The intensity of characteristic X-rays as a TEP Related topics Characteristic X-radiation, energy levels, Bragg s law, and intensity of characteristic X-rays Principle The X-ray spectrum of an X-ray tube with a copper anode is selected based on the wavelength with the aid of a LiF monocrystal as the analyser, and registered with a Geiger-Müller counter tube. The intensity of the characteristic K α and K β lines is determined as a function of the anode current and voltage. Equipment 1 XR 4.0 expert unit 09057-99 1 X-ray goniometer 09057-10 1 X-ray plug-in unit with a Cu X-ray tube 09057-50 1 Counter tube, type B 09005-00 1 X-ray lithium fluoride crystal, mounted in a holder 09056-05 1 X-ray diaphragm tube, d = 2 mm 09057-02 1 measure XRm 4.0 X-ray software 14414-61 1 Data cable USB, plug type A/B 14608-00 Additional equipment PC, Windows XP or higher This experiment is included in the XRP 4.0 X-ray solid state, XRS 4.0 X-ray structural analysis, and XRC 4.0 X-ray characteristics upgrade sets. Note: As an option, the experiment can also be performed with a tungsten X-ray tube (09057-80). Fig. 1: XR 4.0 expert unit 09057-99 www.phywe.com P2540401 PHYWE Systeme GmbH & Co. KG All rights reserved 1
TEP The intensity of characteristic X-rays as a Tasks 1. Analyse the intensity of the X-radiation as a function of the Bragg angle and with the aid of a LiF monocrystal. 2. Determine the intensity of the characteristic X-ray lines as a function of the anode voltage and current. 3. Compare the results of the experiment to the results that can be expected theoretically. The parameters for the experiment with a tungsten tube are shown in the appendix. Set-up Connect the goniometer and the Geiger-Müller counter tube to their respective sockets in the experiment chamber (see the red markings in Fig. 2). The goniometer block with the analyser crystal should be located at the end position on the right-hand side. Fasten the Geiger-Müller counter tube with its holder to the back stop of the guide rails. Do not forget to install the diaphragm in front of the counter tube (see Fig. 3a). Insert a diaphragm tube with a diameter of 2 mm into the beam outlet of the tube plug-in unit for the collimation of the X-ray beam. Fig. 2: Connectors in the experiment chamber Note Details concerning the operation of the X-ray unit and goniometer as well as information on how to handle the monocrystals can be found in the respective operating instructions. GM-counter tube Goniometer at the end position Diaphragm tube Counter tube diaphragm Mounted crystal Fig. 3: Set-up of the goniometer 2 PHYWE Systeme GmbH & Co. KG All rights reserved P2540401
The intensity of characteristic X-rays as a TEP Procedure - Connect the X-ray unit via USB cable to the USB port of your computer (the correct port of the X-ray unit is marked in Fig. 4). - Start the measure program. A virtual X-ray unit will be displayed on the screen. - You can control the X-ray unit by clicking the various features on and under the virtual X-ray unit. Alternatively, you can also change the parameters at the real X-ray unit. The program will automatically adopt the settings. Task 1: Analyse the intensity of the X-radiation as a function of the Bragg angle and with the aid of a LiF monocrystal. Fig. 4: Connection of the computer - Click the experiment chamber (see the red marking in Figure 5) to change the parameters for the experiment. Select the parameters as shown in Figure 6 (scanning range: 4-55 ). - If you click the X-ray tube, you can change the voltage and current of the X-ray tube. Select the following parameters: anode voltage U A = 35 kv; anode current I A = 1 ma. - Start the measurement by clicking the red circle - After the measurement, the following window appears: For setting the X-ray tube For setting the goniometer Fig. 5: Part of the user interface of the software - Select the first item and confirm by clicking OK. The measured values will now be transferred directly to the measure software. - At the end of this manual, you will find a brief introduction to the evaluation of the resulting spectra. Fig 6: Settings of the goniometer; LiF crystal www.phywe.com P2540401 PHYWE Systeme GmbH & Co. KG All rights reserved 3
