1

Use of gratings in neutron instrumentation

F. Ott, A. Menelle, P. Humbert and C. Fermon Laboratoire Léon Brillouin CEA/CNRS Saclay

2

Objective Study of the neutron diffraction on periodical gratings.

(produced by lithographic techniques).

Theoretical calculation of the diffraction intensities:– Born / DWBA approximation (fails for large diffraction intensities)– matrix formalism : full dynamical calculation.– Comparison with simulations (!?, getting worse)

Application of gratings in neutron optics.– Example: energy analyser for time of flight neutron reflectometer– Fabrication and tests of small prototypes (20x20mm²)

(choice of materials, periodicities, shape of the grating, optimisation in the resolution, useful q range)

Extension to large surfaces (100x50mm²)Integration on the EROS reflectometer for measurements on liquids.Data processing (deconvolution)

3

Outline

Some experiments on D17

Commercial ruled gratings

Holographic gratings

Energy analysis in a magnetic field gradient

4

Modelisation of the grating

medium 2, vacuum

medium 1, grating

medium 0, substrate

specular reflexion

diffracted mode +1

diffracted mode -1

n2

n2n1

n0

indices

n0

periodicity d

x

z

5

Increase of the diffraction efficiencies

Increase of the contrast between the incidence medium and the diffraction grating.

Three possibilities :– grating made out of a high index material (Nickel)– incidence medium with an index >1 (Titanium)– use of materials with an «high artificial index» : supermirrors.

Results– under some conditions, efficiencies > 20%– increase of the “diffraction bandwidth”:

- high efficiency for a wide wavelength spectrum- or for a large range of incidence angles.

6

Glass grating with and without a Ni coating

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

0 0.01 0.02 0.03 0.04 0.05 0.06

qz (A°-1)

Réfl

ectiv

ity (lo

g sc

ale)

bare glass

Ni coating

Modes 1 (x 10-2)

Modes 2 (x 10-2)

Specular

7

Titanium coating(1st order diffraction mode efficiencies)

-3

-2.5

-2

-1.5

-1

-0.5

0

0 0.005 0.01 0.015 0.02 0.025 0.03

qz (A°-1)

Ref

lect

ivity

(lo

g)

0.4°0.75°1.2°

30%

3%

10%

Rocking curves around

8

Time of flight reflectivity

k1

q1

q2k2

x

z

kii r

kr

q

échantillon0.00001

0.0001

0.001

0.01

0.1

1

0 0.5 1 1.5

qz (nm-1)

Refl

ectivi

ty

Cu (30nm) sur Si

q

5 µs pulse Spatial spread

= 2 - 0.2 nm

9

Application in neutron instrumentation: Energy analysis.

r i d2 2 2

The diffraction directionis a function of the wavelength

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5

Incidence 0.8°

Diff

ract

ion

dir

ect

ion

(d

eg

ree

s)

Wavelength (nm)

20 µm

10 µm

5 µm

2 µm

10

Application on a time of flight spectrometer for energy analysis.

sample

grating

Position sensitivedetector

white beam = 4 to 25 A°

specular reflexion(white beam)

m=0m=+1

m=-1

11

Detector view

Specular reflection

Mode 1

200

mm

Mode -1

1.5 nm

0.2 nm

1.5 nm

0.2 nm

Sample horizon

I

12

Intensity gain

Use of a white beam a reflectivity curve in a single “shot”.

Study of the evolution of materials or liquids on a time scale of a few minutes

Examples: – liquid interfaces– diffusion, sticking, breaking– anything with a “smooth” reflectivity curve.

13

Experiments on the D17 reflectometer

Some test experiments on the new reflectometer D17 at the ILL on various types of gratings

14

Ni grating on glass (Bob Cubbit and Alain Menelle on D17)

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

0

5

10

15

20

25

2 theta (°)

lam

bda (

A°)

-3.00-2.75-2.50-2.25-2.00-1.75-1.50-1.25-1.00-0.75

toto_s2_x

4.00 3.50 3.00 2.50-3.00

-2.25

-1.50

-0.75

2 Theta

Inte

nsi

ty

Specular line

No broadening of the diffraction lines is observed

15

Ruled gratings

(Edmund Scientific Corp.)

16

Holographic gratings

(Edmund Scientific Corp.)

17

Holographic gratings efficiencies

(Edmund Scientific Corp.)

18

Ruled and holographic gratings

Main providers:– Edmund Scientific Co. (www.edsci.com)

– Instrument SA Inc. (www.isainc.com)

Blaze angles and available periodicities:– Holographic : from 200 nm to 5 µm– Ruled gratings : from 0.5 µm to 50 µm with blaze

angles de blaze from 1° to 20°

Large surface available, cheap but on epoxy

19

Field gradient energy analysis: principle

zz BµW gradBgradgradF )()(

x

L

B'=dB/dz

222

'2

LBh

mz

2

2' LB

h

m

v

v

x

z

20

Basic simulation

00.20.40.60.8

11.21.41.61.8

0 1 2 3

(nm)

défle

xion

(deg

rés)

0

20

40

60

80

100

120

0 1 2 3

(nm)po

sitio

n (m

m)

Angular beam deflexion at the output of the field gradient region as a function of the wavelength.

Position on the PSD at 4m (EROS configuration)

Hypothesis: length 400mm and dB/dz = 0.3T/mm

21

Field gradient creation

Halbach type quadrupôle based on permanent magnets(Mr = 1.14T => dB/dz = 0.25T/mm)

0°

-90°-22.5°

45°

112.5°

180°

-112.5°

-45°

22.5°90°-202.5°

-135°

-67.5°

67.5°

135°

202.5°

22

-0.01-0.005

00.005

0.01

-0.01

0

0.010

1000

2000

3000

B(m

T)

X(m)Y(m)

-6 -4 -2 0 2 4 6

x 10-3

0

0.5

1

1.5

2

2.5

Y(m) at x=0

B [

Tes

la]

-6 -4 -2 0 2 4 6

x 10-3

260

280

300

320

340

360

380

State of the art prototype– Use of high remanent field permanent magnets

(NdFeB); ‘ www.magnetic-solutions.com ’

ID=13mm (magnet only)OD=60mm (magnet only)Height=400mmWeight: ~20kg (in can)

23

Example

0 2 4 6 8 10

4

8

12

16

20

Position (mm)

Longueur

d'o

nde (

A°)

0.0 0.2 0.4 0.6 0.8 1.0

Normalised intensity

0 2 4 6 8 10

4

8

12

16

20

Position (mm)Longueur

d'o

nde (

A°)

0.10 0.20 0.30 0.40 0.50

Normalized intensity

aimant (longueur 200mm)

8 mm

M

dB/dz

direction du faisceaude neutrons

zone de passagedes neutrons

20 m

m

Gradient 80 mT/mm

24

Conclusion

Near future work– efficiencies of optical ruled and holographic gratings

(experiments on EROS and PRISM at the LLB)– supermirror deposition on 20x20mm glass gratings (home-made)

and efficiency tests

Field gradient device– assess the problem of magnetic field and field gradient

inhomogeneity and the limited resolution effects– Larger bore device (?)