X-Ray Scattering Studies of Thin Polymer Films

Transcription

1 X-Ray Scattering Studies of Thin Polymer Films Introduction to Neutron and X-Ray Scattering Sunil K. Sinha UCSD/LANL Acknowledgements: Prof. R.Pynn( Indiana U.) Prof. M.Tolan (U. Dortmund)

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3 Wilhelm Conrad Röntgen : Discovery of X-Rays

4 Nobel Prizes for Research with X-Rays 1901 W. C. Röntgen in Physics for the discovery of x-rays M. von Laue in Physics for x-ray diffraction from crystals W. H. Bragg and W. L. Bragg in Physics for crystal structure determination C. G. Barkla in Physics for characteristic radiation of elements K. M. G. Siegbahn in Physics for x-ray spectroscopy A. H. Compton in Physics for scattering of x-rays by electrons P. Debye in Chemistry for diffraction of x-rays and electrons in gases M. Perutz and J. Kendrew in Chemistry for the structure of hemoglobin J. Watson, M. Wilkins, and F. Crick in Medicine for the structure of DNA A. McLeod Cormack and G. Newbold Hounsfield in Medicine for computed axial tomography K. M. Siegbahn in Physics for high resolution electron spectroscopy H. Hauptman and J. Karle in Chemistry for direct methods to determine x-ray structures J. Deisenhofer, R. Huber, and H. Michel in Chemistry for the structures of proteins that are crucial to photosynthesis.

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6 Brightness & Fluxes for Neutron & X-Ray Sources Brightness de/e Divergence Flux ( s m ster ) (%) ( mrad ) ( s m ) Neutrons Rotating Anode Bending Magnet Undulator (APS)

7 Why Synchrotronradiation? Intensity!!!

8 Synchrotronand Neutron Scattering Places

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10 The photon also has wave and particle properties E=hν =hc/l= hck Charge = 0 Magnetic Moment = 0 Spin = 1 E (kev) λ (Å)

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16 d 2 Intrinsic Cross Section: Neutrons 0 Ω d const. b = = σ

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18 Intrinsic Cross Section: X-Rays m : radius) electron (classical Electron the of Length Scattering Thomson cos ) ( ), ( cos ) ( ) / ( ) / ( 4 ), ( i 0 in rad / i in 2 0 rad = = = = = mc e r R e r E t R E e E m e c R t x c R t x R c e t R E kr c R πε ψ ω α ψ ω α πε ω && && ) i( 0 in t r k e E E ω = r r r r E r rad

19 in rad ) ( ) cos (1 2 1 d d ) ( ) ( ) ( ), ( ω α ψ σ ψ ω α r R f P R r E t R E + = Ω Ω = = Intrinsic Cross Section: X-Rays 0 d d Ω σ ω r ω ηω ω ω ω ω α i ) ( 2 2 r 2 = Resonance Scattering ω r ω Thomson Scattering r 2 P 0 0 r d d = Ω >> σ ω ω 4 ω Rayleigh Scattering

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21 k k

22 Adding up phases at the detector of the wavelets scattered from all the scattering centers in the sample:

23 Wave vector transfer is defined as q = k f - k i

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26 X-rays dσ = r 02 [1 + Cos 2 (2θ)] S(q) dω 2 S(q) = Σ ij exp[-iq.(r i -r j )] {r i } == electron positions.

27 Now, Σ i exp[-iq.r i ] = ρ N (q) Fourier Transform of nuclear density [ sometimes also referred to as F(q) ] Proof: ρ N (r) = Σ i δ( r - R i ) ρ N (q) = ρ N (r) exp[-iq.r] dr = Σ i δ( r - R i ) exp[-iq.r] dr Similarly, = Σ i exp[-iq.r i ] Σ i exp[-iq.r i ] = ρ el (q) Fourier Transform of electron density So, for neutrons, S(q) = ρ N (q) ρ N* (q) And, for x-rays, S(q) = ρ el (q) ρ el* (q)

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48 q z q y q x

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61 X-Ray Scattering Scheme Scattering ~ Power Spectral Density I(q x,q y ) ~ S(q x,q y ) = FT ( C(X,Y) )

62 Scattering Geometry & Notation q x Reflectivity: q x = q y = 0 q z = (4π/λ π/λ)sinα i q q z k f k i Wave-Vector: q = k f k i

63 Reflection of Visible Light

64 Perfect & Imperfect Mirrors

65 Basic Equation: X-Rays Helmholtz-Equation & Boundary Conditions

66 Refractive Index: X-Rays & Neutrons + magnetic part + magnetic part Minus!! Dispersion Absorption

67 Refractive Index: X-Rays E = 8 kev λ = 1.54 Å Electron Density Profile!

68 Formal Solution Refractive Index of the sample n(x,y,z) n(x,y,z) = n(z) + δn(x,y,z) Refractive Index Profile Lateral Distortions Reflectivity Diffuse Scattering

69 X-Ray Reflectivity: Principle Visible Light Reflectivity: n 2 > 1 n 1 n 2 n 1 <n 2 X-Ray Reflectivity: n 2 < 1 n 1 n 2 n 1 >n 2

70 Total External Reflection cos α i = (1 δ) cos α t α t =0 Critical Angle: α c 2δ ~ 0.3 GRAZING ANGLES!!!

71 Single Interface: Vacuum/Matter Fresnel- Formulae Reflected Amplitude Transmitted Amplitude Wave- Vectors

72 Fresnel Reflectivity: R F (α i ) Total External Reflection Regime

73 The Master Formula Reformulation for Interfaces Fresnel-Reflectivity of the Substrate Electron Density Profile

74 Roughness Damps Reflectivity σ j = 10 Å λ = 1.54 Å

75 X-Ray Reflectivity: Water Surface Difference Experiment- Theory: Roughness!! Braslau et al. PRL 54, 114 (1985) Measurement Fresnel Reflectivity

76 Example: PS Film on Si/SiO 2 X-Ray Reflectivity (NSLS) λ = 1.19Å d = 109Å Data & Fit Density Profile

77 Calculation of Reflectivity Slicing of Density Profile Slicing & Parratt-Iteration ε ~ 1Å Reflectivity from Arbitrary Profiles! Drawback: Numerical Effort!

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80 Grazing-Incidence-Diffraction

81 X-Ray Reflectometers Laboratory Setup Synchrotron Setup HASYLAB: CEMO

82 Reflectivity from Liquids I Synchrotron Setup (APS)

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97 Photon Correlation Spectroscopy coherent beam sample detector X-ray speckle pattern from a static silica aerogel

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