1. ME 330 Engineering Materials
Lecture 5
Material Structure
Crystalline vs. Amorphous
Crystals and Crystallographic planes
Metallic structures (BCC, FCC, HCP)
Single Crystal vs. Polycrystalline Structure
Please read Chapter 3

2. Next Lecture ... Please read Chapter 4 Theoretical Strength
Point Defects
Linear Defects
Planar Defects
Volume Defects
Microscopy
Please read Chapter 4

3. Atomic Packing Crystalline: Amorphous
3-D arrangement of atoms in which every atom has the same geometrical arrangement of neighbors
Long-range, periodic array over large length scales
Most solids are crystalline (metals, most ceramics, some polymers)
Amorphous
Arrangement over which no long range order exists
Often clear - not enough order to diffract light
Rarely purely amorphous - have regions of crystallinity
Many polymers and some ceramics

4. Crystal Structure Definitions
Unit cell: Smallest repeating unit of the crystal.
Lattice: 3–D framework of a crystal where atoms are located
Lattice parameters: Dimensions (a,b,c) and angles (,,) of the lattice b c a   

5. Bravais Lattices French Crystallographer Bravais (1848)
7 crystal systems using primitive unit cells
Primitive - one lattice point at origin
14 distinguishable point lattices
P - simple
F - face centered
I - body centered
C - base centered
For now, interested in BCC, FCC, HCP
Metallic crystal structures
Metallic bond is non-directional
No restriction on nearest neighbors
Very dense packing
First need to collect some definitions
Tetragonal
FCC
Monoclinic
Rhombohedral
BCC
Cubic
Hexagonal
Orthorhomic
Triclinic
HCP

6. Crystallographic Directions
Determining direction indices
Start vector at crystal axis
Draw to any point in the 3-D crystal
Project vector on each xyz axes
measure a in x-direction
measure b in y-direction
measure c in z-direction
Multiply by common factor to achieve smallest integer value
Enclose in [ ] without commas
Negative directions indicated with -
Family of directions indicated by < >
Hexagonal crystals have 4 indices
x [100]
y [010] z
[001]
[111]
a = 1
b = ½
c = 0
[110]
[210]
When atoms “touch” this is close packed plane
In a cubic crystal, are
all in the <100> family.

7. Crystallographic Planes
Determining Miller indices
Look at plane in unit cell which does not pass through the origin
Determine length of planar intercept with each axes (again, a,b,c)
Take reciprocal of a,b,c
Reduce to smallest integer value
Enclose in ( ) without commas
Any parallel planes are equivalent
x [100]
y [010] z
[001]
c = 1/3
b = 1/2
a = 1
(123)
Bring in unit cells to show packing between HCP and FCC as well as different structures (BCC, FCC, HCP)
do in class assignment closely related to a homework problem z z y z x x
(012) -1

8. Crystallographic Planes
Important for understanding deformation
Important planes to note
The direction [hkl] is normal to the plane (hkl) for cubic systems only!
Negative directions indicated with -
Family of planes indicated by { }
x [100]
y [010] z
[001]
(110)
(111)
(100) x y z
{111} family
Bring in unit cells to show packing between HCP and FCC as well as different structures (BCC, FCC, HCP)
do in class assignment closely related to a homework problem

9. Crystal Characteristics
Cube length (a)- dimension of unit cell
Volume of unit cell - Vc= a3
Coordination number (Nc) - number of atoms in contact with a single atom (nearest-neighbors)
Atomic Packing Factor (APF) - fraction of solid sphere volume in a unit cell where
n = number atoms in a unit cell, R is radius of atom
True Density- weight per unit volume

10. Body Centered Cubic Structure
Atoms “touch” along body diagonal <111>
Cubic unit cell ( )
n = 2
Nc = 8
APF = 0.68
“ABAB” stacking
Iron (RT), Tungsten, Molybdenum, Chromium
{110}
{110} is the closest packed plane
When atoms “touch” this is close packed plane

11. Face Centered Cubic Structure
Atoms “touch” along face diagonal <110>
Cubic unit cell ( )
n = 4
Nc = 12
APF = 0.74
A “close-packed” structure
“ABCABC” stacking
Aluminum, Copper, Gold, Silver, Iron (high temp)*
{111}
{111} is the close packed plane
*Allotropic form- crystal structure depends on temperature and pressure

12. Hexagonal Close-Packed Structure
Hexagonal unit cell
n = 6
Nc = 12
APF = 0.74
A “close-packed” structure
“ABAB” stacking
Cadmium, Magnesium, Titanium, Zinc
{001}
{0001} is the close packed plane

13. Stacking of Close-Packed Planes
HCP (A-B-A)
FCC (A-B-C)
Can stack second plane in locations B or C
Can stack third plane in locations A or C
Difference between FCC and HCP?
FCC stacking sequences is ABCABC
HCP stacking sequence is ABABAB

14. Density Definitions Deformation depends on density
x [100]
y [010]
z [001]
Deformation depends on density
Examples for BCC crystal
Linear Density: Fraction of line length filled by atoms.
Planar Density: Total area of atoms in given unit plane.
Volumetric Density: Total volume of atoms in given unit cell. Same as APF.
[111] ao
[100] ao
(100)

15. Metals Are Polycrystalline

16. Macroscopic Packing (Single Crystal vs. Polycrystalline)
Though we show only single cube, these are small portion of larger, repeating structure
Single crystals can be grown to macroscopic size
Si crystals for microchips
GaAs wafers for semiconductors
Turbine blades for aircraft
Polycrystalline metals
Much more common than single crystals
Solidification from various sites leads to grains
Grains: Patches of single crystal material essentially randomly oriented with respect to each other
Grain boundary: Atomic mismatch in region between grains