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

2. 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

3. 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

4. E1 R E2 y O T 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.

5. Laue vs. Bragg, perfect vs. bent Symmetric Asymmetric qB qB c Bragg c qB qB Laue Order-of-Magnitude 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

6. Diffraction of 8-keV X-rays by Si Crystal • 511 or 440 can be used to provide 10-5 energy resolution • Absorption length ~ 68 microns

7. 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

8. 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

9. Anisotropic elastic bending of silicon crystal Displacement due to bending

10. For Sagittally-bent crystals Lattice-angle change d-spacing change Rocking-curve width

11. For Meridionally-bent Crystals Lattice-angle change d-spacing change Rocking-curve width

12. E1 E2 0.5 mm E1 E2 E1 E2 0.5 mm Three Laue Options Meridionally bent, “whole” beam Meridionally bent, pencil beam • Sagittally bent, whole beam

13. E1 R E2 y O T 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

14. E1 R E2 y O 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. • Disadvantages • Different beam locations contribute to different energies in the spectrum

15. E1 R E2 y O T Meridionally bent, “whole” beam • Our choice • Assuming y=0.5 mm • Si (001) wafer • 440 symmetric Laue reflection • T=5 microns • R=200 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

16. E1 E2 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/E~3x10-3 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

17. E1 E2 Meridionally bent, Pencil Beam • Our pick (out of many winners) • Si (001) wafer • 333 reflection, =35.3 • T=50 microns • R=125 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.

18. E1 E2 0.5 mm 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/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.

19. E1 E2 0.5 mm Sagittally bent, whole beam • Our choice • Si (111) wafer • 4-2-2 symmetric Laue reflection • T=20 microns • R=10 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.

20. 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

21. 1 cm h=15 mm h=0 h=15 mm h=–12 h=–12 On the wall at 2.8 meters from crystal Observation of previous data • 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. Behind the crystal

22. 0.11 m 0.37 m 0.75 m 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

23. 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)

24. 0.8 40 keV 30 keV 0.6 25 keV 20 keV Reflectivity 0.4 0.2 0.0 -200 -100 0 100 200 Rocking Angle (microradians) 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.

25. Depth-resolved Rocking-curve Measurement Rocking-curve width

26. Rocking-curve width Two crystals, many reflections tested 18 keV incident beam, 20 micron slit size 0.67 mm thick crystal, bent to Rs=760 mm

27. 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:0=92-16=76 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: 0=177-35= 141 rad

28. 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

29. 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 …

30. 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

31. Condition for Inverse-Cauchois 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 100’s micro-radians • Source and virtual image are on the Rowland circle. • No energy variation across the beam height