Engineering 45
Crystalline
MicroStructure
Bruce Mayer, PE
Registered Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Learning Goals
 Learn How atoms assemble
into solid structures
•
Use metals as Prototypical Example
 Determine Relationship Between
Material density and material
MicroStructure
 Understand how material properties
vary with the sample (i.e., part)
orientation
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Properties of Solid Materials
 Mechanical: Characteristics of
materials displayed when Forces
and/or Moments are applied to them.
 Physical: Characteristics of materials
that relate to the interaction of materials
with various forms of Energy.
 Chemical: Material characteristics that
relate to the e− structure of a material.
 Dimensional: Size, shape, and finish
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Material Properties
Chemical
Physical
Mechanical
Dimensional
Composition
Microstructure
Phases
Grain Size
Corrosion
Melting Point
Thermal
Magnetic
Electrical
Optical
Tensile properties
Toughness
Ductility
Fatigue
Hardness
Standard Shapes
Standard Sizes
Surface Texture
Stability
Mfg. Tolerances
Crystallinity
Molecular Wt
Flammability
Acoustic
Gravimetric
Creep
Compression
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Energy and Atomic Packing
 NonDense, Random Packing
Energy
typical neighbor
bond length
typical neighbor
bond energy
 Dense Regular Packing
r
Energy
typical neighbor
bond length
r
 Regular Structures typical neighbor
bond energy
Tend to have
LOWER Energy → Energetically Favored
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Materials and Atomic-Packing
 CRYSTALLINE Materials
• atoms pack in periodic, 3D arrays
• typical of: Metals, many
Ceramics, and some Polymers
crystalline SiO2
 NONcrystalline Materials
• atoms have no periodic packing
• occurs for:
– Complex structures
– Rapid Cooling
 "Amorphous"  Noncrystalline
Engineering-45: Materials of Engineering
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noncrystalline SiO2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Crystal Basics
 Crystalline Material
• atomic arrangement
in solid:
– periodic and repeating
3D array
– Long Range Order
 Unit Cell  Smallest
Repeating Entity
Within a Lattice
• Geometry
lattice
Engineering-45: Materials of Engineering
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– Lattice Constants:
a, b, c
– interaxial angles:
a, b, g
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Crystal Structure
 Crystal Structure 
geometry + atom-positions
• i.e.; the spatial arrangement of Atoms,
Ions, or Molecules
 Some Types
Crystal Type
Face Centered Cubic (FCC)
Body Centered Cubic (CCC)
B
Hexagonal Close Packed (HCP
Typical Metal Typical Ceramics
Cu, Al
Cr, W
Ti, Zn
NaCl
CsCl
ZnS
polymer
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Example Crystal Systems
 Tab 3.2 In Text
Shows the 7 Most
Common Crystal
Systems
 Hexagonal
• a=bc
• a = b = 90°, g = 120°
• Some Examples
 Cubic
• a=b=c
• a = b = g = 90°
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Simple Cubic Stucture (SC)
Rotate
 Rare due to poor
packing (only Po
has this structure)
 Close-packed
directions are cube
edges.
 Coordination No. = 6
• CoOrd No. (CN) = the
No. of Nearest
Neighbors
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
 HardSphere Model
 Reduced Sphere Mod
Lattice Constants
InterAxial 's
a (pm) b (pm) c (pm) a  b  g 
335.9
335.9
335.9
90
90
90
 Note: 100 PicoMeters = 1 Å
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
http://www.webelements.com/webelements/index.html
http://www.webelements.com/webelements/elements/text/Po/key.html
http://www.webelements.com/webelements/elements/text/Po/xtal.html
Polonium, Z = 84, SC Structure
Atomic Packing Factor, APF
 Assuming HardSphere Model
Volume of ATOMS In a Unit Cell
APF 
TOTAL Volume of Unit Cell
 APF For Simple Cubic Structure = 52%
atoms
unit cell
a
R=0.5a
close-packed directions
contains 8 x 1/8 =
1atom/unit cell
Engineering-45: Materials of Engineering
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APF =
volume
atom
4
p(0.5a) 3
1
3
a3
volume
unit cell
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Body Centered Cubic (BCC)
 HardSphere Model
 Atoms per Unit Cell =
1 + (8 x 1/8) = 2
 CoOrd No. = 8
Rotate
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• 8 Atoms Touch the
“Center” Atom
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Atomic Packing Factor: BCC
 Find Radius, r, in
terms of Lattice
Const, a
 Thus r in Terms of a
3
3a  4r  r 
a  0.433a
4
 And Vsphere = (4/3)pR3
 So the BCC APF
 Atoms Touch On
Cube Diagonal, L
• L = a3 = L = 4r
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 4  3 3

3

2 at cell   p  a  m at 
3  4 


APF 
a 3 m3 cell
APFBCC  68.02%
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Face Centered Cubic (FCC)
 HardSphere Model
 Atoms per Unit Cell =
6x½ + (8 x 1/8) = 4
 CoOrd No. = 12
Rotate
Engineering-45: Materials of Engineering
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• CN = 4top + 4bot + 4mid
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Atomic Packing Factor: FCC
 Find Radius, r, in
terms of Lattice
Const, a
 Thus r in Terms of a
2 a  4r  r 
1
2 2
a  0.3536a
 And Vsphere = (4/3)pR3
 So the FCC APF
 Atoms Touch on
Face Diagonal, f
• f = a2 = 4r
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 4  1 3 3 
4 at cell   p 
a  m at 

