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cusing monochromators/analyzers symmetric diffraction geometry of the monochromator ispersive double crystal monochromator wo wavelength sandwich monochromator FAD geometry of the monochromator ispersive „umweganregung“ monochromator nergy dispersive neutron diffraction transmission ent perfect crystals in TOF diffractometry? Other applications and proposals ? Possible contribution of NPI Rez Possible contribution of NPI Rez Neutron Bragg Diffaction Optics for High- Neutron Bragg Diffaction Optics for High- Resolution Neutron Scattering Instrumentation Resolution Neutron Scattering Instrumentation Pavel Mikula Nuclear Physics Institute, Academy of Sciences of the Czech Republic 250 68 Řež near Prague, Czech Republic

Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

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Page 1: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Focusing monochromators/analyzers•Asymmetric diffraction geometry of the monochromator•Dispersive double crystal monochromator•Two wavelength sandwich monochromator• FAD geometry of the monochromator•Dispersive „umweganregung“ monochromator•Energy dispersive neutron diffraction transmission•Bent perfect crystals in TOF diffractometry?• Other applications and proposals ?

Possible contribution of NPI RezPossible contribution of NPI Rez

Neutron Bragg Diffaction Optics for High-Resolution Neutron Bragg Diffaction Optics for High-Resolution Neutron Scattering InstrumentationNeutron Scattering Instrumentation

Pavel Mikula Nuclear Physics Institute, Academy of Sciences of the Czech Republic

250 68 Řež near Prague, Czech Republic

Page 2: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

R

B en t p e rfec t c ry s ta l

(h k l)

Reflectivity properties of bent perfect crystals

Page 3: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Output beam compression

Output beam extention

Assymetric diffraction geometries

Page 4: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Comparison on powder and solid -Fe samples

Missouri Missouri

NPI NPI

Page 5: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

PSD

S i(111 )B en t P e rfect

G e(331)M osa ic

Inc iden t neu tron beam

2.7 m

1 .5 m(1 .2 m )

(2 .0 m )

Dispersive Double-Crystal Monochromator

Page 6: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

S i (111)

S ym m etric d iffraction geom etryo f S i (111)

S i (111 )

A sym m etric d iffrac tion geom etryo f S i (111 )

S i (331 )

S i (331 )

S ym m etric d iffraction geom etryo f S i (331 )

A sym m etric d iffrac tion geom etryo f S i (331)

S i (33 -1 )

S i (331 )

Dispersive Double-Crystal Monochromator

Page 7: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

S i (111)

S ym m etric d iffraction geom etryo f S i (111)

S i (111 )

A sym m etric d iffrac tion geom etryo f S i (111 )

S i (331 )

S i (331 )

S ym m etric d iffraction geom etryo f S i (331 )

A sym m etric d iffrac tion geom etryo f S i (331)

S i (33 -1 )

S i (331 )

Dispersive Double-Crystal Monochromator

Page 8: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Dispersive Double-Crystal Monochromator

Page 9: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

S i(111 )B en t P e rfe c t

G e(3 3 1 )M o sa ic

P o ly cry s ta llin e A u s ten ite S am p le

(111 )(2 0 0 )

(2 2 0 )(2 2 2 )

P a r a lle lG eo m etr y

A n tip a ra lle lG eo m etr y

N eu tro n B eam

2 .7 m

1 .5 m

1 .2 m

Experimental setup for the estimation of resolution of powder diffractometerunder the dispersive setting of the double-crystal monochromator

Dispersive Double-Crystal Monochromator

Page 10: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Mosaic Ge331) + bent Si(111) + -Fe(220)

Page 11: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Horizontally focusing two wavelength sandwich monochromator

Sandwich monochromatorSi111(2.7 A) & Si220(1.65 A)Si111(2.7 A) & Ge311(1.45 A)

hkl1

hkl2

21

Advantage:For strain measure-ments of two phase materials, composi-tes etc.

Page 12: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

b M

k b a M

k a

k b

bM

k b aM

k a

k b

Sing le c rysta l sa m p le

FADG

Two possible scans:• -scan, k┴

• -2 scan, k||

Special case of single crystal diffractometry

B ent S i crysta l

Incident po lychrom atic beam

(H K L)

Page 13: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

B en t S i crysta l

Inc iden t po lych rom atic beam

(hkl)

(hk l)M(hk l)M(hk l)M

B en t S i crysta l

Inc iden t po lych rom atic beam

(hkl)

W

Schematic drawing of the case of the symmetric diffraction geometry – (a) and of the fully asymmetric diffraction geometry – (b).

Comparison of two diffraction geometries

Page 14: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Diffraction profiles as imaged by IP for curved crystals set in the symmetric diffraction geometry (R=8.8 m) and the fully asymmetric diffraction geometry (R=7.5 m).

10 20 30 40 50

0

5

10

15

20

25

30

Inte

nsi

ty (

rela

tive

un

its)

Spatial beam distribution / mm

SD-geometry FAD-geometry

Beam profiles at the sample position

Page 15: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Ba sic reflec tion(h ,k ,l ) (fo rb idden)1 1 1

(h ,k ,l ) Sec onda ry reflec tion

2 2 2

(h ,k ,l ) Tertia ry reflec tion

3 3 3

g1 = g2 + g3

Bent perfec tc rysta l

“Umweganregung“ monochromator

Double reflection realized on (h2,k2,l2) and (h3,k3,l3) in a bent perfect or mosaic single crystal simulates the forbidden one corresponding to (h1,k1,l1) and can provide a good intensity of highly monochromatic and highly collimated beam for a further use.

