The energy separations between electron levels in atoms range typically from eV to keV meaning that the photons emitted or absorbed in transitions between these states range from infrared light to x-rays. The radiation emitted when electrons accelerate due to Coulomb interactions with heavy nuclei in solids can range from 0 eV up to the initial kinetic energy of the electron. The separation between atoms in crystalline solids is comparable to x-ray wavelengths. For all these reasons, x-ray photons are used extensively for probing material structure and characterizing atomic processes.

This experiment will study x-rays in several different contexts, including Bragg scattering, emission and absorption spectra, and x-ray fluorescence.

This experiment studies x-ray emission and absorption phenomena. In particular, the objectives of this experiment include the following:

• Study the emission spectrum of x-rays produced by accelerating a beam of electrons into a copper slug.
• Study the absorption of x-rays by different metals.
• Test Mosley's Law using x-ray florescence techniques.

Prior to your Pre-Meeting with the TA for this experiment familiarize yourself with the following concepts, all of which are central to the experiment. Much of the relevant material can be found in this wiki page and in the supplemental materials section of the course wiki home page. Google and Wikipedia are also your friends when doing preparatory research for an experiment.

Characteristic Radiation. Make sure you understand what characteristic radiation is, how it is produced and what its spectrum looks like.

Proportional Counter. This is the x-ray detector you will be using. Make sure that you have a good conceptual understanding of how it works.

Bragg Diffraction. You should know and understand the physics of Bragg diffraction. Bragg diffraction is the key aspect of the experimental technique being employed.

The energy resolution of the proportional counter is not sufficient to resolve the spectral features we are interested in, particularly the $K_{\alpha}$ and $K_{\beta}$ emission lines. Bragg diffraction of x-rays from a LiF crystal is used to achieve the required degree of energy resolution. Make sure you understand how this works before the pre-meeting. Assume you have a source which emits x-rays over a wide range of energies, a crystal suitable for Bragg scattering and an x-ray detector which can record the number of x-rays which strike it but cannot measure their energy. How would you use these three elements to count x-rays at different energies? Having a hand drawn sketch prepared for the meeting would be very helpful.

The following links provide some of the theoretical background related to the emission and absorption of x-ray energy photons.

X-ray emission

X-ray absorption

X-ray fluorescence

Moseley's Law

Bragg Scattering

You do not need to study the details of how to operate the apparatus prior to coming to lab. Lab staff and TA's will show you in the lab. But you do want to have a conceptual understanding of the tools which you will be using to make measurements.

The image above shows a typical setup for the X-Ray experiment. From left to right you have:

• A digital multi meter for monitoring the Tel-X-Ometer accelerating voltage.
• A Tel-X-Ometer apparatus which comprises the X-ray source and detector.
• An old fashioned galvanometer for measuring the current in the electron tube.
• A NIM bin, which is simply a power supply and chassis with three modules mounted inside it, displayed below. The modules include:
  • A Ratemeter which displays the rate of pulses on its input.
  • An Amplifier which is used to amplify the pulses from the detector in the Tel-X-Ometer.
  • A High Voltage Supply which powers the detector in the Tel-X-Ometer.

You will use a Tel-X-Ometer x-ray spectrometer. It provides several features described below. In the following, all identifying letters refer to Fig. 5.

Figure 5: The Tel-X-Ometer and associated electronics.

The X-ray tube is a glass vacuum tube (a) containing an electron gun and a copper target. The electron gun accelerates a beam of electrons upward toward the target, through a potential difference in the range of about 8 kV to 30 kV. An exit port (b) with a lead collimator produces a collimated beam of X-rays directed towards the crystal post holder (c).

At the center of the unit, a LiF crystal may be mounted on the crystal post holder (c). A $\theta:2\theta$ table maintains the Bragg condition of equal angles of incidence and reflection. The carriage arm (d) has slots for holding collimators or for some of the experiments.

The LiF crystal acts as the diffraction grating to give the spectrometer high wavelength resolution. LiF has a lattice spacing of

$d = 0.2008 \pm 0.0001$  nm (source: F. W. C. Boswell, Proc. Phys. Soc. A 64, 465-476 (1951).)

