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## Development of Spin-Echo Scattering Angle Measurement

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**Development of Spin-Echo Scattering Angle Measurement**Wai Tung Hal Lee1, Roger Pynn1,2, Paul Stonaha2, Adam Washington2, Shah Valloppilly2, Rana Ashkar2, Mike Fitzimmons3, Brian Maranville4, Lowell Crow1, Alexandru Stocia1, Xin Tony Tong1, Michael Fleenor1, J. Lee Robertson1, Wen Ren Chen1. 1 Oak Ridge National Laboratory 2 Indiana University Cyclotron Facility 3 Los Alamos National Laboratory 4 National Institute of Standards and Technology**Conventional Off-Specular Scattering**f Final Angle Off-Specular Specular Incident Side view Off-Specular i f Horizon Diffraction Intensities are not normalized to the incident spectrum l Wavelength 10μm x 2μm x 100 Å Permalloy arrays**Measured by conventional off-Specular scattering (Probe**structure along X) Incident Beam (Specular) Reflection (Probe structure along Z) Measured by conventional off-Specular scattering (Probe structure along X) Off-specular scattering measured by SERGIS (Probe structure along Y) Z Y X Spin-Echo Resolved Grazing Incident Scattering (SERGIS) It is difficult to collimate the beam to measure the off-specular scattering that is transverse to the scattering plane of incident-specular reflection. Spin echo labeling of the scattering angle can measure very small scattering angle without collimating the beam. Using SERGIS, off-specular scattering, and specular reflectivity, we can obtain a 3-dimensional “map” of the surface structure of the sample. More importantly, the length scale of the lateral surface structures measured by SERGIS ranges from 10 nm to several microns which is the length scale of nano-materials. Length scales below 500 nm are difficult to measure using conventional off-specular scattering technique.**sample**+B precess precess -B Polarized neutrons of wavelength, l Y D f p/2 flipper produces How SESAME works? Classical: For the neutron beam that goes through the sample without being scattered, the precessions through the two parallelogram shape magnetic fields cancel. For scattered neutrons, the path-lengths through the two parallelogram-shape magnetic fields are different, resulting in a net precession angle of the neutron spin. Quantum: The boundaries of parallelogram shaped magnetic field are birefringent for neutrons and cause splitting (D) and phase lag (Y) between the two neutron spin states. Using Snell’s law we can show that dY/df=(2p/l) D for light or neutrons. If a sample between the two field-regions causes scattering through an angle2q, the net phase is DY = (dY/df) ·2q = (2p/l) 2qD = Q · Z for small scatttering angles.**Polarized**neutrons of wavelength, l Y D f p/2 flipper produces How SESAME works? The ratio of neutron beam polarization with sample P to polarization without sample P0 is related to the real space correlation function G(Z) Z is the spin-echo length and is proportional to the phase difference in the two spin states. The polarization ratio varies with Z with a period close to the characteristic length scale of the sample being measured.**How to set up SESAME?**• The main practical issue is how to produce the parallelogram field region. Our approach is to use triangular coils. • Simulations show fields are uniform within numerical accuracy • For the Asterix test, the coil gives**z**y x A B B A How to set up SESAME? Creating a gap in one face of each solenoid gives smooth transitions between internal and external fields. No neutron depolarization due to boundary BUT – does it work properly i.e. does it give the correct Larmor phase? For any neutron traveling parallel to the average direction (x), the field integrals (& hence the Larmor phase) through a pair of prisms is the same for “ideal” (closed) prisms and “gapped” prisms, by symmetry. Even for neutrons with finite divergence angle, simulations show that the difference is expected to be small. Difference between fields of “ideal” and “gapped” prism-pair**SESAME Setup at Asterix, LANSCE**V T/T T/T V S p V T/T T/T V T/T = triangular coil pair V = v-coil (p/2 “flipper”) p = p flipper S = sample**SESANS Test on Asterix, LANSCE**Intensity (arb. Unit, same scale) Wavelength (Å) Wavelength (Å) Wavelength (Å) Polystyrene spheres suspended in D2O: Comparison of 40 nm sphere (white) with 100 nm sphere (green). 100 nm polystyrene spheres suspended in D2O: Comparison of 10% (green) with a 20% sample (white). Through beam with spin-echo, no sample. G(ζ) correlation functions obtained using triangular solenoids for three different samples of polystyrene spheres suspended in D2O. Solid squares are for ~100 nm spheres at 8.3 % concentration; open circles are for the same spheres at 10.2% concentration and filled triangles are for ~40 nm diameter spheres at 2.8% concentration. The solid curves are the theoretical curves for uncorrelated spheres of 40 nm and 100 nm diameter.**S**p/2 T T p T T p/2 SERGIS Test on AND/R at NIST SERGIS setup on AND/R. The neutron beam went from right to left in the picture. Label: T = triangular coil pair, p/2 = p/2 flipper, p = p flipper, S = sample 140 nm The results from the measurement on AND/R and from a previous test on Asterix, LANSCE. On AND/R The spin-echo length was selected by varying the B-fields in the triangular coils at a fixed neutron wavelength of 0.55 nm.. On Asterix, the spin-echo length varied during a time-of-flight frame with wavelength at a fixed coil field. Electron microscope picture of grating cross section**Next: SERGIS Test Beam Line at HFIR CG1**We are constructing a SERGIS Test beam line at the HFIR Cold Source CG1 Beam Guide position to serve as a test bed for exploring the technologies for SERGIS. (1) Explore the characteristics and develop the methodology for analyzing SERGIS data. (2) Enhancing the signal-to-noise ratio by exploring designs that will better preserve the neutron polarization and further reduce the beam attenuation. (3) Explore different methods for SERGIS. Key Characteristics: (1) Fixed wavelength l = 4.2 Å (PG), 11 Å (intercalated PG); (2) Vertical scattering plane geometry (i.e. Sample lays flat horizontally); (3) 1.5 m-long distance available along the incident and the scattered arm for SERGIS coils (distance excludes polarizer, analyzer, and sample stages). Total instrument length from shutter to beam stop = 5 m; (4) Polarized 3He based polarizer and analyzer SERGIS Layout of CG1 Instrument development Beam lines Post-Doc Position: Contact: J. Lee Robertson (RobertsonJL@ornl.gov)