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Understanding Specular Reflectivity: Concepts, Applications, and Measurement Techniques

This document explores the principles of specular reflectivity, including its critical angles and the impact of surface roughness on intensity. It delves into quantitative information regarding film thickness and scattering length density (SLD) in the Z direction, highlighting the effects of footprint in total external reflection. The text discusses the nuances of reflectivity profiles in both single-layered and multilayered systems, utilizing methods like X-ray and neutron reflectivity. Additionally, practical tools and experimental setups for calculating and analyzing reflectivity are introduced.

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Understanding Specular Reflectivity: Concepts, Applications, and Measurement Techniques

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  1. Specular reflectivity – Examples and applications Sandip Argekar

  2. Specular reflectivity Footprint, Critical angle Ѳrefl=Ѳincident q-4 decay, roughness Quantitative information of thickness and SLD in Z direction 7 to 8 orders of magnitude drop in intensity Background

  3. Features - Footprint effect In the regime of total external reflection, some intensity is lost as the footprint on the surface is too large Low q High q Foot print depends on beam width & sample geometry

  4. Critical edge The refractive index for x-rays and neutrons in materials is less than 1. Total external reflection occurs

  5. Double critical edge – Better guestimation of layer SLD 2 critical edges observed

  6. Effect of roughness on the reflectivity profile Smooth surface Maximum specular reflection Rough surface Increased non-specular reflection Loss of intensity and sharpness Effect of roughness depends on coherence length lc Only If roughness features < , reflectivity profile is affected

  7. X-ray reflectivity single layered system Fringes with uniform spacing Thickness of the layer : Kiessig fringes SLD of the layer pushes the curve up or down

  8. Multilayered systems – PS 19 • Identify critical edge • Calculate substrate SLD • Guess number of layers • Based on practical expt • Calculate approx SLD • Guess preliminary thickness 7 crests

  9. Neutron reflectivity Utilize contrast between H and D to understand polymeric and biological systems Swelling studies under dueterated solvents Neutrons penetrate through Si D2O becomes the new substrate For Neutrons Liquid cell configuration Si D2O

  10. Courtesy - Peng Wang presentation

  11. Temperature dependent swelling of poly (N-isopropylacrylamide) • Swelling of a hydrogenated polymer with D2O • Water penetration shows a diffuse profile • Non-swollen polymer at the substrate interface Critical temperature Diffuse layer

  12. Panalytical XRD pro MD setup – X-ray reflectivity – Goniometer based LANSCE –SPEAR - Neutron reflectivity – Time of flight approach

  13. Handy tools – SLD calculator http://www.ncnr.nist.gov/resources/sldcalc.html

  14. Handy tools – Reflectivity data fitting Parratt 32

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