UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS Level 1: Experiment 2F THE ABSORPTION, DIFFRACTION AND EMISSION OF X- RAY RADIATION 1 AIMS 1.1 Physics These experiments are intended to give some experience of the generation and properties of X-rays. The very short wavelength of X-rays will be exploited to cause Bragg diffraction from a NaCl crystal. The emission of X-rays will be studied and used to calculate a value for Planck's constant. 1.2 Skills The particular skills you will start to acquire by performing this experiment are: Use of a low power, biologically safe, X-ray source. Use of a Geiger-Müller tube and appropriate equipment to detect and measure X-rays. Use of a Sodium Chloride crystal as a diffraction grating for short wavelengths. Adjustment of an X-Ray spectrometer to measure small angles accurately. Graphing and calculating skills. Last updated on 4/2/05 by JLK
2 X-RAY PRODUCTION, DETECTION, ABSORPTION AND DIFFRACTION 2.1 Production of X-rays X-rays are generated when fast moving electrons are slowed down rapidly on collision with a metal target [1]. In the Tel- X-Ometer equipment the electrons are accelerated through 20kV or 30kV in a vacuum tube and then collide with a copper target. The accelerating voltage is selected by a switch on the top of the instrument. The current carried by the electron beam is typically 60-80µA, as can be observed on the meter provided. n= n=4 n=3 n=2 K α2 K α1 K β1 K β2 L α M α 0 ev N M L The spectrum of radiation produced consists of sharp lines characteristic of the target material superimposed on a background of continuous radiation. For a Figure 1: K, L and M energy levels in the copper atom. copper target the most intense lines are the K α and K β lines, corresponding to the transitions indicated in Figure 1. 2.2 X-Ray Detection Photographic methods are frequently used particularly when observing X-ray diffraction patterns. However, when quantitative measurements of intensity are required either an ionisation chamber together with a sensitive current detector, or a Geiger-Müller (GM) tube connected to a ratemeter or counter, are more suitable. 2.3 Absorption n=1 K When X-rays pass through matter they lose energy both by scattering and by true absorption, the net effect is termed the total absorption. The true absorption is the larger effect and varies as the cube of the wavelength of the radiation. If a beam of intensity I traverses a layer of thickness dx the intensity decreases according to the relationship di = µ dx (1) I where µ is the absorption coefficient for the material through which the rays have passed. Integrating the above relation gives: ( x) I = I0 exp µ (2) Page 2 of 11
The true absorption coefficient is a function of wavelength and changes abruptly at the characteristic absorption edges. For example, the transmission of Ni varies with the wavelength of the radiation as shown in Figure 2. By using a thin layer of nickel in the X-ray beam it is possible to have the absorption edge just on the short wavelength side of the K α line, hence producing much more nearly monochromatic radiation. Figure 2: Transmitted X-radiation through a thin Ni foil, showing strong absorption at an angle corresponding to a characteristic K β absorption energy. 2.4 Diffraction The wavelength of X-rays is so short that in order to produce diffraction patterns a grating with a spacing of the order of a nanometer would be required. While such a grating would be difficult to manufacture artificially, this value is typical of the interplanar spacing in crystal lattices, and therefore a crystal of known lattice structure can be used as a grating to determine X-ray wavelengths. Alternatively, if the wavelength of the radiation is known, then the lattice spacing can be found. This technique is of great importance in crystallography [2]. 3 EXPERIMENTAL EQUIPMENT In the Tel-X-Ometer the entire experimental zone is enclosed in a transparent plastics scatter shield. It is impossible to turn on the extra high voltage (EHT) supply, and thus to generate X-radiation, unless this shield is locked down in the safe position. In addition this shield is fitted with an Aluminium and Lead back-stop directly in line with the X-ray source. The EHT may be set to either 20kV or 30kV, and the tube current may be adjusted with a screwdriver - do not exceed 80µA. You are advised to spend about half an hour becoming familiar with the Tel-X-Ometer and its controls. Connect the Tel-X-Ometer to the mains supply and switch on at the POWER ON switch. Note that nothing will happen unless the timer knob on the front panel is rotated clockwise to start a timed period. Throughout the experiment, keep an eye on the timer. When it gets close to zero, increase the time, so that the X-ray source does not switch off during an experiment. The X-ray tube filament and power on indicators will then illuminate. The equipment should be allowed to warm-up for 3 minutes after initial switch on to eliminate any condensation. During this period examine the functioning of the scatter shield interlocks. To release the shield displace it sideways in either direction at its hinge. To close the shield lower it until the ball ended spigot engages with its locking plate and then displace the shield at the hinge to centralise this Page 3 of 11
