Question

In a face centered unit cell, the number of nearest neighbours?
(a) 8
(b) 12
(c) 6
(d)14

Answer 1

Hint: In Fcc, there are a number of four spheres per unit cell i.e. there are four corners and four centers of the four vertical faces each on the top and bottom of the cube. Now, identify the nearest neighboring atoms in it.

Complete step by step answer:
First of all, we should know what a space lattice is. It is the regular arrangement of the constituents i.e. the atoms, molecules and the ions of a crystalline solid in three dimensions. In the space lattice we can select a group of lattices or points which when repeated over and over (i.e. unit cell) give rise to the formation of the space lattice.
In FCC i.e. the face centered crystal lattice, there are 12 nearest neighbors to each lattice point. And thus, the coordination number (i.e. the number of spheres touching a given spheres is called its coordination number) of a lattice point in the FCC lattice is 12. And the distance of each lattice point from the center is i.e. the radius of the atom is 2​a​. Here, a is the distance between the two nearest spheres.
In FCC, one lattice point is in the center of the face and all the four corners in FCC are nearest to this central lattice point. In a three- dimensional packing, a unit cell will be placed on the top of the central unit cell and the centers of four vertical faces of the top cube is the nearest to the central lattice point. And thus, it gives 12 nearest neighbors in the Fcc space lattice.
So, the correct answer is “Option B”.

Note: Don’t get confused in the space lattice and the unit cell. Unit cell is that smallest repeating unit which when repeated over and over again gives rise to the formation of the space lattice whereas on the other hand, space lattice is the regular arrangement of the particles of crystalline substance in the three dimension and is formed by the repetition of the unit cells.