Understanding the in uence of incidence and exit optics of a diractometer on the quality and
eciency of measurements
Jimmy Gladh September 20, 2019
Abstract
The purpose of this project has been to streamline the use of the new diractometer, the Bede D1, on the department of material physics. A number of experiments have been done to nd out how to avoid sources of errors, and how to use the machine eciently.
In the rst series of experiments, it was found that the choice in slit setup had a signicant eect on the resolution of the scan. Using the thinnest slits available cost 29 minutes, compared to a total scan time with the widest slits of 5 hours and 41 minutes. In addition to this, the background was well above an order of magnitude higher with the wider slit.
In conjunction with the above experiment, scans were made with an extra, shorter vertical slit on the tube side of the machine. Not using this slit increased the background by a factor of ten.
Using the thinnest slits available combined with the vertical one decreased the background with about a factor of fty, compared to the background while using the widest slits tested, without an extra slit.
Contents
1 Introduction 3
2 Theory 4
2.1 K-shell copper electrons, X-rays and you . . . 4
2.2 Diraction . . . 5
3 Method 7 3.1 Experiments with dierent slit setups . . . 7
3.1.1 Slit experiment - Extra vertical, shorter slit . . . 8
3.1.2 Slit experiment - Diering slits on both side . . . 8
3.1.3 Slit experiment - Same slits on both sides . . . 8
3.2 Copper attenuator . . . 8
3.3 Experiment - Varying the amount of counts . . . 9
4 Results 10 4.1 Slit experiment results . . . 10
4.1.1 Experiment - Extra vertical, shorter slit . . . 10
4.1.2 Experiment - Varying width on each side . . . 11
4.1.3 Experiment - Measurements with varying slit widths . . . 12
4.2 Experiment - Varying the amount of counts . . . 13
4.3 Copper dampener . . . 14
5 Discussion 15
1 Introduction
This project has revolved around the use of the Bede D1 x-ray diractometer, both the physics of x-ray diraction and the general use of the machine. A number of measurements have been done on a sample with dierent setups to streamline using the machine, and to discover potential sources of errors and how to avoid them.
First and foremost a series of measurements has been done with dierent slit setups, to examine how this aects the results in terms of the background radiation and resolution. Three slits with varying widths, with and without an extra shorter vertical slit was used. These measurements were also done to determine how the slit width aected the time needed for the machine to scan the sample.
A minor part of the project has been to determine the strength of a number of copper lters, used to keep the detector to saturate with high beam intensities. This lter is needed when scanning at very low angles, as around half of the initial beam either passes the sample or is transmitted through it.
2 Theory
2.1 K-shell copper electrons, X-rays and you
X-rays are a category of electromagnetic radiation with wavelengths around an order of magnitude of 1 Angstrom m. In the scope of this report, the x-rays from the characteristic K emission, generated from excitation of the inner electron in copper are used.
Figure 1: A schematic picture of energy levels in an atom, with emissions and excitations. [1]
The K-shell electrons are excited by bombarding a target copper plate in an x-ray tube with very energetic electrons. To achieve this the bombarding electrons have to have an energy equal to or greater than the energy needed for the electron in the K-shell to escape the atom. Not all electrons convert its kinetic energy completely, a vast majority hit other particles than the K-electrons, or simply collide with glancing collisions.
In order to accelerate electrons to sucient energies, a high voltage is needed. In an x-ray tube, voltages of the order of magnitude of tens of thousands of volts are used. The lowest limit voltage needed to generate a photon of a given wavelength is described by;
SW L= hc
eV (1)
where SWL stands for short wavelength limit, h is Plancks constant, c the speed of light, e the electron charge and V is the tube voltage.
2.2 Diraction
Diraction essentially uses the phase relation of two waves re ected by two dierent surfaces in a material, as the wavelength of x-rays is suciently short to move between the atoms. A surface, in the scope of this report, is the interface between two materials, and the measurement technique is called XRR. It is also possible to do XRD measurements with the machine used in this report, in which case the surfaces are the atomic planes of the crystal lattices. As the beam re ecting of a deeper layer inside of the material will have moved farther, it will cause destructive or constructive interference at certain angles of the incident light. If the path dierence of the two re ected beams is an integer multiple of the wavelength, there will be constructive interference.
Figure 2: Schematic view of two beams of light re ecting of two layers in a material.
[2]
Using Snell's law and an expression for the path dierence, a formula can be derived. Snell's law:
n1sin(1) = n2sin(2) (2)
The distances traveled by the light and the path dierence:
P D = n2( ~AB + ~BC) n1AD~ (3) Where,
AB = ~~ BC = d
cos(2) (4)
and, AD = 2d tan(~ 2) sin(2) (5)
Using these expressions leads to the formula:
n = 2n2d cos(2) (6)
Where is the wavelength of the x-rays, d is the thickness of a layer, n is an integer multiple and is the angle the incident light makes with the inner layer.
3 Method
Except the experiment concerning the amount of counts, all measurements in this report are done on a 20x20 mm iron vanadium superlattice, Fe/V [4/28]*32. During the project it was found that the results were very uneven and rough at low angle scans, 0 - 3 degrees. It was found that this was caused by the machine not keeping up at high motor speed, and the problem was solved by xing the scan time. The counting time was generaly xed to 2 seconds per measuring point at these angles.
All measurements were done with a step size of 0.01 degrees unless otherwise stated, and all data was normalized with the initial beam intensity.
As the detector has an upper limit of around 1.5 million counts per second, a copper absorber was also used to lower the beam intensity at these angles. At intensities higher than this, the detector does not funtion linearly.
For general information on how to use the Bede D1, see appendix A.