3 2 2 


APF 
a 3 m3 cell
APFFCC  74.05%
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
FCC Stacking Sequence
 An ABCABC... Stacking Sequence
• The 2D
projection
A sites
B sites
B
A
B
C
B
C
B
B
C
B
B
C sites
 The FCC
Unit Cell
Engineering-45: Materials of Engineering
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A
B
C
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Hexagonal Close Packed (HCP)
 Built Up in an A-B
Stacking Pattern
 Exhibits NonCubic
Symmetry on a & c axes
• c:a Ratio  1.633
 Atoms per Cell = 6
• (12 x 1/6)corners +
(2 x ½)top/bot + 3mid = 6
c
 APF and CN are the
SAME as the FCC
Structure
• APF = 74.05%
a
Engineering-45: Materials of Engineering
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– Close Packed
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
HCP CoOrdination Number
 For 3 Stacking
Planes Below,
Consider the
CENTER Atom
 Observe The Center
Atom’s Nearest
Neighbors
• 6 Surrounding in the
Center Plane
• 3 Touching From Below
• 3 Touching From Above
 Thus
CN HCP  3  6  3  12
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Structure of Compounds
 Compounds: Often
have similar closepacked structures
 Expand Na+ ions to
Reveal Close-Packed
X-tal Structure
 NaCl Structure
• Ionic Radii
– Na+ = 116 pm
– Cl– = 167 pm
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Theoretical Density, r
 Atomic Radii for Crystals are Measured by
X-Ray Diffraction
• Can use The Data From XRD Measurements to
Calc Density for Crystals
Fcn of Ratom
 On the Macro Scale Densities are Calc’d by
Weight & Measure of Chunks of Crystals
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Theoretical Density Example
 For Copper
 FCC Cu has 4 atoms
per Unit Cell; so r
• Ratom = 128 pm
• Acu = 63.54 g/mol
nACu
r
VC N A
• Xtal Structure = FCC
4  63.54

3


16 2  128pm  6.023 10 23
 Recall From FCC
APF Calc
R
1
2 2

r  8.893 10 30 g/pm 3  8893 kg/m 3
a  a  2 2R
 rmacro = 8940 kg•m-3
 And The VC = a3


3
a  2 2R  8  2 2  R
3
Engineering-45: Materials of Engineering
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
3
•  0.53% HIGHER than
Theoretical Value
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Characteristics of Some
Elements
at
20
°C
Density
At. Weight
Element
Symbol (amu)
Aluminum Al
26.98
Argon
Ar
39.95
Barium
Ba
137.33
Beryllium
Be
9.012
Boron
B
10.81
Bromine
Br
79.90
Cadmium
Cd
112.41
Calcium
Ca
40.08
Carbon
C
12.011
Cesium
Cs
132.91
Chlorine
Cl
35.45
Chromium Cr
52.00
Cobalt
Co
58.93
Copper
Cu
63.55
Flourine
F
19.00
Gallium
Ga
69.72
Germanium Ge
72.59
Gold
Au
196.97
Helium
He
4.003
Hydrogen
H
1.008
Engineering-45: Materials of Engineering
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(g/cm3)
2.71
-----3.5
1.85
2.34
-----8.65
1.55
2.25
1.87
-----7.19
8.9
8.94
-----5.90
5.32
19.32
-----------
Atomic radius
(nm)
0.143
-----0.217
0.114
----------0.149
0.197
0.071
0.265
-----0.125
0.125
0.128
-----0.122
0.122
0.144
----------15
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Densities Of Material Classes
rmetals > rceramics > rpolymers
Why?
Metals have...
• close-packing
(metallic bonding)
• large atomic mass
Ceramics have...
• less dense packing
(covalent bonding)
• often lighter elements
Polymers have...
• poor packing
(often amorphous)
• lighter elements (C,H,O)
Composites have...
• intermediate values
Engineering-45: Materials of Engineering
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Data from Table B1, Callister 6e.
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
16
SINGLE Crystal Applications
 Most Crystalline
Materials Are
Composed of many
Small Crystals
• i.e., they are
POLYcrystalline and
exhibit a GRAIN
Structure
 Grain Structure
Introduces
Weakness into the
Material
Engineering-45: Materials of Engineering
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 But Making LARGE
Single Crystals is Very
Difficult; i.e., Expensive
 Single Xtal Examples
• SemiConductor
wafers
• Turbine
Blades
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
1-Material; Several Crystal Types
 Polymorphism  More Than One
Crystal Structure
• Often Found in Compounds
 Allotropy  Polymorphism in
ELEMENTAL Solids
 Examples
• Carbon Allotropes
– Graphite
– Diamond
– Bucky Balls/Tubes
Engineering-45: Materials of Engineering
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• Iron Allotropes
– BCC Ferrite (RT)
– FCC Austenite (> 912 °C)
– BCC Delta (~TMelt)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Cabon
Allotropes
 Graphite – Layers of
Hexagonally Bonded
C-atoms
 Diamond - tetrahedral,
covalent bonds, SingleElement Form; the
ZincBlende Crystal
structure
 C60 Fullerenes
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
WhiteBoard Work
 Example 
similar to P3.15
 → FIND APF
• Uranium
• Orthorhombic
• Lattice Constants
– a = 286 pm
– b = 587 pm
– c = 495 pm
• ratom = 138.5 pm
• r = 19050 kg/m3
• AU = 238.03 g/mol
Engineering-45: Materials of Engineering
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SR Case
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Uranium Unit Cell (BCR)
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Uranium Unit Cell (BC)
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Uranium Unit Cell (SR)
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
All Done for Today
Uranium has
the Highest Z
Of Any Natural
Element
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
P3-15
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-03_Crystal_Structure.ppt