Bent crystals for focusing Bent crystals for focusing cosmic hard x-rays and cosmic hard x-rays and

gamma rays ingamma rays insatellite-borne experimentssatellite-borne experiments

V. Guidi, E. Bagli, V. Bellucci,R. Camattari, I. Neri

University of Ferrara – Ferrara - Italy

Royal Holloway, Spetember 15, 2011

N. Barrière University of California – Berkeley - USA

OutlineOutline

Curved crystals and some applications Scientific motivations Crystals bent by superficial

indentations Experimental results Modelling Discussion and conclusions

Göbel mirrorsGöbel mirrors

Curved crystals can be used as Goebel mirrors Curved crystals can be used as Goebel mirrors in Bragg geometry to transform a divergent x-ray in Bragg geometry to transform a divergent x-ray beam into an intense parallel beambeam into an intense parallel beam

Bragg geometry

DiffractionDiffraction ofof neutronsneutrons

Neutron diffractionNeutron diffraction

Curved crystals can be used as neutron monochromatorsover a wide energy band to analyze magnetic structure of materials

Sample

detector

Curved crystalin Bragg geometry

Neutron beam

Particle steering via channelingParticle steering via channeling

Channeling is confinement of charged particles travelling through a crystal by atomic planes or strings (planar or axial mode)

2

0,5

Channeled particles in a bent crystal follow the curvature of the crystal thereby they are diverted like an equivalent magnetic filed of thousands of Tesla would do!!!

The UA9 experiment at CERNThe UA9 experiment at CERN

Crystals fabricated at Ferrara

experimented at SPS (CERN)

Phys Lett. B 692 (2010) 78

Laue lensLaue lens

• Space-borne telescope to concentrate radiation over selected energy bands in the hard x-ray domain.• Crystals are arranged as

concentric rings to diffract radiation in Laue geometry from celestial sources to the focus.• Mosaic crystals are normally

considered for application

Curved crystals allow focusing and concentrating high-energy x-rays at high diffraction efficiency and increasing the energy bandwidth of the lens

Crystals with curved diffracting planes as an alternative to mosaic crystals in diffraction of high-energy raysin Laue geometry.

Re-diffraction within the crystal is prevented, thus the 50%-limit is overcome.

Curved crystals offer a continuum of possible diffraction angles over a finite range, leading to a rectangular-shape energy passband directly owing to the curvature.

Curved crystals for a Laue lens

vs.

Imaging in nuclear medicine

Curved crystals would improve gamma-ray detection in SPECT with better resolution and

lower radioactive dose to the patient than for the standard case with a gamma-camera system.

Curved crystal Optics in LAUE

geometry

Detector

Gamma-ray source

511-keV line for PET in nuclear medicine

Positron Emission Tomography scheme

A Laue lens made of curved

crystals would concentrate 511-keV photons due to

annihilationproviding higher resolution

with respect to existing instruments.

Self-standing bent crystals through indentations

Grooves manufactured on the surface of a crystalGrooves manufactured on the surface of a crystal

by a diamond saw induce a uniform and permanent by a diamond saw induce a uniform and permanent curvature curvature

within the crystal with no need for external deviceswithin the crystal with no need for external devices

Indented crystal with a numberof indentations onto its surface

Optical profilometry scannig of the surface without grooves (Si crystal S71)

Principles and features

Plastic compression of the material beside indentations deforms the whole crystal, leading to a net curvature within the crystal itself.

Final curvature can be modulated by adjusting the process parameters (advance speed, blade grit, geometry of the grooved path on the sample).

High accuracy and reproducibility. Separate control of the

two principal curvatures.N. Barrière V. Guidi et al J. Appl. Cryst. 43 (2010) 1519

Experimental session at ESRF (May 2010)

Grooved crystals were tested by x-ray diffraction of their (111) planes,in Laue geometry.

Aim of the experiment was to assess the performance of such crystals

European Synchrotron Radiation Facility(Grenoble, France)

A quasi-parallel and highly monochromatic pencil beam was set at energy ranging from 150 to 700 keV. Measurement consisted in Rocking Curves.

