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Cf a 1134å 19 4943å this is inconsistent with the d

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cF: a 0 =1.134Å* 19 = 4.943Å; this is inconsistent with the d-spacings for the sixth peak, with a d-spacing of 1.225Å and should be d 400 =4.943Å/ 16=1.236Å 1.225Å; … and also inconsistent with d 111 =4.943Å/ 3=2.854Å 3.000Å, the d-spacing for the first diffraction peak; …etc. for all the other experimentally observed diffraction peaks… This is not a cF crystal . […. On the next page an alternative approach to answering the question…] Alternatively… students are prone to use the d-spacings associated with the smaller diffraction angles and check for consistent values for a single lattice parameter.
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cP: For a cP lattice, the lattice parameter should be a 0 =3.00Å=3Å/ 1=d 100 , associated with the first diffraction maximum. If cP then for seventh peak, d 220 = a 0 / 8 = 3.00Å/ 8 = 1.061Å 1.134Å !!!! Inconsistent with the measured d-spacing associated with the seventh peak; So, likely we can rule out the cP lattice. However…and for the sixth peak d 211 = 1.225Å = a 0 / 6 = 3Å/ 6 1.225Å , which would be OK! … similar, for the other first five peaks good agreement would be obtained for a lattice parameter of 0.300nm=3Å. cI: For a cI lattice, the lattice parameter should be a 0 =4.243Å= a 0 = 2d 110 = 2 *(3.000Å), where the first diffraction maximum is associated with d 110 =3.000Å. If cI then for seventh peak, d 321 = a 0 / 14 = 4.243Å/ 14 = 1.134Å ! …and for the sixth peak d 211 = 1.225Å = a 0 / 6 = 3Å/ 6 1.225Å , … similar, for the other first five peaks good agreement would be obtained for a lattice parameter of 0.4243nm=4.243Å. The pattern is entirely consistent with a cI lattice with a 0 =4.243Å. cF: For a cF lattice, the lattice parameter would be a 0 = 2 (d 200 ) = 2 * 2.122Å= 4.244Å, where d 200 is associated with the second diffraction maximum. If cF then for seventh peak, d 331 = a 0 / 19 = 4.244Å/ 19 = 0.974Å !!!! Inconsistent with the measured d-spacing associated with the seventh peak; similar, the measured diffraction angles and this associated d-spacings are not consistent with those of the allowed diffraction maxima for a cF lattice. We can rule out the cF lattice.
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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 structural phase transformation from a high-temperature cubic structure to the ferroelectric tetragonal structure. The cubic crystal structure, lattice parameter a
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