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• Crystallinity
– Unit Cell
– Crystallographic Points, Directions, and 
Planes.
• Noncrystallinity (Amorphous) 
STRUCTURES OF 
METALS
Issues To Address….
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• atoms pack in periodic, 3D arrays
Crystalline materials...
-metals
-many ceramics
-some polymers
• atoms have no periodic packing
Noncrystalline materials...
-complex structures
-rapid cooling
crystalline SiO2
noncrystalline SiO2"Amorphous" = Noncrystalline
Materials and Packing
Si Oxygen
• typical of:
• occurs for:
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• Non dense, random packing
• Dense, regular packing
Dense, regular-packed structures tend to have
lower energy.
Energy 
r 
typical neighbor 
 bond length 
typical neighbor 
 bond energy 
Energy 
r 
typical neighbor 
 bond length 
typical neighbor 
 bond energy 
Energy And Packing
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• 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.
Metallic Crystals
• Unit Cell is the basic structural unit of crystal 
structure. It is generally defined in terms of 
atom (ion) positions within a parallepiped 
volume. 
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Unit Cell
• The atomic order of 
the crystalline solids 
is represented by 
the cell
• Various structural 
units that describe 
the crystalline 
structure
• The simplest 
Structural Unit is the 
unit cell 6
• Rare due to poor packing (only Po has this structure)
• Close-packed directions are cube edges.
• Coordination # = 6 (# nearest neighbors)
Simple Cubic Structure (SC)
contains 8 x 1/8 = 
 1 atom/unit cell
close-packed directions
a
R=0.5a
2
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• Coordination # = 12
• Close packed directions are face diagonals.
--Note: All atoms are identical; the face-centered atoms are shaded
differently only for ease of viewing.
Face Centered Cubic Structure 
(FCC)
Unit cell contains: 
 6 x 1/2 + 8 x 1/8 
 = 4 atoms/unit cell
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• Coordination # = 8
• Atoms touch each other along cube diagonals.
--Note: All atoms are identical; the center atom is shaded
differently only for ease of viewing.
Body Centered Cubic Structure (BCC)
ex: Cr, W, Fe (α), Tantalum, Molybdenum
2 atoms/unit cell: 1 center + 8 corners x 1/8
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• Coordination # = 12
• ABAB... Stacking Sequence
• 3D Projection • 2D Projection
Hexagonal Close-Packed Structure 
(HCP)
6 atoms/unit cell
ex: Cd, Mg, Ti, Zn
c
a
A sites
B sites
A sites Bottom layer
Middle layer
Top layer
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Crystallographic directions
• Can determine atom positions in unit cell
• Certain direction in unit cell are important with 
respect to deformation in metals
• Metals deform in directions along which atoms 
are in closet contact
• Miller indices are used to describe these 
directions
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Point Coordinates (position)
Point coordinates for unit 
cell center are
a/2, b/2, c/2 ½ ½ ½
Point coordinates for 
unit cell corner are 111
z
x
y
a b
c
000
111
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Directions
• [uvw]
• Directions are vectors
• Neg. directions are 
possible
• Fractions may also be 
used
• [111]
y
x
z
3
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Crystallographic Directions
z
x
y
-
a3
a1
a2
z
-
a3
a1
a2
z
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Crystallographic Planes
z
x
y
a b
c
2. Miller Indices (110)
example a b c
z
x
y
a b
c
2. Miller Indices (100)
1. Intercepts 1 1 ∞
1. Intercepts 1/2 ∞ ∞
example a b c
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Crystallographic Planes (HCP)
• In hexagonal unit cells the same idea is used 
example a1 a2 a3 c
2. Miller-Bravais Indices (1011)
1. Intercepts 1 ∞ -1 1
a2
a3
a1
z
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• Most engineering materials are polycrystals.
• Each "grain" is a single crystal.
• If grains are randomly oriented,
overall component properties are not directional.
• Grain sizes typ. range from 1 nm to 2 cm
(i.e., from a few to millions of atomic layers).
1 mm
Polycrystals
Isotropic
Anisotropic
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• Single Crystals
-Properties vary with
direction: anisotropic.
-Example: the modulus
of elasticity (E) in BCC iron:
• Polycrystals
-Properties may/may not
vary with direction.
-If grains are randomly
oriented: isotropic.
(Epoly iron = 210 GPa)
-If grains are textured,
anisotropic.
200 μm
Single vs Polycrystals
E (diagonal) = 273 GPa
E (edge) = 125 GPa
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Polymorphism 
• Two or more distinct crystal structures for the same 
material (allotropy/polymorphism)
titanium
α, β-Ti
carbon
diamond, graphite 
BCC
FCC
BCC
1538ºC
1394ºC
912ºC
δ-Fe
γ-Fe
α-Fe
liquid
iron system