Question

1. (a) Find the packing density (total atomic volume/unit cell volume) for fcc copper (Cu, a - 0.3624 nm), assuming a hard sphere model for these atoms. (b) Now find the packing density of NaCl see details about this structure in problem 1.11 (4th Ed) (or look it up directly in the Inorganic Crystal Data Base). Explain why NaCl is NOT "simple cubic. What is the bravais lattice?

Answer 1

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In fcc unit cell Number of effective atoms = 4 a = 4r/squareroot 2 Packing fraction/density = 4 times (4/3 pi r^3)/a^3 = 4(4/3 pi r^3) 2 squareroot 2/4 r^3 = 0.74 NaCl crystals have FCC lattice/structure. There are four Na^+ and four cl^- ions per unit cell. R = radius of Cl^- = 0.181 nm r = radius of Na^+ = 0.102 nm packing fraction: 4(4/3 pi r^3) + 4 (4/3 pi R^3)/(2r + 2R)^3 packing density = 0.67