Introduction to symmetry operations and symmetry elements: screw axis



September 1, 2023

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  • In this video, Hallam Greene introduces us to the screw axis symmetry element. Many of the symmetry elements of a crystal are the same as those of discrete molecules: mirror planes, rotation axes, inversion centres and improper rotation axes, which we introduced in our previous video "Introduction to Symmetry Operations and Point Groups". However, crystal structures also have another class of symmetry operations that involve a translational element: screw axes and glide planes. In this video we look at screw axes. First, we describe the symmetry operation performed by a screw axis by comparing it to the behaviour of a screw. Then, we see the nomenclature and we look in detail at the 2-1 screw axis (twofold), the 3-1 screw axis (threefold), the 4-1, 4-2, and 4-3 screw axes (fourfold), and the 6-1 screw axis (sixfold). Resources: - Explore symmetry operations, and in particular screw axes, in 3D by manipulating crystal structures from the Cambridge Structural Database (CSD) using the CCDC's visualisation software Mercury. A free version of CCDC's Mercury is available to download: - Structures in the CSD are identified with refcodes. You will find of interest structures with refcode: ADRENL, AECLPA10, DAWGOX, NUCKOL, HYDTML, LCYSTI10, JAGREP, ESAMOA, APRETS01, UGOQAL, LOLWIS. All refcodes for the crystal structures displayed are shown in the video. Download from Access Structures: In this video: - 00:14 Brief review of symmetry operations and symmetry elements seen in our previous video. - 00:44 What is a screw axis? Definition and example in 2D. - 01:29 The 2-1 screw axis. Explanation and definition of the screw axis nomenclature. - 02:47 The 3-1 screw axis. - 03:30 The 4-1 screw axis and how it forms a right-handed screw. - 04:03 The 4-3 screw axis and how it forms a left-handed screw. - 04:32 The mirror image of a structure with a 4-1 screw axis is a structure with a 4-3 axis, describes as enantiomorphic structures. - 05:26 The 4-2 screw axis and the importance of making sure to replicate the unit cell. - 06:08 The 6-1 screw axis. - 06:33 Examples of screw axis symmetry element in small molecules crystal structures and in polymeric structures. - 08:38 All the screw axes. - 09:00 Time to explore more examples by yourself! Examples of relevant structures from the Cambridge Structural database and free Mercury software. The images and animation frames of these molecules are prepared using Mercury, the CCDC visualisation software. A free version is available to download. More advanced functionality from the CCDC enables you explore molecules and structures in more detail. To find out how to access more advanced functionality with a CSD-Core license see Follow us on social media: Instagram: @ccdc_cambridge Twitter: @ccdc_cambridge Facebook: Cambridge Crystallographic Data Centre (CCDC)


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