The proportional counter (e) is a Xe-CO2 filled tube with a central wire held at about +2100 V. X-rays which enter the counter, through a delicate beryllium side window, will ionize the gas in the tube, releasing excited electrons. These electrons are in turn accelerated towards the positively charged central wire.  As they pass through the Xe-CO2 gas, these electrons liberate more electrons thus creating a cascade.  The more energetic the incident x-ray, the more electrons which will be liberated in the cascade.  The resulting pulse of electrons striking the central wire produces a dip in the voltage which is proportional to the energy of the incident x-ray. These pulses, after passing through an amplifier, can be viewed on a scope or sent into a pulse height analyzer for further analysis.

The plastic dome contains lead and is a good shield for x-rays. The spectrometer is interlocked so that the electron accelerating voltage should not turn on (therefore, no x-rays can be generated) unless the dome is closed and centered.

On the side of the Tel-X-Ometer are dials to control the electron accelerating voltage and the electron current. The accelerating voltage (which is on the order of kV) can be safely read by a digital multimeter (which measures on the order of V) by using a 1/1,000 voltage divider (f) mounted on the back of the unit. The current can be read on an ammeter which is plugged into the side of the unit.

The charge-sensitive pre-amp collects the total charge and shapes the pulses from the proportional counter. The amplifier provides further shaping and variable gain.

To open or close the dome, slide the absorber holder on top of the dome to its uppermost position. Slide the plastic dome to the same side as the carriage arm, at which point you should hear a click as see the red X-ray light turn off indicating that the X-ray source no longer active. Lift the front of the cover, if you feel resistance to opening the cover jiggle it side to side to ensure that it is fully disengaged from the interlock mechanism.

The LiF crystal is used for most of the measurements and is likely already mounted in the central post as shown in Fig. 6. If it is not you can easily mount it as shown.

Figure 6: Mounting the LiF crystal in the post

In order to use Bragg scattering to select X-ray energy, the detector and crystal are attached to a Two Theta table. Notice how rotating the carriage arm containing the detector through an angle $\theta$ causes the crystal post to rotate through $\frac{\theta}{2}$. When properly aligned this insures that the angle of incidence of the X-ray beam and the angle of the detector with respect to the normal to the crystal face meet the Bragg condition. The following procedure will allow you to align the two theta table if necessary.

To check the alignment open the dome and rotate the carriage arm to the $2\theta = 0^\circ$ position. When the carriage arm is set to $2\theta = 0^\circ$ the scribe line scribe lines on both sides of the crystal post should be aligned as shown.

If the alignment needs to be adjusted loosen the knurled clutch plate beneath the crystal post. Move the slave plate holding the crystal post until the two scribed lines are as close as possible to the zeros on the $\theta$ scale. If the scribed lines cannot be exactly aligned with the zeros, the lines should both be displaced to the same side (i.e., a slight centering offset is ok, but a rotation offset is bad). This adjustment is critical. Carefully retighten the clutch plate. (See Fig. 7.)

Figure 7: Aligning the θ:2θ table

This collimator can be rotated to be either horizontal or vertical. Anytime you are using Bragg diffraction off of the LiF crystal it should be aligned vertical. If you are irradiating foils in the rotary radiator this collimator should be oriented horizontal for maximum illumination of the foils.

Additionally there are a pair of collimating slits which can be placed in the carriage arm, in between the detector and the LiF crystal. When using Bragg diffraction you should also use these collimators with the 3mm slit placed nearest to the crystal and the 1mm slit closest to the detector.

Check that the proportional counter is mounted so that the beryllium window faces the crystal holder. Note that the sensor may be rotated or moved from side to side to a degree, and that misalignment may result in a very low count rate (on the order of 10 counts/s).

When you have the detector powered up and the X-ray source on it is good to check the detector output to verify that everything is operating properly. To do so look at the output of the amplifier in the NIM bin on the scope with the detector set to an angle somewhere near 40º or 45º. The proportional counter should be recording X-rays from the source which have diffracted off of the crystal. These pulses should look something like this.

