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Structural distortion analysis Determination of regular and irregular distorted octahedral molecular geometry; Octahedral distortion parameters [5] [6] [7] Volume of the octahedron; Tilting distortion parameter for perovskite complex [8] Molecular graphics. 3D modelling of complex; Display of the eight faces of octahedron
The Jahn–Teller effect (JT effect or JTE) is an important mechanism of spontaneous symmetry breaking in molecular and solid-state systems which has far-reaching consequences in different fields, and is responsible for a variety of phenomena in spectroscopy, stereochemistry, crystal chemistry, molecular and solid-state physics, and materials science.
The defect of any of the vertices of a regular dodecahedron (in which three regular pentagons meet at each vertex) is 36°, or π/5 radians, or 1/10 of a circle. Each of the angles measures 108°; three of these meet at each vertex, so the defect is 360° − (108° + 108° + 108°) = 36°.
A perfect octahedron belongs to the point group O h. Examples of octahedral compounds are sulfur hexafluoride SF 6 and molybdenum hexacarbonyl Mo(CO) 6 . The term "octahedral" is used somewhat loosely by chemists, focusing on the geometry of the bonds to the central atom and not considering differences among the ligands themselves.
(To some extent rotation influences the geometry via Coriolis forces and centrifugal distortion, but this is negligible for the present discussion.) In addition to translation and rotation, a third type of motion is molecular vibration , which corresponds to internal motions of the atoms such as bond stretching and bond angle variation.
A cube has the same set of symmetries, since it is the polyhedron that is dual to an octahedron. The group of orientation-preserving symmetries is S 4 , the symmetric group or the group of permutations of four objects, since there is exactly one such symmetry for each permutation of the four diagonals of the cube.
Most Goldberg polyhedra can be constructed using Conway polyhedron notation starting with (T)etrahedron, (C)ube, and (D)odecahedron seeds. The chamfer operator, c, replaces all edges by hexagons, transforming GP(m,n) to GP(2m,2n), with a T multiplier of 4.
If a non-isomorphic pair is used for the meridional profile then the normal to the yield surface will not appear normal in the meridional profile. Any pair of coordinates that differ from ( z , r ) {\displaystyle (z,r)} by constant multiples of equal absolute value are also isomorphic with respect to principal stress space.