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

1
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

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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

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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 _at_ 100 m
• Source size 82 microns
• N (1010 assumed) ph/pulse

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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.

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Laue vs. Bragg, perfect vs. bent
Symmetric
Asymmetric
qB
qB
c
Bragg
c
Laue
qB
qB
Order-of-Magnitude
Angular acceptance Energy bandwidth

(micro-radians) (?E/E) Perfect Crystal a
few-10s 10-4- 10-5 Meri. Bent Laue
xtal 100s-1000s 10-3 - 10-2 Sag. Bent Laue
xtal 100s 10-3
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Diffraction of 8-keV X-rays by Si Crystal
Reflection Bragg Angle (deg) Darwin Width (micro-radians) Extinction length (microns) dE/E
111 14.3 34 3.0 13?10-5
220 23.8 25 2.6 5.7 ?10-5
311 28.3 14 4.1 2.7?10-5
400 34.8 17 3.2 2.4?10-5
511 47.9 9.1 5.4 0.83?10-5
440 53.8 13 4.1 0.91?10-5
533 69.4 10.7 6.7 0.40?10-5

• 511 or 440 can be used to provide 10-5 energy
  resolution
• Absorption length 68 microns

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Diffraction of X-rays by Bent Laue Crystal

• 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

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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
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Anisotropic elastic bending of silicon crystal
Displacement due to bending
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For Sagittally-bent crystals
Lattice-angle change
d-spacing change
Rocking-curve width
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For Meridionally-bent Crystals
Lattice-angle change
d-spacing change
Rocking-curve width
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Three Laue Options
Meridionally bent, whole beam
Meridionally bent, pencil beam
Sagittally bent, whole beam
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Meridionally bent, whole beam

• How it works
• Using very thin (a few microns) perfect Silicon
  crystal wafer.
• Use symmetric Laue diffraction, with S530, to
  achieve perfect crystal resolution
• Bandwidth
• Easily adjustable by bending radius R, R 100 mm
  to achieve ?E/E3x10-3.

• Resolution
• dE/E10-5 for thin crystals, T extinction
  length, or a few microns

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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.

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

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Meridionally bent, whole beam

• Our choice
• Assuming y0.5 mm
• Si (001) wafer
• 440 symmetric Laue reflection
• T5 microns
• R200 mm

• Yields (theoretically)
• 3?10-3 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
  

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Meridionally bent, Pencil Beam

• 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/E3x10-3 with large ?.

y

• Resolution
• dE/E is dominated by beam size y, dE/E
  y/(Rtan?B)
• Y must be microns to allow 10-5 resolution

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Meridionally bent, Pencil Beam

• Our pick (out of many winners)
• Si (001) wafer
• 333 reflection, ?35.3
• T50 microns
• R125 mm
• Yields
• 3?10-3 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
  

• 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.

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Sagittally bent, whole beam

• 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/E1x10-3.

• 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.

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Sagittally bent, whole beam

• Our choice
• Si (111) wafer
• 4-2-2 symmetric Laue reflection
• T20 microns
• R10 mm
• Yields
• 0.6?10-3 bandwidth
• 1 ?10-5 dE/E
• Dispersion at 10 m is 21 mm
• 70 reflectivity
• 109 ph/pulse on detector

• Advantages
• Uses most of the photons
• Disadvantages
• Limited bandwidth due to the crystal breaking
  limit.

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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

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Observation of previous data

• 0.67 mm thick, 001 crystal (surface
  perpendicular to 001), Rs760 mm
• 111 reflection, 18 keV
• Focusing effects Fs5.7 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.

Behind the crystal
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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
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Measuring the Rocking-curves

• NSLSs 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 Rs760 mm, active width50 mm
• Rm18.8 m (from rocking-curve position at
  different heights)
• Rocking curves measured with 1 mm wide slit at
  different locations on crystal (h and x)

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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.

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Depth-resolved Rocking-curve Measurement
Rocking-curve width
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Two crystals, many reflections tested
18 keV incident beam, 20 micron slit size 0.67 mm
thick crystal, bent to Rs760 mm
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Comparison 001 crystal and 111 crystal
Upper-case
Lower-case
100 xtal, 111 reflection ? 35 deg S31'-0.36,
S32'-0.06, S36'0 Upper-case?092-1676
?rad Lower-case ?0-73-16-89 ?rad
111 xtal, 131 reflection ?32 deg S31'-0.16,
S32'-0.26, S36'0 Upper-case?0-73-35-108
?rad Lower-case ?0177-35 141 ?rad
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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

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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 -gt 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

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Focal Length

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

Real Space

• 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

Reciprocal Space
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Inverse-Cauchois in the meridional plane
Meridional plane

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