3.1 Experiments with dierent slit setups
A number of measurements were systematically done with dierent slit setups. In total six measurements, three with varying widths on the slits, identical on both the detector side and x-ray side. These scans were all made twice, with and without an extra shorter slit. This shorter slit can be seen in gure 3 below, bottom plate, second one from the left. A schematic diagram of the setup can be seen in gure 4.
The measurements was split into three sections, 0-3, 3-8 and 8-16 degrees. The rst section was done with a xed counting time as explained above, the second section with a variable method with a maximum of 10000 counts and the last with 1000 counts, both with a max scan time of 99 seconds.
Figure 3: A photograph of the slits used in the experiments.
Figure 4: Schematic diagram of the setup.
3.1.1 Slit experiment - Extra vertical, shorter slit
In this experiment the eect of the shorter slit was examined. Two identical measurements, same alignment, sample and settings in the software was done, with and without the extra vetical slit, seen in gure 3 on the bottom plate. A schematical representation of the position of the slit in the machine can be seen in gure 5.
Figure 5: Diagram showing the position of the slit.
3.1.2 Slit experiment - Diering slits on both side
Two scans were made with dierent slits on the detector and tube side of the machine.
The two slits used can be seen on the upper plate from the right, in gure 3 above, and are highlighted in gure 6. Both measurements were done with the extra shorter slit.
Figure 6: Diagram of the setup.
3.1.3 Slit experiment - Same slits on both sides
Three scans with the same width slits on the detector and tube side was done. The slits in question can be seen on the top plate in gure 3 and are highligthed in gure 6 above. The scans were done with the same settings in the software, and with the extra vertical slit.
3.2 Copper attenuator
Ten measurements were done with and without the copper attenuator. A sample was set in a position for re ection to keep the detector from saturating. Data on
the intensity was gathered with the machine in this position. The position of the attenuator in the machine can be seen in gure 8 below, and the attenuator in gure 7.
Figure 7: A photograph of the copper dampener used to keep the detector from saturating.
Figure 8: Diagram showing the position of the copper plate.
3.3 Experiment - Varying the amount of counts
Three measurements were done on a sample while varying the maximal amount of counts in the software, 10, 50 and 100k. All other settings were identical. The data were moved slightly to improve visibility.
4 Results
4.1 Slit experiment results
4.1.1 Experiment - Extra vertical, shorter slit
This is the results from doing two measurements with and without an extra, shorter vertical slit, blocking some of the radiation from the x-ray tube. The results can be seen in gure 9 below. Scanning 10-16 degrees took about 2 hours and 50 minutes without, and 4 hours and 14 minutes with the slit.
Figure 9: Results from doing two re ectivity measurements with and without an extra vertical, shorter slit on the x-ray tube side of the machine.
4.1.2 Experiment - Varying width on each side
The results of the measurements with varying slit widths on the detector and x-ray side of the machine can be seen in gure 10 below. In the blue colored line, a thinner slit was used on the detector side than on the tube side, and in the other plot the relationship was reversed.
Figure 10: Varying slits on each side.
4.1.3 Experiment - Measurements with varying slit widths
The results from scanning a sample with the same size slits on both sides of the machines can be seen in gure 12 below, and the slits used can be seen in gure 11.
Figure 11: The slits in question.
Figure 12: Measurement results with varying slits widths.
4.2 Experiment - Varying the amount of counts
In gure 13 below is the results from scanning the same sample multiple times with diering amounts of maximum counts. The maximum exposure time of each data point was 99 seconds. (Note again that the data was moved slightly to improve visibility.)
Figure 13: Three measurements done on an iron, nickel grid with varying amount of counts.
4.3 Copper dampener
Below is a table with the measurement results from using the copper dampener.
Copper [cps] None [cps]
76401 694188
76230 694587
75449 695644
75823 695381
75343 694210
74714 694602
75050 693760
74920 694139
75065 694203
74935 694999
Table 1: Measurements with and without a copper dampener.
This gives a dampening of a factor 9.2130:005.
5 Discussion
As can be seen i gure 9 the beam are far from perfect after passing through the air and hitting the area of the sample. Using the extra slit decreases the background by almost a factor of 10. The extra noise is actually strong enough to completely drown the peak at around 15.5 degrees. This saves a lot of time, though, as scanning the background took almost 50 percent longer with the slit.
In gure 10 are scans done with the before mentioned slit, but with dierent widths on the detector and tube side. As can be seen in the gure, not surpisingly having a wider slit on the detector let's in more diuse radiation. The intensity of this noise is proportional to the strength of the initial beam and lowers the resolution of the measurement. The radiation is much more diuse after hitting the target.
Using a wider slit on the tube side also introduces more diuse radiation in the measurements from scattering in the air, and from the sample holder.
Lastly, in gure 12 the measurements made with the same width slits on both sides can be seen. Clearly the wider setup, 33 in the legend, has a profound impact on the data, completely drowning the peaks at around 9 degrees. This setup does decrease the time it takes for the machine to nish, but only with about 7 percent.
A thinner slit improves the angular resolution of the scan, making the fringes and minimas more pronounced.
In conclusion the shorter initial beam slit increases the time it takes to record data with low intensity, with the benet that it might make it possible to distinguish see additional data in the background. The other slits helps with the resolution of the measurements by removing diuse light. Another thing that helps with the resolution is the counts setting in the software, at a low cost of time where there is more than background in the data. Further more; as Possion distributions has an error that is proportional to p1n you would not expect a whole lot of improvement in the measurments, which is consistant with the result shown in 13. There's barely a visible improvement.
References
[1] Cullity, B. D, (1956)
[2] By Nicoguaro - Own work, CC BY 4.0,
https://commons.wikimedia.org/w/index.php?curid=49324857
Acknowledgements
Thanks for the opportunity, Gunnar and Vassilios. And thank you for all your help, Ange. :)