Nanostructuring by annealing Spray coating Sputter deposition Stephan V. Roth SAXS Lecture Page 26

$Aerogels > Highly porous materials: OLED: matching of refractive indices molecular sieves sensors > Challenges Generation of$

27 Aerogels > Highly porous materials: OLED: matching of refractive indices molecular sieves sensors > Challenges Generation of pores with dimensions greater than 100 nm, yet submicron Characterization of size Stephan V. Roth SAXS Lecture Page 27

28 Quantitative analysis > Bimodal distribution particles > Δ > Porod law: Particle size ~ 30nm Pore size estimate >1300nm Stephan V. Roth SAXS Lecture Page 28 Eggers, SVR et al., Langmuir 24, 5887 (2008)

29 Outline > SAXS Introduction > Instrumentation PETRA III > Bulk materials Transmission U/SAXS: Porous materials Ni-base superalloys Droplet drying > Thin films Grazing incidence SAXS : A Primer Nanostructuring by annealing Spray coating Sputter deposition Stephan V. Roth SAXS Lecture Page 29

1Mo) > Ni-Al solid solution Matrix ( ), fcc > Precipitates ( Al, ), Ni 3

30 Ni-base superalloys Ni-base superalloys > Ni-base W-rich experimental single crystal superalloy (Ni-4.6Al-6.4Ta-5.7Cr-10.8W-2.1Mo) > Ni-Al solid solution Matrix ( ), fcc > Precipitates ( Al, ), Ni 3 (Al,Ti) > TEM: -precipitates R > 50 nm > D > 100 nm Stephan V. Roth SAXS Lecture Page 30

ID2 0.275 nm -1 Fit noc_4: P. Strunz et al., J. Appl. Cryst.

round edges D max =(139± 59) nm R = 52 nm (consistent with TEM)

] 10000 1,00E+05 1000 1,00E+04 100 1,00E+03 10 1,00E+02 1 Beam: 100 m

31 ID nm -1 Fit noc_4: P. Strunz et al., J. Appl. Cryst. 36, 854 (2003) Courtesy: Gilles Strunz Only phase visible : cuboids, round edges D max =(139± 59) nm R = 52 nm (consistent with TEM) Intensity [a.u.] ,00E ,00E ,00E ,00E+02 1 Beam: 100 m resolution form factor Structure factor Maximum Stephan V. Roth SAXS Lecture Page 31 q [nm -1 ] 1,00E+01 1,00E-02 1,00E-01 1,00E

32 Local precipate morphology µsaxs [320] [320] [100] R. Gilles et al. Scripta Mat. 39, 715 (1998) > phase precipitate: embrittlement of alloy crack formation and propagation - streaking: correct orientation - phase: stack - distance 5-15 m diameter 2R < 10 m thickness t > O(100 nm) y = 5 m k 0 [001] Stephan V. Roth SAXS Lecture Page 32-1 z = 5 m Q=1.5 nm

33 Microfocus: local - particle size distribution Roth et al., Nucl. Instr. Meth. B 200, 255 (2003) Porod-law Q -4 SAXS: TEM: USAXS: R > 55 nm R 50 nm R = 52 nm I [a.u.] resolution Q [nm -1 ] Lower minimum of particle size distribution Stephan V. Roth SAXS Lecture Page 33

34 Outline > SAXS Introduction > Instrumentation PETRA III > Bulk materials Transmission U/SAXS: Porous materials Ni-base superalloys Droplet drying > Thin films Grazing incidence SAXS : A Primer Nanostructuring by annealing Spray coating Sputter deposition Stephan V. Roth SAXS Lecture Page 34

The drying droplet > Self-organisation: attractive capillary forces > correlated nano-structures > industrial processes spray drying (see also GISAXS

35 The drying droplet > Self-organisation: attractive capillary forces > correlated nano-structures > industrial processes spray drying (see also GISAXS part) food processing, pharmaceuticals Paintings/coatings Stephan V. Roth SAXS Lecture Page 35

Porod Invariant - practical application > Colloidal solution: drying thick droplet 1mm > Evaporation of water: Irradiated volume becomes smaller: shrinking Distance of

36 Porod Invariant - practical application > Colloidal solution: drying thick droplet 1mm > Evaporation of water: Irradiated volume becomes smaller: shrinking Distance of colloidal partices decreases, 1 increases (air!), as water removed from interstitial sites Chen et al., Soft Matter 8, (2012) Stephan V. Roth SAXS Lecture Page 36

The drying droplet > Microbeam: local concentration of colloids > Q~ (1 )( R x ) 2 2 0.

