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Sub-meV optics for medium energy X-ray spectroscopy: Principles and preliminary studies
XianRong Huang
Advanced Photon Source, Argonne National [email protected]
I. Angular dispersion optics using grazing backscattering
II. Multi-cavity Fabry-Perot interferometry
Thanks to Yuri Shvyd’ko (APS) and D. Peter Siddions (NSLS) …
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Sub-meV-resolution optics at medium energy (5-10 keV)
Inelastic X-ray Scattering (IXS):
• Higher energy transfer resolution
• Higher momentum transfer resolution, filling the gap between high and low frequency probes
• Higher brightness at medium energy for many synchrotrons, particularly for NSLS-II
For ~1 nm focusing, may also need narrow energy bandwidths Coherent imaging (coherent length = 2/) High resolution X-ray diffraction…
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Backscattering has the highest resolution:
Even ~1 meV mono/analyzer for E <10 keV not realized yet!
• FWHM 1meV for E 20 keV• but FWHM > 30 meV for E < 10 keV• Overall, FWHM when E
High energy resolution optics:a) Monochromator b) Analyzer c) …
based on single-crystal diffraction
Toellner et al, APL 71, 2112 (1997). E = 14.4 keV, E = 0.8 meV Acceptance 8.6 rad
E = 14.4 keV, E ~ 0.1meV!!! Acceptance 6.4 rad Yabashi et al, Rev. Sci. Instrum. 72, 4080 (2001) How about <10 keV???
For E >10 keV, 1 0.1 meV possible using multi-crystal diffraction, but small angular acceptance, a few rad, so NOT for analyzers!
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Goals: Sub-meV at E < 10 keV with wide angular acceptance Applicable for both Mono and Analyzer
I. Angular dispersion optics using grazing back diffraction
Backward CDS geometry
Shvyd’ko’s designsPRL 97, 235502 (2006); NSLS-II
In-line (forward) CDDS geometry
Optics does not depend on Darwin Curve Width
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In asymmetric x-ray diffraction,the crystal is a natural “prism”.
Dispersion of light by prism:
Incident white light decomposed into component colors. Red light refracted less than violet, so propagating in different directions.
White incidence
Polychromatic
Refraction-based
Diffraction-basedX-ray dispersion
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0 0
0 0
, h hx x x
x x hx hx
k k h
K k K k
k k h 0hx x xK K h
Conservation of tangential momentum
2 2 2cos cos sine d
sincos cose d
Relationship between wavelength and incident/exit angles
Bragg law: Kh K0 + h
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Angular dispersion in asymmetric diffraction
sincos cose d
sin
sine
ed
= const
No dispersion in symmetric reflection ( = 0 e )
Dispersion coefficient increases with e 0, grazing-exit geometry
DuMond diagramS. Brauer et al. JSR 2, 163 (1995)
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sin tan
sin(90 )e
d d
2 tane
H
E
E
2H
hcE
dwhere
A geometry effectIndependent of the Structure Factors and Darwin curve, so also applicable to higher energy optics!
sin
sine
ed
To maximize resolution: 90°, e 0
Grazing backscattering
e
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2 tane
H
E
E
For Si 008 reflection: EH 9.1 KeV
If angular acceptance of selector e = 5106 rad
= 88.5 E = 0.6 meV = 89.6 E = 0.16 meV
for a single dispersing crystal
90°
We can use (1) two dispersing crystals (described later) or (2) reduce e or (3) further increase (but must not exceed the critical angle ~89.8°) to achieve 0.1 meV!
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CDS scheme
DuMond DiagramShvyd’ko et al., PRL 97, 235502 (2006)
C S
D
Transmission through the thin crystal due to
Bormann effect
Si 220, B = 20.7Asymmetric factor |b| 20
Acceptance ~100 rad 5rad divergence of diffracted
Si 008
Angular acceptance~ 5 rad
0.6 meV 2
CDS scheme
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Si 220, B = 20.7
R(E, 1)
sincos cos
d
Full calculation using dynamical theory
R(E, 1) = R1(E, 1) T2(E, 2) R3(E, 3) R4(E, 4)
Totalreflectivity
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= 88.5 E = 0.6 meV = 89.6 E = 0.16 meV
Predicted
Calculated with 1 = const
Back diffraction reflectivity ~ 90% for 89.79º, close to the critical angle!!!Because b -1.
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1
Angular acceptance~ 87 rad
> 100 rad for = 88.5°
= 89.6°
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Energy Tuning
Selectorfixed
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Energy tuning
Tuning rate 0.07 meV/rad
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2 tanH
E
E
for a single dispersion crystal
In-line (forward) CDDS scheme
4 tanH
E
E
Resolution doubledfor two D-crystals
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Full dynamical theory calculations
Inline forward CDDS
steep wingone side
Backward CDS
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Horizontal divergence?
