Crystalline Structures

CHAPTER 3: CRYSTAL
STRUCTURES & PROPERTIES
ISSUES TO ADDRESS...
• How do atoms assemble into solid structures?
(for now, focus on metals)
• How does the density of a material depend on its structure?
• When do material properties vary with the sample (i.e., part) orientation?

Chapter 3- 1

ENERGY AND PACKING
• Non dense, random packing

Energy typical neighbor bond length

typical neighbor bond energy

• Dense, regular packing

r

Energy typical neighbor bond length

typical neighbor bond energy

r

Dense, regular-packed structures tend to have lower energy.
Chapter 3- 2

MATERIALS AND PACKING
Crystalline materials...
• atoms pack in periodic, 3D arrays
• typical of: -metals
-many ceramics
-some polymers

crystalline SiO2
Adapted from Fig. 3.22(a),
Callister 7e.

Si

Oxygen

Noncrystalline materials...
• atoms have no periodic packing
• occurs for: -complex structures
-rapid cooling
"Amorphous" = Noncrystalline

noncrystalline SiO2
Adapted from Fig. 3.22(b),
Callister 7e.
Chapter 3- 3

METALLIC CRYSTALS
• tend to be densely packed.
• have several reasons for dense packing:
-Typically, only one element is present, so all atomic radii are the same.
-Metallic bonding is not directional.
-Nearest neighbor distances tend to be small in order to lower bond energy.

• have the simplest crystal structures.
We will look at three such structures...

Chapter 3- 4

Chapter 3-

α=β==90o

Cubic

a=b=c

Hexagonal

a=b≠c α=β=90o,=120o

Tetragonal

a=b≠c

Rhombohedral a=b=c

α=β==90o α=β=≠ 90o

Orthorrhombic a≠b≠c α=β==90o
Monoclinic
Triclinic

a≠b≠c α==90o,β ≠ 90o a≠b≠c α≠β≠≠90o

Chapter 3-

SIMPLE CUBIC STRUCTURE (SC)
• Rare due to poor packing (only Po has this structure)
• Close-packed directions are cube edges.
• Coordination # = 6
(# nearest neighbors)

(Courtesy P.M. Anderson)
Chapter 3- 5

ATOMIC PACKING FACTOR
APF =

Volume of atoms in