### Solid State Physics Lecture 2 of 20

May 9, 2012 by Sandro Scandolo

S. Scandolo, ICTP

This lesson starts by recalling the concept of crystals introduced in the previous lesson, then it is introduced the concept of Bravais lattice an infinite array of discrete points generated by a set of discrete translation operations. Then it was given some examples in two dimensions like the square lattice, the rectangular lattice and the triangular lattice. As an example of an structure that is not a Bravais lattice it is introduced the Honeycomb lattice because if a Bravais lattice vector belong to the lattice then any integer multiple of that vector must belong to the lattice and this property does not hold on the Honeycomb lattice. Thus a more general definition of lattice is needed to describe the Honeycomb lattice for this porpoise is introduced the concept of crystal structure or "lattice with a basis" is a Bravais lattice to witch are adding more points for each Bravais lattice point. This new points are given as a basis set on n vectors. Then it was shown how the Honeycomb lattice is describe by using a lattice with a basis. Finally some examples of the Bravais lattice in three dimensions were given like the cubic, the tetragonal, the orthorhombic, the hexagonal and the triclinic lattices

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