Upgrades and Development for XES
at CHESS
Robert Cope, Colorado State University
Ken Finkelstein, CHESS
Motivation and Goals Set for Summer
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Want to improve XES capabilities and enhance user
experience at beam line.
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Implementing multilayer mirrors in the monochromator
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Improve User experience
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Goal: Model the multilayer mirrors and integrate into current
simulations of beam line.
Goal: Automate calibration procedure, and produce easily usable
calibration constants file.
Goal: Add all necessary functionality to beam line data analysis tools.
Add to current calibration procedure:
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Goal: Help implement secondary X-Ray source, reducing dependence
on “precious synchrotron time.”
CHESS and X-Ray Emission Spectroscopy
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XES works by looking at X-ray fluorescence coming from the
source. Incident X-rays have enough energy to eject an inner
shell electron, often a K-shell electron. The atoms fluoresce
when an electron drops from a higher energy state down into
the vacancy in a lower energy state.
Transition energies vary from element to element, thus XES is
“element sensitive.”
XES is a good method of probing the electronic structure of
atoms and crystals.
The C1 XES setup has been used to probe high energy
electronic transitions, including K-α and K-β lines in samples
such as iron.
Right: Atom with Ligands. Source: Chris Pollock
X-rays and Emission Spectra
K-β Lines
We are interested specifically in the K-β
lines, which are some of the highest
energy emission lines. K-β lines result
from an electron dropping from the M
or N shells (principal numbers n = 3 and
4) down into the K shell (principal
number n =1), and emitting X-rays.
Source: Lawrence Berkeley National Laboratory X-ray Data Booklet
Improving XES efficiency.
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Certain electronic transitions, such as the satellite K- β
lines fluoresce very weaking compared to K-alpha.
Low flux silicon optics in the monochromator mean
longer wait times to probe transitions.
We need a way to resolve transitions faster.
Solution: Multilayer Monochromator
Some Background: Beam Path
Top Down View
Analyzer
Detector
Sample/
Detector
Vortex
Laue Xtal
I0
Analyzer
I1
Sample
Incident Beam
from CESR
Monochromator
Side View
Rowland Geometry
L = R sinQB
P = R sin2QB
H = R sin(2QB)
R = 85cm
QB (Mn Kb) ~ 84.3 deg
QB (Mo Kb) ~ 81.1 deg
Calculate detector & crystal vertical
motion about H & H/2 center position
using dE/E=DQB /tanQB-center .
detector
Crystal bend
radius = R
H
P
P
R/2
L
QB
sample
P
Side view
Top view
Source: Ken Finkelstein
OD ~115mm
Detector Mechanism
Left: The sample, analyzer crystals and the detector as they are setup at C1
Right: A picture of the spectrometer sitting inside the Helium chamber at C1
Source: Ken Finkelstein
Multilayer Optics
Multilayer Mirror
Θ
Top Layer
Θ
Air/Vacuum
Cell N
Bottom Layer
Cell N-1
Cell N-2
In order to model the
Multilayer mirror, we
can treat each cell as
a set of two classical
optical layers.
Modified Fresnel
relations can then be
used to determine
reflectivity. We must
account for multiple
reflections in our
theory.
Cell 1
r = Er / E0
Substrate (R =0)
R = Ir / I 0
Modeling Multilayer Optics
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Need to model and simulate Multilayer optics so we
know the angle to align the mirrors at, and how much
reflectivity we will see for a given energy.
Bmad is a library developed by David Sagan originally for
charged particle simulation. It has been adapted for
modeling synchrotron radiation.
Bmad allows us to simulate the entire beam line, along
with CESR to get a fuller prediction of what will happen
when we change parameters and elements in the beam
line.
Bmad Logo Source: David Sagan
Modeling Multilayer Optics
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Three models for Multilayer Optics:
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Kinematic Approximation [1]
Parratt Recursion Formula [1],[3]
V.G. Kohn’s Analytic Formula [2]
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Advantages/Disadvantages:
Kinematic:Very Simple/Rough approximation, fails in low-angle
Parratt: Simple, Accurate/Long computation time
Kohn: Accurate, Quick/Difficult to implement correctly
First Task: Accurately Implement Reflectivity
Simulations
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Kinematic formula was not used because we need
accurate data.
Parratt and Kohn’s equations were coded into a Python
script and evaluated, debugged and modified until results
were produced that matched those provided by CXRO,
and then used to check against Tao data.
Simulations were tested with the proposed MLM, which is
formed from multiple W/B4C bilayers, at many different
angles and energies.
Simulating Multilayer Mirror Reflectivity
Kohn’s Analytic Formula
Parratt Recursion Formula
Notice, Kohn’s analytic formula takes a order of magnitude less time to give results.
