Question

In a face centerd cubic lattice the number of nearest neighbours for a given lattice point

Answer 1

(The way we did it in class) We know that the fcc structure is a close packed one — it’s also known as cubic close packed — so we have six nearest neighbours in one layer, three in the layer above, and three in the layer below:



(Looking along an axis) If we consider an atom at the centre of some face, it has four nearest neighbours that are at the corners of that face, four that are at the centres of adjacent faces in one unit cell, and four that are at the centres of adjacent faces in another unit cell:



(Using the properties of a lattice) We know that since the fcc structure is a lattice (strictly speaking, there is only one atom in the motif) every atom has to be in an equivalent position. Thus we can simultaneously consider our black atom to be at the centre of a face perpendicular to the x axis (giving four nearest neighbours), at the centre of a face perpendicular to the y axis (giving another four), and at the centre of one perpendicular to the z axis (giving a further four

Answer 2

The number of nearest neighbour for giving lactic is also known as cubic close structure