Materials Engineering – Day 5
• Crystallinity in Metals
• Types of Metallic Crystals
1. Face-centered cubic (FCC)
2. Body-centered cubic (BCC)
3. Hexagonal close-packed (HCP)
• Crystalline Imperfections
• Dislocations
1. Edge
2. Screw
3. Mixed
• Relationship of Dislocations and Plasticity
You need to know/be able to
• Describe the difference between amorphous
and crystalline and state how that structure
affects properties.
• Name the three most common types of unit
cells for metals and explain how the unit cell
affects properties
• State the relationship of dislocation motion
and planar slip on the behavior of metals, and
explain how it affects strength and ductility.
Amorphous
• No repeating structure (amorphous is pile of
bricks compared to a brick wall (crystalline))
• Must cool very rapidly from the liquid to prevent
diffusion or combine a number of incompatible
(size,crystal structure, electronegativity) atoms.
• Currently marketed by Liquidmetal
http://www.liquidmetal.com/index/ in bulk and
Metglas http://www.metglas.com/products in
ribbon, but still a niche market.
Crystallinity in Metals
• First discovered, using x-ray diffraction, in the
early years of the 1900’s.
• The crystallinity of metals is simple. Why?
Strong, non-directional, metallic bonding. (We
are not dealing with positive and negative ions of
different size.) We are dealing with spheres of
about the same size.
• It involves several concepts. Here are two of
them.
1. The close-packed plane.
2. The unit cell.
Section 3.4 – Metallic Crystal Structures
• How can we stack metal atoms to minimize empty
space?
2-dimensions
vs.
Now stack these 2-D layers to make 3-D structures
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Metallic Crystal Structures
• Tend to be densely packed.
• 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.
- Electron cloud shields cores from each other
• Have the simplest crystal structures.
We will examine three such structures...
7
Body Centered Cubic Structure (BCC)
• Atoms touch each other along cube diagonals.
--Note: All atoms are identical; the center atom is shaded
differently only for ease of viewing.
ex: Cr, W, Fe (), Tantalum, Molybdenum
• Coordination # = 8
Adapted from Fig. 3.2,
Callister 7e.
2 atoms/unit cell: 1 center + 8 corners x 1/8
(Courtesy P.M. Anderson)
8
Atomic Packing Factor: BCC
• APF for a body-centered cubic structure = 0.68
3a
a
2a
Close-packed directions:
R
atoms
unit cell
APF =
length = 4R =
a
Adapted from
Fig. 3.2(a), Callister 7e.
4
2
p ( 3 a/4 ) 3
volume
atom
3
a3
3a
volume
unit cell
9
Face Centered Cubic Structure (FCC)
• Atoms touch each other along face diagonals.
--Note: All atoms are identical; the face-centered atoms are shaded
differently only for ease of viewing.
ex: Al, Cu, Au, Pb, Ni, Pt, Ag
•
Coordination # = 12
Adapted from Fig. 3.1, Callister 7e.
4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8
(Courtesy P.M. Anderson)
10
Atomic Packing Factor: FCC
• APF for a face-centered cubic structure = 0.74
maximum achievable APF
Close-packed directions:
length = 4R =
2a
2a
Unit cell contains:
6 x 1/2 + 8 x 1/8
= 4 atoms/unit cell
a
Adapted from
Fig. 3.1(a),
Callister 7e.
atoms
unit cell
APF =
4
4
p ( 2 a/4 ) 3
3
a3
volume
atom
volume
unit cell
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FCC Stacking Sequence
• ABCABC... Stacking Sequence
• 2D Projection
B
A
A sites
B sites
B
C
B
C
B
B
C
B
B
C sites
• FCC Unit Cell
A
B
C
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Hexagonal Close-Packed Structure
(HCP)
• ABAB... Stacking Sequence
• 3D Projection
• 2D Projection
c
a
Top
layer
B sites
Middle layer
A sites
Bottom layer
Adapted from Fig. 3.3(a),
Callister 7e.
