Related topics: X-rays, Bragg s law, Duane-Hunt relation, lattice constant and NaCl structure.

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1 FYSIK X-RAY DIFFRACTION 17/ Version 2.0 FYSA30, FYSA17&FYSL41 Vt07 Goal: The first goal of this experiment is to understand the X-ray spectra as a superposition of the continuum of bremsstrahlung radiation and the characteristic X-ray lines of the anode material. The second goal is to gain experience in using X-ray diffraction for identification of unknown crystal structures. Related topics: X-rays, Bragg s law, Duane-Hunt relation, lattice constant and NaCl structure. Principle and task: In this experiment we investigate the energy spectrum of x-rays as a function of the voltage and the emission current of the anode and we verify Bragg s law by studying the diffraction of x-rays from a single crystal. Background: X-rays are created when fast-moving electrons are rapidly decelerated in matter. A typical X-ray spectrum consists of bremsstrahlung and characteristic peaks. The bremsstrahlung radiation has a continuous spectrum which extends to a certain maximum frequency υ max (or a minimum wavelength λ min ). The characteristic X- radiation appears in the spectrum as individual lines in addition to the continuous bremsstrahlung spectrum. These lines are generated when high-energy electrons penetrate deep into the atomic shells of the anode material and eject electrons from the innermost orbitals by collision. The gaps created in this process are filled by electrons from the outer orbitals under emission of X-rays. Figure 1 illustrates the orbital model of the atomic shell for the lines of the characteristic X-radiation: the orbitals are characterized by a particular binding energy and are designated from the innermost to the outermost with the letters K, L, M, N, etc. 1

2 Fig. 1 The lines of the characteristic x-radiation Electrons can move between the orbitals. These transitions entail the absorption or emission of radiation, depending on the direction. For example, radiation from transitions to the K-shell (n=1) occurs as a series of sequential lines named K α, K β, K γ, etc. In this experiment, we verify Bragg s law of reflection by investigating the diffraction of X-rays at a NaCl monocrystal in which the lattice planes are parallel to the cubic surfaces of the unit cells of the crystal. The lattice spacing d of the face-centered cubic NaCl crystal is half the lattice constant a 0. We can thus say 2 d = a 0 = pm. Bragg s law of reflection: n λ = 2 d sinθ Fig.2 Bragg s reflection The bremsstrahlung continuum in the emission spectrum of an x-ray tube is characterized by the limit wavelength λ min, which becomes smaller as the tube high voltage, U, increases. It can be explained by using Duane-Hunt relationship: 2

3 λ = min hc 1 e U This relation can also be used to determine Planck s constant h when the quantities c and e are known. Tasks: 1. Record the energy spectra of an x-ray tube with metal anode 2. Determine the wavelength for the characteristic K α and K β x-ray radiation of the anode. 3. Investigate how the bremsstrahlung radiation and the characteristic radiation depend on the high voltage and the emission current. 4. Investigate Bragg reflection at a NaCl monocrystal using the characteristic X- ray radiation of the anode and confirm Bragg s law of reflection. 5. Measure the lattice constant of an unknown monocrystal. 6. Determine the limit wavelength λ min of the bremsstrahlung continuum as a function of the high voltage, U, of the x-ray tube and confirm the Duane-Hunt relation. 7. Determine Planck s constant. Set-up and experiment: This experiment records the energy spectrum of an x-ray tube with a metal anode. The x-rays are detected using a GM counter tube (end-window counter) which is swiveled in tandem with the NaCl crystal in a 2θ coupling with respect to the incident light; this means that the counter tube always advances by an angle which is twice that of the crystal. Important Notes! NaCl crystals are hygroscopic and fragile. Keep the crystals in a dry place. Avoid mechanical stresses on the crystal; handle the crystal by the short faces only and use latex gloves. If the counting rate is too low, you can reduce the distance s 2 between the target and the sensor somewhat. However, this distance must not be too small, as otherwise the angular resolution of the goniometer is no longer great enough to separate the characteristic K α and K β lines. 3

