Crystallography - Introduction to lattices and symmetries

Abstract

The properties of crystals, which make up a large part of solid materials, are closely related to the symmetry of their internal structure. The objective of the crystallography lecture is to provide concepts and mathematical fundamentals of symmetry theory, structure-property relationships, and the basic principles of structure determination. Simple crystal structures will be discussed.

Objective

Students are able to, - mathematically represent the geometry of a crystal lattice and derive and understand its symmetry. - apply concepts of group theory to classify crystal lattices based on their symmetry. - analyse simple crystal structures in terms of their symmetry. - develop a basic understanding of the relationships between crystal structure, symmetry and physical properties of solids. - understand the concept of X-ray diffraction as an elementary experimental technique for determining crystal structures. - apply the methods and concepts presented in the lecture and communicate the results in written and oral form.

Content

Symmetry and crystal lattices: symmetry operations and lattices in two and three dimensions, point groups, space groups. Crystal structures: symmetry and typical simple crystal structures. Structure/property relationships: Neumann's principle; examples: piezoelectricity, ferroelectric. Materials characterization: diffraction techniques.

Resources