Time-of-flight spectroscopy and the Disk Chopper Spectrometer

John R.D. Copley

NCNR Neutron Spectroscopy TutorialDecember 4, 2007

Time-of-flight spectroscopy

Detectors

SampleMonochromator

Pulser

SourceBeam stop

Beam monitor

Monochromatic bursts of neutrons strike the sample. Some of the neutrons are scattered.Some of the scattered neutrons are detected. The time between pulses, T, is divided into N time channels of

width Δ=Τ/Ν. (Αt the DCS, N=1000). Detector events are stored in a 2-d histogram I(i,j); i labels the detector, j labels the time channel.

( )2dI i, j I(2 , t) N t

d dt⎡ ⎤σ

⇔ θ = Φ ΔΩΔ⎢ ⎥Ω⎣ ⎦

Number of neutrons per second scattered at angle 2θ into solid angle ΔΩ, reaching detector within time interval [tD,tD+Δt]

Number of atoms illuminated

Double differential scattering cross section (w.r.t. time)

Number of neutrons per second per unit area in the incident beam (incident flux)

Solid angle subtended by detector

Width of time channel

2dTo the extent that and t (and N and ) are constants, I(2 , t)d dt

σΔΩ Δ Φ ∝ θ

Ω

How do we obtain S(Q,ω) from I(i,j)?

2 2

f f

d d dtd dE d dt dE

σ σ= ⋅

Ω Ω

( )2

1S ff SD

f i

kd S Q, and k td dE 4 k

−σσ= ω ∝

Ω π

( )SD SD SD

22 3 3f

ff

dE dSince E t , t , and I 2 , t t .dt d dE

− − σ∝ ∝ ∝ θ

Ω

Double differential scattering cross section w.r.t. energy

Double differential scattering cross section w.r.t. time

4SDHence S(Q, ) I(2 , t) tω ∝ θ ⋅

How do we obtain S(Q,ω) from I(i,j) (contd.)?

SD

SD

2

f 2

LmE2 t

=

PS i S

SD S D f

Knowing D and v , we obtain t .Knowing D , t , t , and 2 , we obtain v .θ

2θ

DSD Detector, tD

Sample, tS

Monochromator

Pulser (t=0)

DPSSource

vf

How do we obtain Q and ω?

vi

i f

i f

Hence E Eand Q k k

ω = −= −

21E mv2

=mvk =

26.8m6.9m

12.0m

Guide width60mm

Guide width30mm

Cold sourceChoppers

Crystalfilter

Sampleposition

Neutron Guide Hall (G100)ConfinementBuilding (C100)

9.0m1.5m

Detectorsat 4.0m

0.25

Localshutter

Plan view (to scale)

The Disk Chopper Spectrometer

Neutron Guide

Optical FilterSample Chamber

913 3He detectors,400x31x11mm3

MonochromaticBeam Monitor Radial Collimator

Sample

Monochromating Choppers

Frame OverlapChopper

Order Removal Choppers

Pulsing Choppers

Argon gas-filledFlight Chamber

White BeamMonitor

Crystal Filter

TransmittedBeam Monitor

BeamStop

Shutter

The Disk Chopper SpectrometerSchematic (not to scale)

The choppers and the guide

The pulsing and monochromating choppers are counter-rotating pairs, permitting a choice of pulse widths; they normally run at 20,000 rpm. The order removal choppers remove contaminants (also 20,000 rpm). The frame removal chopper alleviates the problem of frame overlap; it runs at 20,000/m or 20,000(m-1)/m rpm, where m is a small integer.

The flight chamber and detectors

The flight chamber is argon-filled to reduce scattering of neutrons traveling the 4 m distance from sample to detectors.There are 913 detectors in 3 banks, from -30ºto +140º.

What can one study using the DCS?

such as metals, insulators, semiconductors, glasses, magnetic materials, heavy fermions, superconductors, solid and liquid helium, plastic crystals, molecular solids, liquid metals, molten salts, biomolecules, water in confined geometries, polymer systems, micelles, microemulsions, etc., etc.,

See the NCNR annual reports for examples.

– the length and time scales (Q and ω ranges) are consistent with instrument capabilities

– the scattering (and absorption) cross sections are acceptable– the quantity of material is acceptable

such as (at the NCNR) T ≈50 mK to ≈1900K, P to ≈1.0 GPa, B to ≈11.5T, also strong electric fields, controlled humidity, etc., etc.,

Single particle and/or collective motions in all sorts of materials

under all sorts of conditions

provided that

http://www.ncnr.nist.gov/AnnualReport/

Considerations when running an experiment:

choice of wavelength, chopper speeds, and

resolution mode

Considerations when running an experiment

Intensity at sample I(E) Resolution width ΔE

Quantities that can be varied/chosen:Chopper period T*Wavelength λ

Chopper slot widths W“Speed ratio denominator” m=TS/T

(TS is period at sample)* Normally T=3000μs

3

I(E) peaks around 2.5-4.5Å; at long λ, I(E) drops 50% for every 2Å. Energy resolution width ΔE varies roughly as 1/λ Q range and Q resolu

Ch

ti

oice o

o

f wavelen

n 1/λ Bragg pea

gth

k

s

• ≈

•∝

•

λ

•

2S

Choice of chopper period T and/or speed rati can be troublesome at short λ (4.8Å is a popular choice)

I(E) T /T T / m ΔE T range increases wit

o denominat

h m (frame

or

overlap le

m

ss

• ∝ =

• ∝• ω

3

of a problem)

I(E) varies roughly as

Choice of chopper slot widths

W ΔE varies roughly

W

as W••

Considerations when running an experiment

Time-distance diagrams

Time-distance diagrams - single pulse

Choppers

Sample

Detectors

Time

Distance

0ω <

0ω =

0ω >

Time-distance diagrams - multiple pulses

Choppers

Sample

Detectors

Time

Distance

Choppers

Sample

Detectors

Time

Distance

What is frame overlap?

Frame overlap

Choppers

Sample

Detectors

Time

Distance

“Removal” of frame overlap

Frame overlap removal chopper

What are contaminant wavelengths (“orders”)?

Choppers

Sample

Detectors

Time

Distancek 0

12

h Tkm D

λ = λ +

12D

T

Choppers

Sample

Detectors

Time

Distance

Removal of contaminant wavelengths

Order removal chopper