Uppsala University Department of Physics and Astronomy Laboratory exercise X-ray spectroscopy: Experimental studies of Moseley s law (K-line x-ray fluorescence) and x-ray material s composition determination Summary of exercise: 1. Record the K α and the K β lines emitted from different metals and make an energy calibration of the spectra.. Determine the energies of the observed K lines. 3. Verify Moseley s law in a diagram. 4. Measure the x-ray spectrum of an unknown material. 5. Determine the material s elemental composition from measured K, L, or M lines. 6. Make an oral report on the results. 1
Laboratory exercise in Quantum Physics X-ray spectroscopy 1. Introduction Author/date: Lage Hedin, Filip Heijkensköld /008-04-18/ 011-09- Vacancies in inner shells (electron holes) of an atom can be created by absorption of x-ray radiation or by collisions with energetic particles. The atom ionised in this way then has an electron hole, which rapidly will be filled with an electron from other, less strongly bound shells of the atom. E.g., a vacancy in the K-shell can be filled by the transition of an electron from the L-shell. Such a transition is connected with the emission of a photon. This radiation has only particular discrete photon energies corresponding to the energy difference of the levels involved and it is characteristic for every chemical element. Radiation like this is called x-ray fluorescence. In the laboratory exercise the radiation to be investigated is emitted from some different metals in which vacancies are created in K shells using the radiation from an x-ray tube equipped with a molybdenum (Mo) anode. The designations of the characteristic x-ray lines are a combination of the symbol for the electron shell (K, L, M, etc) and a Greek letter α, β, γ, etc). The electron shell being referred to is the one where a vacancy was created before the transition of an electron from an outer shell. Preparatory exercises and questions 1. Formulate Moseley s law? What are characteristic x-rays?. Draw an energy level diagram, with level terms, e.g., for copper. Mark allowed transitions in the diagram and label the terms for corresponding emission lines. 3. Calculate the cut-off limit of the bremsstrahlung from a molybdenum anode in an x- ray tube with an accelerating voltage of 35 kv. 4. What is the lowest possible voltage over the tube which still generates molybdenum s K α radiation?. Theory.1 Characteristic radiation In the present laboratory exercise characteristic K α and K β x-ray fluorescence (see explanation of designations in the section Moseley s law ) from some different metals will be investigated. The process may be described in the following way, where the atom is represented by its electron configuration and a 1s electron is assumed to be emitted from the atom with a kinetic energy of free E kin e - in ( E kin ) + 1s s p 6 3s 3p 6 3d 10 4s e - out ( E kin ) + 1s 1 s p 5 3s 3p 6 3d 10 4s + e - ( E free kin ) In the metal the outer electron shells aren t strictly atomic, but form valence and conduction
bands. The other electrons can, however, be considered to be primarily atomic. By the interaction, a vacancy in the 1s-shell in a copper atom will be created. Due to the selection rule Δl = ±1, only electrons from the p and 3p shell come into consideration in the case of copper. The former give rise to the K α radiation, and the latter to the K β radiation (see lecture notes). The energies of these radiation components can be calculated from the binding energies for different electrons. These energies are tabulated below: Orbital 1s s p ½ p 3/ 3s 3p ½ 3p 3/ Energy (ev) 8979 1096,7 95,3 93,5 1,5 77,3 75,1 Thus, an energy of at least 8979 ev to release a 1s electron, has to be supplied e.g. by means of x- ray photons. The energy of the state has been raised with the same value. For example, when the 1s vacancy is filled by an electron from the p shell, the following configuration appears: 1s s p 5 3s 3p 6 3d 10 4s This state has an energy of about 94 ev higher than the ground state energy (mean value of the two spin-orbit components). The difference in energy is: ΔE = 8979-94 = 8037 ev If the electron relaxation is followed by the emission of a photon, then the photon will have the energy 8037 ev. (Another possibility is that an electron leaves the system in a so-called Auger process.) If we calculate this energy more accurately, taking the spin-orbit interaction into account, we will actually get two transitions with the energies 8047 ev (Cu K α1 ) and 807 ev (Cu K α ). These components are close in energy, and are difficult to resolve in the used x-ray spectrometer.. Moseley s law The designations of the characteristic x-ray lines are a combination of the symbol for the electron shell and a Greek letter. The electron shell being referred to is the one where a vacancy is created before the electron transition. For example, the designation K α -line describes the transition from the L-shell into the K-shell, K β -line refers to the transition from the M-shell to the K-shell. The L α - and L β -lines refer to the transitions from the M-shell and the N-shell, respectively, to the L-shell. For the energies E of the characteristic lines Moseley found in 1913 the following relations. E = Z 1 Ry n 1 1n (1) with the atomic number Z, the screening constant σ, the constant Ry=m e e 4 /8e 0 h = 13,6 ev and the principal quantum numbers n 1 and n for the electron shells involved ( n 1 <n ). This equation can be rewritten as 3