Indented crystals have shown significantly high

diffraction performance!

Indented sample S71 (Indented sample S71 (25.5 x 1 x 10 mm25.5 x 1 x 10 mm33)) was measured at was measured at 150 keV, through its 150 keV, through its 10 x 1 mm10 x 1 mm22 (a) or 25.5 x 1 mm (a) or 25.5 x 1 mm2 2 (b) (b) surfacesurface. . The pencil beam entered the sample at several depths from The pencil beam entered the sample at several depths from the grooved side.the grooved side.

Measured morphological curvature was nearly 16 arcsec, Measured morphological curvature was nearly 16 arcsec, thereby expected passband is 16 arcsec. thereby expected passband is 16 arcsec.

Silicon samples

(a) Beam quasi-parallel to the grooves

(b) Beam perpendicular to the grooves

Rocking Curves at 150 keV

40 20 0 20 400.0

0.2

0.4

0.6

0.8

1.0

20 10 0 10 200.0

0.2

0.4

0.6

0.8

1.0

40 20 0 20 400.0

0.2

0.4

0.6

0.8

1.0

20 10 0 10 200.0

0.2

0.4

0.6

0.8

1.0

Norm

ali

zed

cou

nts

Norm

ali

zed

cou

nts

Angle of incidence (arcsec)

Parallel configuration Perpendicular configuration

Angle of incidence (arcsec)

93 %

71 %94 %

53 %

z=0.4 mm

z=0.85 mmz=0.8 mm

z=0.15 mm

13 ”

15 ”

60 ”

54 ”

Discussion

All RCs exhibitedAll RCs exhibited rectangular and homogenous rectangular and homogenous shapes with an energy passband of the order of shapes with an energy passband of the order of crystal bending (about 16 arcsec for the parallel crystal bending (about 16 arcsec for the parallel case and 57 arcsec for the perpendicular case).case and 57 arcsec for the perpendicular case).

At 150 keV diffraction efficiency is significantly high At 150 keV diffraction efficiency is significantly high in all cases and close to unity in the parallel case. in all cases and close to unity in the parallel case.

This performance is representation that a bent This performance is representation that a bent crystal can overcome the 50%-efficiency limit that crystal can overcome the 50%-efficiency limit that holds for a mosaic crystal.holds for a mosaic crystal.

Insight into the method of indentations

Perpendicularly to the grooves, efficiency varies Perpendicularly to the grooves, efficiency varies over the crystal depth, being lower than predicted over the crystal depth, being lower than predicted especially near the grooved region. especially near the grooved region.

This fact is ascribed to fabrication process of This fact is ascribed to fabrication process of indentations with selected parameters. indentations with selected parameters. Generation of mosaicity perpendicularly to the Generation of mosaicity perpendicularly to the translation of the blade is easier to form than translation of the blade is easier to form than longitudinally because of the stronger action longitudinally because of the stronger action exerted by the blade on the side walls of the exerted by the blade on the side walls of the groove.groove.

Efficiency vs. energy beam parallel to the grooves

20 10 0 10 200.0

0.2

0.4

0.6

0.8

1.0

20 10 0 10 200.0

0.2

0.4

0.6

0.8

1.0

20 10 0 10 200.0

0.2

0.4

0.6

0.8

1.0

20 10 0 10 200.0

0.2

0.4

0.6

0.8

1.0

Norm

ali

zed

cou

nts

Norm

ali

zed

cou

nts

Angle of incidence (arcsec)

Angle of incidence (arcsec)

200 keV

400 keV

300 keV

500 keV

92 %

54 %68 %

84 %

Efficiency vs. energy beam perpendicular to the

grooves

Norm

ali

zed

cou

nts

Norm

ali

zed

cou

nts

40 20 0 20 400.0

0.2

0.4

0.6

0.8

1.0

40 20 0 20 400.0

0.2

0.4

0.6

0.8

1.0

40 20 0 20 400.0

0.2

0.4

0.6

0.8

1.0

40 20 0 20 400.0

0.2

0.4

0.6

0.8

1.0

Angle of incidence (arcsec)

