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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 @ 100 m Source size: 82 microns N (10 10 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. y E1E1 E2E2 R O T

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Laue vs. Bragg, perfect vs. bent Bragg Laue SymmetricAsymmetric BB BB BB BB Angular acceptance Energy bandwidth (micro-radians)( E/E) Perfect Crystala few-10’s10 -4 - 10 -5 Meri. Bent Laue xtal100’s-1000’s10 -3 - 10 -2 Sag. Bent Laue xtal100’s10 -3 Order-of-Magnitude

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Diffraction of 8-keV X-rays by Si Crystal Reflecti on Bragg Angle (deg) Darwin Width (micro-radians) Extinction length (microns) dE/E 11114.3343.0 13 10 -5 22023.8252.6 5.7 10 -5 31128.3144.1 2.7 10 -5 40034.8173.2 2.4 10 -5 51147.99.15.4 0.83 10 -5 44053.8134.1 0.91 10 -5 53369.410.76.7 0.40 10 -5 511 or 440 can be used to provide 10 -5 energy resolution Absorption length ~ 68 microns

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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

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Sagittally-bent Laue crystal : asymmetry angle R s : 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 0.5 mm E1E1 E2E2 Meridionally bent, “whole” beam Meridionally bent, pencil beam Sagittally bent, whole beam E1E1 E2E2 0.5 mm E1E1 E2E2

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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 S 53 ’ =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 y E1E1 E2E2 R O T

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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. y E1E1 E2E2 R O T Disadvantages –Different beam locations contribute to different energies in the spectrum

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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 E1E1 E2E2 R O T Yields (theoretically) – 3 10 -3 bandwidth – 2.6 10 -5 dE/E, dominated by xtal thickness contribution – Dispersion at 10 m is 80 mm – 10 7 ph/pulse on detector, or 10 4 ph/pulse/pixel

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Meridionally bent, Pencil Beam E1E1 E2E2 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/(Rtan B ) Y must be microns to allow 10 -5 resolution y

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Meridionally bent, Pencil Beam E1E1 E2E2 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 – 3 10 -3 bandwidth – 0.8 10 -5 dE/E, – Dispersion at 10 m is 71 mm – 10% reflectivity – 10 6 ph/pulse on detector, or 10 3 ph/pulse/pixel

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Sagittally bent, whole beam 0.5 mm E1E1 E2E2 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.

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Sagittally bent, whole beam 0.5 mm E1E1 E2E2 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 – 0.6 10 -3 bandwidth – 1 10 -5 dE/E – Dispersion at 10 m is 21 mm – 70% reflectivity – 10 9 ph/pulse on detector

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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 1 cmh=15 mm h=0 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: F s =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.

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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 m0.37 m0.75 m 0.11 m

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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 R s =760 mm, active width=50 mm R m =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)

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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 Rs=760 mm Rocking-curve width

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Comparison: 001 crystal and 111 crystal 100 xtal, 111 reflection =35 deg S 31 ' =-0.36, S 32 ' =-0.06, S 36 ' =0 Upper-case: 0 =92-16=76 rad Lower-case: 0 =-73-16=-89 rad 111 xtal, 131 reflection =32 deg S 31 ' =-0.16, S 32 ' =-0.26, S 36 ' =0 Upper-case: 0 =-73-35=-108 rad Lower-case: 0 =177-35= 141 rad Upper-case Lower-case

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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 -> 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 Real Space Reciprocal Space Diffraction vector, H, precesses around the bending axis change in direction of the diffracted beam F s is positive (focusing) if H is on the concave side No focusing for symmetric Laue: At =0 F s is infinity - H points along the bending axis

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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 Meridional plane Condition for Inverse-Cauchois

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