Extra Credit AssignmentIn the lecture given by Professor I. Cevdet Noyan, I learned about the ongoing analysis of powder diffraction from nanostructures and how these structures are analyzed. In order to yield the best results for his experiments, he needs to have ideal specimens. With an ideal specimen, the scattering pattern is known, so the Patterson analysis can give results that is truly representative of the specimen. Additionally, the absolute error of the X-ray techniques is a small 1nm. However, because nanoparticle powders were used, obtaining a single, average shape was difficult, and it influenced the results of the X-ray diffraction. To determine the acceptable error of using such non-ideal specimens, statistical analysis of the data obtained was done.In order to measure the diffraction patterns of the x-rays on the specimens, particular equations such as Braggs Law are necessary. Professor Noyan noted that the basic theories in introductory books for such mathematics are insufficient. For example, the application of Braggs Theory requires x-ray layers, and it does not allow multiple scattering nor say anything about x-ray peak slopes. On the other hand, if the sample being used in the experiment fits all assumptions, then transmission electron microscopy can be used to analyze the results by obtaining cross sections of the SOI substrate layer of the sample. Sample results obtained by the transmission electron microscope should be close to values obtained from the Scherrer equation and the Fourier analysis. They are not accurate at first, however, because these values are not corrected for the broadening of the instrument being used. Once broadening is altered appropriately, the analysis thickness of the sample will be more accurate.