37 The drying droplet > Microbeam: local concentration of colloids > Q~ (1 )( R x ) > Dried droplet: different gradient in > Homogenous distribution > Agglomeration in shell > Continuous gradient Sen, SVR et al., Soft Matter 10, 1621 (2014) Stephan V. Roth SAXS Lecture Page 37

38 The drying droplet part 2 > Slow / fast drying > Concentration of colloids: Arresting of colloids Homogenous Core shell effect ( coffee ring ) > Follow concentration profile in-situ Porod invariant (arb. unit) Experiment Model X (mm) Q~ (1 )( R x ) a Porod invariant (arb. unit) Experimental Model X (mm) b Sen, SVR et al., Soft Matter 10, 1621 (2014) Stephan V. Roth SAXS Lecture Page 38

39 Outline > SAXS Introduction > Instrumentation PETRA III > Bulk materials Transmission U/SAXS: Porous materials Ni-base superalloys Droplet drying > Thin films Grazing incidence SAXS : A Primer Nanostructuring by annealing Spray coating Sputter deposition Stephan V. Roth SAXS Lecture Page 39

$y z Sample horizon Refracted pattern BS q y Stephan V. Roth SAXS Lecture 14.8.$

40 Grazing incidence small-angle x-ray scattering q z Reflected pattern SBS Y( i,f = c ) x y z Sample horizon Refracted pattern BS q y Stephan V. Roth SAXS Lecture Page 40

41 T-SAXS vs. GISAXS z y x 2 q z q y q x Beamstop i z y x f 2 q z q y q x i Si f - Easy measurement - Easy analysis - In-plane information (q y,q z ) - Any possible scattering from substrate - Transparency of substrate - High energy Lee et al., Macromolecules, 38, 8991 (2005) 2 - Strong intensity - Easy preparation of samples - Full information (q x,q y,q z ) - Scattering from surface / internal structure - Scattering from reflected AND transmitted beam - Refraction effects (DWBA) Stephan V. Roth SAXS Lecture Page 41

42 GISAXS: Tuning of penetration depth > Scattering depth: ² ² ² ² ² i z y x f 2 q z q y q x > Tune depth sensitivity Lee et al., Macromolecules, 38, 8991 (2005) 2 - Strong intensity - Easy preparation of samples - Full information (q x,q y,q z ) - Scattering from surface / internal structure - Scattering from reflected AND transmitted beam - Refraction effects (DWBA) Stephan V. Roth SAXS Lecture Page 42

43 Total reflection Yoneda peak > Refractive Index for X-rays 1 Real part: 1 1 ; N = Number density of atoms, Z = Atomic number Imaginary Part: > Snell s Law / Total reflection: 2 ~ > Maximum of the Fresnel transmission function > Electrical field on surface: 2xE i > Increased scattering at surface > Yoneda peak [Yoneda, 1963] Occurs when, > Material sensitive Renaud et al., Surf. Sci. Rep. 64, 255 (2009) Stephan V. Roth SAXS Lecture Page 43

44 Theory > k f Courtesy: R. Lazzari (U Paris VI/VII) Stephan V. Roth SAXS Lecture Page 44

pair correlation function 2) Regular bidimensional lattice 3) Bidimensional paracrystal

45 Theory - Simulation > * Particle form factor: multiple scattering DWBA Shape, Size, Orientation, Distribution Interference function Three main cases 1) Disordered lattice - pair correlation function 2) Regular bidimensional lattice 3) Bidimensional paracrystal Courtesy: R. Lazzari (U Paris VI/VII) Manual IsGISAXS Stephan V. Roth SAXS Lecture Page 45

46 Grazing incidence small-angle x-ray scattering cos cos 2Θ cos 2 cos sin 2Θ sin beamstop Stephan V. Roth SAXS Lecture Page 46 Mueller-Buschbaum, Anal. Bioanal. 376, 3 (2003)

47 GISAXS A Primer cut at constant cut at constant f c q z [nm -1 ] q y [nm -1 ] Correlation perpendicular to surface, e.g. height of clusters, roughness, layer thickness H 2R In-plane structures, e.g. distances D, Radius R D q z =2 / sin ( i + f ) q y =2 / sin(2 )cos( f ) Salditt et al.; Phys.Rev.B 51, 5617 (1995) Naudon et al.; Physica B, 283, 69 (2000) Renaud et al.; Science, 300, 1416 (2003) Stephan V. Roth SAXS Lecture Page 47

48 Outline > SAXS Introduction > Instrumentation PETRA III > Bulk materials Transmission U/SAXS: Porous materials Ni-base superalloys Droplet drying > Thin films Grazing incidence SAXS : A Primer Nanostructuring by annealing Spray coating Sputter deposition Stephan V. Roth SAXS Lecture Page 48

49 Annealing > Au on glass > Parameters: Au layer mass thickness: 3nm, 5nm, 8nm Annealing time approaching critical coalescence thickness (cluster -> metal character) 0min 10min 20min 1h 3h 7h 24h Log (Annealing T anneal =300 C < 1064 C (bulk melting point) Stephan V. Roth SAXS Lecture Page 49

[a.u.] p p 400 600 800 Wavelength [nm] J.C. Hulteen et al., J Phys.

