LAUE DIFFRACTION INTRODUCTION CHARACTERISTICS X RAYS BREMSSTRAHLUNG

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1 LAUE DIFFRACTION INTRODUCTION X-rays are electromagnetic radiations that originate outside the nucleus. There are two major processes for X-ray production which are quite different and which lead to different X-ray spectra. CHARACTERISTICS X RAYS If electrons striking a target are sufficiently energetic to ionize some of the inner electron shells of the target atoms, the atoms themselves emit electromagnetic radiations in the X-ray energy region when the holes in the inner shells are filled. The X-rays produced in this manner are monochromatic, that is, they exhibit a line spectrum just as the visible (optical) spectra emitted by atoms. These X-rays are characteristic of the target atoms, hence the name characteristic X-rays. BREMSSTRAHLUNG Electromagnetic radiations are also produced when electrons are decelerated upon passing through matter. (Bremsstrahlung is a German word meaning deceleration radiation.) These X-rays are characterized by a continuous spectrum. The maximum quantum energy of the X-rays emitted is equal to the maximum energy of the electrons. The wavelengths of X-rays are of the same order of magnitude as the dimensions of an atom and therefore that a regular array of atoms (as in a crystal) should behave much like an optical diffraction grating. Just as there is a relation between the slit width and the wavelength of light in an optical grating, there will be a similar relation between the lattice spacing of the crystal and the X-ray wavelength. The geometry of the situation is illustrated in Fig. 1, where the horizontal rows represent the crystal planes. Assume that a collimated beam of X-rays is directed at the crystal surface, making an angle θ with the surface. The X-rays will interact with the electrons of the crystal lattice and will be scattered. Some will suffer a change in frequency (Compton scattering) and thus will Page 1 of 9

2 be lost from the coherent beam, but most of the photons in the region of a few kiloelectron volts quantum energy are scattered without change in frequency (Rayleigh scattering). Since the electrons in the crystal (i.e., electrons belonging to the lattice atoms) are arranged in an ordered manner, coherent Rayleigh scattering can be observed. The condition for a diffraction maximum is that the path difference between rays 1 and 2 in Fig. 1 is an integral number of wavelengths. This is expressed by nλ = 2d sin θ (1) where λ is the wavelength, d is the lattice spacing, and n is an integer. Figure 1 Bragg reflection from two crystallographic planes This condition is known as Bragg s law and is the fundamental relation used in X-ray analysis to measure crystal lattice spacings. The condition in Eq. (1) will be used to determine the symmetry properties of the crystal. Page 2 of 9

3 The first X-ray diffraction experiments were carried out by M. von Laue. Using the continuous X-ray spectrum and the geometry shown in Fig. 2, he obtained a picture containing a pattern of spots, each of which corresponds to coherent reflection of the X-ray beam from one set of the crystal planes. Figure 2 Transmission X-ray diffraction pattern This experiment is a striking demonstration of the wave nature of X-rays. The pattern of the spots was characteristic of the crystal structure of the material being examined. In the case of Laue diffraction a continuous spectrum is used to irradiate the crystal; thus every crystal plane contributes to the diffraction pattern, since it picks out the proper frequency (wavelength) component in the initial beam which satisfies the Bragg condition [Eq. (1)]. This situation is illustrated in Fig. 3. Each of the reflected beams will be monochromatic, with a wavelength determined by the d spacing of the particular planes. Also, the angles θ 1 and θ 2 and the symmetry pattern of reflections on the photographic plate make it possible to deduce whether cubic, hexagonal, or other crystal structures exist in the sample. Page 3 of 9

4 Photographic plate Crystal showing the diffracting planes Monochromatic diffracted beams Incident X-ray beam containing all wavelength Diffracting planes Figure 3 Schematic representation of various crystallographic planes contributing to X ray diffraction Page 4 of 9

5 X-RAY UNIT The apparatus is designed as a horizontal counter tube goniometer with rotatable carriage arm and a sample post in the axis of rotation. The angles of rotation of carriage arm and sample post are coupled in a proportion 2:1, so that when demonstrating Bragg reflection and recording X-ray spectra the counter tube fastened on the carriage arm is always in correct position for receiving the reflections. The coupling can be detached e.g. for measuring a scattering indicatrix. A slide carriage is fitted to the carriage arm. Measuring equipment and sample materials are fixed in slide frames or have the shape of a slide. An additional small slide carriage can optionally be fitted on the lead glass dome or on the crystal post. Sample materials and measuring equipment, such as e.g. counter tube, X-ray film cassette, welded seam, ionization chamber, are placed into the path of rays by simply sliding them into one of these slide carriages. The collimators are positioned by introducing them into the opening in the lead glass dome. Crystals or powders are fastened on the sample post by means of a screw clamp. Figure 4 Page 5 of 9

