Optical Analogy to Diffraction of Electrons in Polycrystalline Lattice PDF

LD Atomic and Nuclear Physics Physics Introductory experiments Dual nature of wave and particle Leaflets...

LD Atomic and Nuclear Physics Physics Introductory experiments Dual nature of wave and particle Leaflets P6.1.5.2 Optical analogy to diffraction of electrons in a polycrystalline lattice Objects of the experiment  Understanding the deformation of the spot diffraction pattern into a ring-shaped pattern  Determination of the ring diameter as function of the wave length Principles This experiment illustrates the Debye-Scherrer method used for instance in the electron diffraction method by means of visible light. To show the optical analogy to diffraction parallel, mono- chromatic light passes through a cross grating. The diffraction pattern of the crossed grating at rest consists of spots of light which are arranged around the central beam in a network-like pattern (Fig. 1 (a) left). By rotating the cross grating the dif- fraction pattern is deformed into rings arranged concentrically around the central spot (Fig. 1 (b) right). Thus the rotation of the cross grating simulates a powder situation where all pos- sible orientations of the cross grating in one plane contribute to the diffraction pattern. At rest the diffraction pattern of the cross grating is compara- Fig. 1: Schematic illustration of the diffraction pattern of a cross- ble to a Laue diagram of single crystals (see experiment grating at rest for monochromatic light (a), rotating the cross- P7.1.2.2). The lattice spacing g (i.e. slit spacing) can be de- grating changes the spot like pattern into a ring pattern (b). termined by using equation (III) of experiment P5.3.1.3: The rotation corresponds to diffraction of light on randomly orientated 2-dimensional lattices in a plane. (a) (b) x1 x2 Bi 1113 1 P6.1.5.2 LD Physics leaflets Apparatus Setup Note: The experiment can be performed with different light 1 Cross-grating, 5000/cm, rotatable...................... 555 629 sources and various optical benches. In this setup the small 1 Halogen lamp, 12 V/90 W.................................. 450 63 optical bench is described for both the halogen lamp and the 1 Halogen light...................................................... 450 64 laser. For setting up with optical bench 460 32 refer also to 1 Picture Slider...................................................... 450 66 the instruction sheet 555 629. If using the optical bench 1 Transformer 2 …12 V, 120 W............................ 521 25 460 310 the instructions for optical bench 460 32 can be 1 Pair of cables 1m, red and blue.......................... 501 46 followed. 1 Lens, f = +100 mm............................................. 460 03 1 Holder with spring clips...................................... 460 22 1 Translucent screen............................................. 441 53 a) Assembly with halogen lamp 1 Tape measure 1m / 1mm................................... 311 78 - Mount the halogen light and the translucent screen on opposite sides of the optical bench according Fig. 2 (a). 1 Small optical bench............................................ 460 43 5 Leybold multiclamp............................................ 301 01 - Adjust the halogen light in such a manner that the light 1 Stand base V-shape........................................... 300 01 from the lamp is parallel. or - Insert the 1 mm diaphragm into the image slider of the 1 Optical bench with standardised profile, 1 m...... 460 32 halogen light. 5 Optic riders......................................................... 460 373 - Place the lens f = +100 mm on an optic rider between halogen lamp and translucent screen and move the lens until the aperture is focused on the screen sharply. It is recommended to use the 2f configuration, i.e. adjust the k distance between lens and screen to approx. 200 mm. g   d with k = 1, 2, 3... (I) xk - Place the cross grating on an optic rider between lens and translucent screen. The flywheel has to be on the side of : monochromatic wave length the translucent screen. g: slit or lattice spacing (the same in x- and y-direction) - Place the holder with spring clips between the translucent d: distance between the screen and the cross grating screen and the cross-grating and insert the red color filter. xk; distance of the k-th spot from the center beam - It might also be necessary to adjust the halogen lamp or the lens to obtain sharp spots. in x- or y-direction For a rotating cross grating the lattice constant g of the “ran- domly orientated 2-dimensional lattices in one plane” can thus be determined by measuring the diameter 2r of the rings. Fig. 2: Optical setup for observing a light spot pattern and a ring- shaped pattern. (a) Using a halogen lamp and a red or green color filter al- lows to compare the rings for different wave lengths at the same time. (b) Setup for observing the light spot pattern and a ring- shaped pattern using the laser. 2 P6.1.5.2 LD Physics leaflets b) Assembly with laser Measuring example - Mount the laser on the optical bench according Fig. 2 (b). The following data have been obtained by using the setup - Arrange the cross-grating in the path of the laser beam in with an halogen lamp: such a manner that the flywheel is on the side that points away from the laser. Table 1: Diameter 2r of red rings - Direct the laser beam to the opening of the cross-grating to observe the diffraction pattern on a wall at some dis- 2r tance. mm first ring Safety notes second ring The He-Ne laser meets the requirements according to class 2 of EN 60825-1 “Safety of laser equipment”. If the corre- third ring sponding notes of the instruction sheet are observed, exper- imenting with the He-Ne laser is safe.  Never look into the direct or reflected laser beam. Table 2: Diameter 2r of green rings  No observer must feel dazzled. 2r mm Carrying out the experiment first ring second ring 1. Observation of light spots and ring pattern third ring - After the optical adjustment which usually includes also the rotation of the cross-grating a red light spot pattern accord- ing Fig. 1. (a) should be visible. Distance between translucent screen and cross-grating: - Now gently turn the cross-grating and observe how the red d = 55 mm. spots start to move on a circular path as depicted in Fig. 1 (b). Evaluation and results - Put the cross-grating into rapid rotation. Gently rotating the cross-grating shows how the light spots Note: Two rings are visible. Depending on the darkness of the move on concentric circles (rings) around the central beam. laboratory and the adjustment a third ring might be visible. From the observation of the ring pattern with no color filter While the solid rings depicted in Fig. 1 (b) have a high intensi- follows that the diameter of the red rings is larger than for the ty, the dotted rings are hardly visible. blue rings. - If using a halogen lamp repeat the experiment with no col- The measurement of the diameter 2r allows to estimate the or filter. lattice constant g of the cross-grating by using equation (I): 2. Determination of the ring diameter for different color filters (for halogen lamp only) red color filter  average wave length:  = 630 nm - Insert the red color filter into the holder with spring clips. average lattice constant: g = 9.9 m - Put the cross-grating into rapid rotation and measure the diameter of the red rings and the distance d between the green color filter  average wave length:  = 550 nm cross grating and the translucent screen. average lattice constant: g = 11.4 m - Repeat the experiment with the green color filter. Hint: For direct observation of red and green rings at the same time the red and the green color filter has to be insert- This result is within the limits of error in accordance with the ed according Fig. 2 (a). Putting the cross grating into rapid 1000 lines / cm of the cross-grating, i.e. g ~ 10 m. rotation allows to observe a ring pattern of green and red half rings. Supplementary information For the diffraction of electrons on a poly-crystalline graphite sample the diameter of the diffraction rings depends on the kinetic energy of the electrons (compare experiment P6.1.5.1). The larger the kinetic energy of the electrons the smaller is the diameter of the rings in the Debye-Scherrer diffraction pattern. This can be compared with this experiment where the ring diameter for green light (i.e. smaller wave length, larger energy) is smaller then for red light (i.e. larger wave length, lower energy). From the ring-shaped diffraction pattern the lattice parameters can be determined. LD DIDACTIC GmbH  Leyboldstrasse 1  D-50354 Huerth / Germany  Phone: (02233) 604-0  Fax: (02233) 604-222  E-mail: [email protected]  LD DIDACTIC GmbH Technical alterations reserved