Download Understanding Crystal Symmetry: Elements, Notation, and Forms and more Lab Reports Environmental Science in PDF only on Docsity! Earth Materials Lab 3 – Crystal Symmetry and Form Covered in chapter 4 in textbook (Wenk and Bulakh) Symmetry, the repeatability of a point or group of points through reflection or movement, is a fundamental property of the natural world. Plants and animals exhibit symmetry, as do crystalline solids. Because crystalline solids are made of atoms bonded in a repeated framework (lattice), their external form is the expression of this internal order. Minerals, naturally occurring inorganic crystalline solids, exhibit a limited range of symmetry that is diagnostically useful. Elements of symmetry Only three elements and one combination term are required to describe the external symmetry of a crystal. Mirror plane (3D) or line (2D) This element divides an object into two halves, one the mirror reflection of the other. For every point on one side of a plane, there exists a point on the other side at equal distance from the plane. Rotational axis (3D) or point (2D) A rotational axis is a line (or in 2D a point) around which an object may be rotated such that the features are repeated more than once in 360o. For example, if an object can be rotated to 180o and appears the same as previous, the object has two-fold rotational symmetry. In contrast, if an object can be rotated to 120o and appears the same as it did previously, and then may be rotated another 120o, and again appears as it did the previous two times, the object has three-fold rotational symmetry. Inversion point Just like a mirror plane, an inversion point relates two identical points at equal distance from the symmetry element. Whereas mirror planes change the handedness of the point (your left hand in a mirror appears to be your reflection’s right hand), an inversion center completely flips the point. Think of an optical lens - at the correct distance the image is identical but inverted (see diagram). The focus point is the point where the object and its image converge, and this is similar to an inversion point. However, unlike a lens, where the object must be projected through the lens, a true inversion point is equal distance from both the original and inverted object. Rotoinversion axis (3D) or point (2D) This fourth element is just a combination of rotation and inversion. A rotoinversion axis or point occurs when you are able to rotate an object to an angle less that 180o, invert it, and end up with it looking the same as it did at the starting point. Writing it down There is a shorthand used by crystallographers for recording the symmetry elements of an object. You will find the following notations and symbols useful for documenting symmetry. Element Notation Symbol Rotational Axes 2-fold A2 3-fold A3 4-fold A4 6-fold A6 Rotoinversion Axes 3-fold A3 4-fold A4 6-fold A6 Mirror planes m Inversion point i Inversion of an image through a lens A mirror reflection across a line. Inversion symmetry ERTH 2330 Lab 3 - Symmetry and Form 2 The symmetry of an object may be written by enumerating the number of symmetry elements contained in the object. For instance, if you found an object to have one inversion point, one six-fold rotational axis, six two-fold rotational axes, and seven mirror planes (such an object is shown right), then you would write "i 1A6 6A2 7m". Exercise 1 Defining symmetry Mark the diagrams below with mirror lines and rotational points. Additionally, use the shorthand notation to describe all of the marked elements. After completing the 2D drawings, check your answers with the instructor. 2D representation of a 3D object Side Base Symmetry i 1A6 6A2 7m , , , , , , , , , , , , , , , A S
