Instytut Fizyki Doświadczalnej Wydział Matematyki, Fizyki i Informatyki UNIWERSYTET GDAŃSKI
Experiment 13 : Electron beam diffraction on a layer of polycrystalline graphite I. Background theory. 1. Wave particle duality of matter: a) De Broglie postulate; b) experimental confirmation of the electron s wave properties; c) properties of de Broglie waves. 2. Crystallographic structures: a) types of lattices and crystallographic structures; b) lattice planes and Miller indices; c) the crystal structure of graphite and copper. 3. Wave diffraction in crystals: a) types of diffraction in crystals, focussing in particular on electron beams; b) Bragg s law; scattering angles of the incident beam; c) experimental methods for studying diffraction in crystals, with emphasis on the method of Debye Scherrer. 4. Construction and operation of electron guns: a) thermoemission; b) forming an electron beam; Wehnelt cylinder. II. Experimental tasks. 1. Familiarise yourself with the experimental setup to measure electron beam diffraction by layer of polycrystalline graphite, as shown in Picture 1 and the circuit diagram of the lamp and power supply in Figure 2. Picture 1. Experimental setup for studying electron diffraction in graphite: 1 high-voltage power supply 0 10 kv ; 2 tube with electron gun ; 3 multi-function power supply 0 600 V DC. Instytut Fizyki Doświadczalnej 1.
2. Obtain sharp diffraction rings on the screen for accelerating voltages U A ranging from 4 to 10 kv in steps of 0,5 kv. To do this, turn on the power supplies (1 and 3, Picture 1). Turn off all cellular telephones! They disrupt the operation of the high voltage power supply displays. Set the voltages on the multi-function power supply as follows (according to Figure 2): for G1 U₁ = 25 V; for G2 U₂ = 300 V; for G4 U₄ = 300 V. Use the callipers to measure the internal and external diameters of the diffraction rings appearing on the lamp s screen by changing the accelerating voltage U. After each change in high voltage, the image sharpness can be improved by adjusting the voltage across the Wehnelt cylinder (up to 50 V). Because of the possibility of damage to the electron gun above 10 kv and damage to the screen below 4 kv, the accelerating voltage must be kept in the range 4 to 10 kv. 3. Calculate the electron wavelength λ for a range of accelerating voltages U A. 4. Calculate the average radii of the observed diffraction rings. 5. Plot graphs of r = ƒ( λ ) (including errors) for each observed diffraction ring. Determine the interplanar distances in the graphite using linear regression. When calculating the angle of deflection, refer to Figure 3. 6. Discuss errors. 7. Compare the values obtained with the data given in the literature. III. Apparatus. 1. High-voltage power supply 0 10 kv. 2. Lamp with electron gun and 10 MΩ resistor. 3. Multi-function power supply 0 600 V DC. The electron gun meets German safety regulations of January 8 1987 ( 5(2) - RöV) on the X-ray dose allowed by electron guns. Instytut Fizyki Doświadczalnej 2.
IV. Literature. 1. Handbook Laboratory Experiments Physics, Phywe System GmbH & Co. K.G. 2. H. Ibach, H.Lϋth Solid State Physics, Springer, Berlin 1993. 3. B.K. Vainsthein Fundamentals of Crystals. Springer, Berlin 1996. 4. A.P. Arya Fundamentals of Atomic Physics, Allyn & Bacon, Inc., Boston 1971. 5. Ch. Kittel Introduction to Solid State Physics, Wiley, 2004. 6. H. Haken, H.Ch. Wolf The Physics of Atoms and Quanta, Springer, Berlin, Heidelberg 2000. 7. J.H. Moore, Ch.C. Davis, M.A. Coplan Building Scientific Apparatus, Westview Press, 2003. Instytut Fizyki Doświadczalnej 3.
Appendix Electron gun diagrams Figure 2. Circuit diagram of measuring apparatus: H cathode heating circuit; K cathode wire; G1 Wehnelt cylinder; G2 and G4 electrode to accelerate and shape the beam; G3 anode (from PHYWE). grafit Figure 3. Schematic diagram of electron gun (from PHYWE). Instytut Fizyki Doświadczalnej 4.