1. Crystalline Structure of Metals

2. ISSUES TO ADDRESS... • How do atoms assemble into solid structures?
• How does the density of a material depend on
its structure?
• When do material properties vary with the
atom(i.e., part) orientation?

3. Concept
is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of these elements. Allotropes are different structural modifications of an element;[1] the atoms of the element are bonded together in a different manner.
is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties (absorbance, refractive index, conductivity, tensile strength, etc.) An example of anisotropy is the light coming through a polarizer. Another is wood, which is easier to split along its grain than against it.

4. Energy and Packing • Non dense, random packing
typical neighbor
bond length
bond energy
• Dense, ordered packing
Energy r
typical neighbor
bond length
bond energy
Dense, ordered packed structures tend to have lower energies.

5. Materials and Packing Si Oxygen Crystalline materials...
• atoms pack in periodic, 3D arrays
• typical of:
-metals
-many ceramics
-some polymers
crystalline SiO2
Adapted from Fig. 3.23(a),
Callister & Rethwisch 8e. Si
Oxygen
Noncrystalline materials...
• atoms have no periodic packing
• occurs for:
-complex structures
-rapid cooling
"Amorphous" = Noncrystalline
noncrystalline SiO2
Adapted from Fig. 3.23(b),
Callister & Rethwisch 8e.

6. 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

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. Simple Cubic Structure (SC)
• Rare due to low packing density (only Po has this structure)
• Close-packed directions are cube edges.
• Coordination # = 6
(# nearest neighbors)

9. Atomic Packing Factor (APF)
Volume of atoms in unit cell*
APF =
Volume of unit cell
*assume hard spheres
• APF for a simple cubic structure = 0.52
close-packed directions a
R=0.5a
contains 8 x 1/8 = 1
atom/unit cell
atom
volume
atoms
unit cell 4 3 p
(0.5a) 1
APF = 3 a
unit cell
volume

10. 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 & Rethwisch 8e.
2 atoms/unit cell: 1 center + 8 corners x 1/8

11. Atomic Packing Factor: BCC
• APF for a body-centered cubic structure = 0.68 a R a 3 a a 2
length = 4R =
Close-packed directions:
3 a
Adapted from
Fig. 3.2(a), Callister & Rethwisch 8e.
APF = 4 3 p (
a/4 ) 2
atoms
unit cell
atom
volume a

12. 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 & Rethwisch 8e.
4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8

13. 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 & Rethwisch 8e.
APF = 4 3 p ( 2
a/4 )
atoms
unit cell
atom
volume a

14. 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

15. 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 & Rethwisch 8e.
• Coordination # = 12
6 atoms/unit cell
• APF = 0.74
ex: Cd, Mg, Ti, Zn
• c/a = 1.633

16. The reason that metals form different crystal structures is to minimize the energy required to fill space
At different temperatures the same metal may form different structures

17. Theoretical Density, r Density =  = n A  = VC NA
Cell
Unit of
Volume
Total in
Atoms
Mass
Density =  =
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

18. Theoretical Density, r  = a R Ex: Cr (BCC) A = 52.00 g/mol
R = nm
n = 2 atoms/unit cell
a = 4R/ 3 = nm
Adapted from
Fig. 3.2(a), Callister & Rethwisch 8e.
 = a3
52.00 2
atoms
unit cell
mol g
volume
6.022 x 1023
theoretical
= 7.18 g/cm3
ractual
= 7.19 g/cm3

19. Densities of Material Classes
In general
Graphite/ r
metals r
ceramics r
polymers
Metals/
Composites/
>
>
Ceramics/
Polymers
Alloys
fibers
Semicond 30
Why? B
ased on data in Table B1, Callister
Metals have...
• close-packing
(metallic bonding)
• often large atomic masses 2
Magnesium
Aluminum
Steels
Titanium
Cu,Ni
Tin, Zinc
Silver, Mo
Tantalum
Gold, W
Platinum
*GFRE, CFRE, & AFRE are Glass,
Carbon, & Aramid Fiber-Reinforced
Epoxy composites (values based on
60% volume fraction of aligned fibers 10
in an epoxy matrix). G
raphite
Silicon
Glass -
soda
Concrete
Si nitride
Diamond
Al oxide
Zirconia
Ceramics have...
• less dense packing
• often lighter elements 5 3 4
(g/cm ) 3
Wood
AFRE *
CFRE
GFRE*
Glass fibers
Carbon
fibers A
ramid fibers H
DPE, PS
PP, LDPE PC
PTFE
PET
PVC
Silicone
Polymers have...
• low packing density
(often amorphous)
• lighter elements (C,H,O) r 2 1
Composites have...
• intermediate values
0.5
0.4
0.3
Data from Table B.1, Callister & Rethwisch, 8e.

20. Crystals as Building Blocks
• Some engineering applications require single crystals:
-- diamond single
crystals for abrasives
-- turbine blades
Fig. 8.33(c), Callister & Rethwisch 8e. (Fig. 8.33(c) courtesy of Pratt and Whitney).
(Courtesy Martin Deakins,
GE Superabrasives, Worthington, OH. Used with permission.)
• Properties of crystalline materials
often related to crystal structure.
-- Ex: Quartz fractures more easily along some crystal planes than others.
(Courtesy P.M. Anderson)

21. Single vs Polycrystals
E (diagonal) = 273 GPa
E (edge) = 125 GPa
• 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.
-If grains are textured,
anisotropic.
200 mm

22. Grains and Grain Boundaries
When molten metal solidifies, crystals begin for form independently of each other. They have random and unrelated orientations. Each of these crystals grows into a crystalline structure or GRAIN.
The number and size of the grains developed in a unit volume of the metal depends on the rate at which NUCLEATION (the initial stage of crystal formation) takes place
Schematic illustration of the stages during the solidification of molten metal; each small square represents a unit cell. (a) Nucleation of crystals at random sites in the molten metal; note that the crystallographic orientation of each site is different. (b) and (c) Growth of crystals as solidification continues. (d) Solidified metal, showing individual grains and grain boundaries; note the different angles at which neighboring grains meet each other.

