MATERIALS SCIENCE & ENGINEERING

1. MATERIALS SCIENCE & ENGINEERING Part of A Learner’s Guide AN INTRODUCTORY E-BOOK Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email:anandh@iitk.ac.in, URL:home.iitk.ac.in/~anandh http://home.iitk.ac.in/~anandh/E-book.htm

2. Connection between Geometry & Symmetry • From reading some of the topics so far one might get an impression that the:“Geometry of the unit cell has no connection with the symmetry” !! • One may even be tempted to conclude (e.g.) that choice of:“Square Prism Unit Cell (Tetragonal UC) for the Tetragonal Crystal is purely coincidental • Let us consider an example to clarify the matter • The crux of the issue lies in the fact that many of the examples considered are “ideal geometrical” examples  which have been used to illustrate basic concepts • In real crystals with atomic entities  nature decides the final outcome and we are left to analyze the outcome in the language of crystallography

3. Let us consider a cubic unit cell decorated with a two atom motif + = UC of cubic lattice This is an ideal geometrical example If the entities are atomic a better picture would be We will use two views

4. But then these atoms will not be hanging loosely in space!  The atoms would be touching each other  an even better picture would be Side View Front View New Unit Cell • As you can see this automatically leads to an unit cell in which a = b  ci.e. a Square Prism unit cell of Tetragonal crystal system • Hence a lower symmetry motif can lead to an altered geometry of the unit cell (of lower symmetry)