Question: The number of tetrahedral and octahedral voids in CCP unit cells are respectively. (A) \[4,8\] (...

Question

The number of tetrahedral and octahedral voids in CCP unit cells are respectively.
(A) $4,8$
(B) $8,4$
(C) $12,6$
(D) $6,12$

Answer 1

Solution

Further the tetrahedral voids= $2N$ where N is the number of particles. Moreover when we talk about the octahedral voids we found that the void is surrounded by six spheres and is called the octahedral void. So, we can say that the number of octahedral voids= $N$ where N is the number of particles. When we talk about the CCP further known to contain the atoms at the corners as well as the centre of the cube.

Complete step-by-step answer: When we talk about the CCP we should know that we are talking about the FCC structure only. So it is the face centred cubic unit cell which is further known to contain the atoms at the corners as well as the centre of the cube. Then as suggested in the question we need to consider the tetrahedral and the octahedral voids. So voids are nothing but the empty spaces that are left behind when the packing is supposed to take place. The spaces that are left behind are further of two more types: tetrahedral and octahedral. When the void is surrounded by the four spheres occupying the corners of the tetrahedron is called the tetrahedral voids. Further the tetrahedral voids= $2N$ where N is the number of particles. Moreover when we talk about the octahedral voids we found that the void is surrounded by six spheres and is called the octahedral void. So, we can say that the number of octahedral voids= $N$ where N is the number of particles. We can solve the given question as:
$8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 4$
Where eight are the number of corners and six are the number of spheres.From this we have calculated the number of particles which is further equal to the octahedral voids and that is four.Further the tetrahedral voids are given as = $2N$
$2 \times 4 = 8$

Hence the correct option is (B).

Note: from here we found that the number of tetrahedral voids is eight and that of octahedral voids is four . hence, option B is correct. Moreover we should know how to calculate the number of atoms or particles because it is a basic step for further calculation.