Concept:
Metals organize themselves into distinct crystal structures to minimize their total cohesive free energy. The most common metallic structures are Body-Centered Cubic (BCC), Face-Centered Cubic (FCC), and Hexagonal Close-Packed (HCP). Aluminum (\(\text{Al}\)), with an atomic number of 13, forms a stable Face-Centered Cubic lattice configuration under normal standard ambient temperature and pressure conditions.
Step 1: Structural features of FCC Aluminum.
The stable phase of Aluminum exhibits the following crystallographic parameters:
• Lattice Configuration: Atoms are positioned at the 8 vertices of the unit cube and at the centers of the 6 square faces.
• Coordination Number: Each aluminum atom is tightly bounded, touching exactly 12 nearest-neighbor atoms, which represents the maximum possible packing efficiency for spherical objects.
• Atomic Packing Factor (APF): The volume occupied by the hard spheres relative to the total volume of the unit cell is:
\[
\text{APF} = \frac{\pi}{3\sqrt{2}} \approx 0.74 \text{ or } 74%
\]
Step 2: Linking structure to physical behavior.
Because of its FCC geometry, aluminum contains four distinct sets of closely packed \(\{111\}\) planes, and each plane possesses three close-packed \(\langle 110 \rangle\) slip directions. This provides a total of 12 independent, highly symmetric slip systems. The presence of these numerous intersecting slip paths allows aluminum to undergo easy dislocation glide without structural fracturing, explaining its excellent ductility, formability, and softness at room temperature.
Step 3: Verification.
Comparing with options, Aluminum is universally known to crystalize in an FCC matrix, matching option (B).