Flash Spectroscopy using Meridionally- or Sagittally-bent Laue Crystals: Three Options

Zhong Zhong National Synchrotron Light Source, Brookhaven National

Laboratory

Collaborators: Peter Siddons, NSLS, BNL

Jerome Hastings, SSRL, SLAC

Agenda• The problem we assume• X-ray diffraction by bent crystals

– Meridional– Sagittal

• Sagittally bent Laue crystal– Focusing mechanism, focal length– Condition for no focusing

• Three Laue approaches– Meridionally bent, whole beam – Meridionally bent, pencil beam– Sagittally bent, whole beam

• Some experimental verification • Conclusions

The problem we “assume”• Would like to measure, in one single pulse, the

spectrum of spontaneous x-ray radiation of LCLS

• Energy bandwidth: 24 eV at 8 keV, or 3X10-3 E/E

• Resolution of dE/E of 10-5, dE= 100 meV

• 5 micro-radians divergence, or 1/2 mm @ 100 m

• Source size: 82 microns

• N (1010 assumed) ph/pulse

The general idea

• Use bent Laue crystals to disperse x-rays of different E to different angle.

• Go far away enough to allow spatial separation.

• Use a linear or 2-D intensity detector to record the spectrum.

• Un-diffracted x-rays travel through and can be used for “real” experiments.

y

E1

E2

R

O

d2

T

Laue vs. Bragg, perfect vs. bent

Bragg

Laue

Symmetric Asymmetric

B B

BB

Angular acceptance Energy bandwidth (micro-radians) (E/E)Perfect Crystal a few-10’s 10-4- 10-5

Meri. Bent Laue xtal 100’s-1000’s 10-3 - 10-2

Sag. Bent Laue xtal 100’s 10-3

Order-of-Magnitude

Diffraction of 8-keV X-rays by Si CrystalReflection

Bragg

Angle (deg)

Darwin

Width (micro-radians)

Extinction length (microns)

dE/E

111 14.3 34 3.0 1310-5

220 23.8 25 2.6 5.7 10-5

311 28.3 14 4.1 2.710-5

400 34.8 17 3.2 2.410-5

511 47.9 9.1 5.4 0.8310-5

440 53.8 13 4.1 0.9110-5

533 69.4 10.7 6.7 0.4010-5

• 511 or 440 can be used to provide 10-5 energy resolution

• Absorption length ~ 68 microns

• What bending does? – A controlled change in angle of lattice planes and d-spacing of

lamellae through the crystal• Lattice-angle change- determines dispersion• D-spacing change – Does not affect the energy resolution,

as it is coupled to lattice-angle change …diffraction by lamellae of different d-spacing ends up at different spot on the detector.

• Both combine to increase rocking-curve width - energy bandwidth

• Each lamella behave like perfect crystal –resolution• Reflectivity: a few to tens of percent depends on diffraction

dynamics and absorption– Small bending radius: kinematic – low reflectivity– Large bending radius: dynamic – high reflectivity

• A lamellar model for sagittally bent Laue crystals, taking into account elastic anisotropy of silicon crystal has recently been developed. (Z. Zhong, et. al., Acta. Cryst. A 59 (2003) 1-6)D

Diffraction of X-rays by Bent Laue Crystal

Sagittally-bent Laue crystal

• : asymmetry angle • Rs: sagittal bending radius • B: Bragg angle• Small footprint for high-E x-rays• Rectangular rocking curve• Wide Choice of , and crystal thickness, to control the energy-resolution•Anticlastic-bending can be used to enable inverse-Cauchois geometry

Side View

Top view

Anisotropic elastic bending of silicon crystal

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Three Laue Options

0.5 mm

E1

E2

Meridionally bent, “whole” beam

Meridionally bent, pencil beam

Sagittally bent, whole beam

E1

E2

0.5 mm

E1

E2

Meridionally bent, “whole” beam• How it works

– Using very thin (a few microns) perfect Silicon crystal wafer.

– Use symmetric Laue diffraction, with S53

’=0, to achieve perfect crystal resolution

• Bandwidth:

– Easily adjustable by bending radius R, R~ 100 mm to achieve E/E~3x10-3.

• Resolution

dE/E~10-5 for thin crystals, T~ extinction length, or a few microns

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tan/

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E1

E2

R

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d2

T

Meridionally bent, “whole” beam• Advantages

– Wide range of bandwidth, 10 –4 - 10-2 achievable.

– High reflectivity ~ 1.– Very thin crystal (on the

order of extinction length, a few microns) is used, resulting in small loss in transmitted beam intensity.

y

E1

E2

R

O

d2

T

•Disadvantages–Different beam locations contribute to different energies in the spectrum

Meridionally bent, “whole” beam• Our choice

– Assuming y=0.5 mm– Si (001) wafer– 440 symmetric Laue

reflection– T=5 microns– R=200 mm

y

E1

E2

R

O

d2

T

• Yields (theoretically) – 310-3 bandwidth– 2.6 10-5 dE/E, dominated by xtal thickness

contribution– Dispersion at 10 m is 80 mm– 107 ph/pulse on detector, or 104 ph/pulse/pixel

Meridionally bent, Pencil BeamE1

E2

• How it works– Bending of asymmetric crystal

causes a progressive tilting of asymmetric lattice planes through beam path.

• Bandwidth: – Adjustable by bending radius

R, thickness, and asymmetry angle , possible to achieve E/E~3x10-3 with large .

• Resolution• dE/E is dominated by

beam size y, dE/E ~ y/(RtanB)

• Y must be microns to allow 10-5 resolution

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'13 ss

R

TB

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y

Meridionally bent, Pencil BeamE1

E2

• Advantages– Can perform spectroscopy

using a small part of the beam

• Disadvantages: – Less intensity due to cut in

beam size, and typically 10% reflectivity due to absorption by thick xtal.

