Question

The packing sequence of atoms in FCC is

• A. AB AB AB...
• B. BC BC BC...
• C. AC AC AC...
• D. ABC ABC ABC....

Hint:

HCP Stacking Sequence: AB AB AB...
FCC Stacking Sequence: ABC ABC ABC...
Both have a coordination number of $12$ and a packing efficiency of $74\%$.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the specific stacking sequence of close-packed atomic planes in a Face-Centered Cubic (FCC) crystal structure.

Step 2: Key Formula or Approach:
Both FCC and HCP (Hexagonal Close-Packed) are close-packed structures with a maximum atomic packing factor (APF) of $0.74$.
The difference between them lies in how the close-packed planes are stacked on top of each other.

Step 3: Detailed Explanation:

• Let the first close-packed layer of atoms be layer 'A'.

• The second layer of atoms is placed in the hollows of the first layer, which we designate as layer 'B'.

• For the third layer, there are two choices:
1. Place the atoms directly above the atoms of layer 'A'. This creates an AB AB AB... sequence, which corresponds to the HCP structure.
2. Place the atoms in the alternative set of hollows that do not lie directly above layer 'A'. This creates a third distinct layer, designated as layer 'C'. This results in an ABC ABC ABC... sequence, which corresponds to the FCC structure.

• In the FCC lattice, this stacking direction is perpendicular to the $\{111\}$ family of close-packed planes.

Step 4: Final Answer:
The packing sequence of atoms in an FCC crystal is ABC ABC ABC....