Packing Efficiency of Unit Cells
-- packing efficiency of simple cubic unit cells = 52%
-- packing efficiency of body-centered cubic unit cells = 68%
-- packing efficiency of face-centered cubic unit cells = 74%
-- the packing efficiency is the percentage of the volume of the unit cell occupied by atoms
-- packing efficiency = [V(atom) / V(unit cell)] x 100%
-- V(atom) is the number of atoms in the unit cell times the formula for the volume of a sphere
-- number of atoms: -- simple cubic = 1 -- face-centered cubic = 4 -- body-centered cubic = 2
-- volume of a sphere is found using the formula (4/3)πr^3
-- V(unit cell) is the edge length cubed
-- edge lengths: -- simple cubic = 2r -- body-centered cubic = 4r/√3 -- face-centered cubic = 2√2r
-- V(unit cell) values -- simple cubic = 8r^3 -- body-centered cubic = 64r^3 / (√3)^3 -- face-centered cubic = 8 (√2)^3 r^3
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