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HOMEWORK5-MEMS1054AY2111 - HOMEWORK#5 Return by Next...

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HOMEWORK #5 MEMS1054 AY2111 Return by: Next WEDNESDAY! NAME: 1) A diffraction pattern has been obtained from a powder sample of a material with a cubic crystal structure using an X-ray powder diffractometer instrument with Cu-K α X-radiation, wavelength λ =0.1542nm=1.542Å. The experimental X-ray diffraction pattern exhibits seven maxima for the following angles θ : 14.89 ˚ 21.31 ˚ 26.43 ˚ 30.93 ˚ 35.08 ˚ 39.01 ˚ 42.84 ˚ Determine the Bravais lattice and the corresponding lattice parameters of this material with a cubic crystal structure. You can assume that it has a mono-atomic (elemental) motif. The interplanar spacing of a plane (hkl), d hkl , for a cubic crystal relates to the lattice parameters as d hkl 2 = a 0 2 /(h 2 + k 2 + l 2 ).
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2) Barium titanate, BaTiO3, exhibits ferroelectric behavior at room temperature, which is only possible for crystal structures belonging to one of the ten non-centrosymmetric point groups that possess a crystallographically unique direction. At T T C =393K, Barium titanate undergoes a
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