Civil Engineering Reference
In-Depth Information
By inspection, the diagonal of the face of an FCC unit cell
=
4
r
Length of each side of unit cell
=
2
2
2
r
b
3
Volume of unit cell
=
a
2
2
2
r
a
16
3
pr
3
b
volume of atoms in the unit cell
total unit volume of the cell
APF
=
=
b
3
=
0.74
a
2
2
2
r
Similar geometric considerations allow for the calculation of the atomic
packing factor for the BCC and HCP structures as 0.68 and 0.74, respectively.
The density of a metal is a function of the type of lattice structure and
can be determined from
nA
V
c
N
A
r
=
(2.3)
where
r
=
density
of the material
of equivalent atoms in the unit cell
mass of the element (grams/mole)
of the unit cell
number
n
=
number
A
=
atomic
V
C
=
volume
10
23
atoms/mole
N
A
=
Avogadro's
1
6.023
*
2
Sample Problem 2.2
Calculate the radius of the aluminum atom, given that aluminum has an FCC crystal
structure, a density of and an atomic mass of 26.98 g/mole. Note that the
APF for the FCC lattice structure is 0.74.
2.70 Mg/m
3
,
Solution
nA
V
c
N
A
r
=
For an FCC lattice structure,
n
=
4,
so
4
*
26.98
10
-
29
m
3
V
c
6.636
=
10
23
=
*
10
6
2.70
*
*
6.023
*
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