E=RyZ 1 eff n 1 1n where Z eff =Z () which is the Bohr model applied to many-electron atoms. Like the Schrödinger equation it gives the energies of the emitted photons. 3. The x-ray spectrometer When high-energy electrons hit the anode of the x-ray tube two different processes may take place leading to x-ray emission. On the one hand, electrons can be decelerated by the anode atoms, and radiation emitted as bremsstrahlung. This radiation is continuous and the onset of the distribution occurs at maximum kinetic energy of the electron. On the other hand, vacancies can be created in inner shells and filled by electrons from outer shells. Transitions of this kind lead to emission of characteristic radiation (the wavelengths are characteristic of the anode material). The experimental set-up is shown on the front page and in figure 1 and. The essential components are an x-ray tube equipped with a molybdenum anode and a hot cathode, a goniometer and a cooled detector which directly gives the energy of each incoming photon. The anode is seated in a copper block to dissipate heat. The voltage across the x-ray tube should, in these experiments, be adjusted to 35 kv and the emission current should be adjusted to 1 ma. The goniometer is used for mounting the target and setting it at proper angles. The apparatus is equipped with two independently controllable stepping motors, which move the detector and target arms. Do not block the target arm and sensor arm of the goniometer and do not use force to move them. 4. Procedures 4.1 Start up procedure Turn on computer and log in as a student without password. Turn on the x-ray apparatus. Push the sensor button (see figure ) and adjust to 90. Be careful and do not override the angle. The equipment has no automatic stop. Push the target button (see figure ) and adjust to 45. Open the sliding glass window to access the target compartment. Start the Cassy lab program in the computer by double-clicking the icon on the desktop. Click in the middle lower figure in the context menu on the screen to select a new diagram. A green LED on the detector and the Cassy interface shows that they are ready to be used. Change the setting on in the Measuring Parameters. Set number of channels to 104 and set pulse height to -000 mv. 4. Calibration procedure Load the sample holder with an iron sample. Close all sliding glass windows. Turn on the high voltage for the x-ray tube, set it to 35 kv. Adjust the current to 1.0 ma. Use F9 on the computer to start the measurement. After the measurement is ready turn off high voltage, open windows and change to a molybdenum sample. Use F9 on the computer to start the measurement. 4..1 Open in the context menu of the diagram (right-click mouse button) the Energy calibration, select global energy calibration and enter on the right-hand side the energies of the Fe K α -line (6.40 kev) and of the Mo K α -line (17.48 kev). Do not close the Energy calibration window. 4
4.. In the context menu of the diagram select under Other evaluations use Calculate peak center, mark the Fe K α -line and enter the result in the left-hand side of the energy calibration (e.g., with drag & drop from status line). Then determine the center of the Mo K α -line and also enter the result on the left-hand side. 4..3 Close the Energy calibration window. The scale of the x-axis is now in kev! 4.3 Measurement of other samples 4.3.1 Replace the sample with the next sample, close all windows, turn on high voltage and push the F9 button at the computer to start a new measurement. Repeat the measurements for other remaining known (marked) samples. Measure the characteristic energy for unknown samples and try to identify the elements the samples contain. 4.4 Evaluation As the atomic number Z increases the energy of the characteristic lines also increases and so does the separation between the α- and the β- component in the K spectral series. For a quantitative analysis, the energies of the individual K α -line can be determined. Click on top of the lines to determine the energy and read the energy of the peak positions from the status line and enter them together with the atomic numbers Z of the different metals. Make a diagram by using Excel for the energies E Z 1, i.e. the x-ray energy as a function of the square the effective charge. Add a linear regression line with the equation for the regression line to the graph. 4.5 Investigation of the unknown samples Your task is to find out what elements the other samples are made from. Look for L- or M- lines when you suspect heavy elements. 4.6 Examination You are expected to work in groups of two students, to be prepared and be present in the laboratory at your allocated time. You have to print out the instructions and read the instructions before going to the lab. Bring your own copy of the instructions with you. You have to make a short oral presentation of your experiment and of the results of your laboration on x-ray spectroscopy. This presentation you will present at the allocated time the day after your lab. You do your presentation together with your group partner. Your report has to contain the answer to the following questions: How does the energy of the measured emission lines correspond to what you get from energy tables? Specify the amount of deviation. Why is it necessary to use the screening constant σ in the calculation of the energy of the characteristic radiation? Have you verified Moseley s law with your measurement and calculation? What are the elements you detected in your unknown sample, and how did you establish this? You have to hand in your presentation in electronic form by uploading it in pdf format to your folder in the Studentportalen. Each student has to upload his/her material into her/his personal folder. The name of the file has to be the same as yours and your lab-partner's name, e.g., Anna_Sevedsson_Hezekiel_Hansson.pdf could do. 5
Sensor Target Figure 1: Sample compartment with x-ray detector. Figure : Control panel. 6