Materials Engineering – Day 5

1
Materials Engineering Day 5

• Crystallinity in Metals
• Types of Metallic Crystals
• Face-centered cubic (FCC)
• Body-centered cubic (BCC)
• Hexagonal close-packed (HCP)
• Crystalline Imperfections
• Dislocations
• Edge
• Screw
• Mixed
• Relationship of Dislocations and Plasticity

2
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.

3
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.

4
Crystallinity in Metals

• First discovered, using x-ray diffraction, in the
  early years of the 1900s.
• 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.
• The close-packed plane.
• The unit cell.

5
 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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Close-Packed Planes

• Here is a picture close packed planes.
• Note that one set of atoms is close packed.
  Another set is not. Close packed planes are
  found in some, but not all, metal crystals.

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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...
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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)
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Atomic Packing Factor BCC
APF for a body-centered cubic structure 0.68
a
Adapted from Fig. 3.2(a), Callister 7e.
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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)
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Atomic Packing Factor FCC
APF for a face-centered cubic structure 0.74
maximum achievable APF
Adapted from Fig. 3.1(a), Callister 7e.
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FCC Stacking Sequence
ABCABC... Stacking Sequence 2D Projection
FCC Unit Cell
13
Hexagonal Close-Packed Structure (HCP)
ABAB... Stacking Sequence
3D Projection
2D Projection
Adapted from Fig. 3.3(a), Callister 7e.
6 atoms/unit cell
Coordination 12
ex Cd, Mg, Ti, Zn
APF 0.74
c/a 1.633
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Theoretical Density, r
Density ?
where n number of atoms/unit cell
A atomic weight VC Volume of unit
cell a3 for cubic NA Avogadros
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

a 4R/ 3 0.2887 nm
?theoretical
7.18 g/cm3
ractual
7.19 g/cm3
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Unit Cells Start with Face-Centered Cubic (FCC)
The lattice is the mathematical skeleton of the
crystal. It has points at each corner of the
cube and points in the center of each face. 4
atoms/cell. APF 74. It can be thought of as
close-packed planes stacked in sequence
ABCABCABC.
Aluminum, Gold, Silver, Copper, etc.
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Body-Centered Cubic (BCC)
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Hexagonal Close-Packed (HCP)
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Overview
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• 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

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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.

22
Slip Systems and Ductility
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!
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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

Adapted from Fig.4.14 (b), Callister 7e.

• Crystals grow until they meet each other

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Imperfections in Crystals

• Point imperfections
• Vacancy. Lattice point not occupied by an atom.
  Position of nearby atoms slightly affected.
• 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.
• Impurity atom interstitial. A much smaller
  atom is dissolved in the unoccupied space in the
  lattice. Eg. Carbon in iron as in steel.

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Polycrystalline Materials

• Grain Boundaries
• regions between crystals
• transition from lattice of one region to that of
  the other
• slightly disordered
• low density in grain boundaries
• high mobility
• high diffusivity
• high chemical reactivity

Adapted from Fig. 4.7, Callister 7e.
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Point Defects
Vacancies
-vacant atomic sites in a structure.
Self-Interstitials
-"extra" atoms positioned between atomic sites.
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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
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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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Line Defects - Dislocations

• The dislocation was first connected with plastic
  deformation in the 1930s. It was first observed
  experimentally in the late 1940s.
• Here is an edge dislocation. Observe extra ½
  plane.

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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 its
  motion, the value is about G/180. This agrees
  with experiment.
• Slip occurs locally by dislocation movement.

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Dislocation Motion

• Schematic, and picture of slip in a crystal.

Slip paralled to direction dislocation moves.
Dislocations Bubble raft movie
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More on Dislocations The screw dislocation.

• Various concepts

Slip produced by a screw dislocaton
Notice that slip is perpendicular to the
direction the dislocation moves.
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Imperfections in Solids

• Dislocations are visible in electron micrographs

Adapted from Fig. 4.6, Callister 7e.
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Dislocations can have both edge and screw
components.

• It is handy to think of a dislocation as a loop.
• The more the dislocation moves, the more the loop
  expands.
• As the loop expands and gets longer, the
  dislocation density increases.
• Dislocation density increases inevitably with
  plastic deformation.
• Dislocation density before plastic deformation is
  about 1010 m-2.
• Dislocation density after plastic deformation is
  about 1015 m-2.

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Secret to understanding how to make metals strong.

• BLOCK THAT DISLOCATION!
• If a dislocation moves easily through the crystal
  structure of the metal, it will be weaker than if
  there are obstruction, effects that create
  thermodynamic road blocks which impede the
  dislocation motion.
• You can see that two edge dislocations will repel
  each other. This is the kind of thing that we
  will be talking about.