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 in bulk and Metglas in ribbon, but still a niche market.

4. 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.
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

6. 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.

7. 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...

8. 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)

9. Atomic Packing Factor: BCC
• APF for a body-centered cubic structure = 0.68 a 3 a a 2
length = 4R =
Close-packed directions:
3 a
Adapted from
Fig. 3.2(a), Callister 7e.
APF = 4 3 p (
a/4 ) 2
atoms
unit cell
atom
volume a

10. 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)

11. Atomic Packing Factor: FCC
• APF for a face-centered cubic structure = 0.74 a
2 a
maximum achievable APF
Close-packed directions:
length = 4R =
2 a
Unit cell contains:
6 x 1/2 + 8 x 1/8 =
4 atoms/unit cell
Adapted from
Fig. 3.1(a),
Callister 7e.
APF = 4 3 p ( 2
a/4 )
atoms
unit cell
atom
volume a

12. FCC Stacking Sequence • ABCABC... Stacking Sequence • 2D Projection
A sites B C
sites A B
sites C A C A A B C
• FCC Unit Cell

13. Hexagonal Close-Packed Structure (HCP)
• ABAB... Stacking Sequence
• 3D Projection
• 2D Projection c a
A sites B
sites
Bottom layer
Middle layer
Top
layer
Adapted from Fig. 3.3(a),
Callister 7e.
• Coordination # = 12
6 atoms/unit cell
• APF = 0.74
ex: Cd, Mg, Ti, Zn
• c/a = 1.633

14. Theoretical Density, r Cell Unit of Volume Total in Atoms Mass
VC NA
n A
 =
where n = number of atoms/unit cell
A = atomic weight
VC = Volume of unit cell = a3 for cubic
NA = Avogadro’s number
= x 1023 atoms/mol

15. Theoretical Density, r  = Ex: Cr (BCC) A = 52.00 g/mol R = 0.125 nm
a = 4R/ 3 = nm
 = a 3
52.00 2
atoms
unit cell
mol g
volume
6.023 x 1023
theoretical
= 7.18 g/cm3
ractual
= 7.19 g/cm3

16. 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.

17. Body-Centered Cubic (BCC)

18. Hexagonal Close-Packed (HCP)

19. Overview Type Name Properties Example FCC Face-Centered-cubic
Ductile at all temps
Aluminum, copper, Nickel
BCC
Body-centered-cubic
ductile-brittle transition with temp or strain rate
Iron (steel) tungsten
HCP
Hexagonal-close-packed
less ductile
Magnesium, zinc

20. 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

21. 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
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!

23. 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
crystals growing
grain structure
liquid
Adapted from Fig.4.14 (b), Callister 7e.
Crystals grow until they meet each other

24. 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.

25. 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.

26. Point Defects Vacancy self- interstitial
• Vacancies:
-vacant atomic sites in a structure.
Vacancy
distortion
of planes
• Self-Interstitials:
-"extra" atoms positioned between atomic sites.
self-
interstitial
distortion
of planes

27. 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.

28. Area Imperfections
The most common area imperfections are grain boundaries. (The grains adhere tightly.)
photomicrograph

29. Imperfections in Solids
Edge Dislocation
Fig. 4.3, Callister 7e.

30. Imperfections in Solids
Screw Dislocation
Screw Dislocation b
Dislocation
line
Burgers vector b
(b)
(a)
Adapted from Fig. 4.4, Callister 7e.

31. Line Defects - Dislocations
The dislocation was first connected with plastic deformation in the 1930’s. It was first observed experimentally in the late 1940’s.
Here is an edge dislocation. Observe extra ½ plane.

32. 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.

33. Dislocation Motion Schematic, and picture of slip in a crystal.
Slip paralled to direction dislocation moves.
Dislocations
Bubble raft movie

34. 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.

35. Imperfections in Solids
Dislocations are visible in electron micrographs
Adapted from Fig. 4.6, Callister 7e.

36. 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.

37. 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.