Neutron Spin Echo Spectroscopy NSE Dobrin P Bossev
Neutron Spin Echo Spectroscopy (NSE) Dobrin P. Bossev, Steven Kline, Nicholas Rosov NCNR, NIST Gaithersburg, MD 20899 E-mail: dbossev@nist. gov Internet: http: //www. ncnr. nist. gov/
Why precession? • Goal: E = 10 -5 – 10 -2 me. V (very small !!!) • We need low energy neutrons. Cold neutrons: = 5 – 12 Å, E = 0. 5 – 3. 3 me. V • The problem: neutron beam wavelength spread / = 5 – 20%, E/E = 10 – 40%, E = 0. 05 – 0. 2 me. V >> E = 10 -5 – 10 -2 me. V • In fact, to measure neutron energy we need to measure the neutron velocity: E = m. V 2/2 V = l/t t? • The solution: We need neutron precession in magnetic field. We are going to attach “internal” clock for each neutron. Thus, we can observe very small velocity changes of a neutron beam, regardless of the velocity spread
Neutrons in magnetic fields: Precession Mass, mn = 1. 675 10 -27 kg Spin, S = 1/2 [in units of h/(2 )] Nuclear g number, gn = n/ N = -1. 9130 where ( N = 5. 0508 10 -27 J/T) Gyromagnetic ratio g = n/[S h/(2 )] = 1. 832 108 s-1 T-1 (29. 164 MHz T-1) B L • The neutron will experience a torque from a magnetic field B perpendicular to its spin direction. • Precession with the Larmor frequency: L = g. B • The precession rate is predetermined by the strength of the field only. S N
Spin flippers /2 flipper Precession L flipper B B B Send S n Sini B /2 B B B
NSE Spectrometer schematic 1 2 3 4 7 5 6 8 9 � 1. Velocity selector 6. Sample 2. Polarizer 7. Second main solenoid (polarizing supermirrors) (phase and correction coils) 3. /2 flipper 8. /2 flipper (selects neutrons with certain 0) (starts Larmor precession) 4. First main solenoid (field integral ~0. 5 T. m) 5. flipper (provides phase inversion) (stops Larmor precession) 9. Polarization analyzer (radial array of polarizing supermirrors) 10. Area detector (20 20 cm 2) 10
Monochromatic beam • elastic scattering /2 flipper B • inelastic scattering sample B /2 flipper S # of cycles 0 2 N + -(2 N + )± J – field integral At NCNR: Jmax = 0. 5 T. m N ( =8Å) ~ 3 105 Analyzer 0 measures ± cos(± ) !
Polychromatic beam /2 flipper S < 0 0 B sample B /2 flipper f( ) # of cycles 0 > 0 2 N( ) + ( ) ± ( ) 0 The analyzer projects out the spin component parallel to the beam, cos( ( )): Energy change Asymmetry between coil field integrals Neglect 2 nd order terms for small asymmetries or quasielastic scattering. Neglected
Intensity at the detector For a single wavelength: At small N 0 vary N 0: - Oscillations give 0 - Envelope gives f( ) For wavelength distribution, f( ), with mean wavelength, 0:
How to deal with the resolution? In the energy domain, the energy resolution of the spectrometer is convoluted with the scattering properties of the sample In the time domain the deconvolution is simply a division.
Measuring I(Q, t) • The difference between the flipper ON and flipper OFF data gives I(Q, 0) • The echo is fit to a gaussiandamped cosine.
Experimental system AOT Surfactant molecule Hydrophobic tail Hydrophilic head Experiment II Diffusion of AOT micelles in C 10 D 22 (5. 4 % vol. fraction) Shape fluctuations in AOT/D 2 O/C 10 D 22 microemulsion (5. 4/4. 6/90 % vol. fraction) Inverse spherical micelle ~ 25 AOT C 10 D 22 Translational diffusion Inverse microemulsion droplet D 2 O AOT C 10 D 22 Shape fluctuations Translational diffusion
Data analysis Shape fluctuations Expansion of r in spherical harmonics with amplitude a: Frequency of oscillations of a droplet:
Summary of data analysis Experiment I AOT micelles in C 10 D 22 Experiment II AOT/D 2 O/C 10 D 22 microemulsion Goal: Bending modulus of elasticity 2 – the damping frequency – frequency of deformation <|a|2> – mean square displacement of the 2 -nd harmonic – amplitude of deformation p 2 – size polydispersity, measurable by SANS or DLS
- Slides: 13