Chapter 12, Problem 70A

Interpretation Introduction

(a)

Interpretation:

The number of particles in 1 unit cell for simple cubic needs to be determined.

Concept introduction:

In simple cubic unit cell, each atom in the lattice has 6 neighboring atoms arranged in octahedral arrangement. It is an inefficient way to pack atoms in the given space. In simple cubic lattice, 52% of the total space is occupied by atoms. The example is NaCl in which each cation is surrounded by 6 anions and vice versa.

Answer to Problem 70A

8

Explanation of Solution

In simple unit cell, there are 8 atoms at corners sharing 1/8^th of the original volume of the cube. $8\times \frac{1}{8}=1$

The number of atoms at centers and faces is equal to zero. Therefore, the total number of atoms per unit cell will be 8 that is present on 8 corners of the lattice.

Thus, the number of particles per unit cell is 8.

Interpretation Introduction

(b)

Interpretation:

The number of particles in 1 unit cell for body-centered cubic needs to be determined.

Concept introduction:

In body-centered cubic unit cell, the spheres are packed together more efficiently. There are 8 nearest neighbors in the unit cell and 68% of the volume is occupied by atoms.

Answer to Problem 70A

9

Explanation of Solution

In a simple unit cell, there are 8 atoms at the corners sharing 1/8^th of the original volume of the cube. $8\times \frac{1}{8}=1$

The number of atoms at centers and faces is equal to 1 and zero respectively. Therefore, the total number of atoms per unit cell will be 9 which includes 8 atoms present at 8 corners of the lattice and 1 at the center.

Thus, the number of particles per unit cell is 9 that is one more than simple cubic.