Transcript Chemical Bonding - California Institute of Technology

Types of Primary Chemical Bonds
Isotropic, filled outer shells
• Metallic
– Electropositive: give up electrons
• Ionic
– Electronegative/Electropositive
• Colavent
– Electronegative: want electrons
+
+
e-
e+
+
+
+
+
+
+
+
-
+
-
+
-
+
-
+
e-
– Shared electrons along
bond direction
Close-packed
structures
mirror plane
Definitions
• Lattice point
• Unit cell
• Lattice
parameters
• Atoms per
unit cell
• Symmetry
operations
• Fractional
coordinates
• Coordination
number
(glide plane)
unit cell
not a unit cell
2-fold rotation axes
a2
a1
6-fold rotation axis
3-fold
rotation
axes
high symmetry locations are good candidates for lattice points
B
A
C
A
ABABABABA….
ACACACACA….
ABCABCABC….
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
ABABABABA….
2-D fractional coordinates
A at (0,0)
B at (2/3, 1/3)
C at (1/3, 2/3)
a2
A
c
A
C
B
a1
A
A
What are the unit cell dimensions?
let atomic radius be R |a1| = |a2| = 2R
R
A
2R
2R
3R  face diagonal = 23R = AA
A
AB = 1/3 (face diagonal) 
2
R
3
4 2
R  x2  4R2
3
8
x2  R2
3
x
8
R
3
½c
{
A
 c 2
8
R
3
2
R
3
B
C
A
Hexagonal Close-packed Structure
c 2
|a1| = |a2| = 2R
8
R
3
a1 = a2 = 90°; g = 120°
ideal:
c

a
8
3
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
lattice type of HCP is called “primitive hexagonal”
reminder: the hexagon is not an acceptable unit cell shape
HCP
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
ABCABCABC….
What are the unit cell dimensions?
a
face diagonal is
close-packed
direction
2a  4R
a  2 2R
|a1| = |a2| = |a3|
a1 = a2 = a3 = 90°
Cubic Close-packed Structure
|a1| = |a2| = |a3|  2 2R
a1 = a2 = a3
only one cell parameter to
be specified
coordination number?
12
atoms per unit cell?
4
lattice points per unit cell?
4
atoms per lattice point?
1
CCP
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)
Cubic “Loose-packed” Structure
Body-centered cubic (BCC)
a
coordination number?
8
atoms per unit cell?
2
lattice points per unit cell?
2
atoms per lattice point?
1
another example of a non-primitive cell
body diagonal is closestpacked direction
4

a

R
3a  4R
3
|a1| = |a2| = |a3|
a1 = a2 = a3 = 90°
lattice type of ‘CLP’ is “body-centered cubic”
no common name that distinguishes
lattice type from structure type
Summary: Common Metal Structures
hcp
ccp (fcc)
ABABAB
ABCABC
Hexagonal unit cell
Specify: a, c
Hexagonal implies:
|a1| = |a2| = a
g = 120°; a = b = 90°
bcc
not close-packed
Cubic unit cells
Specify: a
Cubic implies:
|a1| = |a2| = |a3| = a
a = b = g = 90°
Metals