zhiyangwang
Hi All,
I did some in situ synchrotron x-ray diffraction measurements on bulk samples in reflection geometry. The sample surface is fixed in a cell during measurements. I'd like to refine the Specimen_Displacement value in TOPAS to confirm sample surface is not moving. Seems it must be very dependent on the sample surface angle to the beam, but I don’t see where that’s taken into account in the TOPAS macro. Does anyone has idea about the macro I require?
Thanks
Zhiyang
zhiyangwang
@ Alan
Could you please give me some advices about my question? Many thanks.
alancoelho
Specimen displacement as defined in the SD macro in TOPAS.INC is for parafocusing geometry where the sample in the equitorial plane is at Th with the primary beam and the detector at 2Th with the primary beam; note the beam is divergent.
What you have is a parallel beam hitting a sample that does not move. If you have analyser/Soller slits that keep the beam parallel in the equitorial plane then specimen displacement would not move the peaks.
You would need to describe the instrument; the instrument scientist should be able to help. You may want want to look at the paper:
Cheary, R. W.; Coelho, A. A. and Cline, J. P. (2004). Journal of Research-National Institute of Standards and Technology 109 (2004): 1-26. "Fundamental parameters line profile fitting in laboratory diffractometers."
In that paper search for the term parallel.
cheer
alan
zhiyangwang
Hi Alan, thanks for your help.
rowlesmr
Have a look at these two papers. The first looks at instrument profiles for synchrotrons in flatplate reflection, and has the specimen displacement function in it (from earlier work). The second as specimen displacement calcs for capillary samples.
Whole-pattern profile fitting of powder diffraction data collected in parallel-beam flat-plate asymmetric reflection geometry
By: Rowles, Matthew R.; Madsen, Ian C.
JOURNAL OF APPLIED CRYSTALLOGRAPHY Volume: 43 Pages: 632-634 Part: 3 Published: JUN 2010
DOI: 10.1107/S0021889810007673
Sample-displacement correction for whole-pattern profile fitting of powder diffraction data collected in capillary geometry
By: Scarlett, Nicola Vivienne Yorke; Rowles, Matthew R.; Wallwork, Kia S.; et al.
JOURNAL OF APPLIED CRYSTALLOGRAPHY Volume: 44 Pages: 60-64 Part: 1 Published: FEB 2011
DOI: 10.1107/S0021889810047461
zhiyangwang
Hi Alan,
For the instrument I used with the synchrotron source and Mythen detector, we don't have the analyser/Soller slits.
I would like to refine the Specimen_Displacement values to check that the sample is not moving during the cyclic measurements. In the experimental setup, the beam is incident along a certain angle to the sample surface. I'm wondering whether this angle affect the refinement of the Specimen_Displacement values? If so, is it taken into account in the macros? And what instrument conditions I need to describe?
Sorry I'm still not clear... thanks!
alancoelho
The diagram in the attached image shows your situation. The sample is red and the dashed red line is the sample displaced by an amount t in a direction perpendicular to the sample. omega is the angle the sample makes with the incident beam in the equatorial plane. 2Th_Bragg is the diffraction angle of some peak.
The length of the green line (del) is what you are after or from geometry we have:
del = t Cos(2Th_Bragg-omega)
If the detector is moving in an arc with radius R then the change in 2Th (which we will call 2Th_measured) due to a movement in the sample del is:
2Th_measured = 2Th - (del / R) Pi/180
Angles 2Th_measured and 2Th are in radians. To refine on t then use:
prm t 0
prm !radius = whatever that happens to be;
th2_offset = -t Cos(2 Th- omega) (180/Pi) / radius;
th2_offset is in degrees 2Th. Check the geometry as mistakes do occur.
rowlesmr
Hi Zhiyang
I'm assuming this is for the PD beamline at the AS?
The equation you're after is equation 4 is the first paper I referenced.
The attached picture details its derivation.
O is the goniometer centre. O' is the centre of diffraction for the displaced specimen. R is the diffractometer radius. a is the angle of the specimen. 2T is the diffraction angle.
If the specimen is at the centre of goniometer, then an X-ray diffracted at 2T is detected at 2T.
If the specimen is displaced some distance s from the centre, where the distance is perpendicular to the sample surface, then an X-ray diffracted at 2T is detected at (2T + d).
The distance O-O' is given by s/sin(a).
R/sin(2T) = O-O'/sin(d) --> sin(d) = (s/R)(sin(2T)/sin(a))
If you then invoke the small angle rule, then the 2T offset is equal to (s/R)(sin(2T)/sin(a)).
Yes, the specimen angle affects the refined specimen displacement.
You'll also have line broadening due to the geometry, and my first paper linked above goes over this.
Matthew
alancoelho
zhiyangwang
Matthew is correct - I'm wrong; thanks Matthew. It shows the importance of peer review.
zhiyangwang
Thanks Matthew for you helpful instructions, yes, this is for the PD beamline at the AS.
I've read through your paper which address this problem. I've incorporated the correction function to refine the specimen displacement.
cheers
Zhiyang
zhiyangwang
Thanks Alan
johnsoevans
Anybody fancy putting a summary of the above on the wiki? Perhaps in the topics section?
mfisch
BTW: There is a similar approach as in Scarlett et al., for capillaries, which can be found in
Gozzo et al., Z Kristallogr 225 (2010) 616-624.
The corresponding Topas Macro is
th2_offset =(Rad ArcSin( (VD Cos(2 Th))/Rs) )+(Rad ArcSin( (HD Sin(2 Th))/Rs) ) + Ze;
for data measured from 0 to positive 2Th, and
th2_offset =(Rad ArcSin( (-VD Cos(2 Th))/Rs) )+(Rad ArcSin( (HD Sin(2 Th))/Rs) ) - Ze;
for data from 0 to negative 2Th.
Refineable parameters are consequently:
prm HD 0 = horizontal displacement (along to the beam)
prm VD 0 = vertical displacement (perpendicular the beam)
prm Ze 0 = zero error
Determining all three parameters requires high intensity data up to high angles in both negative and positive 2Th from a standard material. Once the zero offset is determined, it gives very robust results.