Relation for scattering vectors

Page 16: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

0 10 20 30 40 50 60 70100

1000

10000

Main face of the slabparallel to (110)

Inte

nsity

/ 60

sec

- angle / deg

Umw 222 Flat crystal Background

R=10 m, t = 5 mm

scan taken with the Si crystal slab set for 222 diffraction

in symmetric transmission geometry; guide tube, 3x3 m2 Cd slit

“Umweganregung“ monochromator

Page 17: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

“Umweganregung“ monochromator

scan taken with the Si crystal slab set for 222 diffraction in symmetric transmissiongeometry and bending dependences taken with

on the umweg-peak at =47.9o.

Page 18: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

“Umweganregung“ monochromator

0 10 20 30 40 50 60 70

100

1000

10000

Main face of the slabparallel to (110)

Umw OO2 Background

R = 9 m, t = 4 mm

Inte

nsity

/ 60

s

- angle / deg

scan taken with the Si crystal slab set for 002 diffraction

in symmetric transmission geometry

Page 19: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Fully asymmetric diffraction geometry

B ent S i crysta l

Incident po lychrom atic beam

(H K L)

bM

kb a M

ka

Kb

K a

Page 20: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

2dhklsin hkl=

hkl==2dhklDiffraction edge I() modulation

Instrumental resolutiond/d=5.7x10-

4

Energy-Dispersive Neutron-Transmission Diffraction

Page 21: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Bragg diffraction edge of a 8 mm thick standard sample.

Sample thickness dependence of Ao

FWHM=5.7x10-4 rad

FWHM=12.5x10-4 rad

EDNTD examples

Page 22: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

High resolution bent perfect crystal analyzer in High resolution bent perfect crystal analyzer in

fully asymmetric diffraction geometryfully asymmetric diffraction geometry

Extremely low attenuation factor for neutrons in the wavelength range of 0.15-0.4 nm

Page 23: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

TOF experimental testTOF experimental test

B ent S i crysta l I

(331 )(220 )

(551 )

(400 )

(511 )

Inc iden t beam

D iffracted beam s

Generally, different lattice planes (hkl) at different asymmetry angles can operatesimultaneously. The beam that should be analyzed enters the bent crystal slab through its end face and passes along its longest edge. Due to the bending, on the path through the crystal it meets homogeneously changing diffraction angle hkl with respect to the planes (hkl).

Page 24: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

TOF experimental testTOF experimental test

(h k l)B en t S i c ry s ta l

D e te c to rs 15 4 3 2

IP B

xz

Page 25: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Experimental results

1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40

0

50

100

150

200

Si(440)

2=89.5o

R=13 m

=0.017 A

Det. 1Det. 3Det. 5

Inte

nsity (

norm

.)

Wavelength / A

2.60 2.65 2.70 2.75 2.80

0

25

50

75

100

125

=0.035 A

Si(220)

2 = 89.5o

R = 13 m

Det. 1 Det. 3 Det. 5

Inte

nsity (

norm

.)

Wavelength / A

Page 26: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Experimental resultsExperimental results

Page 27: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

OTHER BRAGG DIFFRACTION OPTICS APPLICATIONS

hkl1

hkl2

Hig h re so lutio n sa nd wic h m o no c hro m a to r

Page 28: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Time focusing assemblyTime focusing assembly

D e tec to r

F ro m a sam p le

B e n t c ry s ta ls

Page 29: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Since 1994, we have been developing computer codeRESTRAX for Monte Carlo simulation of three-axisneutron spectrometers (TAS) in collaboration withILL Grenoble (Dr. J. Kulda). RESTRAX containshighly optimised MC ray-tracing code describingneutron-optical components of TAS (neutron guides,collimators, elastically bent perfect and mosaiccrystals). Although the program has primarily beendeveloped as a tool for data evaluation andexperiment optimisation at TAS, it has also beenused for designing new or upgraded instruments(both TAS and powder diffractometers) andmodeling new configurations with focusingmonochromators oranalysers. In the context ofCOST Action P7 program of the working group 1,we could participate in the following tasks:

Summary of activities - Monte Carlo simulationsof neutron scattering instruments

Page 30: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Scattering from diffractive optics elements

Simulation of diffraction on neutronmonochromators/analysers :Models describing neutron transport throughmosaic and elastically bent perfect crystals andtheir focusing assemblies in RESTRAX should becalibrated (and possibly improved) by comparisonwith measured reflectivities. The aim is to have anefficient MC ray-tracing code describing crystalcomponents reliably in a wide range ofexperimental arrangements (wavelengths,diffraction geometries). Such a code should allowfor more accurate simulation of the performance ofnewly built instruments and thus to help indecisions about optimum monochromator/analysermaterial and layout.

Page 31: Focusing monochromators/analyzers Asymmetric diffraction geometry of the monochromator Dispersive double crystal monochromator Two wavelength sandwich

Beam-line modelisation Testing new experimental arrangements with

focusing Bragg optics:Focussing Bragg optics and particularly elasticallybent crystals permits to employ various newarrangements of neutron scattering experiment.However, practical testing is expensive and limitedby the beam time available. We intend to participatein testing newly proposed experimentalarrangements employing focusing Bragg optics bycarrying out corresponding MC simulations.