TEP The intensity of characteristic X-rays as a Task 2: Determine the intensity of the characteristic X-ray lines K α and K β of copper as a function the anode voltage and current. - Click the experiment chamber (see the red marking in Figure 5) in order to change the parameters for the experiment. Select a scanning range of 19-24. - If you want to determine the dependence of the intensity on the anode current, record a spectrum with various different anode currents. Settings: U A = 35 kv = const.; I A = 1 ma...0.1 ma in steps of 0.1 ma. - If you want to determine the dependence of the intensity on the anode voltage, record a spectrum with various different anode voltages. Settings:: I A = 1 ma = const.; U A = 35 kv...11 kv in steps of 2-3 kv. - The evaluation is the same as for task 1. Note: Never expose the Geiger-Müller counter tube to the primary X-radiation for an extended period of time. Theory The electrons coming from the cathode are accelerated towards the anode by the voltage U A between the cathode and anode. Due to the resulting high level of kinetic energy, the electrons are capable of ejecting electrons from the inner shells of the atoms of the anode material. If this occurs on the K shell of the atoms, an electron from a higher shell, e.g. the L or M shell, can take up the free place while emitting an X-ray quantum. The energy of this X-ray quantum corresponds to the energy difference of the two shells that are involved in this process. Since this energy difference is atom-specific, the resulting radiation is also called characteristic X-radiation. X-radiation that is produced following a transition from the L shell to the K shell is called K α radiation, while the radiation that is produced following a transition from the M shell to the K shell is called K β radiation. The intensity I K of the K radiation is: I K = B I A ( U U ) 1. 5 A K Overview of the settings of the goniometer and X-ray unit: - 2:1 coupling mode - Gate time: 2 s; angle step width: 0.1 For recording a complete spectrum: - Scanning range: 4-55 - Anode voltage: U A = 35 kv; anode current: I A = 1 ma For determining the intensity of the characteristic lines as a function of U A and I A : - Scanning range: 19-24 - U A = 35 kv = constant; I A = 1 ma...0.1 ma in steps of 0.1 ma - I A = 1 ma = constant; U A = 35 kv...11 kv in steps of 2-3 kv Detailed information concerning the operation of the software can be found in the handbook and in the Help of the software. (I A = anode current, U A = anode voltage, B = const. and U K = ionisation potential of the K shell) (1) The depth of penetration of the ionising electrons into the anode material as well as the escape depth of the generated X-rays is limited. When they have both reached their maximum, the relationship given in (1) loses its validity. With the aid of Bragg s law: ( 1, 2,3,... ) 2 d sinϑ = nλ n = (2) and the known interplanar spacing of the LiF crystal (d = 201.4 pm), the wavelength λ of the characteristic K α and K β lines can be calculated based on the glancing angles ϑ that were determined experimentally. Based on the relations c = λ f (velocity of light c = 2.9979 10 8 m/s), the frequency f of the lines can be calculated. Then, E = h f finally leads to the energy E of the lines (Planck's constant 4 PHYWE Systeme GmbH & Co. KG All rights reserved P2540401
The intensity of characteristic X-rays as a TEP h = 6.626 10-34 Js). E = ( n h c) ( 2d sinϑ) (3) n =1 n=2 ϑ/ λ/pm ϑ/ λ/pm Cu (Z=29)K 22.6 α 154.8 50.2 154.7 Cu (Z=29)K β 20.4 140.4 43.9 139.6 Evaluation and results In the following section, the evaluation of the data is described based on example results. Your results may differ from the results given below. The evaluation of the results that were obtained with the tungsten tube is described in the appendix. Task 1: Analyse the intensity of the X-radiation of copper as a function of the Bragg angle and with the aid of a LiF monocrystal. Figure 7 shows the X-ray spectrum of copper up to the second-order interference. The table shows the resulting glancing angles ϑ of the characteristic lines as well as the corresponding wavelengths that were calculated based on (2). Fig. 7: X-ray spectrum of copper, LiF monocrystal as the analyser Task 2: Determine the intensity of the characteristic X-ray lines of copper K α and K β as a function of the anode voltage and current. Intensity as a function of the anode voltage Figure 8 shows the relevant scanning range with the pulse rates for various different selected anode voltages. Fig. 8: Scanning range 19 < ϑ < 24 at different anode voltages In Figure 9, the lower curves show the measured intensity (pulse rate) of the characteristic lines (intensity maximum of the lines) as a function of the anode current I A at a constant anode voltage U A = 35 kv. However, excessively high pulse rates cause the Geiger-Müller counter tube to become saturated. The deviation of the measurement curves from the expected linearity can be eliminated by taking the dead time of the Geiger-Müller counter tube into consideration at high pulse rate values. These corrected values are represented by the upper curves in Figure 9. If τ (τ 90 μs) is the dead time of the Geiger-Müller counter tube and N 0 is the measured pulse rate, the www.phywe.com P2540401 PHYWE Systeme GmbH & Co. KG All rights reserved 5
