This experiment is included in the upgrade packages: XRC 4.0 X-ray characteristics and XRS 4.0 X-ray structural analysis.

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1 Characteristic X-rays of copper TEP Related Topics X-ray tube, bremsstrahlung, characteristic radiation, energy levels, crystal structures, lattice constant, absorption, absorption edges, interference, the Bragg equation, order of diffraction. Principle Spectra of X-rays from a copper anode are analyzed using different monocrystals and the results plotted graphically. The energies of the characteristic lines are then determined from the positions of the glancing angles for the various orders of diffraction. Equipment 1 XR 4.0 expert unit 35kV Goniometer for X-ray unit, 35 kv Plug-in module with Cu X-ray tube Counter tube, type B Lithium fluoride crystal, mounted Potassium bromide crystal, mounted diaphragm tube 2 mm measure XRm 4.0 X-ray Software USB Data cable USB, plug type A/B PC, Windows XP or higher This experiment is included in the upgrade packages: XRC 4.0 X-ray characteristics and XRS 4.0 X-ray structural analysis. Fig. 1: XR 4.0 expert unit P PHYWE Systeme GmbH & Co. KG All rights reserved 1

2 TEP Characteristic X-rays of copper Tasks 1. Record the intensity of the X-rays emitted by the copper anode as a function of the Bragg angle using a LiF monocrystal as analyzer. 2. Step 1 is to be repeated using the KBr monocrystal as analyzer. 3. Calculate the energy values of the characteristic copper lines and compare them with the energy differences of the copper energy terms. Set-up Connect the goniometer and the counter tube to the appropriate sockets in the experimenting area (seee red marking in Fig 2). Fix a diaphragm tube in the X-ray outlet tube (2 mm tube diameter). Set the goniometer block with mounted analyzing crystal to the right position and the counter tube to the right stop. Do not forget to install the diaphragm of the GM-tube (See Fig. 3a). Note For more information about the X-ray expert unit, the Goniometer and how to handle the crystals please refer to the manuals. Fig. 2: Connections in the experimenta- tion area Mounted crystal Diaphragm of the GMtube GM-tube Goniometer at the right position Fig. 3a and 3b: Set-up of the Goniometer and setting of the diaphragm. 2 PHYWE Systeme GmbH & Co. KG All rights reserved P

3 Characteristic X-rays of copper TEP Procedure - Connect the X-ray unit via USB cable to the USB port of your computer (see red marking in Fig. 4). - Start the program measure. - The X-ray device appears on the screen (see Fig 5). - Click on the experimentation area to adjust the parameters for your experiment. Select the parameters as shown in Fig. 6 for the LiF crystal and for the KBr crystal: scanning range Click on the x-ray tube to adjust the parameters for the voltage and current of anode. Select the parameters as shown in Fig Start the measurement clicking on the red button Fig. 4: Connection to the computer - After the measurement, the following window appears: Set the X-ray tube Set the goniometer - Select the first item and approve with OK. The data is now transferred directly to the software measure. - At the end of this manual a short introduction to the evaluation of data using the program measure is given. Fig. 5: A part of the graphical user interface of the "X-ray Device"-software Note - Never expose the counter tube to primary radiation for a longer length of time. The following settings are recommended for the recording of the spectra: - auto and coupling mode - gate time 2 s; angle step width scanning range 3-55 using the LiF monocrystal, and 3-75 using the KBr monocrystal - anode voltage UA = 35 kv; anode current IA = 1 ma P PHYWE Systeme GmbH & Co. KG All rights reserved 3

4 TEP Characteristic X-rays of copper Fig 6: Measuring parameters of the Goniometer Fig 7: Measuring parameters of anode voltage and current Theory When electrons of high energy impinge on the metallic anode of an X-ray tube, X-rays with a continuous energy distribution (the so-called bremsstrahlung) are produced. X-ray lines whose energies are not deso-called characteristic pendent on the anode voltage and which are specific to the anode materials, the X-ray lines, are superimposed on the continuum. They are produced as follows: An impact of an electron on an anode atom in the K shell, for example, can ionize that atom. The resulting vacancy in the shell is then filled by an electron from a higher energy level. The energy released in this de-excitation process can then be transformed into an X-ray which is specific for the anode atom. Fig. 8 shows the energy level scheme of a copper atom. Characteristic X-rays produced from either the L K or the M K transinot take place due to tions are called Kα and Kβ lines respectively. M 1 K and L 1 K transitions do quantum mechanical selection rules. Accordingly, characteristic lines for Cu with the following energies are to be expected (Fig. 8): Fig. 8: Energy levels of copper (Z = 29) 4 PHYWE Systeme GmbH & Co. KG All rights reserved P

