X-ray practical: Crystallography Aim: To familiarise oneself with the operation of Tex-X-Ometer spectrometer and to use it to determine the lattice spacing in NaCl and LiF single crystals. Background: Prof RW James, the person after whom the building housing the Physics Department is named, was Head of the Department of Physics from 1937-57. He established the first x-ray crystallography research group in South Africa, and later wrote the book The Optical Properties of the Diffraction of X-rays which became the standard work on crystallography of its day. He was a dedicated teacher and was much loved by staff and students alike, and eventually rose to become the Acting Principal of UCT. Prof. James s time at UCT was also notable in that two of his students were subsequently awarded the Nobel Prize: Prof. A. M. Cormack (M.Sc., 1945) and Sir Aaron Klug (M.Sc., 1946), who were awarded Nobel Prizes in Physiology and Medicine (1979) and Chemistry (1982) respectively. In both cases the work for which they were awarded the prize was a direct outgrowth of the X-ray diffraction theory which they had learned from Prof James. It is therefore very fitting that x-ray crystallography is once again part of the undergraduate practical syllabus. Introduction: Students should have read pages 1-8 of the Tel-X-Ometer manual (web link) and pages 9 13 of the Tel-X-Driver manual (web link) before commencing the practical. Particular attention should be paid to the section 8.1 in the Tel-X-Ometer manual dealing with Checking radiation protection equipment. X-rays are produced in the tube of the Tel-X-Ometer by accelerating a beam of electrons over a voltage of 20 or 30 KV and allowing them to impinge on a copper target (often chosen for a target as it is easy to cool). Two types of x-rays are produced in this manner; a broad continuous background spectrum and superimposed on this background are sharp intense peaks, depending whether the impinging electron collides with the copper nucleus or its electrons. Collisions with nuclei cause a very rapid deceleration of the electron and the emission of electromagnetic radiation. This is the origin of the broad continuous background known as Bremsstrahlung which is German for braking radiation. Electrons that loose all their kinetic energy in a single collision give rise to the maximum energy of the Bremsstrahlung radiation (and with E = hc/ they are represented by x-rays with lowest
wavelength). If the impinging electron collides with core electrons of the target Cu atoms this will result in the core electrons being ejected from the inner shell, giving rise to a vacancy. These vacancies are quickly filled by electrons dropping down from higher levels, emitting x-rays that have a sharply defined frequency determined by the difference in energy of the atomic levels of the Cu atom. As the energies of these x-rays are fixed by the atomic structure of the target atom they are referred to as characteristic x-rays. It is the emission of these characteristic x-rays which give rise to the sharp peaks in the energy spectrum Most solids are crystalline in nature, with atoms arranged in a regular and ordered format. We can therefore consider the crystal as being made up of a collection of planes of atoms, separated by a distance d. X-rays of wavelength will be scattered from these planes (i.e. the scattered radiation from the atoms in the planes will be in phase at the detector) if the path difference between adjacent planes is an integer number of wavelengths, n. Given that the path difference between adjacent planes is 2d sin the condition for diffraction is n = 2d sin with n known as the order of diffraction. This condition is referred to as Bragg Diffraction after Sir Lawrence Bragg who first proposed it. If we were to place a single crystal in the path of the x-ray beam and rotate the sample by an angle we will then detect scattered radiation at an angle 2 for those x-rays of wavelength which satisfy the Bragg diffraction condition, and where d is the separation between the planes which are parallel to the face of the crystal. 2
If we sweep the crystal through a range of (and the detector through a range of 2) we will then sample a range of x-ray wavelengths. Since E = hc/ the apparatus therefore acts as a spectrometer, and we are thus able to determine the energy distribution of the x-rays. Preparatory Measurements: Make sure that the x-ray source and main power to the Tel- X-Ometer are switched off and then carry out the radiation protection check described in the Tel- X-Ometer manual. Then open the lid and check that there is a vertical 1 mm slit in front of the x- ray tube, a 3 mm vertical slit in position 13 of the magazine of the measuring arm, and a 1 mm vertical slit in position 22, directly in front of the Geiger counter. Mount the LiF single crystal, taking care not to touch the crystal itself. Check that the high voltage selector switch under the Tel-X-Driver is set to 30 kv. Close the lid and switch the powers on and switch on the x-ray tube. In this experiment only two characteristic x-rays will be observed, namely the copper K and K x-rays. These characteristic x-rays have wavelengths of 154 pm and 138 pm respectively. Crystallographers, however, traditionally measure crystals dimensions in angstroms, symbol Å (1Å = 10-10 m) so these x-rays would normally be described as having wavelengths of 1.54 Å and 1.38 Å. We will begin by using the diffraction peak of the K characteristic x-ray from the LiF single crystal to calibrate the Tel-X-Ometer as described in pages 9-12 of the Tel-X-Ometer manual. Use the ROI button on the data collection window of the Tel-X-Driver to set the range of interest to 38 o 48 o, and after setting the HV on the detector to 650 V begin the scan. After the scan has completed the data collection window should appear similar to the figure shown below. Two peaks should appear in this range, the smaller peak around 40.5 o corresponds to K diffraction from the LiF(100) planes and the large peak situated around 45.0 o due to K diffraction. Once the run is complete open up setup and check that the larger peak has appeared at position 45.0 o (as it should if the equipment is properly calibrated). If not set the
