Which crystal structure is less densely packed with a packing factor around 0.68 and includes iron at room temperature?

Study for the Material Science Exam 1. Explore flashcards and multiple choice questions with explanations. Prepare for your exam effectively!

Multiple Choice

Which crystal structure is less densely packed with a packing factor around 0.68 and includes iron at room temperature?

Explanation:
Atomic packing factor is the fraction of a crystal’s unit cell that is actually occupied by atoms. For the body-centered cubic (BCC) structure, there are 2 atoms per cell (one at each corner contributes 1/8, totaling 1, plus one in the center). With the relationship a = 4r/√3 between the lattice parameter and atomic radius, the APF becomes (2 × (4/3)πr^3) / a^3, which simplifies to π√3/8 ≈ 0.68. Iron at room temperature exists as ferrite with a BCC lattice, so its packing factor is about 0.68. In comparison, simple cubic is about 0.52, while both FCC and HCP are about 0.74, more densely packed. Therefore, the structure that fits the given packing factor and aligns with iron at room temperature is body-centered cubic.

Atomic packing factor is the fraction of a crystal’s unit cell that is actually occupied by atoms. For the body-centered cubic (BCC) structure, there are 2 atoms per cell (one at each corner contributes 1/8, totaling 1, plus one in the center). With the relationship a = 4r/√3 between the lattice parameter and atomic radius, the APF becomes (2 × (4/3)πr^3) / a^3, which simplifies to π√3/8 ≈ 0.68. Iron at room temperature exists as ferrite with a BCC lattice, so its packing factor is about 0.68. In comparison, simple cubic is about 0.52, while both FCC and HCP are about 0.74, more densely packed. Therefore, the structure that fits the given packing factor and aligns with iron at room temperature is body-centered cubic.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy