Metallic

1
Types of Primary Chemical Bonds
Isotropic, filled outer shells

• Metallic
• Electropositive give up electrons
• Ionic
• Electronegative/Electropositive
• Colavent
• Electronegative want electrons
• Shared electrons along bond direction

Close-packed structures
2
(glide plane)
mirror plane
unit cell

• Definitions
• Lattice point
• Unit cell
• Lattice parameters
• Atoms per unit cell
• Symmetry operations
• Fractional coordinates
• Coordination number

not a unit cell
2-fold rotation axes
From 2-D to 3-D
a2
6-fold rotation axis
a1
3-fold rotation axes
high symmetry locations are good candidates for
lattice points
3
B
A
4
C
A
5
AB
BABABA.
A
6
AC
CACACA.
A
7
(No Transcript)
8
AB
ABCABC.
C
9
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
10
AB
BABABA.
A
11
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
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
12
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
13
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
14
AB
ABCABC.
C
Cubic???
15
What are the unit cell dimensions?
a
face diagonal is close-packed direction
a1 a2 a3 a1 a2 a3 90
16
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)
17
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
18
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