Simulating Multilayer Mirror Reflectivity
Kohn’s Analytic Formula
Parratt Recursion Formula
Implementing in Bmad
My Simulations
Bmad Simulations
Kohn’s Analytic Formula is now implemented in BMAD, and matches my simulations
Note: The Bmad x-axis is not angle, but instead the sin of the angle, which
Corresponds to the normalized x-momentum, px = Px/P0, where P0 is the total
Momentum, and Px is the x component of the total momentum.
Multilayer Optics
Kohn’s multilayer formula is now implemented
in Bmad. It matches the “golden standard,”
Parratt’s recursion formula, and is an order of
magnitude quicker.
 The next step will be to debug Laue geometry
in Bmad, and begin simulating the proposed
MLM setup in C1.
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New Calibration Procedure
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The drawback to using an MLM: Increase in flux
proportional to increase in bandwidth. MLM has 100x
more bandwidth, with ΔE/E = 1%.
Since the analyzer has a bandwidth roughly the same as
the silicon optics, calibrating MLM energy to analyzer
energy is difficult.
Solution: Use a Laue diffraction crystal in the beam path
to resolve energy. The Laue crystal cuts a notch out of
the incident beam given approximately by the Bragg
relation:
λ = 2d sin(Θ)
Laue Geometry in Diffracting Crystals
Laue
Scattering
Bragg
Scattering
Image Source: wikipedia.org
Right: Artist’s
rendition of beam
profile after Laue
diffraction.
When we talk about a crystal utilizing Laue
geometry, diffraction planes are near normal to
the surface for Laue geometry and near parallel
to the surface for Bragg geometry. In both cases,
the diffracted beam is emitted at an angle ~Θ,
where Θ is the Bragg angle defined by λ =
2dsin(Θ). Also typically associated with Bragg
scattering is the reflection of the incident
waveform. A crystal in the Laue geometry
produces scattering at the transmission
interface, rather than reflection.
Calibration
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As discussed in previous talk, calibration procedure has
been coded into a SPEC script
SPEC is the X-ray data taking tool, which drives motors
and reads detectors.
Calibration procedure generates a file containing analyzer
and detector motor positions and corresponding Laue
energies.
File is read in by my data analysis program or can be used
later by beam line user in their own analysis
On to the Beamline
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Now that we know how the reflectivity should look, and
how to calibrate, how do we incorporate this at the beam
line? Also how do we make it easier for users to make
sure data is good?
Energy calibration from SPEC script (last presentation) is
used in one of a couple of new PyMca modules for data
analysis at the beam line.
New module fits Laue energy-analyzer position, and
automatically changes spec scans in PyMca to energy
space.
Left: Workstation at C1 Beamline
PyMca: X-Ray Data Analysis
Summing, Averaging, Scaling, Error Bars,
etc.
More Data Analysis
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Certain features such as error bars not stock on PyMca
Feature Implementation List:
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Square Root of N Error Bars
Summing, Averaging, and Standard Deviation of Mean for
selected curves
Scaling to Monitor Curve with error bar propagation
First and Second Derivatives of multiple curves
Normalization of curve integral to 1.
Most new features wrapped into convenient GUIs
Everything built on QT4 and Python, thus portable and
free.
Completed Tasks:
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Finished:
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Calibration procedure for MLM ready, scripts written
Data analysis modules written, PyMca ready for Beam line
MLM reflectivity modeled with Parratt Forumla and Kohn’s
Formula, integrated into Bmad
X-Ray tube ready to be physically mounted in Beam line for
calibration without synchrotron:
To Be Completed:
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Test simulations, scripts and modules with Synchrotron running
Get power supply for X-Ray tube, test with current setup.
Finish integrating Laue diffraction into Bmad
Acknowledgements:
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Ken Finkelstein
David Sagan
Serena DeBeer
Armando Sole
Georg Hoffstaetter, Ivan Bazarov, Lora Hine, and Monica
Wesley
CHESS staff
NSF
The End
Questions?
Sources:
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[1] – J. Als-Nielsen & D. McMorrow, “Elements of Modern
X-Ray Physics”, 2001
[2] – V.G. Kohn, “On the Theory of Reflectivity by an XRay Multilayer Mirror”, Phys. Stat. Sol. 187
[3] – L. G. Parratt, “Surface Studies of Solids by Total
Reflection of X-Rays”, Phys. Rev. 95, 359 (1954)
[4] - Ken Finkelstein, private communications.
[5] - Chris Pollock, Development of Kβ X-ray Emission
Spectroscopy
[6] - Kazmirov et al., “Multilayer Optics at CHESS”
X-Ray Tube Adaptor Plate
In order to use the calibration X-ray tube with the beam line, an adaptor for the current
tube holder had to be designed to allow it to be inserted easily in to existing beam line
clamps.
Assembled X-Ray Tube Holder
The X-Ray tube holder adapter was machined and then fitted up to the
enclosure. The fit is good, and the X-ray tube will be ready to be used on the
beamline once a suitable power supply has been found.