This lesson begins by recalling the concept of crystals introduced in the previous lesson, then the notion of a Brallais network is introduced, an infinite network of discrete points generated by a set of discrete translation operations. Then, some two-dimensional examples were given such as the square lattice, the rectangular lattice and the triangular lattice. As an example of a structure that is not a Brallais network, we introduce the Honeycomb network because if a vector of the Brallais network belongs to the network then any integer multiple of this vector must belong to the network and this property does not apply to the network Honeycomb. . Thus, a more general network definition is needed to describe the honeycomb network for this porpoise. The concept of crystal structure or "lattice with a base" is a Brviens lattice to which more points are added for each point of the Brviens lattice. These new points are given in base form placed on n vectors. Then it was shown how the Honeycomb network is described using a network with a basis. Finally some examples of three-dimensional Brallais lattices were given such as cubic, tetragonal, orthorhombic, hexagonal and triclinic lattices.

The Abdus Salam International Center for Theoretical Physics (CIPT) is a “school of excellence” in Italy, in Trieste. This is a course given by prof. Sandro Scandolo (CIPT professor) in the winter semester 2012. The official webpage of this course and all associated videos are available at the following link

http://mediacore.ictp.it/categories/solid-state-physics

These are NOT my videos! All credits for these videos go to the CIPT Institutes

https://www.ictp.it/

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