Hi everyone, Could anyone help me with this. Why is that the Darwin reflectitivity curve plotted versus rotation angle (in text books for example) and rocking curve plotted against rotation angle (observed in the oscilloscope at XAS beamlines for example) look different? I understand that the double crystal rocking curve (photon counts in Ionization chamber1 as a function of Bragg angle) is obtained by rotating the second crystal and recording the photon count. Is it right? Regards, Sankaran Anantharaman
The curve observed on beamlines is the convolution of the curves of the two crystals in the mono, which is why it looks different
from the single -bounce curve in the textbooks.
mam
----- Original Message -----
From: "sankaran anantharaman"
Hi everyone,
Could anyone help me with this.
Why is that the Darwin reflectitivity curve plotted versus rotation angle (in text books for example) and rocking curve plotted against rotation angle (observed in the oscilloscope at XAS beamlines for example) look different?
I understand that the double crystal rocking curve (photon counts in Ionization chamber1 as a function of Bragg angle) is obtained by rotating the second crystal and recording the photon count. Is it right?
Regards, Sankaran Anantharaman _______________________________________________ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
Just to follow up a little on Matthew's answer: The Darwin width is the angular width over which a particular reflection will diffract. A rocking curve measurement usually leaves one crystal at a fixed angle and rotates the second crystal. For a perfectly collimated beam, the resulting intensity would be a convolution of the two Darwin widths. In addition, real x-ray sources have a finite angular spread of the incident beam, so that the rocking curve profile is further blurred. For bending magnet beamlines on older sources, the angular spread of the source can dominate the rocking curve. Many such sources use a collimating mirror before the monochromator in order to reduce the angular spread of the beam on the monochromator. In most cases, both contributions (natural Darwin width of the reflection and angular spread of the source) need to be included to get an accurate rocking curve. --Matt
Following up on Matt's following up on my answer:
Let's pretend that the Darwin curve is a simple rectangle, reflectivity=1 within the Darwin band and 0 outside. Now consider a
given energy, with the source having a wide angular
distribution. The first crystal will select a range of angles to reflect. Now, if the second crystal is exactly parallel to the
first, it will reflect all of the rays. If it's off by the Darwin width, then it will reflect none.
In between, the range of angles the two crystals have in common will be linearly related to the angular offset, so that the rocking
curve of the one with respect to the other will be a triangle. Now, at other energies, the
same thing happens, so with a white incident beam, you still get a triangle.
A useful tool for visualizing this is the Dumand diagram, which is a plot of angle vs. wavelength or energy. The passband of a
single crystal is a curve with a width to it (Darwin width). For the
non-dispersive case (common in monochromators) the curves for the two crystals are parallel and offset in the angle direction by the
angular offset. The transmission of the system is proportional to the overlap
area of the two curves. Books on X-ray diffraction should have examples of these diagrams, which will make it clearer than I can do
with words alone.
mam
----- Original Message -----
From: "Matt Newville"
Just to follow up a little on Matthew's answer:
The Darwin width is the angular width over which a particular reflection will diffract. A rocking curve measurement usually leaves one crystal at a fixed angle and rotates the second crystal. For a perfectly collimated beam, the resulting intensity would be a convolution of the two Darwin widths.
In addition, real x-ray sources have a finite angular spread of the incident beam, so that the rocking curve profile is further blurred. For bending magnet beamlines on older sources, the angular spread of the source can dominate the rocking curve. Many such sources use a collimating mirror before the monochromator in order to reduce the angular spread of the beam on the monochromator.
In most cases, both contributions (natural Darwin width of the reflection and angular spread of the source) need to be included to get an accurate rocking curve.
--Matt _______________________________________________ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
Hi Matthew and Matt, Thanks for your rapid replies and explanation describing the reason for the difference between the rocking curve and the Darwin. I indeed only have little bit of idea about DuMond diagrams and not much and would have to seek further help to understand it better other than that it is a transfer function and its application in a symmetric Bragg reflection. In the meantime, the figure attached as PDF file and caption given in quotations is what I am trying to understand with the help of the text in the book in addition to what Matthew explained. I hope that over the weekend I am still confused but at a higher level. Thanks once again. Regards, Sankaran Start quote" Figure Caption: Non-dispersive geometry (left): X-rays from a white source are incident on two crystals aligned in the same orientation. The central ray (full line) will be Bragg reflected by both the crystals and will emerge parallel to the original ray. A ray incident at a higher angle than that of the central ray will only be Bragg reflected if it has a longer wavelength. The angle of incidence this ray makes with the second crystal is the same as that it made with the first, and will be Bragg reflected. The DuMond diagram in the lower part shows that a scan of the second crystal has a width equal to the convolution of the Darwin widths of the two crystals, independent of the incident angular divergence. Dispersive geometry (right): A ray incident at a higher angle than the central ray at the first crystal will be incident at a lower angle at the second crystal . The second crystal must be rotated by the amount 2(DELTAtheta)in for Bragg's law to be fulfilled. " End quote. Jens Als-Nielsen -- Universität Stuttgart Institute of Physical Chemistry Pfaffenwaldring 55 70569 Stuttgart Tel.: +49 711/685-64463 Fax: +49 711/685-64443
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sankaran anantharaman