5 Characteristic X-rays of copper TEP EKα* = EK 1/2 (EL2 + EL3) = kev (1) EKβ = EK EM2.3 = kev K α* is used as the mean value of the lines K α1 and K α2. The analysis of polychromatic X-rays is made possible through the use of a monocrystal. When X-rays of wavelength λ impinge on a monocrystal under glancing angle, constructive interference after scattering only occurs when the path difference Δ of the partial waves reflected from the lattice planes is one or more wavelengths (Fig. 9). This situation is explained by the Bragg equation: Fig. 9: Bragg scattering on the lattice planes 2 = (2) (d = the interplanar spacing; n = the order of diffraction) If d is assumed to be known, then the energy of the X-rays can be calculated from the glancing angle, which is obtainable from the spectrum, and by using the following relationship: =h =h / (3) On combining (3) and (2) we obtain: = (4) Planck's constant h = 6, Js Velocity of light c = 2, m/s Lattice constant LiF (200) d = 2, m Lattice constant KBr (200) d = 3, m and the equivalent 1 ev = 1, J Evaluation Task 1: Record the intensity of the X-rays emitted by the copper anode as a function of the Bragg angle, using a LiF monocrystal as analyzer. Fig. 10 shows that well-defined lines are superimposed on the bremsspectrum continuum. The angles at which these lines are positioned remain unaltered on varying the anode voltage. This indicates that these lines are characteristic copper lines. The first pair of lines belongs to the first order of diffraction (n = 1), whilst the second pair belongs to n = 2. P PHYWE Systeme GmbH & Co. KG All rights reserved 5

6 TEP Characteristic X-rays of copper Fig. 10: X-ray intensity of copper as a function of the glancing angle; LiF (100) monocrystal as Bragg analyzer Task 2: Record the intensity of the X-rays emitted by the copper anode as a function of the Bragg angle, using a KBr monocrystal as analyzer. When the LiF monocrystal is replaced by the KBr monocrystal for the analysis of the copper X-ray spec- 11). The structures trum, Bragg scatterings are allowed up to an order of diffraction of 4 (n = 4) (Fig. which are additional to those in Fig. 10 result from the higher lattice constant of the KBr monocrystal. Fig. 11: X-ray intensity of copper as a function of the glancing angle; KBr (100) monocrystal as Bragg analyzer 6 PHYWE Systeme GmbH & Co. KG All rights reserved P

7 Characteristic X-rays of copper TEP The bremsstrahlung spectrum in Fig. 11 is subject to a noticeable drop in intensity in the direction of smaller angles at 8.0 and This drop coincides with the theoretically expected bromide K absorption edge (E K = kev) in the 1 st and 2 nd order of diffraction. The K absorption edges of potassium, lithium and fluorine cannot be observed, since the intensity of the bremsstrahlung spectrum is too low in these energy regions. (For K and L absorption edges, refer to experiment P ). Task 3: Calculate the energy values of the characteristic copper lines and compare them with the energy differences of the copper energy terms. The energy values of the characteristic copper X-ray lines are calculated using (4). They are listed in the Table. Taking the energy values from the Table, the mean values of the energies of the characteristic lines are: E Kα = 8,010 kev and E Kβ = 8,862 kev. Both of these experimental values correspond to better then 1% with literature values (see (1) and Fig. 8). Table of results / Linie E exp /kev LiF-analyzer n=1 22,7 Kα 7,974 20,4 Kβ 8,830 n=2 50,3 Kα 8,005 44,0 Kβ 8,857 KBr- analyzer n=1 13,6 Kα 8,018 12,3 Kβ 8,831 n=2 28,0 Kα 8,015 25,1 Kβ 8,870 n=3 44,7 Kα 8,041 39,4 Kβ 8,902 n=4 69,1 Kα 8,069 57,7 Kβ 8,919 Note A variation of the evaluation is possible by using the calculated characteristic copper X-ray lines from one spectrum in order to derive the corresponding lattice constant from the other spectrum. The atomic energy values were taken from the "Handbook of Chemistry and Physics", CRC Press Inc., Florida. P PHYWE Systeme GmbH & Co. KG All rights reserved 7

8 TEP Characteristic X-rays of copper Measure How to determine the peaks with the software measure : Refer to the help of the soft- to get more - Klick on the button and select an appropriate area of the ware measure curve. detailed information about the program. - Klick on the button Peak analysis. - The window Peak analysis appears (see Fig. 12). - Then, klick on Calculate. - If not all the peaks are identified (or too many), set the error tolerance. With high error tolerance, fewer peaks and therefore only important peaks, are displayed. With lower error tolerance, on the other hand, all peaks will be displayed, even those resulting from noise. - Sign visualize results, to transferr the calculated values to the spectrum. Fig. 12: Automatic peak analysis with Measure 8 PHYWE Systeme GmbH & Co. KG All rights reserved P

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