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Lecture

Symmetry Operations in Materials Science

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 introduces the concept of symmetry in materials science, focusing on the invariance of objects under geometric operations. It covers symmetry elements, groups, and operations, including rotations, roto-inversions, and rotoréflexions. The presentation also discusses helical axes and screw axes, as well as glide planes and their symbols.

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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

Ontological neighbourhood

Mathematics

Geometry: Symmetry

Related concepts (32)

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 (geometry)

In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). Thus, a symmetry can be thought of as an immunity to change. For instance, a circle rotated about its center will have the same shape and size as the original circle, as all points before and after the transform would be indistinguishable.

Molecular symmetry

In chemistry, molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain many of a molecule's chemical properties, such as whether or not it has a dipole moment, as well as its allowed spectroscopic transitions. To do this it is necessary to use group theory. This involves classifying the states of the molecule using the irreducible representations from the character table of the symmetry group of the molecule.

Rotation

Rotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis.

Reflection symmetry

In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line/axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called . In conclusion, a line of symmetry splits the shape in half and those halves should be identical.

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