Lecture

Crystallography Basics: Symmetry and Crystal Classes

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In course

MSE-100: Introduction to materials science

This course relates the structural elements of materials to their mechanical, thermal, electric, magnetic, and optical properties. Hands-on laboratories and team projects offer insight into the profession of materials engineers. ...

Description

This lecture covers the fundamentals of crystallography, focusing on symmetry elements, crystal classes, and their representations. Topics include crystal faces, axes, and coordinate systems, as well as the classification of crystal classes into holoedries and meroedries. The instructor explains the concept of bravais networks, plan groups, and the relationship between point groups and translation groups. Additionally, the lecture delves into the crystal systems of oblique, rectangular, square, and hexagonal, highlighting the importance of symmetry operations and space groups.

Instructors (2)

Pierre-Etienne Bourban

Background 1990 Ingénieur en science des matériaux 1993 PhD in materials science Activities 1993-1994 Research at the Center for Composite Materials, University of Delaware, USA (ccm.udel.edu), SNSF grant Since 1994 Research and teaching at EPFL, Composites, (LTC, LPAC) 1995-1999 Coordination Swiss Priority Program on Materials research: 2.2: Composites Since 1998 Biocomposites 2004-2009 Direction of the EPFL Transdisciplinary programme in Sport and Rehabilitation 2005-2008 Member of the EPFL Vice-Presidency for Innovation and Valorisation and direction a.i.EPFL-LTC Since 2016 Direction Discovery Learning Labs Materials/Bioengineering and Engineering

Francesco Stellacci

Francesco Stellacci graduated in Materials Engineering at the Politecnico di Milano in 1998 with a thesis on photochromic polymers with Prof. Giuseppe Zerbi and Mariacarla Gallazzi. In 1999 he moved to the Chemistry Department of the University of Arizona for as a post-doc in the group of Joe Perry in close collaboration with the group of Seth Marder. In 2002 he moved to the Department of Materials Science and Engineering at the Massachusetts Institute of Technology as an assistant professor. He was then promoted to associate without (2006) and with tenure (2009). In 2010 he moved to the Institute of Materials at EPFL as a full Professor. He holds the Alcan EP Chair. Francesco was one of the recipients of the Technology Review TR35 "35 Innovator under 35" award in 2005, and the Popular Science Magazine "Brilliant 10" award in 2007. He has been a Packard Fellow starting 2005.

Official source

Related concepts (32)

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 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.

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 in mathematics

Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. This can occur in many ways; for example, if X is a set with no additional structure, a symmetry is a bijective map from the set to itself, giving rise to permutation groups.

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