• Coordination # = 12
• APF = 0.74
A sites
6 atoms/unit cell
ex: Cd, Mg, Ti, Zn
• c/a = 1.633
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Theoretical Density, r
Mass of Atoms in Unit Cell
Total Volume of Unit Cell
Density = r =
r =
where
nA
VC NA
n = number of atoms/unit cell
A = atomic weight
VC = Volume of unit cell = a3 for cubic
NA = Avogadro’s number
= 6.023 x 1023 atoms/mol
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Theoretical Density, r
• Ex: Cr (BCC)
A = 52.00 g/mol
R = 0.125 nm
n=2
R
a
atoms
unit cell
r=
a = 4R/ 3 = 0.2887 nm
g
2 52.00
a 3 6.023 x 1023
mol
rtheoretical
= 7.18 g/cm3
ractual
= 7.19 g/cm3
volume
atoms
unit cell
mol
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Overview
Type
Name
Properties
Example
FCC
FaceCenteredcubic
Ductile at all
temps
Aluminum,
copper, Nickel
BCC
Bodycenteredcubic
ductile-brittle
transition with
temp or strain
rate
Iron (steel)
tungsten
HCP
Hexagonalclose-packed
less ductile
Magnesium, zinc
Grand Truth - Strengthening in metals
•
•
•
Yield strength is the onset of plastic flow
Plastic flow results from planar slip
Planar slip results from dislocation motion
Therefore
To increase Strength - Prevent/Impede Dislocation Motion
Ductility Corollary
• Impeding dislocation motion makes slip harder
• Lower slip means lower ductility
Therefore:
Increasing Strength generally Lowers Ductility
Concept of Slip
• Slip in metal crystals is the primary mechanism of
plastic deformation.
• Adjacent planes of atoms slip, or move past one
another. This deformation is not recoverable.
Atoms have new neighbors. It is plastic
deformation.
• A slip system consists of the most close-packed
planes in the crystal and the most close-packed
directions in that plane.
• Crystallographers have studied the geometry of
the crystals and here is the ranking.
Slip Systems and Ductility
Metal Crystalline
structure
Rank in terms of
slip systems
Typical Metal
Typical Ductility
FCC
1
Copper
Pure and annealed
60%
BCC
2
Iron (very Low
carbon steel – hot
rolled)
30%
HCP
3
Magnesium (cast)
6%
The basic ductility is going to be tied to the type of crystallinity. But,
ductility rises and falls within a material type due to the way the material is
processesed. This is a very important lesson!
Imperfections in Solids
• Solidification- result of casting of molten material
– 2 steps
• Nuclei form
• Nuclei grow to form crystals – grain structure
• Start with a molten material – all liquid
nuclei
•
liquid
crystals growing
grain structure
Adapted from Fig.4.14 (b), Callister 7e.
Crystals grow until they meet each other
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Imperfections in Crystals
• Point imperfections
1. Vacancy. Lattice point not occupied by an atom.
Position of nearby atoms slightly affected.
2. Impurity atom – substitutional. An atom of
approximately the same size can, and will, be
found filling a lattice point. Position of nearby
atoms is affected. Eg. Chromium in Iron as in
stainless steel.
3. Impurity atom – interstitial. A much smaller
atom is dissolved in the unoccupied space in the
lattice. Eg. Carbon in iron as in steel.
• Vacancies:
Point Defects
-vacant atomic sites in a structure.
Vacancy
distortion
of planes
• Self-Interstitials:
-"extra" atoms positioned between atomic sites.
selfinterstitial
distortion
of planes
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Point
Defects
in
Alloys
Two outcomes if impurity (B) added to host (A):
• Solid solution of B in A (i.e., random dist. of point defects)
OR
Substitutional solid soln.
(e.g., Cu in Ni)
Interstitial solid soln.
(e.g., C in Fe)
• Solid solution of B in A plus particles of a new
phase (usually for a larger amount of B)
Second phase particle
--different composition
--often different structure.
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Area Imperfections
• The most common area imperfections are grain
boundaries. (The grains adhere tightly.)
photomicrograph
Imperfections in Solids
Edge Dislocation
Fig. 4.3, Callister 7e.
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Imperfections in Solids
Screw Dislocation
Screw Dislocation
b
Dislocation
line
(b)
Burgers vector b
(a)
Adapted from Fig. 4.4, Callister 7e.
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Slip and Dislocation Motion
• It is possible to predict yield strength in perfect
crystals. The value is G/5. This would imply yield
in iron over 1,000,000 psi. Way too high! The
idea that all slip system atoms simultaneously
move in plastic deformation is not correct.
• Instead, if you look at a dislocation moving
through and producing one unit of slip by it’s
motion, the value is about G/180. This agrees
with experiment.
• Slip occurs locally by dislocation movement.
Dislocation Motion
• Schematic, and picture of slip in a crystal.
Slip paralled to
direction dislocation
moves.
Dislocations
Bubble raft movie
More on Dislocations – The screw
dislocation.
• Various concepts
Notice that slip is perpendicular to
the direction the dislocation moves.
Slip produced by a
screw dislocaton
Imperfections in Solids
Dislocations are visible in electron micrographs
Adapted from Fig. 4.6, Callister 7e.
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