(Doc to be updated)

Main result and status

Result

link to main result here that will be displayed in the following text (energy repartition and XANES/EXAFS scans)

Give the commands to create those results:

mxrun SOLEIL_ROCK.instr Etohit=8500,9500 scan=1 nbsample=1 cc=2 -N100

mxrun SOLEIL_ROCK.instr Etohit=5700,6800 scan=1 nbsample=2 sample_file=Mn.txt sample_density=7.21 sample_file_2=Cr.txt sample_density_2=7.15 cc=2 -N100

Status

• Simulate the ROCK beamline
• Use the Single_crystal component as it is used in the glitches project.

The ROCK beamline

Rock is a quick-EXAFS beamline dedicated to the study of rapid kinetic processes on nanomaterials used mainly in the field of catalysis and of batteries. It's energy range goes from 4 to 40 keV, the wavelength selection is done with a two Hertz oscillating channel-cut.

From the source to the sample the beamline is composed of the elements listed in the table I with their characteristics :

Table I

Beamline elements	Bending magnet	Horizontal slit	Vertical slit	Toroidal mirror	Horizontal slit	M2a plane mirror	Horizontal slit	Channel Cut	Vertical slit	Horizontal slit	Focusing mirror
Distance (mm) source / Element	0	8533.6	8648.6	10150	11690.5	16820	18151.2	CC1:18920 CC2:19250 CC3:20000	21135	21250	22440
Element characteristics	Field=1.72T Ec=8.65keV	-	-	Coating:Ir(50nm) Big radius:9.02km Small radius:0.0317m Incidence:2.5mrad Width:0.015m Length:1.1m	-	Coatings:Pt(50nm) ou Pd(50nm) ou B4C(5nm) Width:47mm Length:1.1m Incidence:1.75mrad à 5.2 mrad	-	Channelcut CC1 Crystal:Si(111) d:3.13582Ang Width:25mm Length(C1,C2):70mm Spacing:10mm ----------------- Channelcut CC2 Cristal:Si(220) d:1.92038Ang Width:25mm Length(C1,C2):70mm Spacing:10mm ----------------- Channelcut CC3 Crystal:Si(111) d:3.13582Ang Width:25mm Length(C1):50mm Length(C2):70mm Spacing:10mm	-	-	Coatings:Pt(50nm) ou Pd(50nm) ou B4C(5nm) Width:47mm Length:1.1m Incidence:1.75mrad à 5.2 mrad

Angular attitudes of ROCK's beamline optics. The total angular deviation is of 2.5 mrad (toroidal mirror). The angular deviations due to M2a/M2b on one end and those due to the channel-cut on the other cancel each other out.

McXtrace Rock

Soleil : ROCK beamline with McXtrace

Simulation of the ROCK beamline with the McXtrace software. The beam at the end of the line is then used to simulate an EXAFS spectrum of copper.

Channel cut

Vertical offset

Depending on the attack angle the reflected ray from the first crystal will hit the second at different places.

The vertical offset of the ray is : H1 = 2*e*cos(β) The vertical offset of the center of the second crystal is : H2 = D*sin(α+β) where D = sqrt(e^2+l^2) and α = arctan(e/l).

(the red line is not a ray)

The vertical offset of the center of the second crystal is also of interest because we place the optic that follows the second crystal of the CC relative to it's center.

Further on we present a simulation of a simple case with the CC only. The optic that follows the second crystal of the CC will be placed relative to the centre of the second crystal of the CC.

For the simulation of the ROCK beamline, we follow the ray. Indeed the ray needs to hit the same place of the sample. Therefore we position the optic that follows the second crystal of the CC relative to it's centre modulo h.

((explain also the projection for the horizontal offset))

Energy ranges

We have a long CC Si 220, a long CC Si 111 and a short CC Si 111. The long CC have their crystals equal to a length of 0.07 m.

The short CC has it's first crystal equal to a length of 0.05m, and it's second crystal of length 0.07m.

All have their crystals separated vertically of 0.01m. The long CC turn from 4 to 35 degrees. The short CC turns from 6 to 35 degrees.

E=12398.42/(2*d*sin(β))=(12398.42*sqrt(h^2+k^2+l^2))/(2*a*sin(β))

So in theory, the energy ranges are the following:

Si 220: E_min = 5628.83 and E_max = 46283.37.

Long Si 111: E_min = 3446.94 and E_max = 28342.66.

Short Si 111: E_min = 3446.94 and E_max = 18914.31.

But we've seen that the beam moves on the second crystal, let's calculate the energies corresponding to these maximum movements.

