Crystal Structures in Engineering Materials Science : Practice MCQ Questions & Answers with Explanations

Explanation: Atomic packing factor: In the crystal structure, the atomic packing factor (APF) or packing efficiency or packing fraction is the fraction of volume in a crystal structure that is occupied by constituent particles. It is a dimensionless quantity and always less than unity. The atomic packing factor of different crystal structures is given in the table below: Unit Cell | Coordination No.

Explanation: Unit Cell | Coordination No. | No. of Atoms Per Unit Cell | Atomic packing factor Diagram The unit cell of BCC crystal = 2 The unit cell of HCP crystal = 6 The difference between the number of atoms in a unit cell of HCP crystal and BCC crystal is 6 - 2 = 4

Explanation: Hexagonal closed pack structure: In a hexagonal closed-packed structure, the third layer has the same arrangement of spheres as the first layer. Since the structure repeats itself after every two layers, the stacking for hcp may be described as "a-b-a-b-a-b". The atoms in a hexagonal closed packed structure efficiently occupy 74% of space while 26% is empty space.

Explanation: Atomic Packing Factor: In the crystal structure, atomic packing factor (APF) or packing efficiency or packing fraction is the volume of atoms in a unit cell divided by the volume of the unit cell. It is a dimensionless quantity and always less than unity No of atoms in b.c.c unit cell = 2 For BCC $a = \frac{{4r}}{{\sqrt 3 }}$ where a is the side of the cube and r is the atomic radius. Now APF will be $APF = \frac{{{N{atoms}}{V{atom}}}}{{{V{crystal}}}} = \frac{{2\left( {\frac{4}{3}} \right)\pi {r^3}}}{{{{\left( {a } \right)}^3}}}= \frac{{2\left( {\frac{4}{3}} \right)\pi {r^3}}}{{{{\left( {\frac{{4r}}{{\sqrt 3 }}} \right)}^3}}}$ $APF = \frac {\sqrt {3} \pi}{8}$ Unit Cell | Coordination No.