0hx x xK K h Conservation of tangential momentum
2 2 2cos cos sine d
sincos cose d
To treat incidence deviated by a small angle in the horizontal plane, replace 2/ with
(2/)cos = (2/)(1 2/2...) Modification negligible when < 1 mrad
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Experimental verification
Shvyd’ko et al., PRL 97, 235502 (2006)Shvyd’ko et al., SRI 2007
= 88.5°
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X-ray transmission topographs of selector (thin crystal)
on peak
off peak
X. R. Huang et al., to be published
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Technical issues
1. Long dispersion crystal (segmented)
0.1 meV, E/E ~ 10-8 d/d ~ 10-8
temperature stability and homogeneity ~1 mK
Thermal coefficient of Si: 2.5610-6 K-1
No bending of the entire long crystal, < 1rad How to mount? (gravity)
Surface roughness of long crystals?
No strict requirement for the stability of the undulator beam
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2. Thin crystal
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Alternative designs?
sin
sine
ed
sin80o = 0.985sin89.6o =0.99997563
General CDS
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Spectrum of General CDSfor collimated incidence
compared with 0.18 meV (59%) for CDS
compared with 87 rad for CDS
Unfortunately!
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How to increase acceptance?
Add another collimator C to increase acceptance by a factor b, say 30
But also increases
crystal lengths by b !!!
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The long crystals not shortened (for mono, could be shortened) Efficiency less than CDDS.
Acceptance > 100 rad
More flexible, many variants Avoid multi-beam diffraction Arbitrary energy Scan in wide energy range More suitable for monos!
Pros:
Cons:
More work is undergoing to optimize and to shorten the crystals
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Yabashi et al, E = 14.4 keV, E ~ 0.1meV!!!
C1
C2 D
S
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Conclusion of Angular Dispersion Optics
Sub-meV resolution optics ~ 0.1 meV with angular acceptance ~ 100 rad is feasible based on the Angular Dispersion Principle in asymmetric x-ray diffraction, no doubt in principles.
Backward CDS In-line forward CDDS
o Both using grazing back diffraction: E/E independent of E or Bragg reflection.
o The smaller the photon energy E the smaller is the bandpass E.o For a fixed E, E can be varied by changing (crystal lengths change
though).o Efficiency R and the Acceptance almost constant (while changing ).
Multiple-crystal CCDS For both monos and analyzer (combined with mirrors) Long crystals, strain free, temperature, no bending, mounting
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II. Multi-cavity Fabry-Perot Interferometer
In optics, a Fabry-Pérot interferometer typically made of two parallel highly reflecting mirrors:
For normal incidence = 90º
Free spectral range Ed 0.5hc/tc
Finesse F = Ed /E R1/2/(1 R)
Spectrum
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No large-angle X-ray mirrors!
Using diffraction reflectivity, particularly back diffraction
X-ray interferometer
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Dynamical theory
Dynamical theory simulation
Chang SL et al., PRL 94, 174801 (2005)Shvyd’ko et al., PRL 90, 013904 (2003).
Experiments:
Si (12 4 0), t = 70 m, tc = 520 m
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Tough requirement of pre-monochromator
Solution: Increase Ed. Ed 0.5hc/tc
by shrinking the cavity distance tc
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5 meV pre-monochromator is practical,but spectrum is not clean (and E increased).
tc decreased to 80 m from 520 m
Solution: to increase Finesse? F = Ed /E R1/2/(1 R)
i.e. to increase R, but this is difficult
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True solution: using two cavities
(a) Two-cavity resonaotor.
(b) t1 = 45 m
t2 = 90 m
tc = 81 m.
(c) t1 = 60 m (R increased)
t2 = 120 m
tc = 81 m
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Si (660), E = 9.69 keV
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How to further increase the energy resolution?
Three-cavity interferometer
Compact, single-component,tiny yet powerful
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Si (12 4 0) E = 14.4 keV
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~ eV
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Angular acceptance
t1 = 60 m
t2 = 120 m
tc = 81 m
Physical size limited
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Substantial undercut on the outside wallis largely corrected this time, withoutmessing up the verticality of the inside wall.
Note that we etched deeper than 100 microns.
There is still some bowing near the corner of the structure, but there is a way to address that.
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How to avoid Absorption & Multi-Diffraction?
Multi-cavity interferometers suffer absorption
Diamond
Low absorption
High reflectivity (very close to unity)
High Debye-Waller temperature
Hard, resistance to bending, strains
Fabrication???
Sapphire: avoid multiple diffraction
more energy choices
quality concern
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Thank you!