Question

A tetrahedral void in FCC is formed by atoms at:
a.) 3 corners + 1 face-centre
b.) 3 face-centers + 1 corner
c.) 2 face-centers + 2 corners
d.) 2 face-centers + 1 corner + 1 body-center

Answer 1

Hint: In order to solve the given problem we will first understand the meaning of tetrahedral void and the meaning of FCC of face centered cubic structure. Further we will draw the structure of the tetrahedral void in FCC structure along with the notation. On the basis of the diagram of the FCC and the tetrahedral void structure we will select the correct option amongst the given options.

Complete step by step answer:
First let us understand about the unit cell and FCC.
The unit cell, the building block of a crystal, is the smallest repeating unit of the crystal lattice.
In such a way that they fill space without overlapping, the unit cells that are all similar are described. A crystal lattice is called the 3D arrangement of atoms, molecules or ions inside a crystal. It is composed of a number of unit cells. Per lattice point is taken up by one of the three constituent particles.
At all the corners of the crystal lattice and at the centre of all the faces of the cube, an FCC unit cell comprises atoms. The face-centered atom is divided between 2 neighboring unit cells, and only 1/2 of each atom belongs to a single cell.
In order to find the constituent tetrahedral void in FCC let us draw the figure of FCC lattice along with tetrahedral void.

The given figure shows the tetrahedral void in FCC structure.
In the above figure black spheres represent corner atoms.
Red spheres represent face centered atoms.
And the yellow sphere represents the center of the tetrahedral void.
From the figure it is clear that the tetrahedral void in FCC structure is made up of 3 face centers and 1 corner atoms.
Hence, a tetrahedral void in FCC is formed by atoms at 3 face-centers and 1 corner.
So, the correct answer is “Option B”.

Note: In order to solve such types of problems students must remember the general structure of different types of crystal lattice like face centered cubic, body centered cubic and primitive unit cell. Also students must remember different types of voids like tetrahedral voids and octahedral voids.