MY 3200 Diffraction Spectrum from an X-ray Tube
IntroductionX-rays are produced when any electrically charged particle of sufficient kinetic energy is rapidly decelerated (or accelerated). Electrons are usually used for this purpose, the radiation being produced in an x-ray tube as a result of the electrons being decelerated as they collide with a metal target (the anode). The energy of the x-rays produced will depend on the velocity of the electrons prior to collision with the metal target, which is determined by the voltage applied to the cathode (usually a W filament). In this experiment, x-rays will be generated using different accelerating voltages with the same target material, and the effect of these different accelerating voltages on the properties of the continuous and characteristic x-ray spectrum will be examined. In addition, the effect of absorption by using various filters to modify the intensity of thecharacteristic x-rays lines will be investigated.
X-rays generated using a Cu target tube in a Picker X-ray diffractometer will emerge from the x-ray tube, pass through a 1° beam slit, and focus on a single crystal of LiF.
At this point, Bragg's law of diffraction will apply:
The single crystal will select and diffract only a small fraction of the incoming x-rays at each angle q. The diffracted beam will pass through a 0.02° receiving slit and then into a proportional counter. This signal is amplified and sent simultaneously to a rate meter and a strip chart recorder.
The output on the strip chart is given in "Intensity versus 2q", where q is the angle of diffraction. The specimen at the center of the goniometer is a single crystal of LiF with (200) planes parallel to the large face. The crystal is bombarded by all x-rays, continuous and characteristic, with are emitted from the x-ray tube. However, it passes on, or diffracts, only that wavelength which satisfies Bragg's law. Thus, at 2q = 40°, for example, sinq = 0.342. With 2d = 0.40276 nm, those x-rays diffracted to the counter have a wavelength
Experiments to be carried out...
Characteristics of Spectrum
The following conditions will be used for this portion of the experiment:
- Cu target x-ray tube.
- 1° beam slits.
- 0.02° receiving slit.
- No filter.
- Log scale on rate meter.
- 1 second time constant.
- LiF single crystal sample with (200) cleavage plane parallel to surface (2d = 0.40276 nm)
(a) With the generator at 12 kV and tube current at ~ 2mA, run the counter from 28° 2q to 49° 2q at high speed (2°/min). Record counter output with chart recorder at 2 in/min. Determine the positions of any characteristic peaks on the spectrum and verify that the tube target is Cu. Calculate the error in your measurements of the characteristic peak wavelengths.
(b) Repeat (a) with higher tube voltages of 20, 26, and 30 kV.
(c) Using the Bragg relationship, compute lSWL (the minimum wavelength) for each of these tube voltage settings as well as for 12 kV. As discussed previously, the relationship between lSWL (in units of nanometers) and tube voltage (V) can be described by:
(d) Plot lSWL for the four experimental values you calculated versus the inverse of the tube voltage using a software program and determine the slope of the plot. Compare the slope determined from the experimental data to the value predicted bythe above equation to show that the experimental data are in agreement with that equation; that is, calculate the error between the value of the slope from the above equation and the experimentally determined value of the slope.
(e) LiF has a structure like NaCl. The diffraction observed in the previous experiments was from the (200) planes. Find the second order diffraction of Ka from the (200) planes; that is, from the (400) planes. Calculate the difference in the spacing (that is, D2q) of the Ka1 and Ka2 peaks for the (200) and (400) planes.
(f) Give a reason as to why the doublet is spaced more widely (that is, D2q, is larger for the Ka1 and Ka2 peaks) for diffraction from the (400) planes compared to the (200) planes.
(g) With the counter set for the first order diffraction of Ka from the (200) planes, record the intensity (counts/20 seconds) as the voltage is increased in steps of 2 kV from 12 kV to 40 kV. Use a tube current of 2 mA and enough absorber foils to reduce the intensity diffracted at 12 kV to less than 1000 counts in 20 seconds. The intensity of any characteristic line, measured above the continuous spectrum, depends both on the tube current i and the amount by which the applied voltage V exceeds the critical voltage for that line. For a K line, the intensity is given by
where B is a proportionality constant Vk is the K excitation voltage (which you can calculate), i is the tube current and n is a constant.
(h) Plot ln Ik versus ln (V-Vk) using a software program and obtain the values for n and the product Bi by determining the slope and the intercept of the line, respectively.
Absorption of X-rays
Repeat (a) with a filter of two thicknesses of 0.00889 mm Ni foil.
(i) Briefly comment on the effect that the Ni foil had on the overall spectrum that you found in part (a).
(j) By counting with the scaler for 20 seconds, measure the effect of the Ni foil on Ka and Kb. Repeat this measurement with a Cu foil, 0.127 mm thick.
(k) Compare the measured intensity ratio of Ka /Kb with and without the Ni filter, and then compare these intensity ratios to that obtained with the Cu filter. How do these values compare to the ratio of Ka /Kb = 5 expected for unfiltered radiation?
(l) From the intensities, the filter thicknesses, and known densities, calculate 
(mass absorption coefficient) for the Ka and Kb wavelengths of Ni and Cu. Compare your experimental values to the values tabulated in Appendix 5 of Suryanarayana & Norton by determining the % error using the equation
Take the absolute value of the calculation before multiplying by 100.
(m) Determine the mass absorption coefficient as a function of wavelength by counting for 20 seconds with and without the Ni filter for 1° intervals between 38°and 48° 2q . Plot the calculated mass absorption coefficients of Ni as a function of wavelength using a software program and estimate the wavelength of the observed absorption edge. Compare this value to that given in the attached table (last page of the handout). Discuss briefly how you could improve the accuracy of this measurement.
There is no formal report due from this laboratory assignment. However, a number of exercises were indicated in the procedure section of laboratory (a through m). The questions or calculations indicated in these exercises should be answered or performed, respectively and the answers handed in.
