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MEMS1054 AY2111, Week 7-11, This is not a homework assignment that I will collect and grade. I collated this quite comprehensive list of 20 study questions and problems for you to ponder. I hope that it can help in preparations for the Midterm 2 and review of lecture materials. The problems related to Reciprocal lattice, scattering physics for X-rays and electrons from crystals, point symmetry elements, space groups, indexing of XRD and electron diffraction patterns… subject coverage during the period of week 7/8 to week 11/12 (now). 1) Consider an x-ray powder diffraction experiment from an unknown elemental substance. You have been told that the substance is cubic. How many diffraction lines do you have to collect in your diffraction pattern in order to identify the Bravais lattice of the substance, i.e. determine whether it is cP, cI or cF or diamond cubic? [hint: Also consult chpater 10-3 in Cullity and Stock's text on indexing of diffraction patterns]. 2) (I) Calculate the speed of an electron that moves in the column of a transmission electron microscope that operates with accelerating voltages U=200000 Volts. What is the maximum kinetic energy such electrons could impart to a crystal upon impact? (II) Why does a nanocrystalline material give rise to a so-called ring pattern in electron diffraction in the TEM? When you obtain a spot pattern in the electron diffraction experiment in the TEM, why is this indicative of the single crystalline nature of the material you studied? 3) A crystal of the ionic metal oxide Fe 2 O 3 can be described as a cubic crystal related to the perovskite type structures. The unit cell contains ions of the atoms at five different positions: Fe @ 0,0,0; O @ ½ , ½ , 0; O @ ½ , 0, ½ ; O @ 0, ½ , ½ ; Fe @ ½ , ½ , ½ ;. The valence state of oxygen is doubly negative, O 2- , and the metal ions transfers the appropriate number of electrons to maintain overall charge neutrality. The atomic numbers of atoms of Fe and O are 26 and 16 respectively. a)

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