# Sebastian Electron Diffraction

Steve Koch 21:45, 21 December 2010 (EST): Another excellent lab. Only things missing are statistical comparisons (using SEMs) with the accepted values.

# Purpose

The purpose of this lab is to explore and understand the wave nature of particles such as the electron. Also, by understanding the de Broglie reltaion , $\lambda =\frac{h}{p}$ , we will be able to calculate the lattice spacing of carbon in graphite.

# Equipment

• Calipers - Carrec Precision 6" Digital Caliper
• TEL Universal Stand
• Electron Diffraction Tube - Tel 2555
• 3B DC Power Supply 0-5kV - Model: 433010
• Hewlett Packard Power Supply - 6216B

# Lab Summary

This lab required very easy, but tedious data taking. My lab partner and I took turns taking many data points on both days of the lab. Prof. Koch told us that each group develops their own techniques for measuring the rings that appear on in the bulb, so we thought about how we should collect the data. For the first set of measurements, we decided to measure the outside of the rings. We thought that on the second trial, we would be able to measure the inside of the rings, and then average to two trials together. We quickly realized that this was a terrible idea since the measurements do not have the same parent distribution (not sure if I am using the correct terminology here, but we knew that we would need to analyze both sets of data independently). We began at 5kV for the accelerating voltage, and took measurements in 0.2kV increments. We did this for both trials, and ended up with an enormous set of data. The hardest part of this lab was the data analysis. I first had to correct my measurements for the curvature of the bulb. This consisted of doing some simple geometry (more on this correction can be found in my primary lab notebook). I then used Dext, the corrected or extrapolated D, to plot Dext as a function of VA. The graphs of these functions can be found in my lab notebook, and all of them have the expected linear relationship. Then, using our data, I calculated d, the lattice spacing. Our results can be found below. We did not run into any problems in this lab except for a minor delay in the initial setup (more in lab notebook).

# Calculations and Results

The major comparisons in this lab are the linear relationships for $D_{ext}\left(\frac{1}{\sqrt{V_A}} \right)$, which can be found in my notebook, and the calculations for the lattice spacings, which are as follows:

 do,i = (0.1889 +  /  − 0.0005)nm
do,o = (0.1101 +  /  − 0.0004)nm
di,i = (0.2071 +  /  − 0.0004)nm
di,o = (0.1178 +  /  − 0.0003)nm


where o,i = measuring the outside of the inner ring, o,o = measuring the outside of the outer ring, i,i = measuring the inside of the inner ring, and i,o = measuring the inside of the outer ring.

## Accepted Values

The accepted values from Prof. Gold's Lab manual are:

 douter = 0.123nm
dinner = 0.213nm


## Error

For do,i we had an 11% error.
For do,o we had a 10% error.
For di,i we had a 3% error.
For di,o we had a 4% error.
A more detailed discussion of error can be found in my primary lab notebook.

# Conclusions

Although the data taking was very easy for this lab, I felt like I got a lot of practice with analyzing data. I am also becoming more aware of what I am allowed to do as far as averaging multiple trials and finding the associated error in those trials. I was not completely sure if I should be using a weighted average in this lab, but I am going to find out when it is appropriate to use that method for averaging. The theory behind this lab is well understood since this topic is covered in Physics 330, but we did have a discussion with Prof. Koch about why and how there are only 2 rings visible in the bulb. I am still not quite sure I understand the "how" part because we were trying to figure out how the spinning effect of a crystal could be achieved when there is no spinning crystal in the bulb(I am not even sure if this is the correct description of what Prof. Koch was describing to us). I will have to read up on this topic a little to fully understand it. (Steve Koch 21:41, 21 December 2010 (EST):It's not spinning, of course. But if you were to take a single crystal, and crush it into a powder, then you would randomly have all orientations across a beam of finite width. This is what's going on, and it's called "powder diffraction pattern.")