spigot. Note that the directions of displacement should suit the position of the carriage arm. clutch plate carriage arm ES spring clip Al/Pb Back Stop Figure 3: Photograph of the Tel-X-ometer showing all important components. With the shield closed depress the X-Rays ON button. The EHT will now be applied to the tube and the red indicator lamp will illuminate. Observe that the tube current is in the 60-80µA range. If not, adjust the current using a screwdriver. Should depressing the button have no effect check carefully that the shield is centralised in its locked position. Figure 4: Figure showing the reflecting crystal face against the chamfered post of the Tel-X-ometer. Page 4 of 11
To turn off the EHT simply displace the shield sideways at the hinge. The X-ray beam from the tube is circular with a diameter of 5mm. This beam can be collimated by fitting either the 1mm circular collimator, TEL 580.002, or 1mm slot collimator 582.001, to the tube port, where they will be retained by their O-ring seals. Further collimation may be produced by fitting 1mm or 3mm slot collimators at the appropriate experimental station (ES) on the carriage arm. Crystals can be mounted on the central crystal post using the screw clip provided, as shown in Figure 4. The tube is mounted by slotting the square flange of the tube holder into the spectrometer arm, usually at ES 26. The tube can be connected to the GM inputs of either the ratemeter or the Digicounter, and the power supply should be set to about 480 V. 4 EXPERIMENTAL PROCEDURE 4.1 Experiment 1: Absorption of X-rays by Aluminium When X-rays strike an absorbing material, the softer longer wavelength radiation of the continuous spectrum is absorbed more easily. The mean wavelength of the transmitted radiation therefore progressively decreases, and the X-rays harden. For this experiment the Digicounter and GM tube will be used to measure the intensity of the X- rays. A B C D E F Mount the auxiliary slide carrier over the basic port using the 1mm circular collimator 582.002 to hold it in position. Mount the GM tube at ES22 and connect it to the Digicounter. Set the Digicounter function switch to radioactivity and the range switch to 10s. Set the tube voltage to 480 V and the reading switch to continuous. Mount a 2mm thick Aluminium slide at ES2. This slide will remain in position during the experiment and its thickness is not to be included in the values of absorber thickness x below. Locate the carriage arm in the straight through position, switch on the EHT, set to 30kV, and record the count rate, tabulating three ten second counts and calculating their mean. Mount at ES 13-15 the 0.25mm, 0.50mm, 0.75mm, 1.0mm and 2.0mm aluminum slides, singly or in combination, and repeat the measurements above to record count rates for absorber thickness x from 0.25mm to 3mm. Plot a graph of count rate I against x. This graph should be an exponential curve since I is related to x by the equation (2), where µ is the linear absorption coefficient. Page 5 of 11
G H Find from your plot of I against x the half-value thickness of aluminium for 30kV radiation, i.e. the value of x required to reduce the intensity to I o/2. Find also the tenthvalue thickness. Tabulate and plot ln(i) against x. The equation above implies that this graph should be a straight line. (Do you understand why?) Is it a straight line? Find the value of µ from this graph. What is the meaning of the y-intercept? Try to answer the following questions. Why do you think that the first 2mm of aluminium needs to be placed near to the basic port? What happens if it is omitted? Try it. (See the Appendix for more information about the effect of filters.) Does the fact that the X-ray spectrum contains characteristic lines as well as the continuous spectrum make any difference? Radiographers concerned with the medical effects of soft radiation on outer body tissues commonly work with half-values, while those working with hard radiation more often use tenth-values. Why is this sensible? 4.2 Experiment 2: Bragg diffraction of X-radiation and the Determination of the NaCl Crystal Lattice Spacing When an incident wavefront strikes a series of reflecting layers separated by a distance d the first condition for Bragg reflection is that the angles of incidence and reflection are equal, and therefore the detector of reflected rays must move through an angle of 2θ, where θ is the angle between the incident rays and the reflecting layers. This is shown in Figure 5. Scattering from atoms in a crystal occurs in all directions. The second condition for Bragg reflection is that reflections from several layers must combine constructively. The diagram at the bottom of Figure 5 shows that if two rays reflect from parallel planes (such as planes of atoms in a crystal) separated by a distance of d, then constructive interference will occur only when the lower ray travels an "extra" distance exactly equal to 2dsinθ. This simple geometric argument can thus be used to derive the Bragg equation for diffraction: 2 d sin θ = nλ (3) Figure 5. Constructive interference leading to the Bragg condition. Page 6 of 11