• Our pick (out of many winners)

– Si (001) wafer

– 333 reflection, =35.3

– T=50 microns

– R=125 mm

• Yields– 310-3 bandwidth– 0.8 10-5 dE/E, – Dispersion at 10 m is 71 mm– 10% reflectivity– 106 ph/pulse on detector, or

103 ph/pulse/pixel

Sagittally bent, whole beam

0.5 mm

E1

E2

• How it works– Sagittal bending causes a

tilting of lattice planes– The crystal is constrained

in the diffraction plane, resulting in symmetry across the beam.

– Symmetric reflection used to avoid Sagittal focusing, which extends the beam out-of-plane.

• Bandwidth: – Adjustable by bending

radius R, thickness, and crystal orientation.

– E/E~1x10-3.

• Resolution• dE/E probably will be

dominated by the variation in lattice angle across the beam, must be less than Darwin width over a distance of .5 mm.

Sagittally bent, whole beam

0.5 mm

E1

E2

• Advantages– Uses most of the photons

• Disadvantages: – Limited bandwidth due to the

crystal breaking limit.

• Our choice – Si (111) wafer– 4-2-2 symmetric

Laue reflection– T=20 microns– R=10 mm

• Yields– 0.610-3 bandwidth– 1 10-5 dE/E– Dispersion at 10 m is 21

mm– 70% reflectivity– 109 ph/pulse on detector

Testing with White Beam

• Four-bar bender • Collimated fan of white incident beam • Observe quickly sagittal focusing and dispersion • Evaluate bending methods: Distortion of the diffracted beam variation in the angle of lattice planes

Observation of previous data

1 cmh=15 mm

h=0

h=–12

h=–12

h=15 mm

On the wall at 2.8 meters from crystal

Behind the crystal

• 0.67 mm thick, 001 crystal (surface perpendicular to [001]), Rs=760 mm•111 reflection, 18 keV• Focusing effects: Fs=5.7 m agrees with theory of 6 m• “Uniform” region, a few mm high, across middle of crystal• Dispersion is obvious at 2.8 meters from crystal.

Experimental test: sagittally bent, whole beam

• 4-2-2 reflection, (111) crystal, 0.35 mm thick, bent to 500 mm radius, 9 keV• Exposures with different film-to-crystal distance.• No sagittal focusing due to zero asymmetry.• The height at 0.75 m is larger than just behind the crystal, demonstrating dispersion. • Distortion is noticeable at 1 m, could be a real problem at 10 meters.

4-2-2

0.11 m 0.37 m 0.75 m

0.11 m

Measuring the Rocking-curves

•NSLS’s X15A. 111 or 333 perfect-crystal Si monochromator provides 0.1(v) X 100 mm (h) beam, 12-55 keV• (001) crystal, 0.67 mm thick, 100 mm X 40 mm, bent to Rs=760 mm, active width=50 mm• Rm=18.8 m (from rocking-curve position at different heights)• Rocking curves measured with 1 mm wide slit at different locations on crystal (h and x)

Rocking-curve Measurement

• 111 reflection on the (001) crystal, =35.3 degrees• FWHM~ 0.0057 degrees (100 micro-radians)• Reflectivities, after correction by absorption, are close to unity (80-90%) dynamical limit• Model yields good agreement.

-200 -100 0 100 200Rocking Angle (microradians)

0.0

0.2

0.4

0.6

0.8

Re

flect

ivity

20 keV

25 keV

30 keV

40 keV

Depth-resolved Rocking-curve Measurement

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Bs

Rocking-curve width

Two crystals, many reflections tested

18 keV incident beam, 20 micron slit size0.67 mm thick crystal, bent to Rs=760 mm

Rocking-curve width

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Comparison: 001 crystal and 111 crystal

100 xtal, 111 reflection =35 degS31

'=-0.36, S32'=-0.06, S36

'=0Upper-case:0=92-16=76 radLower-case: 0=-73-16=-89 rad

111 xtal, 131 reflection =32 degS31

'=-0.16, S32'=-0.26, S36

'=0Upper-case:0=-73-35=-108 radLower-case: 0=177-35= 141 rad

Upper-case

Lower-case

Future Directions

• Other crystals?– Diamond? for less absorption– Harder-to-break xtals? To increase energy

bandwidth of sagittally-bent Laue

• Experimental testing– 10 m crystal-to-detector distance is hard to come by– 3-5 m may allow us to convince you

Summary• 3 possible solutions for the “assumed” problem.

• Option 3, sagittally-bent Laue crystal, is our brain child.

• Option 1 has better chance.

• They all require – distance of ~ 10 m

– 2theta of ~ 90 degrees -> horizontal diffraction and square building

– linear or 2-D integrating detector

• With infrastructure in place, it is easy to pursue all options to see which, if any, works.

• Typical of bent Laue, unlimited knobs to turn for the true experimentalists … asymmetry angle, thickness, bending radius, reflection, crystal orientation …

• We have more questions than answers …

Focal Length

Real Space

Reciprocal Space

• Diffraction vector, H, precesses around the bending axis change in direction of the diffracted beam

sinsin2

sin

)2/sin(sin2

B

ss

s

RF

Rx

HH

• Fs is positive (focusing) if H is on the concave side• No focusing for symmetric Laue: At =0 Fs is infinity - H points along the bending axis

Inverse-Cauchois in the meridional plane

• At =0, E/E is the smallest inverse-Cauchois geometry• E/E determined by diffraction angular-width 0~ a few 100’s micro-radians• Source and virtual image are on the Rowland circle. • No energy variation across the beam height

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Condition for Inverse-Cauchois