Close-packed Structures

1
Close-packed Structures

• Metallic materials have isotropic bonding
• In 2-D close-packed spheres generate a hexagonal
  array
• In 3-D, the close-packed layers can be stacked in
  all sorts of sequences
• Most common are
• ABABAB..
• ABCABCABC

Hexagonal close-packed
Cubic close-packed
2
AB
BABABA.
A
3
2-D fractional coordinates
A at (0,0) B at (2/3, 1/3) C at (1/3, 2/3)
c
a2
A
A
C
B
a1
a
A
What are the unit cell dimensions?
a1 a2 2R
let atomic radius be R
A
2R
? face diagonal 2?3R AA
?3R
AB 1/3 (face diagonal)

R
½c
A
A
2R
A
B
C
A
4
Hexagonal Close-packed Structure
a1 a2 2R
a1 a2 90 g 120
ideal
coordination number?
12
atoms per unit cell?
2
lattice points per unit cell?
1
atoms per lattice point?
2
a unit cell with only one lattice point is a
primitive cell
HCP
lattice type of HCP is called primitive
hexagonal
reminder the hexagon is not an acceptable unit
cell shape
5
Close-packed Structures

• Metallic materials have isotropic bonding
• In 2-D close-packed spheres generate a hexagonal
  array
• In 3-D, the close-packed layers can be stacked in
  all sorts of sequences
• Most common are
• ABABAB..
• ABCABCABC

Hexagonal close-packed
Cubic close-packed
6
AB
ABCABC.
C
Cubic???
7
What are the unit cell dimensions?
a
face diagonal is close-packed direction
a1 a2 a3 a1 a2 a3 90
8
Cubic Close-packed Structure
a1 a2 a3 a1 a2 a3
only one cell parameter to be specified
coordination number?
12
atoms per unit cell?
4
lattice points per unit cell?
4
CCP
atoms per lattice point?
1
a unit cell with more than one lattice point is a
non-primitive cell
lattice type of CCP is called face-centered
cubic
CCP structure is often simply called the FCC
structure (misleading)
9
Cubic Loose-packed Structure
Body-centered cubic (BCC)
8
coordination number?
2
atoms per unit cell?
a
2
lattice points per unit cell?
1
atoms per lattice point?
another example of a non-primitive cell
body diagonal is closest-packed direction
lattice type of CLP is body-centered cubic
no common name that distinguishes lattice type
from structure type
a1 a2 a3 a1 a2 a3 90
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Summary Common Metal Structures
hcp
bcc
ccp (fcc)
ABCABC
not close-packed
ABABAB
Hexagonal unit cell Specify a, c Hexagonal
implies a1 a2 a g 120 a b 90
Cubic unit cells Specify a Cubic implies a1
a2 a3 a a b g 90
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Metals