23. Characteristic of Grain Growth
Rapid cooling – smaller grains
Slow cooling – larger grains
Grain boundaries – the surfaces that separate individual grains
Grain size- at room temperature a large grain size is generally associated with low strength, low hardness, and low ductility (ductility is a solid material's ability to deform under tensile stress)
Grain size is measured by counting the number of grains in a given area or by counting the number of grains that intersect a length of line randomly drawn on an enlarged photograph of the grains

24. Anisotropy
Metal properties are different in the vertical direction from those in the horizontal direction
It influences both mechanical and physical properties of metals
Strength is higher for metals with small grains because…
they have larger grain-boundary surface area per unit volume of metal hence more entanglements of dislocations
Plastic deformationis irreversible becauseof the irregular dislocation entanglements which form during its course. Hardening resultsfrom thedeformation process

25. Virtual Materials Science & Engineering (VMSE)
• VMSE is a tool to visualize materials science topics such as
crystallography and polymer structures in three dimensions

26. VMSE: Metallic Crystal Structures & Crystallography Module
• VMSE allows you to view crystal structures, directions, planes, etc. and manipulate them in three dimensions

27. Unit Cells for Metals FCC Structure HCP Structure
• VMSE allows you to view the unit cells and manipulate
them in three dimensions
• Below are examples of actual VMSE screen shots
FCC Structure
HCP Structure

28. VMSE: Crystallographic Planes Exercises
Additional practice on indexing crystallographic planes

29. X-Rays to Determine Crystal Structure
• Incoming X-rays diffract from crystal planes.
reflections must
be in phase for
a detectable signal
spacing
between
planes d
incoming
X-rays
outgoing X-rays
detector q l
extra
distance
travelled
by wave “2”
“1”
“2”
X-ray
intensity
(from
detector) q c
d =
n l
2 sin
Measurement of critical angle, qc, allows computation of planar spacing, d.

30. X-Ray Diffraction Patternz x y a b c z x y a b c z x y a b c
(110)
(211)
Intensity (relative)
(200)
Diffraction angle 2q
Diffraction pattern for polycrystalline a-iron (BCC)
Adapted from Fig. 3.22, Callister 8e.

31. SUMMARY • Atoms may assemble into crystalline or amorphous structures.
• Common metallic crystal structures are FCC, BCC, and
HCP. Coordination number and atomic packing factor
are the same for both FCC and HCP crystal structures.
• We can predict the density of a material, provided we
know the atomic weight, atomic radius, and crystal
geometry (e.g., FCC, BCC, HCP).

32. SUMMARY • Materials can be single crystals or polycrystalline.
Material properties generally vary with single crystal
orientation (i.e., they are anisotropic), but are generally
non-directional (i.e., they are isotropic) in polycrystals
with randomly oriented grains.
• Some materials can have more than one crystal
structure. This is referred to as polymorphism (or
allotropy).
• X-ray diffraction is used for crystal structure and
interplanar spacing determinations.

33. Mechanical Working of Metal

34. Introduction
Mechanical working of metal is defined as an intentional deformation of metals plastically under the action of externally applied force.
Mechanical working of metals is described as:
1. Hot working
2. Cold working

35. Hot Working
The working of metal above the recrystallization temperature is called hot working .
Hot working of metal has following advantage :
1. The porosity of metal largely eliminated .
2. The grain structure of metal is refined .
3. The mechanical properties such as toughness, ductility improved .
4. The deformation of metal is easy.

36. Recrystallization Temperature
Recrystallization is a process in which at a certain temperature range , a new equiaxed & stress free grains are formed . Recrystallization temperature is generally defined as temperature at which complete recrystallization occurs within approximately one hour.

37. Cold Working
Cold working refers to the process of strengthening a metal by plastic deformation.
Also referred to as work hardening, the metal working technique involves subjecting metal to mechanical stress so as to cause a permanent change to the metal's crystalline structure.
The technique is most commonly applied to steel, aluminum and copper.
When these metals are cold worked permanent defects change their crystalline make-up.
These defects reduce the ability of crystals to move within the metal structure and the metal becomes more resistant to further deformation.
The resulting metal product has improved tensile strength and hardness, but less ductility.
The process gets its name because it is conducted at temperatures below the metal's recrystallization point and mechanical stress, not heat, is used to affect change.

38. Advantages of cold working :
1. Residual stresses set up in the metal
2. Strength and hardness of metal are increased.
3. Surface finish improved .
4. Close dimensional tolerances maintained.
Disadvantages …
 Cold working distorted the material
 Requires much higher pressures than hot working .

39. Metal forming processes
 Rolling
 Forging
 Extrusion
 Tube and Wire Drawing
 Deep Drawing
Forging is the process in which the work piece is shaped by compressive forces applied through the various dies and tools . Typically forged product are bolts and rivets , connecting rods , shafts for turbine etc.
In Extrusion Process, a billet is forced through a Die, in a manner similar to squeezing toothpaste from tube. Typical products made by extrusion are tubing's having various cross-sections, structural and architectural shapes.
In Drawing, the cross-section of a round rod, or wire is typically reduced by pulling it through a die. High carbon steel wires for springs , wires for musical instruments.

40. Sequence of operations