Chapter 12, Problem 12.18QP

Interpretation Introduction

Interpretation: The features of simple cubic, body-centered cubic and face-centered cubic crystal structures are to be described.

Concept introduction: The cubic closest-packing structure is divided into three types, which are,

• Body centered cell(BCC)
• Face centered cell(FCC)
• Simple cubic cell

Simple cubic cell contains one lattice point on each corner of the cubic unit cell.

Body centered cubic cell consists of one lattice point in the center with eight corner lattice points.

Face centered cubic cell consists of lattice points on all the six faces of the cubic unit cell with eight corner lattice points.

The packing efficiency of crystal structure is calculated by the formula,

$\text{Packing}\text{efficiency}\left(\text{in}\%\right)=\frac{\text{Volume}\text{occupied}\text{by}\text{the}\text{spheres}}{\text{Total}\text{volume}\text{of}\text{unit}\text{cell}}\times 100$

To determine: The features of simple cubic, body-centered cubic and face-centered cubic crystal structures.