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Symmetry of Crystals, Point Groups and Space Groups
Published in Dong ZhiLi, Fundamentals of Crystallography, Powder X-ray Diffraction, and Transmission Electron Microscopy for Materials Scientists, 2022
Translational symmetry describes the periodic repetition of a motif or basis across a length or through an area or volume. Crystallographic point symmetry, on the other hand, describes the periodic repetition of atoms (ions) around a point. As presented in many textbooks, the symmetry elements in point symmetry are discussed first. By definition, a symmetry element is a geometrical entity about which a symmetry operation is performed.
A kinetic model and parameters estimate for the synthesis of 2-phenyloctane: a starting material of bio-degradable surfactant
Published in Indian Chemical Engineer, 2023
Sudip Banerjee, Md Aurangzeb, Amit Kumar
The symmetry element and operation define the symmetry of molecules. The symmetry element is a theoretical concept that includes the line, plane and point about which the symmetry operation can be performed. The symmetry operation includes rotation, reflection, inversion and rotation-reflection movement about the symmetry element such that the object is indistinguishable after the procedure. The present work is limited to the operation of rotation. It is designated as Cn, which indicates that the rotation by 2π/n brings the object into an equivalent position. It is commonly referred to as n-fold rotation and the corresponding symmetry element as an n-fold rotational axis. For instance, C4 indicates a 4-fold rotation, 4-fold rotational axis and rotation through 2π/4 (=90°) brings the object into an equivalent position. In general, for linear alkene and phenylalkane, there is no internal axes rotation except methyl bond. Also, during protonation and de-protonation of alkene, the shifting of the methyl group does not occur, so the internal symmetry of reactant and activated complex is identical.