Methoden moderner Röntgenphysik II: Struktur und Dynamik kondensierter Materie

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1 Methoden moderner Röntgenphysik II: Struktur und Dynamik kondensierter Materie Vorlesung zum Haupt/Masterstudiengang Physik SS 2011 G. Grübel, M. Martins, E. Weckert et al. SemRm3, Physik, Jungiusstrasse Di: 14:00-15:30 Do: 11:20-12:50 S. Roth (SR) , & finden statt fällt aus 1

2 Summary last lecture Approximations for Form factor: Very useful to get first-hand information about multiple length scales Influence of form factor (concentrated samples) Examples: Colloidal crystals Cracks & crazes I(q) Guinier 1 2 I( q) I(0) exp RGq 3 = 2 Porod s law ~q -4 qr 2

3 Outline SAXS versus GISAXS GISAXS theory Instrumentation Application examples: - Gold on glass - in-situ growth of colloidal crystals - Polymer nanochannels It is important to understand the basic features of the different GISAXS pattern and cuts. 3

4 T-SAXS vs. GISAXS z y 2θ x q z q y q x Beamstop α i z y x α f 2θ q z q y q x Si Lee et al., Macromolecules, 38, 8991 (2005) 4 - Easy measurement - Easy analysis - In-plane information (q y,q z ) - Any possible scattering from substrate - Transparency of substrate - High energy 2θ - 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) - Special setup

5 Surface sensitivity Scattering depth of x-rays: Λ = λ 2π 1 ( 2 2 ) 2 2 ( 2 2 α α + 4β α α ) i c i c α i Λ Vary incident angle α i < α c to probe surface near region only or penetrate large sample volume 5

6 History 1963 Yoneda anomalous Scattering below α i 1988 Sinha rough multilayers 1989 Levine kinetics of gold nanoparticles on glass 1996 Müller-Buschbaum mesoscopic length scales in polymer films 2003 Müller-Buschbaum combination with µfocused beams Since 2006 going nano PETRA III BW4, CCD Au d=5nm t=3h T=300 C 6

7 Outline SAXS versus GISAXS GISAXS theory Instrumentation Application examples: - Gold on glass - in-situ growth of colloidal crystals - Polymer nanochannels 7

8 Grazing incidence small-angle x-ray scattering q z Reflected pattern SBS Y(α i,f =α c ) x y z Sample horizon BS q y 2θ α f α i <1 Refracted pattern 8

9 History 1963 Yoneda anomalous Scattering below α i 1988 Sinha rough multilayers 1989 Levine kinetics of gold nanoparticles on glass 1996 Müller-Buschbaum mesoscopic length scales in polymer films 2003 Müller-Buschbaum combination with µfocused beams Since 2006 going nano PETRA III 9

10 Snell s law The first sucessful experiment α i Specular peak α f =α i A.S.R. Anomalous Surface Reflection (diffuse scattering) Au, 20nm-200nm Si Intensity between α f =0 and α f =α i!!! Why? Yoneda, Phys. Rev. 131, 2010 (1963) 10

11 Refractive index for x-rays n =1 δ + iβ real part δ = 2 λ 2π r 0 { NZ ρ e Number density of atoms Atomic number imaginary part wavelength Absorption coefficient β = λ 4π μ e μ x (Lambert-Beers law) 7 6 λ 1Å δ ~ Very small! α c (Si)=0.2 α c (Au)=0.5 Matter: n(x-rays) <1 optically less dense than vacuum (remember Bragg s law) 11

12 Origin of intensity at α c α i Au, 20nm-200nm α f =α i α f =α c α i =α c Total external reflection α f =0 Si α f (Au) = 0.56 = α c (Au,1.8Å) Reciprocity theorem & critical angle α i =0 α f =α c must stem from wave parallel to surface Yoneda α i >0 α f =α c Yoneda, Phys. Rev. 131, 2010 (1963) 12

13 Hint: Roughness of the sample Yoneda peak = Scattering effect! Etching of SiO 2 with HF 13

14 Basically the same 1963 today α i α i,t Snell s law A.S.R. =Yoneda peak S α i =α f Specular peak 14

15 µgisaxs more details Grazing Incidence Small Angle X-Ray Scattering, GISAXS q z =2π/λ sin(α i +α f ) q y =2π/λ sin(2θ)cos(α f ) q x =2π/λ (cos(α f )-cos(α i )) L SD 2D Detector q z z Specular beam Yoneda peak(s) α f =α c α i α f 2θ q y L SD determines resolution! y 15

16 Grazing incidence small-angle x-ray scattering cut at constant θ cut at constant α f Yon, α c Log intensity q z SBS Log intensity SBS q y 16 Correlation perpendicular to surface, e.g. height of nanoparticles, roughness, layer thickness Detector-scan Salditt et al., Phys.Rev.B 51, 5617 (1995) Naudon et al., Physica B, 283, 69 (2000) Renaud et al., Science, 300, 1416 (2003) Müller-Buschbaum, Anal. Bioanal. Chem 376, 3 (2003) H ξ 2R In-plane structures, e.g. distances ξ, Radius R Out-of-plane scan

