August 2016 Model Answer Written Assignment Group B
GROUP B
MODEL ANSWER
Howard et al., Temperature-induced structural changes in CaCl2, CaBr2 and CrCl2: A synchrotron X-ray powder diffraction Phys. Rev. B 72, 214114 (2005).
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Paragraph 1
The polymorphs involved are the halides in tetragonal rutile (TiO2) structure and the halides in so-called calcium chloride structure. As the name implies, the unit cell of halides in tetragonal rutile structure is tetragonal, with the lattice parameters a=b≠c and α=β=γ=90o. It belongs to the space group P42/mnm. On the other hand, the unit cell of halides in calcium chloride structure is orthorhombic, i.e. a≠b≠c and α=β=γ=90o. The space group of this CaCl2 structured polymorph is Pnnm. To compare symmetry operators in the two polymorphs, we refer to the space group diagrams of P42/mnm and Pnnm space groups. (Figure 1). The positions of the symmetry operators in the unit cell are denoted by the fractional co-ordinate system used in the space group diagrams. Both polymorphs have two a-glide planes at x = 0.25 and x =0.75 respectively and two b-glide planes at y = 0.25 and y = 0.75 respectively. Moreover, the two polymorphs also share twofold roto-inversion operators on (0.5, 0), (0, 0.5), (1, 0.5) and (0.5, 1). However, the roto-inversion operators on (0,0), (0,1), (0.5, ).5), (1,0), (1,1) in the CaCl2-structured polymorph were replaced by operators of higher symmetry, i.e. 42 screw axis with centre of symmetry in the tetragonal rutile structured polymorph. Besides, two diagonal glide lines and four mirror lines which are absent in unit cell of CaCl2-structured polymorph are present in that of tetragonal rutile structured polymorph. CaCl2 and CaBr2 start as a CaCl2-structured polymorph at room temperature. As temperature approaches the transition temperature, the MX6 (M is metal cation while X is the halogen anion) octahedron in the centre of the unit cell rotates about the c-axis, causing the rectangular base of the unit cell to
MODEL ANSWER
Howard et al., Temperature-induced structural changes in CaCl2, CaBr2 and CrCl2: A synchrotron X-ray powder diffraction Phys. Rev. B 72, 214114 (2005).
DO NOT PLAGIARISE THIS MODEL ANSWER
Paragraph 1
The polymorphs involved are the halides in tetragonal rutile (TiO2) structure and the halides in so-called calcium chloride structure. As the name implies, the unit cell of halides in tetragonal rutile structure is tetragonal, with the lattice parameters a=b≠c and α=β=γ=90o. It belongs to the space group P42/mnm. On the other hand, the unit cell of halides in calcium chloride structure is orthorhombic, i.e. a≠b≠c and α=β=γ=90o. The space group of this CaCl2 structured polymorph is Pnnm. To compare symmetry operators in the two polymorphs, we refer to the space group diagrams of P42/mnm and Pnnm space groups. (Figure 1). The positions of the symmetry operators in the unit cell are denoted by the fractional co-ordinate system used in the space group diagrams. Both polymorphs have two a-glide planes at x = 0.25 and x =0.75 respectively and two b-glide planes at y = 0.25 and y = 0.75 respectively. Moreover, the two polymorphs also share twofold roto-inversion operators on (0.5, 0), (0, 0.5), (1, 0.5) and (0.5, 1). However, the roto-inversion operators on (0,0), (0,1), (0.5, ).5), (1,0), (1,1) in the CaCl2-structured polymorph were replaced by operators of higher symmetry, i.e. 42 screw axis with centre of symmetry in the tetragonal rutile structured polymorph. Besides, two diagonal glide lines and four mirror lines which are absent in unit cell of CaCl2-structured polymorph are present in that of tetragonal rutile structured polymorph. CaCl2 and CaBr2 start as a CaCl2-structured polymorph at room temperature. As temperature approaches the transition temperature, the MX6 (M is metal cation while X is the halogen anion) octahedron in the centre of the unit cell rotates about the c-axis, causing the rectangular base of the unit cell to