TEP The intensity of characteristic X-rays as a true pulse rate N is: N N 0 = 1 τ N 0 (3) K α Intensity as a function of the anode current Figure 10 shows the relevant scanning range with the pulse rates for various different selected anode currents. Figure 11 shows the intensity course of the two characteristic lines as a function of the anode voltage U A (I A = const. = 1 ma). The lower curves represent the measured pulse rates while the upper curves show the pulse rates that were corrected in terms of the dead time of the Geiger-Müller counter tube. Task 3: Compare the results of the experiment to the results that can be expected theoretically. If the experimental results are compared to the results that can be expected theoretically, the linear relationship between U A - U K and the pulse rate of (1) is confirmed. If one plots the true pulse rates of the characteristic lines of Figure 12 as a function of (U A -U K ) 1.5 (with U K = 8.979 kev for copper, see the experiment P2540101), a straight line results. K β Fig. 9: Intensity of the K α and K β lines (n = 1) as a function of the anode current I A Fig. 10: Scanning range 19 < ϑ < 24 at different anode voltages K α α K α K β K β K β Fig. 11: Intensity of the K α and K β lines (n = 1) as a function of the anode voltage U A (U A U K ) 3 2 kv 3 2 Fig. 12: The true pulse rates of the K α and K β lines as a function of (U A -U K ) 1.5 ; (I A = const. = 1 ma) 6 PHYWE Systeme GmbH & Co. KG All rights reserved P2540401
The intensity of characteristic X-rays as a TEP measure software With the measure software, the peaks in the spectrum can be determined rather easily: - Click the button and select the area for the peak determination. - Click the button Peak analysis. - The window Peak analysis appears (see Fig. 13). - Then, click Calculate. - If not all of the desired peaks (or too many of them) are calculated, readjust the error tolerance accordingly. Refer to the Help of the measure software for additional, more detailed explanations concerning the program features. - Select Visualise results in order to display the peak data directly in the spectrum. Fig. 12: Automatic peak analysis with measure www.phywe.com P2540401 PHYWE Systeme GmbH & Co. KG All rights reserved 7
TEP The intensity of characteristic X-rays as a Appendix Procedure using a tungsten tube: Task 1: Record the entire spectrum: See P2542801 for the evaluation of the spectrum. Overview of the settings of the goniometer and X-ray unit: - 2:1 coupling mode - Gate time 5-6 s; angle step width 0.1 - Scanning range 4-80 (LiF monocrystal) - Anode voltage U A = 35 kv; anode current I A = 1 ma Task 2: Determine the intensity of a single line For the evaluation, examine the lines α 1 and α 2 appear as one single line. The following settings are recommended: that Determination of the intensity of the characteristic lines as a function of U A and I A : - Gate time 3s - Scanning range: 4-25 - U A = 35 kv = const. ; I A = 1 ma...0.1 ma in steps of 0.1 ma - I A = 1 ma = const. ; U A = 35 kv...11 kv in steps of 2-3 kv Theory and evaluation Since the energy of the K shell is approximately 70 kev, the maximum available energy of the primary beam of the X-ray unit of 35 kev is insufficient for exciting the K shell. Only the L level can be ionised. P2542802 includes the corresponding energy-level-diagram. For the evaluation, the lines α 1 and α 2 are examined. They result from the L 3 M 5 /L 3 M 4 transition. These two lines are so close to each other that they cannot be separated but rather appear as a single line. The evaluation follows that of copper, but in this case with only one single line. For task 3, the ionisation potential of the L 3 shell U K = 10.206 kev is used since the transition takes place to this shell (see the energy-level-diagram of tungsten in P2542801). Fig 14: Scanning range 4 < ϑ < 25 at different anode voltages for the tungsten tube 8 PHYWE Systeme GmbH & Co. KG All rights reserved P2540401