β min	β max

For the long CC Si 220:

tan(β_max)=e/0.035 β_max=arctan(e/0.035)=15.945° β_min=arctan(e/(0.07+0.035))=5.44°

Then, with the relation that links the energy and the attack angle seen above, we have:

E_min =(12398.42*sqrt(8))/(2*5.4309*sin(β_max))=11752.44 eV E_max =(12398.42*sqrt(8))/(2*5.4309*sin(β_min))=34055.4 eV

For the long CC Si 111:

E_min = 7196.87 eV et E_max = 20854.59 eV.

For the short CC Si 111:

E_min = 5323.79 eV et E_max = 18914.31 eV.

We call these energies the "hittable" energies.

This is for the ray arriving "horizontally". Because there's a divergence cone the signal still exists for energies out of these "hittable" energies.

Simulation of a simple case, the CC only

We simulate the simple case where we have the CC and monitors placed after it.

Here the centre of our energy monitor is placed relative to the centre of the CC's second crystal.

Let's take as an example three energies of the CC Si 220, E_min = 11752 eV, E_max = 34055 eV and an intermediate energy of 23keV.

Energy monitors

We see that the bell shaped curve of the energy is cut for the energies 11.752 and 34.055 keV. For 11.752 keV, the lowest energies of the bell are cut. For the second, the highest energies of the bell are cut. And for 23 keV, our bell stays symmetrical, there is no longer any cut from one side or the other.

11.752 keV	23.000 keV	34.055 keV

The reason comes from the fact that the CC cuts only a part of the angular divergence cone of the beam at the extremeties of the second crystal:

β min	β max

(Above drawings are temporary, need to redo them cleaner)

PSD (position sensitive detector)

11.752 keV	23 keV	34.055 keV

We notice that the signal's spot moves vertically as explained before. For a small energy (big attack angle) the spot is towards the bottom because H1-H2 < 0. To be exact, in the case of the long CC, H1-H2>0 from 4 to 8 degrees approximately (exact values to be done), and H1-H2<0 from 8 to 35 degrees.

We also notice that the signal is smaller vertically for a bigger energy.

This is explained by the fact that the divergence cone is smaller for a smaller attack angle, and inversely, bigger for a bigger attack angle of the beam (explain in more detail, show a diagram).

Top and bottom energy monitors

We then have an energy monitor cut in half horizontally at mid-height. We do this to observe the energy repartition of our signal.

We observe that the energy is again cut in half, the part with the highest energies is on the top monitor, and the part with the lower energies is on the bottom monitor.

(maybe insert images here if it's not clear)

The rays that hit the top monitor are of higher energies than those hitting the bottom monitor. The rays forming the beam hit the crystal at different angles, it's our angular divergence, but we also have a divergence in energy with dE = 1% *E.

As explained in page 152 of the book "An Introduction to Synchrotron Radiation" by Willmott, Philip, John Wiley & Sons, 2019:

We allow, however, the incoming polychromatic beam to have a divergence of 𝛿𝜃 in the plane containing both it and the cristal normal. According to Equation (5.25), the cristal will select longer wavelengths from that part of the beam that impinges more steeply (larger 𝜃) on it than that part of the beam that strikes the cristal at a shallower angle.

where the equation 5.25 is Bragg's law: 2*d*sin(β)=n*λ

Simulation of the ROCK beamline

We simulate the whole beamline (without the sample).

Here the center of our energy monitor is positionned relative to the center of the CC's second crystal modulo h. We follow the ray.

Let's take as an example three energies of the CC Si 220, E_min = 11752 eV, E_max = 34055 eV and an intermediate energy of 23keV.

Energy monitors

The energy monitors show the same results as previously.

11.752 keV	23 keV	34.055 keV

PSD (position sensitive detector)

11.752 keV	23 keV	34.055 keV

The presence of the M2b mirror has for main purpose to focus the beam towards the detector's entrance, a ionisation chamber of aperture 10mm. Furthermore, it attenuates the vertical movement of the beam caused by the channel-cut's rotation. Another effect of this mirror is to inverse the beam's spot due to it's concavity.

The presence of the M2b mirror attenuates the beam's vertical movement although we note it is a minimal movement.

We also see this inversion in the following part.

Top and bottom energy monitors

We observe the energy is once more cut in half but this time the part with the higher energies is on the bottom monitor, and the part with the lower energies is on the top monitor.

The M2b mirror is the cause of the inversion.

(...)

Simulation of the ROCK beamline with a sample

We position the sample at the end of the beamline.

Energy scan copper

Here is the XANES/EXAFS graph for an energy scan from 8.5 to 9.5 keV with our copper sample. We can't see the oscillations due to backscattering in the EXAFS part because McXtrace does not simulate that effect.

Energy scan Mn and Cr

Here is the XANES/EXAFS for an energy scan of 5.7 to 7.2 keV with a sample composed of Manganese and Chrome.