CHAPTER 3: CRYSTAL STRUCTURES

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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?
BCC FCC
HCP
From Section 7.4 For a particular
crystal structure, the slip plane is the plane
that has the most dense atomic packing--that is,
has the greatest planar density. The slip
direction corresponds to the direction in this
plane that is most closely packed with
atoms--that is, has the highest linear density.
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MATERIALS AND PACKING
Crystalline materials...
atoms pack in periodic, 3D arrays typical
of
-metals -many ceramics -some polymers
crystalline SiO2
Adapted from Fig. 3.18(a), Callister 6e.
Noncrystalline materials...
atoms have no periodic packing occurs for
-complex structures -rapid cooling
noncrystalline SiO2
"Amorphous" Noncrystalline
Adapted from Fig. 3.18(b), Callister 6e.
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ENERGY AND PACKING
Non dense, random packing
Dense, regular packing
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Solidification
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DENSITIES OF MATERIAL CLASSES
Metals Ceramics Polymers
Data from Table B1, Callister 6e.
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Common Crystal Structures in Metals
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SIMPLE CUBIC STRUCTURE (SC)
Rare due to poor packing (only Po has this
structure) (what element is this?) ?
Does NOT occur in common engineering metals
Close-packed directions are cube edges.
Coordination 6 ( nearest neighbors)
(Courtesy P.M. Anderson)
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ATOMIC PACKING FACTOR
APF for a simple cubic structure 0.52
Coordination
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BODY CENTERED CUBIC STRUCTURE (BCC)
Close packed directions are cube diagonals.
--Note All atoms are identical.
Coordination
APF
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FACE CENTERED CUBIC STRUCTURE (FCC)
HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)
Close packed directions are face diagonals.
Coordination
APF
Coordination
APF
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Close-Packed Crystal Structures

• The only difference between the FCC and HCP
  structures is the sequence of stacking the
  densely packed planes

HCP?
FCC?
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Classifying Crystal Structure a) Crystal
system, b) Coordination number
Ortho-rhombic Monoclinic Triclinic
Cubic Hexagonal Tetragonal Rhombohedral
Coordination Number
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Classifying Crystal Structure c) Atomic packing
factor, d)density
Let material be Aluminum (Atomic radius 0.1431
nm) which has a unit cell as shown. What is the
theoretical density of aluminum? How does this
compare to the measured density?
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Classifying Crystal Structure e) Linear density,
f) planar density
Find the planar density in the plane defined by
the four corners circled in red
Find the linear density for the direction shown
below
Why are we doing this?
For this direction, the direction vector through
the unit cell crosses 3 atoms. Two of these are
shared with 1 other unit cell in this direction
(this is tricky, think about it)