Rotation and Inversion-Solid State Physics-Presentation, Slides of Solid State Physics

Download Rotation and Inversion-Solid State Physics-Presentation and more Slides Solid State Physics in PDF only on Docsity!

MULTIPLE SYMMETRIES

 Symmetry means balance or form.

 It is a precise and well-defined concept of balance or "patterned self-similarity" that can be demonstrated or proved according to the rules of a formal system.

 Rotational symmetry is where you can turn an object so that it looks exactly the same.  It is one of the types of symmetry.  An object with rotational symmetry is an object that looks the same after a certain amount of rotation.

 The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 3600.

 You see that apart from the blob the shape looks exactly the same in 1 and 3. We say that this shape has got rotational symmetry of order 2. ( That just means that there are two positions in which it looks exactly the same.

 All 2-dimensional shapes have some rotational symmetry.

 When rotated around by 3600 it fits itself 3 times so the order of rotational symmetry is

 A square has a rotational symmetry of order

 A regular hexagon has a rotational symmetry of order 6.

 Use your fingers as endpoints of an axis to rotate the cube. Place your fingers in the center of a pair of opposite faces. Rotate 90° and notice that the cube has the same orientation. Repeat this three times to return to the original location. This shows that the cube has an axis of rotational symmetry of order 4.

 1-fold rotoinversion axis is the same as a center of symmetry

 The operation of 2-fold rotoinversion involves first rotating the object by 180o^ then inverting it through an inversion center.

 This involves rotation of the object by 90 o^ then inverting through a center.

 A 6-fold rotoinversion axis () involves rotating the object by 60o^ and inverting through a center.