This equation tells us that for a certain wavelength λ, constructive interference will occur, and we will see a peak in a diffraction pattern, only at values of θ where Equation 3 applies. If λ is known (or can be calculated), and if θ is measured in an experiment, then the spacing between the planes may be found. The Tel-x-ometer uses a copper target to generate the X-rays. Consequently, the energies of the X-rays and their wavelengths can be related to the energy levels in the copper atom. There are a pair of emission lines, called the K α and K β1 lines, that you will use for your diffraction experiment. You can calculate the wavelengths of the Cu K α and K β1 radiation by using the mean energies of the K, L, and M levels of the copper atom: -8979 ev, -951 ev, and -120 ev, respectively. As seen in Figure 1, Cu K α radiation is caused by a transition from the L to K level, whereas K β1 radiation is caused by a transition from the M to the K level. (You should note on Figure 1 that there are actually two transitions that lead to the α radiation, leading to two different wavelengths for α 1 and α 2 emission lines, but you will not be able to resolve these in this experiment, and so it is sufficient to calculate a single wavelength for K α.) In this experiment, you will use a crystal of NaCl as a diffraction grating. The structure of NaCl is shown in Figure 6. It is commonly known that the crystal structure of NaCl is face-centred cubic. The edge length of the cubic repeat unit (e on the Figure) is referred to as the lattice constant. d e Figure 6. The NaCl crystal structure. The small spheres represent Cl ions; the large spheres represent Na ions. Only certain planes in a crystal allow X-ray diffraction, however, because in some cases, there are other planes that cause interference of the diffraction. In NaCl, diffraction does not occur between the top and bottom planes of the repeat unit (separated by a distance of e), because of this effect. Can you see why by looking at Figure 6? Diffraction does occur, however, from the planes separated by a distance of e/2. In your Solid State Physics lectures in the Second Year, you will learn that crystallographers use Miller indices to refer to these planes as (020) planes. In this experiment, you will find e for NaCl. A Mount the NaCl crystal, 582.004, colour coded yellow, in the crystal post, ensuring that the face containing the major planes is in the reflecting position, i.e. against the chamfered post. Refer to Figure 4. The crystal is now mounted so that diffraction will occur from the (020) planes. Page 7 of 11
B C D Mount the collimator 582.001 on the tube port with its slot vertical, the 3mm collimator 562.016 in ES 13 and the 1mm collimator 562.015 in ES 18. Set the carriage arm carefully to zero and then release the drive to the crystal post by unscrewing the clutch plate. Push the slave plate (the inner rotating plate engraved with two datum lines) round until the datum lines are accurately aligned with the zeros on the scale. Check that the carriage arm is still at zero and then screw down the clutch plate to engage the 2:1 drive mechanism between crystal and carriage arm positions. Rotate the carriage arm through 90 and verify that the slave plate has moved through 45. Mount the GM tube at ES 26 and connect it to the ratemeter. Set the GM tube supply voltage to 480V and the EHT to 30kV and turn it on. E Track the carriage arm from its minimum angle (2θ = 11 ) to its maximum angle (2θ =120 ) noting the count rate as a function of θ. The idea is to obtain a "survey" of how intensity varies as a means of finding the diffraction peaks. Angular intervals of 5 in 2θ should be sufficient. You will later "hone in" on the angular regions of the peaks. Alter the ratemeter range as appropriate to obtain a sufficient number of counts. Angular settings between 11 and 15 degrees can be obtained by indexing the cursor to 15 and using the thumb wheel indications between 0 and minus 4. F G H I J Plot a graph of count rate against 2θ over the whole range you have measured. Wherever the count rate appears to peak, plot the count rate at intervals of only 10 minutes of arc by using the thumb wheel. At each peak, measure and record the maximum count rate and angle 2θ as accurately as possible. Tabulate values of θ where you observe a peak. Use