Introduction to Reflectometry and Small Angle Scattering under Grazing Incidence

Mitglied der Helmholtz-Gemeinschaft Introduction to Reflectometry and Small Angle Scattering under Grazing Incidence E. Kentzinger Jülich Center for Neutron Science and Peter Grünberg Institut Jülich Research Center Laboratory course, September 2015

Plan Introduction: Nanoscience and Nanotechnology Method: Reflectivity, off-specular scattering and GISAS Specular reflectivity Measurement of neutron reflectivity Crystallography at mesoscopic length scales: GISAXS from a nanoparticle assembly on a surface Conclusion and outlook September 14, 2015 Folie 2

Biological membranes: Semi-permeable phospholipid bilayer Hydrophobic and hydrophilic components Source: http://www.ncnr.nist.gov/programs/reflect/cnbt/ Membrane proteins and other molecules in biomembranes Involved in cell signaling, cell adhesion, cells fusion and ion conductivity September 14, 2015 Folie 3

Magnetic thin films Ultra thin films Anisotropies at surfaces and interfaces Exchange bias Interlayer exchange coupling Giant magnetoresistance Tunnel magnetoresistance Sensor: The Giant Magneto-Resistance effect: New Field of science: Spintronics Nobel Prize 2007 September 14, 2015 Folie 4 A. Fert et al. (1988), P. Grünberg et al. (1989)

Self-organized magnetic nanoparticles for high density storage media S. Sun, C. Murray, D. Weller, L. Folks, A. Moser, Science 287, 1989 (2000) September 14, 2015 Folie 5

Specular reflectivity: flat surface Refraction: θ 1 < θ, if n 1 < n 0 typically n < 1 for neutrons and x-rays reflected beam θ θ θ 1 n 0 =1 n 1 <1 R = r 2 2 T = t transmitted beam c α i September 14, 2015 Folie 7 c α i

Specular reflectivity: layer on surface Interference between reflected beams according to path length difference reflected beam 2 n 0 =1 θ θ θ θ 1 θ 1 reflected beam 1 n 1 <1 θ 2 n 1 <n 2 <1 transmitted beam September 14, 2015 Folie 8

Offspecular scattering: rough interface Broken translational invariance à Off-specular (diffuse) scattering θ=α i θ α f >θ α f =θ θ 1 θ 1 θ 2 September 14, 2015 Folie 9

Reflectivity and off-specular scattering In-plane structure can be investigated by off-specular diffuse scattering: Q = k f k i, k = 2 / If α f = α i then Q = 0: specular reflectivity average over lateral coordinates If α f α i then Q 0: off-specular scattering lateral correlations can be probed September 14, 2015 Folie 10

The two scattering geometries (Grazing Incidence Small Angle Scattering) Q = k f k i Q = Q x Q y z k.(α k.ϕ k.(α 2 i i α + α 2 f f ) ϕ 2 )/2 typically: (neutrons!) September 14, 2015 Folie 11 2π /Qx 1 20 µm 2 π / Qy 1-300 nm

Wave equation in homogeneous medium. Schrödinger equation for the neutron wave function: Small Q values are probed; Potential of the homogeneous medium: Scattering length density: September 14, 2015 Folie 13

Optical index We receive: : wave vector in medium Index of refraction: is positive for most materials and of the order of 10-6 to 10-5 September 14, 2015 Folie 14

Solution for a sharp surface. Fresnel s formulas z General solution: Boundary conditions: l=0: vac. l=1: medium September 14, 2015 Folie 15

Solution for a sharp surface. Fresnel s formulas We receive: Reflectivity R and transmissivity T: Fresnel s formulas: September 14, 2015 Folie 16

Snell s law of refraction. Total external reflection Continuity of the wave vector components parallel to surface: Leads to Snell s law of refraction: Total external reflection for θ < θ c defined by: September 14, 2015 Folie 17

Total external reflection Normal components of the incoming and refracted wave vectors: Reflectivity and transmissivity: R = r 2 T = t 2 c α i Evanescent c α i Propagating wave September 14, 2015 Folie 18

Reflectivity from a layer on substrate Optical path length difference between beams reflected at surface and interface: Ni layer on Si substrate Distance between interference maxima: September 14, 2015 Folie 19

