# Physics307L:People/McCoy/Formal

SJK 05:30, 8 December 2008 (EST)
05:30, 8 December 2008 (EST)
Much of what you have is good, including important part of comparing final value discrepancy from accepted value in relation to the error bars. However, many important sections were completely missing, as I'm sure you were aware. Therefore, make sure to work on these sections very soon, in case you get stuck or more questions arise.

# An analysis of the Graphite Crystal Lattice from Electron Diffraction

SJK 05:09, 8 December 2008 (EST)
05:09, 8 December 2008 (EST)
Very good title / good contact info.

University of New Mexico

Department of Physics and Astronomy

Albuquerque, NM 87131

cmccoy1@unm.edu

## Abstract

SJK 05:12, 8 December 2008 (EST)
05:12, 8 December 2008 (EST)
This is a good abstract structure. If you can think of how to work in an "impact" statement (why is it important), that would be good, but you may find it difficult. Also, some minor comments: (1) I was initially confused by your center-center ring diameter statement and the remainder of the sentence. Perhaps can be improved by including less details of what needs to be accounted for or being more general about it. (2) you say "compared to" but you don't really compare. You can improve this by saying something like "which are not consistent with the accepted values of __ ___"

In this experiment, I measured the internal lattice spacing of graphite using the properties of electron diffraction and measuring the rings formed by the diffracted electron beam at a known distance from the graphite lattice target. Making the measurement of the center-center ring diameter, allowed for me to form an extrapolated diameter as if the measurements were taken on a flat surface and calculate the spacing relative to each of the two diffracted rings. Doing so I calculated answers of d=.109(3)nm and d=.203(6)nm, compared to the accepted answers of d=.123nm and d=.213nm.

## Introduction

SJK 05:13, 8 December 2008 (EST)
05:13, 8 December 2008 (EST)
This is an important section of the paper and will be where you cite most of your references to original research.

The concept of electron diffraction originated the doctoral dissertation of Prince Louis-Victor de Broglie in 1924.

## Materials and Procedure

SJK 05:18, 8 December 2008 (EST)
05:18, 8 December 2008 (EST)
The photo will be helpful. It would be better if you used a drawing program to label parts, or at least in the caption pointed things out. Also, Darrel made a very nice diagram for his informal report this week, so you could probably borrow that from him and give him credit for it.

You will need to revise this section for two major reasons: (1) You have it written as a "how to" procedure, whereas you will need to write a "I did this" style. For example, "I took ten data points in succession, with the bias voltage set to __ for the odd numbered measurements and set to ___ for the even numbered measurements" etc. (2) formal publications do not typically have a list of equipment, but equipment is mentioned in the procedure text. For example, "The high voltage power supply (Model 813 kV power unit, Teltron Limited, CITYNAME" etc.
Figure 1: Apparatus for electron diffraction experiment

### Materials

• Hewlett Packard model 6212B power supply
• Teltron 2555 electron diffraction tube
• Teltron 2501 universal stand
• Teltron Limited 813 kV power unit
• WaveTek Meterman 85XT digital multimeter
• 8 - 4mm banana cables

### Procedure

• With the electron diffraction tube in its stand, connect using banana cables the stand, two power supplies and multimeter as seen in figure 1, with the multimeter connected between the C5 port on the diffraction tube stand and the negative high voltage port.
• Turn on the Teltron power supply with the slider for the high voltage at zero
• After 1 minute, slowly move the slider to the top, setting the high voltage at 5kV
• With the voltage at 5kV, take ten data points, the odd points with the bias voltage as set using the HP power supply at 10V and even points with the bias at 5V
• Take the measurement of the small ring then the large ring, then adjust the bias and check the anode voltage to make sure it is correct for the tests
• Measure the rings from the inside of one edge of the ring to the outside of the other edge, so as to approximate a center-center measurement of the radius
• Repeat with the voltage at 4.5kV using 5V and 2.5V as the biases
• Repeat with the voltage at 4kV using 2.5V and 0V as the biases
• Repeat with the voltage at 3.5kV using 1V and 0V as the biases
• Repeat with the voltage at 3kV using 1V and 0V as the biases (if possible, if unable to see ring at 1V bias, use 0V for all measurements)

## Results and Errors

SJK 05:21, 8 December 2008 (EST)
05:21, 8 December 2008 (EST)
In this section, you have a lot of description of analysis methods which should actually be moved to the "methods" section above. For example, how to calculate the spacing distance. In the analysis methods you will also want to mention the software and the specific algorithms used.