The pulses should be positive polarity and a few $\mu s$ long. Their amplitude will vary with the gain setting on the amplifier, you should be able to get them in the range of a couple volts.

During your pre-lab meeting with the TA you should have developed a plan for what measurements you need to make. Most likely this plan involves some combination of Emission, Absorption and Fluorescence measurements. In the following sections we provide some general advice relevant to making these types of measurements.

When studying the emission spectra from the X-ray source it is easy to get bogged down in a very inefficient data collection process if you have not invested a little bit of time thinking about where to focus your attention before beginning to collect data. A sure fire way to obtain inadequate and mediocre data is to take data from X degrees to Y degrees in Z degree increments, and then look at the results after the data have been collected.

The emission spectra from the copper slug in the electron tube is complex, there are regions where the count rates change very little if at all, regions where the rates change dramatically over a very small range of angles, etc. Based on what your measurement goals are, you should be able to identify important features of the spectrum where you will need to collect data. To aid you in quickly locating features of interest in the emission spectra we have provided a rate meter with an audible output.

Connect the amplifier output to the rate meter input and turn the audio response on (note that depending on which model ratemeter you are using the audio selector switch may be on the back of the module. Now with the X-ray source on you can slowly move the carriage arm across the full range of scattering angles and observe (hear) the increases and decreases in the intensity of X-rays striking the detector. Using this very simple technique you can very quickly identify at which angles, or range of angles, a feature of interest is located BEFORE you spend a lot of time collecting data.

Some additional points to keep in mind are:

• If you are using Bragg diffraction off the LiF crystal make sure that the collimators are placed and oriented appropriately.
• Plot your data literally as you take it so that you can see what your spectrum is looking like as it builds up. There really is no other way to know when you have collected enough data.
• A tube current of about $10 \mu A$ generally works well for emission measurements.
• A ~20keV accelerating voltage on the electron tube generally works well for emission measurements.
• The USX software should be set to Mode → PHA Direct In throughout the experiment. Adjustments to amplification should be done with the NIM module instead.

Absorption measurements are made by placing different metal foils in between the X-ray source and the LiF crystal and then using Bragg diffraction for energy selection. Foils of three different metals have been mounted on a post holder which sticks out the top of the dome on the Tel-X-Ometer apparatus. By loosening and tightening the nut where the post passes through the dome, it can be raised and lowered to put the desired foil in the beam path.

If you are investigating how X-rays are absorbed by different metals as a function of energy there is an additional complication that the energy spectrum of the source varies with energy. This is something you will be familiar with if you have already studied the emission spectra of the source. One way to account for the source spectrum is to normalize the rates measured with the absorber in place to the rate when no absorber is present. It is advised that for each energy that you use for data collection you record both the attenuated and unattenuated rates before moving on to the next angle.

Other factors to keep in mind while making absorption measurements include:

• Don't collect data randomly in energy, searching for where absorption kicks in. If you are looking for the absorption edge for an element, you can look up the energy at which the edge should occur and use this information to determine what angles (ie X-ray energies via Bragg scattering) you should be focusing on.
• A tube current of about $20 \mu A$ is good for absorption measurements.
• An electron accelerating voltage of about 25keV works well for absorption measurements.
• Don't forget to make sure your collimators are setup correctly.
• Plotting the count rate ratios against $2\theta$ as you go can be very helpful in evaluating where you need more data.

For measurements where you are irradiating a foil with X-rays and looking at its fluorescence it is necessary to replace the LiF crystal used for Bragg diffraction with a rotary radiator containing containing foils of different metals. This is accomplished by removing the crystal and its holder and putting the rotary radiator in its place as shown in figure 8. When removing the crystal and holder completely remove the screw that holds the crystal in place and remove all loose pieces of the post. Note that by moving the carriage arm to 90º you maximize both the area of the sample foil being irradiated and the area of the sample being viewed by the detector.

Since we cannot use Bragg diffraction without the crystal in place, you will rely on the size of the pulses from the detector to determine the energy of the fluorescing metal. To calibrate the pulse height response of the detector in terms of energy units you can use fluorescence off of two different metals in the rotary radiator so long as you do not then use those same metals as part of your data set.

