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Using the scree-target distance given by the tube manufacturer, determine for which diffraction ring diameter the small angle approximation used to arrive at Eq. 2 is no longer appropriate. An X-ray diffraction spectrum consists of a number of reflections or "peaks" that correspond to constructive interference of scattered X-rays off specific lattice planes. Thus each peak corresponds to a set of lattice planes and often are labeled with unique sets of Miller indices (Example: X-ray diffraction spectrum of zircon). How do we know which peak goes with which set of hkl? This exercise with demonstrate the procedure for a cubic crystal. Begin by downloading an Excel spreadsheet file (with annotations) which contains the 2-positions of the X-ray diffraction spectrum of lime (CaO). This spreadsheet is set up to guide you through the whole procedure. In the yellow-shaded fields you will have to add a number or a formula. Others are already filled in or will calculate numbers based on your entries. First you will need to calculate and sin2 from the 2 values given in the second column. From page 30 of the lab manual you know that sin2 can be factored in h2+k2+l2 times a constant. Since h, k, and l are integers, h2+k2+l2 will also be integer. Thus the challenge is to find a common factor (the constant) such that all the mutipliers in column 6 are integers or close to an integer. For cubic crystals one can approach this by trial and error. Most spectra have the 100, 200, or 111 line at the lowest angle. You know your "guess" for the common factor is good if the ratio of sin2 and the common factor is close to an integer for all entries in column 6. Continue with steps 4 to 7 to identify the Miller indices for all peaks and determine the lattice parameter for CaO. Based on the rules for Miller indices, is this an cubic face-centered structure? Justify your answer! Print out page 2 of the spreadsheet and hand it in as part of your prelab assignment.
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