QQuestionPhysics
QuestionPhysics
Show that the atomic packing factor of an FCC crystal structure is 0.74. Be sure to include how you obtained the relationship between a, the lattice parameter, and r, the radius of the atoms.
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Answer
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Step 1I'll solve this problem step by step, carefully following the LaTeX formatting guidelines:
Step 2: Understand the FCC Crystal Structure
In a Face-Centered Cubic (FCC) crystal structure, atoms are located at: - The 8 corners of the unit cell (each shared by 8 unit cells) - The center of each of the 6 faces (each shared by 2 unit cells)
Final Answer
The atomic packing factor of an FCC crystal structure is 0.74 or \frac{\pi}{3\sqrt{2}}, which represents the most efficient packing of spheres in three-dimensional space.
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