17 Distorted Wave Born approximation Form factor: multiple scattering Term 1 Term 2 Term 3 Term 4 k i k i α i α f dσ dω P( qy, k fz kiz ) + R( αi ) P( qy, k fz + kiz ) + R( α f ) P( qy, k fz kiz ) + R( αi ) R( α f ) P( qy, k fz + kiz ) r rr Born term with P( q) = exp( iqr ) d V 3 r 2 Coherent interference between four waves along α f Cross section depends on qy and qz Weighting with the reflection coefficients in incidence and emergence 17

18 Now for surfaces (nanoparticles) I(q y,q z )= c P(q y,q z ) 2 x S(q y ) Form factor: multiple scattering Interference function S(q y )=FT(pair correlation function) Spatial arrangement of the particles Shape, size and orientation lattice cylinder pyramid paracrystal ellipsoid + size distributions + mean distance + fluctuation of distances 18

19 Simulations: IsGISAXS (R. Lazzari) I(q y,q z )= c P(q y,q z ) 2 x S(q y ) P(q) 19

20 Outline SAXS versus GISAXS GISAXS theory Instrumentation Application examples: - Gold on glass - in-situ growth of colloidal crystals - Polymer nanochannels 20

21 BW4 / HASYLAB (Hamburg, Germany) L SD ~1m-13m L SD 21

22 ID13 / ESRF (Grenoble, France) Mean information local information Combination of GISAXS with micro-focus beam L SD ~1m Beamstop Microscope Sample Flight tube 2D-goniometer 5 μm collimator+ aperture X-ray Rotation axis x/y/z-stage diameter of micro beam GISAXS experiment at ID13 (ESRF) 5μm footprint (x/y) 300 x 5 μm 2 local information 22

23 GISAXS & GIUSAXS combination of GIUSAXS and GISAXS experiment: GIUSAXS: sample-detector distance 12.8 m GISAXS: 1.9 m 23

24 Outline SAXS versus GISAXS GISAXS theory Instrumentation Application examples: - Gold on glass - in-situ growth of colloidal crystals - Polymer nanochannels 24

25 Tempering Au nanoparticles Optical properties: sharp resonances (visible light) < > plasmon resonances cluster arrangement & shape Absorption [a.u.] λ p λ p Wavelength [nm] J.C. Hulteen et al., J Phys. Chem. B 101, 7727 (1997) 25

26 Annealing S.V.R., H. Walter (CSEM), R. Domnick (identif) et al., (in preparation) 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) 26

27 Surface coverage Detector scan (8nm) SBS q z Y(Au) q y glass α c (Au) Annealing time 7h 24h 3h 1h 20min 10min 0min 27

28 In-plane ordering Out-of-plane scan (8nm) ξ=2π/q q z q y 28

29 Lateral length scales Out-of-plane scan (8nm) ξ=2π/q ξ high 8nm 5nm ξ lo w 3nm ξ low glass T=RT, 0min glass T=T anneal, 0min < t 1h ξ high 29 glass T=T anneal, t>1h

30 Outline SAXS versus GISAXS GISAXS theory Instrumentation Application examples: - Gold on glass - in-situ growth of colloidal crystals - Polymer nanochannels 30

31 In-situ nanostructuring from solution Circuits, solar cells -> printing: electrodes, cost reduction Evaporation of solvent olar.com Decreased temperature Govor et al., PRE 69, (2004) Capillary forces / dewetting Increased nanoparticle concentration Convective flow Control drying-up of colloidal solution layer during inkjet printing Critical step: Transfer of order to substrate 31

32 Real-time results: nanogisaxs/ ID13 ESRF time 2nm Au spheres in water Slow evaporation time 300nm beam by Fresnel Zone plates 25µl First nanobeam in-situ GISAXS t=0s y 100µm x x-ray Droplet Si 32 Roth et al., Appl. Phys. Lett. 91, (2007)

33 Real-time results: nanogisaxs/ ID13 ESRF Domain building: Strong intensity increase before occurence of Bragg peaks! Bragg peaks 33 Roth et al., Appl. Phys. Lett. 91, (2007)

34 Guinier Approximation I(q) lim I( q) q 0 2 = Δρ V 2 exp( q 2 R 2 g 3 ) Radius of Gyration R g Monodisperse spheres of radius R=2nm: R g = 3 / 5 R = 1. 55nm q [nm -1 ] 2nm Colloids domains Very useful to get a hand on length scales! Sometimes only valid in limited q-range 34

35 Real-time results: nanogisaxs/ ID13 ESRF Colloidal solution 2nm Au in water t L (a) t<0s t 0.32±0.06 (b) t=0s Domains: Guinier law t L =0s Non-diffusive behaviour Height growth: Bragg peaks t>>0s 35 Roth et al., Appl. Phys. Lett. 91, (2007)

36 Outline SAXS versus GISAXS GISAXS theory Instrumentation Application examples: - Gold on glass - in-situ growth of colloidal crystals - Polymer nanochannels 36

37 BW4, GIUSAXS 13m, α i =0 Polymeric nanochannels ω d=7µm ω=6.4 37

38 α i =0 ω ω Zero order q y cosω +q x sinω = 0 In direction of d q x =2π/λ (cos(α f )-cos(α i )) q y + 2π/λ 1/2 α f2 / ω = 0 Calculate tilt angle ω 38

39 The End 39