Lecture

Crystal Systems: Unit Cells and Symmetry

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In course

CH-450: Solid state chemistry and energy applications

You will learn about the bonding and structure of several important families of solid state materials. You will gain insight into common synthetic and characterization methods and learn about the applicability of several classes of materials in energy rele ...

Description

This lecture covers crystal systems, focusing on the smallest repeating unit of crystalline material, known as the unit cell. It explains the different crystal systems such as cubic, tetragonal, orthorhombic, hexagonal, and more. The lecture also delves into rotational axes of symmetry, interstitial sites, and voids in close-packed structures.

Instructor

Wendy Lee Queen

Teaching & PhD PhD Students Pratap Narayan Soni, Pattaraphon Rodlamul, Matthieu Meoli, Olivier Thomas Smith, Sanjay Venkatachalam, Anne Faustine Sido Belin, Christopher William Gardner, Lorenzo Meneghin Past EPFL PhD Students Mehrdad Asgari, Daniel Teav Sun, Ilia Kochetygov, Vikram Vinayak Karve, Anita Justin, Till Marian Schertenleib, Jocelyn Richard Roth, Timo Markus Oskar Felder Courses Chemical engineering practice ChE-309 This course provides the students with practical experience wit

Official source

Related concepts (23)

Rotational symmetry

Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids.

Crystal structure

In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. The smallest group of particles in the material that constitutes this repeating pattern is the unit cell of the structure.

Cubic crystal system

In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of these crystals: Primitive cubic (abbreviated cP and alternatively called simple cubic) Body-centered cubic (abbreviated cI or bcc) Face-centered cubic (abbreviated cF or fcc) Note: the term fcc is often used in synonym for the cubic close-packed or ccp structure occurring in metals.

Symmetry

Symmetry () in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.

Symmetry group

In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object X is G = Sym(X). For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space.

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