6 The same considerations as to the counter tube method was given to photographic X-ray techniques. For the X-ray unit, X-ray films are available which are exposed to X-ray radiation at daylight and subsequently developed and fixed. A time switch with max. 2 hours switching time permits easy adjustment and control of exposure time and prevents in addition uncontrolled continuous operation of the apparatus. Mechanical Inspection The transparent plastics radiation scatter shield which completely encloses the experimental zone is normally locked in the safe position by a ballended spigot. This spigot locates in a key-hole slot situated behind the aluminium backstop displaying the international radiation symbol. To open the unit the entire scatter shield should be displaced sideways with respect to the hinge. The spigot will automatically line up with the left hand or right hand release port and the shield can be lifted; the cover is self-supporting when it has been lifted beyond the vertical line of the hinge. Initial Switch On Connect the mains supply to the unit by depressing the MAINS switch (WHITE) on the control panel; the unit will only function when the time switch is rotated to the required time factor. When this is performed both the filament of the X-ray tube and the MAINS lamp (WHITE) will be illuminated. Page 6 of 9

7 X-Rays On/X-Rays Off Procedure To switch off the EHT, displace the scatter shield sideways with respect to the hinge. Replace the shield in the central locked position and depress the X-rays button; the X-rays lamp (RED) will be illuminated. EXPERIMENTAL TECHNIQUES Primary Beam The X-ray emission from the tube is collimated at the lead glass dome to be a circular beam of 5 mm diameter, see Fig 4. This primary beam diverges from the basic port to give a useful beam diameter at the crystal post of 15 mm diameter, at experimental station E.S. 13 of 20 mm diameter and at E.S. 30 of 38 mm diameter. Primary Collimators The primary beam can be collimated to a fine circular beam using the 1 mm diameter collimator ( ) and to a ribbon beam using the 1 mm slot collimator ( ); each of these collimators is installed by inserting the 0 ring shank into the basic port and pushing it home; the 0 ring retains the collimator in position and allows exchange of the collimators even when they become warm. The collimators should be rotated when they are inserted to ensure that they are securely seated. The 1 mm slot collimator can be rotated in position to provide a vertical ribbon of X-rays, a horizontal ribbon or any diametrical ribbon. Auxiliary Slide Carriage ( ) A demountable auxiliary slide carriage is included. Using this carriage, experimental stations 1 to 4 can be placed in the X- ray beam. Page 7 of 9

8 Mode H (horizontal) The hole in the end face of the auxiliary carriage is placed over the basic port in the glass dome and then held in that position by one or other of the primary collimators. With this arrangement the slides used for the experiment are in vertical position and are passed by the X-ray beam. The X-Ray Tube The X-ray tube current should NOT be adjusted without monitoring the current, using the jack-plug provided and an external 100 µa or 150 µa meter. The tube current must not exceed 0.08 ma. When the emission current of the X-ray tube is changed from 0.02 ma to 0.08 ma, the high tension remains within 5% of the selected value, 20 or 30 kv. If on the other hand the EHT is changed from 30 kv to 20 kv, also the tube current remains within 5% of its preset value. EXPERIMENT LAUE DIFFRACTION (a) Mini-crystal of Lithium Fluoride 1) Using tweezers if available, carefully select one of the mini crystal ( ), the crystals are lithium fluoride and are very fragile. 2) By means of clear adhesive tape mount the mini crystal over the existing aperture of the 1 mm diameter primary beam collimator ( ). 3) Fit the auxiliary slide carriage with primary beam collimator ( ) together with the mini crystal to the lead glass dome. Align the longitudinal axis of the mini crystal at an angle of 45. 4) Load the film cassette ( ), without primary beam shield, with a 38 mm x 35 mm film. Page 8 of 9

9 5) A good Laue pattern can be recorded with the cassette located at E.S. 3 and exposed for 40 minutes. 6) Comment on the symmetry of the Laue pattern obtained. (b) Polyethylene Monofilament 1) Set up for the Laue photograph as in (a), but use a polyethylene monofilament ( ) in place of the mini crystal. Ensure that the axis of the monofilament is vertical and that the monofilament is centralised over the 1 mm diameter port. Select 30 kv, 75 µa Expose for 7 minutes at E.S. 3. 2) Remove the monofilament and manually stretched the central portion of the filament until it obtains a clearly drawn form. 3) Replace the monofilament over the 1 mm aperture with the drawn portion centralised over the port. 4) Replace the exposed film with a fresh film. 5) Expose for 7 minutes at E.S. 3. 6) Compare the photographs of the amorphous polyethylene (1) with the oriented material (3). MH Kuok Page 9 of 9

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