Question

Which of the following crystal structure is ductile?

• A. Face centered cubic (FCC)
• B. Body centered cubic (BCC)
• C. Hexagonal close packed (HCP)
• D. Body centered tetragonal (BCT)

Hint:

FCC metals do not exhibit a ductile-to-brittle transition temperature (DBTT).
They remain highly ductile and tough even at cryogenic temperatures, which is why they are widely used in low-temperature applications.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks which of the common metal crystal structures is inherently the most ductile.

Step 2: Key Formula or Approach:
Ductility in metals depends directly on the number of active slip systems available in their crystal structure.
A slip system consists of a slip plane and a slip direction:
\[ \text{Number of Slip Systems} = \text{Number of Slip Planes} \times \text{Number of Slip Directions} \]

Step 3: Detailed Explanation:

• Face Centered Cubic (FCC): FCC has $12$ independent, highly close-packed slip systems ($\{111\}$ planes and $\langle110\rangle$ directions). Because these planes are closely packed, the activation energy for slip is low, allowing easy dislocation movement even at low temperatures. This makes FCC metals (like Al, Cu, Au, Ag) exceptionally ductile.

• Body Centered Cubic (BCC): Although BCC has $48$ potential slip systems, its slip planes ($\{110\}$) are not close-packed. At low temperatures, the stress required to move dislocations increases sharply, leading to a ductile-to-brittle transition.

• Hexagonal Close Packed (HCP): HCP has only $3$ active slip systems at room temperature. Because it has fewer than the $5$ independent slip systems required for arbitrary homogeneous deformation, HCP metals (like Mg, Zn) are relatively brittle.

• Body Centered Tetragonal (BCT): This is a highly distorted structure (like martensite in steel) with limited slip capability, making it very hard and brittle.

Step 4: Final Answer:
The most ductile crystal structure is Face Centered Cubic (FCC).