the values of λ that you have calculated for K α and K β radiation. As the wavelengths for the two types of radiation are similar, their peaks should occur closely together. You should think about which type of peak (K α or K β ) will occur at lower angles. (You will also need to think about the values of n.) Determine values of d using Bragg's equation. The two X-ray lines should give the same values for d. Do they? Estimate the error in your results for d. What is the largest source of error? Now check your result by estimating the atomic spacing between Na and Cl in the NaCl crystal. This distance will equal the spacing between the planes that lead to diffraction. For your calculation, you should make use of the fact that the molar mass of NaCl is 58.44 g/mole, and its density is 2.17 gcm -3. You should also try to find a value of the lattice constant for NaCl in the literature and compare it to the value that you obtain in this experiment. A final word on the X-ray diffraction experiment: take care when analysing your data. You should see diffraction from both K α and K β emission lines. Plus, you should observe higher order diffraction (n = 2 and n = 3). Do not confuse the two. As you know the relevant values of wavelengths, when you find one diffraction peak, you should know where to look for the others. Page 8 of 11
4.3 Experiment 3: X-Ray emission and the measurement of Planck s constant. When the accelerated electrons in the X-ray tube strike the target the majority of them lose their energy by undergoing sequential glancing collisions with particles of the target material, thus simply raising the temperature of the target. A minority of the electrons will be involved in glancing impacts in which some of their energy is imparted to the target particle while some is emitted in the form of quanta of electromagnetic radiation equivalent to the loss of energy on collision. These collisions usually occur at slight depths within the target material, so that the longer, less energetic wavelengths are absorbed in the target and so are not emitted. The braking radiation (or bremsstrahlung,) as it is known, is thus a continuous spread of wavelengths, not characteristic of the target material, whose maximum possible quantum energy will be equal to the kinetic energy of the accelerated electrons. Since few, if any, quanta will have this maximum energy, it is necessary to find the wavelength of maximum energy by extrapolation. A Mount the auxiliary slide carriage 582.005 over the basic port using the 1mm slot primary beam collimator to hold it in position. Ensure that the slot in the collimator is vertical. Position the 1mm slide collimator 562.015 at ES4 and the 3mm slide collimator 562.016 at ES13. B Mount the NaCl crystal to the crystal post as in experiment 2. C D E Mount the GM tube at ES26 and connect it to the Digicounter. Set the function switch to radioactivity and the range switch to 1s. Adjust the GM tube supply to 480V and set the reading switch to continuous. With the EHT set to 20kV measure, tabulate and plot the count rate at every 30 of arc from 11 30 until after the whale back of the curve appears to fall off. For low count rates it is sensible to use the 100 s range on the Digicounter in order to obtain sufficient statistics. These readings are not easy to take accurately - take your time and be as careful as you can. Extrapolate your curve to zero count rate and note the angular settings at which the curve crosses the horizontal axis. Your results should look something like Figure 7. These angles correspond to the minimum wavelengths (and therefore maximum energies) of the X- radiation. Page 9 of 11
Figure 7: Scattering obtained (at two EHT voltages) from NaCl. The broad peaks indicate the broad range of wavelengths produced. F Use your calculated value for the lattice spacing d for NaCl from experiment 2 to find the minimum wavelengths (and hence the maximum frequencies) of X-radiation emitted for both settings of the EHT supply. This minimum wavelength will be produced when all of the energy of the electrons accelerated through the EHT voltage V is converted into quanta of energy hν We can therefore use the relationship Ve = hν (4) to find values for Planck s constant h. Estimate the error in your results. What is the largest source of error? 5 REFERENCES 1) D. Halliday, R. Resnick and J. Walker, J. Wiley & Sons (1997). Ch 41.8. 2) D. Halliday, R. Resnick and J. Walker, J. Wiley & Sons (1997). Ch 37.9. Page 10 of 11
APPENDIX K lines Effect of a filter on an X-ray spectrum. A filter has the following effects on the spectrum: (1) A change in shape with preferential removal of lower energies (beam hardening) (2) A shift in the peak of the spectrum towards higher energies (3) An overall reduction in X-ray output (4) A shift in the minimum photon energy (Emin) to higher energies (5) No change on the maximum photon energy (Emax). Page 11 of 11