Reflectivity from a multilayer 10 Ni/Ti bilayers on Si ΔQ = 2π D ΔQ = 2π d September 14, 2015 Folie 20

Reflectivity from a supermirror FeCoV #100 TiN #100 FeCoV #99 FeCoV #3 TiN #3 FeCoV #2 TiN #2 FeCoV #1 TiN #1 Gd Glass nuclear sld. September 14, 2015 Folie 21

Reflectivity from a supermirror [FeCoV/TiN] 50 [FeCoV(6 nm)/tin(5.5 100 75 90 nm)] 50 With t FeCoV from 6 to 7.5 9.3 70 13 nm t Ti Ti from 5.5 to 12.6 6.5 7.6 9.2 nm September 14, 2015 Folie 22

Reflectivity from a supermirror: Application The S-shape supermirror-coated guide of KWS-3 @ JCNS Casemate wall (800 mm) Straight guide R=30m R=-30m Movable part of the ANSI shutter Trumpet α NL3 100 cm 1191 mm 2883 mm 3918 mm 2 mm to KWS-2 to KWS-1 to KWS-3 (10x50) mm 2 September 14, 2015 Folie 23

Roughness and interdiffusion z is a gaussian random variable with distribution function: Profile of refraction index between layers j and j+1: with: September 14, 2015 Folie 24

Roughness and interdiffusion Reflectivity from such a surface obtained by averaging: : root mean squared deviation from the nominal position of the interface Si substrate Ni on Si September 14, 2015 Folie 25

Monochromatic instrument Fixed λ, varying θ MARIA of the JCNS at FRM-II September 14, 2015 Folie 27 Courtesy of S. Mattauch, JCNS

Time-of-flight instrument Fixed θ, varying λ λ encoded by time of flight t over distance L: Magnetism reflectometer of the SNS: September 14, 2015 Folie 28 Courtesy of V. Lauter, ORNL

Resolution Aim: Maximize intensity on sample by relaxing resolution in Q Dispersion in wave vector transfer: 400 Å thick Ni layer on Si substrate (Monochromatic instrument) September 14, 2015 Folie 29

Crystallography at the nanoscale: GISAXS from nanoparticle assemblies Self assembled nanoparticles: materials with new functions In plane structure by surface sensitive techniques: SEM, AFM Full 3D structure by GISAXS S. Disch, E. Wetterskog et al. Nano Letters 11, 1651 (2011) September 14, 2015 Folie 31

In-plane 2D Structure 100 nm 5 nm Nanoparticles: Iron oxide Single crystalline Truncated cubes Mesocrystals: Obtained by solvent evaporation in magnetic field Height: 300 nm Lateral: µm s 10 µm Square lattice with a = 13.10(5) nm Whole sample film: 2D powder S. Disch, E. Wetterskog et al. Nano Letters 11, 1651 (2011) September 14, 2015 Folie 32

Possible 3D structures Five different cubic and tetragonal Bravais lattices are possible: sc, st, bcc, bct and fcc bcc and fcc are excluded from packing and geometrical considerations S. Disch, E. Wetterskog et al. Nano Letters 11, 1651 (2011) September 14, 2015 Folie 33

3D structure determined by GISAXS: bct 100 nm 10l Extinction rule: h+k+l = 2n Tetragonal lattice: (! 2 + * 4π 2 h 2 + k 2 + l $ Q z = k i,z + k c,z # & Q 2 a 2 c 2 y ± k 2 2 i,z k c,z " % September 14, 2015 )*,- Folie 34 C = 17.80(5) nm α c = 0.125 2 + - 11l

Conclusion Reflectometry and grazing incidence scattering: depth-resolved investigation of the chemical (and magnetic) order parameter(s) and its (their) lateral fluctuations September 14, 2015 Folie 36

Outlook : GALAXI@JCNS High brillance laboratory GISAXS diffractometer Ulrich Rücker 1M Pilatus from Dectris Metaljet from Bruker AXS Flux: 10 9 ph/mm 2 /s September 14, 2015 Folie 37

Thank you for your attention September 14, 2015 Folie 38