# Presentation: 778836

## Neutron Spin Echo Spectroscopy(NSE)

*Gaithersburg, MD 20899*
- E-mail:
- dbossev@nist.gov
- Internet:
- http://www.ncnr.nist.gov/

**Neutron Spin Echo Spectroscopy****(NSE)**

**Dobrin P. Bossev, Steven Kline, Nicholas Rosov**

## Why precession?

- •  **Goal:**	 *******E***** = 10****-5**** – 10****-2**** meV** (very small !!!)
- •  We need low energy neutrons. Cold neutrons: ** = 5 – 12 Å, *E* = 0.5 – 3.3 meV
- •  **The problem:** neutron beam wavelength spread ***/*** = 5 – 20%,
- *E/E *= 10 – 40%, *******E***** =  0.05 – 0.2 meV**
*******E***** =  0.05 – 0.2 meV**  **>>**  *******E***** = 10****-5**** – 10****-2**** meV**
- •  In fact, to measure neutron energy
- we need to measure the neutron velocity:
*   **E = mV*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, *m*n = 1.67510-27 kg
- Spin, *S* = 1/2 [in units of *h*/(2)]
- Nuclear *g* number, *g*n = **n/**N = -1.9130
- where (**N = 5.050810-27 J/T)
- Gyromagnetic ratio *g* = **n/[S*h*/(2)] =
- 1.832108 s-1T-1 (29.164 MHz T-1)

- •  The neutron will experience a torque from a magnetic field *B *perpendicular to its spin direction.
- •  Precession with the Larmor frequency:
**L = *gB*
- •  The precession rate is predetermined by the strength of the field only.

***B***

********L**

***S***

***N***

## Spin flippers

******/2 flipper**

**Precession**

***B***

********L**

***S***

***n***

****** ****flipper**

## NSE Spectrometer schematic

## Monochromatic beam

- • elastic scattering            • inelastic scattering

*J – *field integral
- At NCNR:
*J*max* = *0.5 T.m
*N *(**=8Å) ~ 3105

***S***

***B***

***B***

******/2**
**flipper**

**sample**

******/2**
**flipper**

- # of
- cycles

- 0

- 2*N*+**

- 2*N*+**
- 2*N*+**

- -(2*N*+**)
- -(2*N*+**)±**

- 0
- ± **

- Analyzer
- measures
- cos(± **)

**!**

## Polychromatic beam

- Energy
- change

- Asymmetry between
- coil field integrals

- Neglect 2nd order terms
- for small asymmetries
- or quasielastic scattering.

- The analyzer projects out the spin
- component parallel to the beam, cos(**(**)):

- Neglected

***S***

***B***

***B***

******/2**
**flipper**

**sample**

******/2**
**flipper**

*f*(**)

***>***0

***<***0

**0

## Intensity at the detector

## How to deal with the resolution?

- 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 gaussian-damped cosine.

## Experimental system

- Hydrophobic tail

- Hydrophilic head

**Surfactant molecule**

**AOT**

**Experiment I**
**Diffusion** of AOT micelles in C10D22
- (5.4 % vol. fraction)

**Experiment II**
**Shape fluctuations** in
- AOT/D2O/C10D22 microemulsion
- (5.4/4.6/90 % vol. fraction)

**Inverse microemulsion droplet**

- D2O

- C10D22

- AOT

**Inverse spherical micelle**

- C10D22

- ~ 25 AOT

- Translational
- diffusion

- Translational
- diffusion

- Shape
- fluctuations

## Data analysis

## Summary of data analysis

**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