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The cubic crystal structure lattice parameter a 04nm

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tetragonal structure. The cubic crystal structure, lattice parameter a 0 0.4nm, and a motif of Ba 2+ at 000, Ti 4+ at 1/2 1/2 1/2, O 2- at 1/2 0 1/2 and 1/2 1/2 0 and 0 1/2 1/2. The tetragonal structure (T) is closely related to the cubic structure (C) and the lattice parameters a T and c T do not differ greatly from a 0 . A powder photograph of BaTiO 3 taken at 20˚C with Cu-K α radiation ( λ =1.5418Å) shows two closely spaced lines at θ =22.73˚ and θ =22.49˚. The line at θ =22.73˚ has about twice the intensity of the line at θ =22.49˚. (a) Determine the unit cell dimensions of tetragonal BaTiO 3 and describe the six lattice parameters. (b) Determine the structure factor for the first four maxima (or diffracted peaks) observed in an X- ray diffractometer experiment where powdered cubic BaTiO 3 has been used. (c) Explain why the intensity ratio of the two closely spaced lines is found to be about 2:1. Re a)
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Re b) Re c)
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3) List the expression for the intensity observed in diffraction peaks obtained from powder samples using the Powder X-ray diffractometer instument and clearly describe each factor in this expression. See textbook Cullity and Stock… Five of the six factors that affect the Intensity in diffraction peaks for Powder X-ray diffraction matter for the diffractometer instrument… Namely, Structure factor, Multiplicity factor, the Temperature factor and the combination of the Polarization factor and Lorentz Factor, the Lorentz-Polarization factor.
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