Beauty And Geometry Research Paper

Name: Hee Wei Qian
Matriculation Number: U1430449B
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Beauty and Symmetry Writing Exercise
Each ReO3 molecule forms a octahedral shape in 3D as each rhenium atom is surrounded by 6 oxygen atom. Like Pervoskite, ReO3 has the general formula of ABO3. However, they have different structure in that ReO3 has an empty A unit cell in its centre. At low temperatures, nonlinear behaviour of the Fermi-surface cross-sections were observed at pressures close to 3kbar. There is thus a pressure-induced phase transition which is termed “compressibility collapse” as compressibility is around 10 times larger in the high-pressure. Transition pressure Pc is observed to be around 5.0kbar at room temperature. In the high pressure phase, there is a large volume strain which is proportional to (P-Pc)2/3 . This can be explained by the buckling of the Re-O-Re

Positive strain is contributed partially by the rigid rotation of the ReO3 crystal structure. This is associated with tilt. In addition to that the octahedron structure also undergoes distortion due to changes in Re-O bond length as well as the buckling of the Re-O-Re bond. This contributes to negative strain. Tilt of the octahedron structure is quantified by rotation angle as mentioned above and the value of β=0.322 is obtained via linear regression via approximation of the graph of ln ɸ vs ln (P-Pc). The rotation angle ɸ is a function of pressure, increasing smoothly with increasing pressure above the transition pressure 27.40KBar. M3 phonons degenerate on 3 different levels and there is a phase transition to P4/mbm, I4/mmm or Im3 structures from the original Pm3m structure via the condensation of either 1,2 or 3 M3 phonons respectively. Since these structures are all subgroups of the Pm3m structure, a phase transition from Pm3m to any of these structures can be regarded as of a 2nd order