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ECE 440
Homework I Solutions
Fall2008
1.
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 zincbelnde 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?
1
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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