THE EXPERIMENT
Equipment
- Electron diffraction tube with carbon thin film target.
- High and low voltage power supplies.
- Digital voltmeter for monitoring anode current.
- Calipers for measuring diffraction ring diameters.
CAUTION
- The 5kV power source can give you a very nasty shock. Verify that your
circuit is correctly wired before turning on power. Have your instructor or TA
check the circuit.
- Check that the anode current monitoring meter is on the grounded side of
the circuit as shown in the diagram below.
- Never permit the anode current to exceed 0.2 mA; otherwise the target may
be damaged.
Procedure
Figure 10: The electron diffraction tube
The electron diffraction tube is sketched in Fig. 10. The carbon film
is mounted in the anode as shown. The variable anode voltage is provided by the
5kV dc supply. Use the outer high voltage terminals. The electrons are emitted
from an indirectly heated oxide coated cathode. The heater voltage,
VF, is supplied by the 6V output on the 5kV supply. VF is
applied to the 4 mm terminals in the plastic cap at the end of the tube. The
external bias for the can surrounding the cathode is provided by the separate
power supply. The negative biasing of the can surrounding the cathode serves to
focus the electron beam. The beam current varies with both anode and bias
voltages. Be sure to keep the beam current below 0.2 mA as monitored on the DVM
in the grounded side of the anode circuit. The 2 mm pin on the back of the tube
is the terminal for the negative side of the anode voltage. The positive side
of the anode voltage is connected to the 4 mm pin on the side of the tube. The
diffraction rings are viewed on the phosphor screen on the glass bulb. After
having your circuit checked, start the experiment by stabilizing the heater
current for about a minute before turning on the anode voltage. The external
bias voltage helps to focus the diffraction rings as well as limiting the anode
current to 0.2 mA.
Figure 11: Atom arrangements in carbon showing the two sets of
planes that produce the diffraction rings.
Figure 11 shows the arrangement of the atoms in a carbon crystal. They are
located on the corners of a hexagon and two principal spacings of the atom
planes are indicated. These spacings are 0.123 nm and 0.213 nm. As you turn up
the anode voltage you will see two rings on the screen, as shown in Fig. 12.
Each ring corresponds to one of the carbon d spacings. As explained in the
text, the diffraction condition for the polycrystalline carbon film is
Measure the ring diameter D on the screen with the calipers. To determine
, you must calculate the extrapolated ring diameter D', as shown in the
figure. Take into account both the curvature and thickness of the glass bulb.
Hint: start with the fact that D is the chord of a circle with a 66 mm
radius.
The value for D' permits you to calculate from the small angle
approximation
Writing 
in terms of the anode voltage gives
for the Bragg condition. For each ring, plot V-1/2 as a function of
D' for a number of values of V. Determine d1 and d2 from
the slopes of these curves. Using error analysis, compare your values to the d
spacings for carbon.
Figure 12: Sketch of the geometry involved in determining
the extrapolated ring diameter, D'.