Angle of incidence (arcsec)

200 keV

400 keV

300 keV

500 keV

59% 35%

24% 17%

Theory vs. experimentsTheory vs. experimentsParallel configuration Perpendicular configuration

Modelling with current theories on diffraction in a curved Modelling with current theories on diffraction in a curved crystal was carried out (SPIE 8147-50 by R. Camattari)crystal was carried out (SPIE 8147-50 by R. Camattari)

Satisfactory agreement of the curves was achievedSatisfactory agreement of the curves was achieved

Samples of germanium

Indented sample 2_G32 (Indented sample 2_G32 (18.6 x 2 x 9.8 mm18.6 x 2 x 9.8 mm33)) was was measured at 300 keV, through its measured at 300 keV, through its 9.8 x 2 mm9.8 x 2 mm2 2

surfacesurface. The pencil beam entered the sample at . The pencil beam entered the sample at different depth (coordinate z) from the grooved different depth (coordinate z) from the grooved side and quasi-parallel with respect to the side and quasi-parallel with respect to the grooves.grooves.

Expected angular distribution was Expected angular distribution was 42.4 arcsec. 42.4 arcsec.

zy x

Beam quasi-parallel to the grooves

Rocking curves at 300 keV N

orm

ali

zed

cou

nts

Angle of incidence (arcsec)

Angle of incidence (arcsec)

Norm

ali

zed

cou

nts z=1.25 mm

z=0.25 mm z=0.85 mm

Performance limited by intrinsicmosaicity of the sample

Diffraction efficiency averaged 58%

DiscussionDiscussion

The FWHM of the The FWHM of the angular distribution is always of angular distribution is always of the order of crystal bending (45 arcsec) the order of crystal bending (45 arcsec) throughout the whole throughout the whole crystal depth.crystal depth.

Diffraction efficiency averaged 58% and kept Diffraction efficiency averaged 58% and kept constant as a function of coordinate z.constant as a function of coordinate z.

Although this figure of merit is far lower than the Although this figure of merit is far lower than the theoretically predicted 93%, this is still a good theoretically predicted 93%, this is still a good performance. Efficiency drops probably due to performance. Efficiency drops probably due to non-perfect crystalline quality of base material.non-perfect crystalline quality of base material.

Possible configuration for a Laue lens

Indented crystals can be piled up Indented crystals can be piled up onto the lens to form a stack with the onto the lens to form a stack with the diffracting planes parallel to the diffracting planes parallel to the major major surfaces of the crystal. surfaces of the crystal.

Proper welding Proper welding of neighboring plates of neighboring plates would be realized to ensure a good would be realized to ensure a good alignment of the alignment of the indented plates. indented plates.

[111]

x-ray beam

V. Bellucci et al. Exp. Astron. 31 (2011) 45–58

Conclusions The technique of indentations proved to yield self-The technique of indentations proved to yield self-

standing homogeneous and standing homogeneous and controlled curvature in controlled curvature in Si and Ge (111) crystals.Si and Ge (111) crystals.

Crystals have shown significantly high efficiency Crystals have shown significantly high efficiency and broad-band response when subject to x-ray and broad-band response when subject to x-ray diffraction.diffraction.

The morphological curvature measured by optical The morphological curvature measured by optical profilometry is in good agreement with the profilometry is in good agreement with the curvature of the crystalline planes as determined by curvature of the crystalline planes as determined by x-ray diffraction.x-ray diffraction.

Energy bandwidth of bent crystals can be very well Energy bandwidth of bent crystals can be very well controlled controlled by by proper curvature to the sample.proper curvature to the sample.

Cylindrically deformed crystals due to indentations Cylindrically deformed crystals due to indentations can be piled up to form a stack with the diffracting can be piled up to form a stack with the diffracting planes parallel to the major planes parallel to the major surfaces of the crystal. surfaces of the crystal.

Thank you for your Thank you for your attention!attention!