Of course, you will also want to add figures to show the data and the linear fits.

### Data

Ring Diameter (inches) for Anode Voltage
5 kiloVolts 4.5 kiloVolts 4 kiloVolts 3.5 kiloVolts 3 kiloVolts
Trial # Ring 1 Ring 2 Ring 1 Ring 2 Ring 1 Ring 2 Ring 1 Ring 2 Ring 1 Ring 2
1 0.839 1.576 0.945 1.662 0.966 1.780 1.023 1.944 1.181 2.064
2 0.856 1.559 0.909 1.651 0.976 1.753 1.044 1.960 1.133 2.022
3 0.882 1.580 0.922 1.681 0.946 1.778 1.059 1.963 1.173 2.021
4 0.895 1.575 0.928 1.652 0.942 1.784 1.063 1.976 1.127 2.031
5 0.898 1.586 0.960 1.655 0.973 1.736 1.024 1.941 1.156 2.051
6 0.859 1.595 0.913 1.659 0.984 1.748 1.021 1.938 1.128 2.061
7 0.863 1.572 0.891 1.664 0.988 1.759 1.022 1.956 1.161 2.054
8 0.886 1.582 0.915 1.662 0.942 1.781 1.039 1.941 1.131 2.064
9 0.884 1.580 0.922 1.661 0.981 1.755 1.052 1.936 1.121 2.072
10 0.871 1.599 0.914 1.662 0.939 1.766 1.026 1.947 1.101 2.003

Because these ring diameters are based on a curved surface, I had to calibrate them to take the curved surface into account, along with converting them from inches to metric units so they could be used in the calculations and return standard units.

To calculate the spacing distance I used the formula: $d=\frac{2{L}{h}}{D\sqrt{2{m_{e}}{e}{V_{a}}}}$ with $D=2{L}{tan(\frac{arcsin(\frac{h_{0}}{C})}{2})}$ in which Va is the anode voltage, h0 is the uncalibrated height of the rings, L is the distance from the graphite to the end of the diffraction tube, and C is the radius of curvature of the diffraction tube.

I did my calculations using the program MatLab, with the results published to a word file that can be accessed here

### Final Result

Calculated spacing by voltage
Voltage d (outer) d (inner)
3kV .1081nm .1993nm
3.5kV .1053nm .2034nm
4kV .1097nm .2051nm
4.5kV .1019nm .2023nm
5kV .1102nm .2027nm

From these values I was able to find the mean and standard error of the mean, and by doing so I was able to develop a confidence interval in which the known value should lie. By doing that I came up with the final value for the lattice spacing of: d = .109(3)nm and d = .203(6)nm

The error margin given in my final answer is that of one standard error of the mean, thereby being a 68% confidence interval for the "true" value.

Comparing my answers to the accepted values of d = .123nm and d = .213nm, it can be seen that for the larger spacing, my answer of d = .203(6)nm holds the accepted value within 2 standard errors of the mean, as that produces the range d = [.191nm,.215nm]. On the other hand, the accepted value d = .123nm is more than 4 standard errors away from my value as it lies 4.67 standard errors above the mean, meaning that if my values were correct, the accepted value would be found less than 1/1000th of the time.

### Errors

The errors that I used in my calculations were the standard error of my data points, and the error in the length of the tube. I did not use the error in measurement as that would involve a subjective approximation of an error and not a statistical error.

## Conclusion

SJK 05:23, 8 December 2008 (EST)
05:23, 8 December 2008 (EST)
You would not typically have sub-sections in your conclusions, and it doesn't have to be that long. Take a look at some other papers to get an idea of what to put here.

### Errors

The errors that would have affected this experiment are the actual measurement of the ring diameter, the accuracy of the power supply and bias, the alignment of the rings relative to center of the phosphorescent coating on diffraction tube.

## Acknowledgements

SJK 05:22, 8 December 2008 (EST)
05:22, 8 December 2008 (EST)
This section is good.

I would like to thank my lab professor, Dr. Steven Koch, and the lab assistant, Aram Gragossian, for all their help fixing the different apparatus if I was getting incorrect data. I would also like to thank the UNM Physics Department for allowing us to use the lab and providing the apparatus so that we can operate.

## References

SJK 05:27, 8 December 2008 (EST)
05:27, 8 December 2008 (EST)
references will be very important, and you should make sure to have a few citations to original peer-reviewed research publications, which you will likely cite in your introduction.