Other things to keep in mind:

• To maximize the irradiation of the metal foils the X-ray source collimator can be rotated horizontal.
• To maximize the collection of fluorescence radiation from the foil the collimating slits in the detector carriage can be removed.
• There is a subtlety involved in using the rotary radiator which is best explained in person. Ask a TA or one of the lab staff to help you with this.

Figure 8: Tel-X-Ometer with x-ray fluorescence sample holder (rotary radiator) mounted on crystal post.

Your final report will be evaluated based on the following rubric. The rubric is not a format for your analysis, you are not expected to have a specific section on Data Handling or Presentation of Data. Elements of the different rubric categories will appear at different points through out your analysis writeup. For example you will be presenting data in your discussion of the calibration, your discussion of determining peak locations, and likely in your final results. Your writeup of your analysis should be structured in a way that is clear and readable, there should be a logic to the flow of it.

Each item below is graded on a 0-4 point scale:

• 4 – Good (A): completes all listed tasks and provides appropriate context; thinks carefully about data and analysis; addresses all concerns raised by the results (where appropriate).
• 3 – Adequate (B): misses one or more minor element or lacks appropriate context; leaves a problem or ambiguity unaddressed; does not present analysis clearly enough.
• 2 – Needs improvement (C): omits or mishandles one or more item which renders the analysis fundamentally incorrect or incomplete; presents results in an incorrect or unclear way.
• 1 – Inadequate (D): omits or mishandles multiple items or treats them at an insufficient level; presentation is overall muddled or inaccurate; flaws in logic or process.
• 0 – Missing (F): omits all elements or makes no meaningful attempt.

All rubric items carry the same weight. The final grade for the analysis will be assigned based on the average (on a 4.0 scale) over all rubric items.

• [1] J. H. Sparrow and C. E. Dick, "The development and application of monoenergetic x-ray sources", National Bureau of Standards Special Publication 456, 41-45, (Nov. 1976).
  • This paper details the intensity of x-ray emissions as a function of atomic number, Z, and electron accelerating voltage for thick targets
• [2] S. Fine and C. F. Hendee, (Philips Laboratories, Irvington on Hudson, New York), "X-Ray Critical-Absorption and Emission Energies in keV", Ortec publication.
  • This paper lists x-ray emission lines and absorption edges for all elements.
• [3] Electron Binding Energies, from the X-Ray Data Booklet, “Section 1-1: X-Ray Properties of the Elements”, Lawrence Berkeley National Laboratory, http://xdb.lbl.gov/Section1/
• [4] Reuter-Stokes Proportional Counters Performance and Specifications Guide.
  • This is the information guide for the proportional counter detector used in this experiment.

The activity of a radioactive source is the number of decays per unit time of that source and is therefore a measure of how much radiation is being released. A common unit of measure for activity is the curie, where $1 \textrm{Ci} = 3.7 \times 10^{10}$ disintegrations/sec. This is a very large unit! For comparison, the small button sources used in the Gamma Cross Section experiment are typically 1-10 microcuries, whereas the sources used in the Compton Scattering or Mossbauer Spectroscopy experiments are on the order of 1-10 millicuries.

In this experiment, you are not working with a naturally radioactive source, but you are working with a source that produces radiation. We can therefore calculate an equivalent strength of the source by determining the number of x-rays produced per unit time.

Your device produces x-rays by bombarding a copper (Z=29) target with electrons. Assume that you produce a current of 10 microamps of electrons and that you accelerate them through a potential of 25 kV before they hit the target. The efficiency of converting electrons into x-rays can be determined from the information plotted in Fig. A. Calculate the total intensity of the x-ray source (emitted in all 4π sr) and express this strength in units of curies. (Don't know what a steradian (sr) is? See here.)

Figure A: Dependence of the K x-ray yield on incident electron energy. (Source: [1])  The figure has been modified to show dependency for copper in red.

Note that the yield is in terms of number of x-rays per steradian (sr) per electron.