Understanding Slip Systems in hcp Zinc

Plastic deformation in crystalline materials occurs via slip, which happens on specific crystallographic planes and in specific directions, known collectively as slip systems. For hexagonal close-packed (hcp) metals like Zinc (Zn), the ease of slip is influenced by factors such as the crystal structure and the ratio of the lattice parameters, commonly denoted as the '$c/a$ ratio'.

Analyzing the c/a Ratio in Zinc

The question provides the actual '$c/a$' ratio for Zn as $1.856$. This value is significantly higher than the ideal '$c/a$' ratio for a perfect hcp lattice, which is approximately $1.633$.

• Ideal hcp $c/a \approx 1.633$
• Zn $c/a = 1.856$

A '$c/a$' ratio greater than the ideal value generally leads to:

• Increased difficulty of slip on prismatic planes ($\{1\overline{1}00\}$).
• Increased ease of slip on basal planes ($\{0001\}$).

Identifying the Most Active Slip System

In hcp metals, the primary slip systems are typically:

• Basal slip: $\{0001\} \langle 11\overline{2}0 \rangle$
• Prismatic slip: $\{1\overline{1}00\} \langle 11\overline{2}0 \rangle$
• Pyramidal slip: e.g., $\{10\overline{1}1\} \langle 11\overline{2}3 \rangle$

Given that Zn has a '$c/a$' ratio ($1.856$) substantially larger than the ideal ($1.633$), slip is most favored on the basal plane ($\{0001\}$) in the $\langle 11\overline{2}0 \rangle$ direction at room temperature. This is a common characteristic of hcp metals with high '$c/a$' ratios.

Conclusion on Zn Slip

Therefore, considering the high '$c/a$' ratio of Zinc, the slip system most active at room temperature is the basal slip system.

Correct Slip System: $\{0001\} \langle 11\overline{2}0 \rangle$