offset, close the tab, click Offset Enabled on the main data collection window and then repeat. The large peak should now appear at position 45.0 0.5 o if not repeat the exercise Next examine the effect of the x-ray tube voltage on the broad background spectrum and the characteristic x-ray peaks. Change the range of interest to 12 50 o and start the scan. Once the scan has been completed save the data, switch off the x-ray beam, turn off the power and open the lid. Change the high voltage selector switch to 20 kv and repeat the scan. (Note best to use a screwdriver to change the switch to prevent moving the driver or else the apparatus will have to be recalibrated.) You should find that changing the voltage affects the background spectrum but does not change the positions of the characteristic peaks. Once completed switch off x-rays and power again, open up and switch back to 30 kv. The final preparatory measurement is to examine the effect various filters have on the x ray spectrum. An ideal x-ray beam for crystallographic determination would be monochromatic. Clearly the x-ray spectrum produced by the Tel-X-Ometer is not which is why diffraction is observed over a large range of angles. The situation can be improved by the introduction of a filter. Ideally one would like the filter to reduce all the background x-rays and one of the two characteristic peaks, preferably the smaller K. There are three filters you should try viz. Zn, Ni, and Co. Begin by opening up the lid and inserting the Zn filter in position 18 of the magazine of the measuring arm. Reset the range of interest to 38 o -48 o and run the scan. Repeat with the Ni and Co filters, then decide which filter would be best to use to produce the most monochromatic x-ray beam. Determination of NaCl and LiF lattice constant. Both NaCl and LiF are ionic crystals meaning that the binding between the elements is ionic. Na has only one electron in the outer shell making it relatively easy to ionize, while the Cl outer shell is short of one electron thus Na readily donates its outer electron to Cl thereby producing Na + and Cl - ions, both of which have filled outer shells. Two of the most common crystal structures for compounds formed by ionic bonding are the CsCl and NaCl crystal structure NaCl crystal structure CsCl crystal structure
As can be seen from the above diagrams, the nearest neighbours of ion at the centre of the cell are ions of the opposite charge needed, of course, if the ions are to bond with an ionic bond. Note that each of the ions in the NaCl crystal structure have six nearest-neighbours while those in the CsCl have eight. Both LiF and NaCl are found to have a NaCl crystal structure. The size of the side of the unit cell, shown as a in figure above, is referred to as the lattice constant, and the purpose of this practical is to use the Tel-X-Ometer to determine this quantity for NaCl and LiF. The NaCl figure also shows how one can consider the crystal to be made up of a collection of planes. Note that the spacing d between the major planes shown in the NaCl figure are ½ the length of the side of the unit cell. Since the spacing between planes is the largest for major planes one generally finds that when NaCl-type crystals are cleaved they tend to cleave along the major planes. These major planes will therefore be aligned parallel to the face of the single crystals, and so any diffraction observed in the - 2 scans carried out in this investigation should correspond to diffraction from these major planes. By scanning the detector over the full range find how many diffraction conditions are observed, determine the spacing between the planes parallel to the faces of the LiF and NaCl single crystals, and hence the lattice constant of these two structures. If the crystal structure is indeed cubic, as shown above, then it should matter which side of the sample was being examined. Rotate one of the crystals in its support by 90 o and repeat the scan to confirm that the diffraction peak appears in the same position from the rotated sample.
The table below gives values of standard radii for ions in filled shell configuration. After ionisation the Na, Li, Cl and F ions are in filled shell configurations so these values should be representative of the size of the ions in the single crystals investigated. Taken from Kittel: Introduction to Solid State Physics, 7 th Ed, Questions. Is the cut off wavelength for the spectra measured at 20 and 30 kv what that one would expect it to be? Are the lattice constants for the two crystal structures that you determined what one would expect from the values given in the above table? What are the inter-ionic lengths of nearest neighbour (unlike ions) and next-nearest neighbours (like ions) in the NaCl crystal structure for your two compounds? What would these inter-ionic lengths be if the two compounds had adopted the CsCl structure (while maintaining the same ionic radii)? Does this suggest why the two compounds investigated don t adopt the CsCl structure in nature? (Note: Given that the ions in the CsCl structure have eight nearest-neighbours, while those in the NaCl structure only have six, one would expect the CsCl structure to have the lowest energy and thus be the natural structure of choice for ionic crystals.)