S. Scandolo, ICTP

Lesson number 4 (lattices / crystals)

This lesson starts with a small test that was given to the students and then discussed in details during the lesson. It was shown how in the case of a lattice with a basis like the **Honeycomb lattice **case the unit cell is the same that the underlying **Bravais lattice **but in this case it contains more than one point and one have to be careful in assigning the lattice points to the unit cell because sometimes they appear in the edges of the unit cell, a solution to this problem could be to assign a fractional number to the points on the edge. Then it was discussed the difference between the unit cell and the **primitive cell **definitions.

In the second part of this lesson it was introduced the **packing fraction **in two and tree dimensions. Several examples were considered the squared and the triangular lattices and the peculiar case of the **Honeycomb lattice **in witch as the unit cell contains two points then each point contribute to the filing area of the unit cell and one has to be more careful. Finally it was calculated the **packing fraction **for the simple **cubic**, the and the **face centered cubic **lattices having this last one the best possible (nearest to one) value.