ECE 440
Homework I Solutions
Spring 2008
11.
How many atoms are found inside a unit cell of a simple cubic (sc), bodycentered cubic
(bcc), facecentered cubic (fcc), diamond structure, and zincblende structure crystal? Find
the maximum fractions of the unit cell volume that can be filled by hard sphere in the sc, bcc,
fcc and diamond lattices. If all unit cells have the same lattice constants, i.e. the unit cell
dimension, which structure among sc, bcc, fcc, diamond and zincblende has the largest
atomic density (atoms/cm
3
)? Which of them has the highest packing density, i.e. highest
volume fraction being occupied by hard spheres?
Simple Cubic (SC)
1/8 of each of the atoms on the corners is within the unit cell.
Since there are 8 corners, 1/8 x 8 atoms = 1 atom.
To find the maximum fraction of the unit cell volume we must
follow the procedure outlined on page 6 of Streetman.
Assuming the atoms touch one another (maximum packing without the spheres intersecting)
the radius of each atom equals a/2. The ratio of volume filled to total volume is the number
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 Spring '09
 Lie
 Cubic crystal system, Diamond cubic, Crystal system, Atomic packing factor

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