For this lab we were experimenting to find the characteristic spacings of graphite by using the wave nature of electrons and the separations as a diffraction experiment. We followed the experimental setup outlined by lab manual: lab 3 which consisted of a preconstructed circuit of a high voltage power supply and an electron gun in a glass bulb that was steered by a magnet across onto a screen of phosphorescent material which illuminated the circles representing our graphite spacings. This seems to be analagous to x-ray crystallography which uses reflected x-rays from a crystalline material at different angles to construct a three dimensional model of the atoms and binding forces in the material. Apparently this same experiment can be done with electrons whose wavelength is on the order of x-rays. The more fundamental reason for conducting this experiment is to prove that electrons have wave like properties as well and our proof is that they are diffracted in this experiment. I am still quite unclear about how exactly we measured only these two spacings as the Bragg pattern indicated that for our sample there should have been several more, as in crystallography, however we failed to bombard the material with electrons from any other angleSJK 09:51, 11 November 2008 (EST)09:51, 11 November 2008 (EST) See comment on your notebook page...related to, "why do you see circles?". Nevertheless, we measured the diameters of these rings for each value of the voltage and then using a relation concocted from DeBroglies equation about energy and wavelength E=hν (Steve Koch:I don't see wavelength in this relation...) we used these data to solve for the spacings. The first set of data refers to taking the diameter from the approximate mean of the widths of the ring and measuring the width separatly and using that as our error. The second set of data we took two measurements: what appeared to be the maximum diameter, and the minimum diameter, we then took the average of these two as our value and the error was the difference between max/min and mean.
The data that we got for the experiment was then used to graph the diameters of each ring versus the inverse square root of the voltage, the slope evaluated for this least squares line was then evaluated for the single quantity of d-the line spacing.
The collection of data went smoothly and I don't think introduced substantial error (as it has in our past experiments). The possible sources of error for our experiment were the material itself - by which i meant that if a layer in the graphite sheet were at an angle to another - then we might get the other previously mentioned spacings we were not expecting, and if these were not of the same intensity as the 2 we were mentioning then we might have interpereted their presence as error in the width of our rings. There was also an error accociated with the geometry of the bulb, but this was probably inconsiquential considering that most of the error, I believe came from the methods that we conducted by eye: the voltage gauge, the diameters, the widths, were all read by eye and these were probably the most substantial.SJK 10:21, 11 November 2008 (EST)
10:21, 11 November 2008 (EST) You have a typo in your error on the second one: 0.2 +/- 0.3 would allow for negative spacing!
0.13(8)nm For the Big Ring
Error from accepted 13%
0.2(3)nm For the Small Ring
Error from accepted 11.9%
value reported fall within the 68% confidence interval
I learned a lot about the structure of crystalline matter and how we as a scientific community go about examining the structure of materials. I read some of the wiki pages about Bragg Diffraction, Powder diffraction, and x-ray crystallography, so I guess I learned a bit about each of these methods. The biggest problem we actually had was with the data analysis - we werent sure which error to report given our new knowledge about error propagation SJK 10:47, 11 November 2008 (EST)10:47, 11 November 2008 (EST) See my comment on Mike's page, and also the excel sheet I uploaded (linked on his page), and we also had a problem with our unit conversions which we eventually decided on being in standard notation, the geometry bit was also confusing we think we solved for the values correctly using trig, but we didn't really know what we were looking for, and ended up just throwing that part out.
Suggestions I guess I heard about making square watermelons by growing them in square glass containers, we could probably evacuate and use one of these for this experiment. SJK 10:48, 11 November 2008 (EST)10:48, 11 November 2008 (EST)
