# Electron Diffraction

## Purpose

Use the De Broglie relation "wavelength = planks constant / momentum" to measure the inner lattice spacing of the crystalline structure of graphite by sending an electron beam through a thin layer of the material and analyzing the diffraction pattern that it produces on a phosphorus Bulb surface.

• The Purpose through the Data are the same as in Emran's notebook.

## Equipment

Electron Diffraction Device and Power Supply 1 and 2
Electron Diffraction Device Emitter
Precise Caliper
• Carrera Precision 6 inch digital caliper alloy # CP8806-T
• DC Power Supply 0-5 kV 3B U33010 6.3V AC/3A
• HP6216B Power Supply
• Electron Diffraction Bulb 5kV .3mA 3B 0185712309003

## Safety

• 5kV of power is very dangerous. We must be careful not to shock ourselves.
• We should not exceed 15 volts for the biasing voltage.
• Make sure the heater doesn't overheat the graphite, it will glow dull red if it is.

## Setup

Golds Lab manual explains how to setup. Basically do the following:

• Match up the banana wires with the leads described in the lab manual on P24.
• Turn on both power supplies
• Turn up Voltage to 5kV.
• Center the rings using the magnet on the neck of the bulb.

## Procedure

Diffraction Rings

You will notice that there are two rings glowing green on the white surface of the bulb (see image).

• Note the voltage
• Measure the inner diameter of the Inner ring using the caliper.
• Measure the inner diameter of the Outer ring using the caliper.
• Adjust the voltage down by 200V and repeat.
SJK 05:36, 21 December 2010 (EST)
05:36, 21 December 2010 (EST)
I can't tell from your procedure how you get the uncertainty on your radii that you show in the graph.

## Data

### Calculations

• We plotted the Diameter of the inner and outer rings verse one over the square root of the voltage and found a linear relationship.
• We then calculated the two different lattice spacing "d" by using the slope of the plots and the equation:
$d=\frac{2Lh}{D\sqrt{2emV_A}}\,\!$
$D=\frac{2Lh}{d\sqrt{2emV_A}}\,\!$
$slope=\frac{2Lh}{d\sqrt{2em}}\,\!$

The values that we obtained for d were:

$d=0.183(10)nm\,\!$SJK 05:38, 21 December 2010 (EST)
05:38, 21 December 2010 (EST)
I think you mean 0.183(1)

and

$d=0.138(7)nm\,\!$
• The standard error I used was the average SE in the Excel sheet calculated by the SE divided by the slope and times the average, or best, value we obtained for d.

The range of values of d I obtained are: 0.173nm<d<0.193nm, and 0.131nm<d<0.145nm The actual values of d are 0.123nm and 0.213nm.

### Error

The values we obtained for d are more than 3 SE away from the actual value for both lattice spacings. The reason for this is because of the difficulty of seeing the two diffraction rings on the bulb. Another reason was because it was hard to hold the calipers steady against the bulb to measure the diameters. The diffraction rings themselves also had a thickness, and we were unsure which diameter to measure. Whether to measure the inner diameter of each pattern or the outer diameter. We decided to measure the inner diameter of both patterns. This was a good choice because as we decreased the voltage from 5kv down to about 2.6kv we noticed that the thickness of each pattern increased, and for our last few measurements at lower voltage we noticed the end to the outer diameter's of the patterns were hard to distinguish. We also did not take into consideration the curvature of the bulb. This was because after studing our data we knew the largest error would be in our measurements of the diameters, and not in neglecting the curvature of the bulb. Therefore, in my opinion the reason for our measurements being more than 3 SE away from the actual values is due to human error trying to determine the diameters of the diffraction patterns.

## Acknowledgments/Citations

Emran was my lab partner again. Emran did most of the code for the Excel sheet. Professor Koch for helping us to visualize what the lattice spacing looked like and why the electrons passing through the graphite produces two diffraction rings.