4 Instructions for setting up the Bragg configuration: Fig. 3 X-ray diffraction apparatus Figure 3 shows some important details of the experiment setup. Most of the setup is already made but check each step to make sure it is done properly: Mount the collimator in the collimator mounts (a) (note the guide groove). Attach the goniometer to the guide rods (d) in such a way that the distance s 1 between the slit diaphragm of the collimator and the target arm is approx. 5 cm. Connect the ribbon cable (c) for controlling the goniometer. Remove the cap of the end-window counter, insert the end-window counter in the sensor seat (e) and connect the counter tube lead to the socket marked GM-Tube. Adjust the sensor seat (b) until the distance s 2 between the target arm and the slit diaphragm of the sensor seat is approx. 6 cm. Attach the target holder with target stage (f). Loosen knurled screw (g), lay the NaCl crystal flat on the target stage, carefully raise the stage as far at it will go and then tighten the knurled screw with care (press against the screw lightly to prevent it from stripping). Adjust the zero position of the goniometer measuring system as necessary (see Instruction Sheet of x-ray apparatus). 4

5 Experiments: a) Varying the tube high voltage: Start the software X-ray Apparatus, check to make sure that the apparatus is connected correctly, and clear any existing measurement data using the button or the F4 key. Set the emission current to I = 1.00 ma, the measuring time per angular step to t = 2 s, and the angular step width to β =0.1 Press the COUPLED key to activate 2θ coupling of target and sensor and set the lower limit of the target angle to 2.5 and the upper limit to 10. Set the tube high voltage U = 15 kv and start measuring and data transmission to the PC by pressing the SCAN key. Conduct additional measurements using a series of tube high voltages, for instance U = 20 kv, 25 kv, 30 kv and 35 kv. To show the wavelength-dependency, open the Settings dialog with the button or F5 and enter the lattice plane spacing for NaCl. Save the measurement series under an appropriate name by pressing the button or the F2 key. b) Varying the emission current: Clear existing measurement data using the button or the F4 key and set the tube high voltage to U=35 kv. Set the emission current I = 0.40 ma and start measuring and data transmission to the PC by pressing the SCAN key. Record additional measurements using a series of emission currents, for instance I = 0.60 ma, 0.80 ma and 1.00 ma. To show the wavelength dependency, open the Settings dialog with the button or F5 and enter the lattice plane spacing for NaCl. Save the measurement series under an appropriate name by pressing the button or the F2 key. c) Bragg reflection Delete any existing measurement data by clicking the button or pressing F4. Set the x-ray high voltage to U = 35.0 kv, emission current I =1.00 ma, measuring time per angular step t = 5 s and angular step width β =

6 Press the COUPLED key on the device to enable 2θ coupling of the target and sensor; set the lower limit value of the target angle to 2 and the upper limit to 25. Start with the NaCl crystal and then change to the other crystal (with a yellow dot on) and do the same measurements as with the NaCl crystal. When the measurement is finished, save the measurement series to a file under a suitable name. d) Planck s constant Set the tube high voltage U = 22 kv, the emission current I = 1.00 ma, the measuring time per angular step t = 3s and the angular step β = 0.1. Press the COUPLED key to activate 2 θ coupling of target and sensor and set the lower limit of the target angle to 5.2 and the upper limit to 6.2. Start measurement and data transfer to the PC by pressing the SCAN key. Additionally record measurement series with the tube high voltages U = 24 kv, 26 kv, 28 kv, 30 kv, 32 kv, 34 kv and 35 kv; to save measuring time, use the parameters from Table 1 for each series. To show the wavelength-dependency, open the Settings dialog with F5 and enter the lattice plane spacing for NaCl. When you have finished measuring, save the measurement series under an appropriate name by pressing the F2 key. In the diagram, click the right mouse button to access the evaluation functions of the software X-ray Apparatus and select the command Best-fit Straight Line. Mark the curve range to which you want to fit a straight line to determine the limit wavelength λ min using the left mouse button. Save the evaluations under a suitable name For further evaluation of the limit wavelengths λ min determined in this experiment, click on the register Planck. Position the pointer over the diagram, click the right mouse button, fit a straight line through the origin to the curve λ min = f (1/U) and read the slope A from the bottom left corner of the evaluation window. 6

7 Table 1: Recommended parameters for recording the measurement series U (kv) I(mA) t Β min (grd) Β max (grd) β (grd)

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