50 Plasmon resonance Optical properties: sharp resonances plasmon resonances (visible light) cluster arrangement & shape Absorption [a.u.] p p Wavelength [nm] J.C. Hulteen et al., J Phys. Chem. B 101, 7727 (1997) Stephan V. Roth SAXS Lecture Page 50

51 Surface coverage > Thickness Au 8nm Annealing time Roth et al., "Gold nanoparticle thin films on glass: Influence of film thickness and annealing time", in: "Synchrotron Radiation and Structural Proteomics", Pan Stanford Series on Nanobiotechnology - Volume 2, Eds.: E. Pechkova and C. Riekel (2010) glass i + f c (Au) 7h 24h 3h 1h 20min 10min 0min Stephan V. Roth SAXS Lecture Page 51

52 Cluster distance high 8nm =2 /q 5nm low 3nm low glass T=RT, 0min glass T=T anneal, 0min < t 1h high Stephan V. Roth SAXS Lecture Page 52 glass T=T anneal, t>1h

53 Outline > SAXS Introduction > Instrumentation PETRA III > Bulk materials Transmission U/SAXS: Porous materials Ni-base superalloys Droplet drying > Thin films Grazing incidence SAXS : A Primer Nanostructuring by annealing Spray coating Sputter deposition Stephan V. Roth SAXS Lecture Page 53

, Langmuir 29, 11260 (2013) Sarkar, SVR et al.

54 In-situ spray deposition > In-situ setup Al-Hussein, SVR et al., Langmuir 29, 2490 (2013) Herzog, SVR, et al., Langmuir 29, (2013) Sarkar, SVR et al., ChemSusChem 6, 1414 (2014) Buffet, SVR et al., Adv. Eng. Mater. 12, 1235 (2010) Stephan V. Roth SAXS Lecture Page 54

, Langmuir 29, 2490 (2013) Perlich, SVR et al.

55 Time-resolved: Optical vs. X-ray > Standard camera > 5 Hz > PILATUS 300k > 10 Hz > Correlation between nanostructure build-up and optical investigation Al-Hussein, SVR et al., Langmuir 29, 2490 (2013) Perlich, SVR et al., in preparation (2013) Herzog, SVR, et al., Langmuir 29, (2013) Stephan V. Roth SAXS Lecture Page 55

56 Colloidal crystals by spray deposition > Multi-stage self-assembly process Herzog, SVR, et al., Langmuir 29, (2013) Stephan V. Roth SAXS Lecture Page 56

57 Outline > SAXS Introduction > Instrumentation PETRA III > Bulk materials Transmission U/SAXS: Porous materials Ni-base superalloys Droplet drying > Thin films Grazing incidence SAXS : A Primer Nanostructuring by annealing Spray coating Sputter deposition Stephan V. Roth SAXS Lecture Page 57

58 Geometry Schwartzkopf, SVR et al., Nanoscale 5, 5053 (2013) > Au on Si (hard substrate) > In-plane structure: q y cut > Out-of-plane structures: q z cut > ~10000 images in 3min > =67fps Stephan V. Roth SAXS Lecture Page 58

distribution S(Q): Distance, distribution, smearing

59 GISAXS results - simulations > From the data to the model and vice-versa > Put in P(Q): Radius, height, shape, distribution S(Q): Distance, distribution, smearing Wavelength, incident angle, Stephan V. Roth SAXS Lecture Page 59

60 GISAXS results - simulations > Watch the film grow > Extract thin film parameters Stephan V. Roth SAXS Lecture Page 60

61 Contact angle > Cluster shape on the nanoscale: wetting > Example: =6.3nm > Try different shapes Stephan V. Roth SAXS Lecture Page 61

62 Towards OLEDs > Soft substrate: small molecule > Used for OLEDs > Al on Alq3 > Observe creation of doping layer Yu, SVR et al., J. Phys. Chem. Lett. 4, 3170 (2013) Stephan V. Roth SAXS Lecture Page 62

4 layer model solar cell production cycle > Preservation of morphology of a self-encapsulated thin titania film Au PEDOT:PSS P3HT Dye Titania > Self-assembly, dip-,

63 4 layer model solar cell production cycle > Preservation of morphology of a self-encapsulated thin titania film Au PEDOT:PSS P3HT Dye Titania > Self-assembly, dip-, spin-, sputter-, spray-coating, fluidic, vacuum deposition Perlich, SVR, Müller-Buschbaum et al., ChemPhysChem 10, 799 (2009) Stephan V. Roth SAXS Lecture Page 63

64 Summary > SAXS > Basics: Porod, Guinier > Extremely versatile method > All areas of materials science Turbine blades Colloids, OE Thin films and surfaces > In-situ & real-time Stephan V. Roth SAXS Lecture Page 64

Methoden moderner Röntgenphysik II Streuung und Abbildung

Methoden moderner Röntgenphysik II Streuung und Abbildung Stephan V. Roth DESY 5.6.14 Two phase Model single particle approximation > Amplitude: Δ 3 > Intensity: = > Closer look at Iq for dilute systems: