quasimosaic crystals

Quasimosaic crystals

Yu.M.Ivanov

Elastic quasimosaic (Sumbaev) effect

• Studied by Sumbaev in 1957

• Resulted in broadening of gamma-ray diffraction peaks from bent quartz plates

• Caused by bending of the reflecting atomic planes (initially flat and normal to large faces of plate) due to crystal anisotropy

• Depends on choice of

crystallographic plane and orientation angle of plate cutting relative to a normal to the chosen crystallographic plane

Figure from article: O.I.Sumbaev, Reflection of gamma-rays from bent quartz plates, Sov. JETP 32(1957)1276

Quasimosaic effect in silicon

• Calculations of deformed crystal plate done by V.M.Samsonov (Preprint No. 278, LIYaF AN SSSR, 1976).

– Resulted in predictions of elastic quasimosaic effect for some other quartz and silicon plate orientations

– Large elastic quasimosaicity for (011) plane of silicon predicted

• Zero result in the first experiments in 1999

• New calculations using Samsonov approach and new measurements:

- (111) plane, not (011) - published in JETP Letters 81, 99, 2005

Figure from article: V.M.Samsonov and E.G.Lapin, On some possibilities and pequliarities of a curved crystal use in crystal diffraction instruments, Preprint No. 587, LIYaF AN SSSR, 1980

Elastic quasimosaic in dependence on cut angle for Si

(111) plane

T – thickness of plate

k9 – deformation coefficient

= 2k9 T , where

Plate bending radius R = 1 m

( formula taken from V.M.Samsonov, E.G.Lapin, Preprint No. 587, LIYaF AN SSSR, 1980 )

Silicon cuts

Cut without quasimosaic

Cut with quasimosaic

Oriented ingot

φ

Rocking curves for Si plate with quasimosaic

before and after bending.

Quasimosaic effect in Si with X-rays

Rocking curves for Si plate without

quasimosaic before and after bending.

Shape of bent Si plate with elastic quasimosaic

Bending device

First quasimosaic silicon crystal prepared in 2002 for channeling experiment with 70 GeV protons

Layout of experiment at IHEP in April, 2002

Crystal 1Magnets

Crystal 2

Emulsion 1

S1

S2 S3

Background

Channeled_1

30 m

35 m 4.6 m

Collimator

1.3 m

Emulsion 2

Channeled_2

70 GeVp-beam

5 m

R=3 m

Profile of 70 GeV proton beam passed through the crystal measured with emulsion: superposition of channeling and volume reflection effects

Explanation of the observed picture on emulsions

Proton trajectories crossing the crystal and emulsions in horizontal plane (top view)

Samples 0.3 mm and 2.7 mm with ~0.4 mrad bending angle

Sample 10 mm with ~100 μrad bending angle

Crystals for experiment on extraction of high entensive proton

beam at IHEP

Plane (111)

Length along beam 2.65 mm

Bending angle 400 μrad

Crystal station at IHEP ring

Crystal mounted on station

Result

Beam in the U-70 ring 5.5∙1012 p

Intensity of extracted beam 4.0∙1012 p

Efficiency 70%

Experiment on observation of volume reflection effect with 1 GeV protons

at PNPI, Gatchina

Beam divergence ~ 160 μrad

Beam size ~ 0.8 mm

Critical angle for channeling ~ 170 μrad

Crystal length along beam ~ 30 μm

Bend angle of (111) planes ~ 380 μrad

One of unsuccessful attempts to bend a 30 μm crystal on 20 mm

radius

Bent crystals in bending devices

Check of crystal shape with laser

~1

m

Measurement of bending angle with X-rays

Collimator

Crystal mounted on goniometer

Horizontal profiles of the p-beam vs. crystal angle measured with

PPC

p-beam

reflection

channeling

p-beamCry

sta

l an

gle

, ste

p 6

2.5

μra

d

Channel number, step 200m

Channeling experiment with 400 GeV protons

H8 beam line

FAR_DETECTOR areaCRYSTAL area

QM2

QM2

2 4 6 8 10 120

50

100

150

200

250

300

350

400

Position, mm

Cry

stal

ang

le, m

krad

Crystal QM2

QM2

Channeling angle (68.2 0.4) μrad

Volume reflection deflection (12.7 0.6) μrad

Volume capture ε (1.8 0.7) %

QM1

QM1

2 4 6 8 10 120

20

40

60

80

100

120

140

160

180

200

Position, mm

Cry

stal

ang

le, m

krad

Crystal QM1

QM1

Channeling angle (77.0 0.4) μrad

Volume reflection deflection (11.6 0.8) μrad

Volume capture ε (2.6 0.8) %

QM2+QM1

QM2+QM1

2 4 6 8 10 120

50

100

150

Position, mm

Cry

stal

ang

le, m

krad

Crystal QM1-QM2

QM2+QM1

Channeling angle

Volume reflection deflection (23.4 0.7) μrad

Volume capture ε (5 1) %

QM3

QM3

2 4 6 8 10 120

20

40

60

80

100

120

140

160

180

Position, mm

Cry

stal

ang

le, m

krad

Crystal QM3

QM3

Channeling angle (72.7 0.8) μrad

Volume reflection deflection (11.9 0.7) μrad

Volume capture ε (5 1) %

QM4

QM4

2 4 6 8 10 120

20

40

60

80

100

120

140

160

180

Position, mm

Cry

stal

ang

le, m

krad

Crystal QM4

QM4

Channeling angle (120.0 0.4) μrad

Volume reflection deflection (12.7 0.5) μrad

Volume capture ε (4.4 0.7) %

Design: sequence of quasimosaic crystals cut from a

single initial plate

p

1 Si plate 0.3 x 30 x 60 mm3

12 Si plates 0.3 x 8 x 14 mm3

Check of plate wedging with optical goniometer

Prototype assembly from 5 plates

0

1000

2000

3000

4000

5000

6000

7000

14,85 14,90 14,95 15,00 15,05 15,10 15,15 15,20 15,25

Check with narrow X-ray beam

ΔN

Δθ≈0.017x ΔN μrad

Δθ < 40 μrad

X, mm

N,

coun

ts

ΔX

N1

N2

Δθ

ΔN=N2-N1

ΔX

Need to provide or to compensate plate wedging

Realization with evaporation technique

Al-layer of 0.14 μm thickness

Δθ = 0.14 μm / 12 mm = 12 μrad

Further steps

• to improve prototype assemly for experimental run in May’07 at CERN

• to prepare larger plates and assemble them for experiments at CERN and IHEP in the Fall’07