Recall

1
Recall

• Engineering properties are a direct result of the
  structure of that material.
• Microstructure
• size, shape and arrangement of multiple crystals
  or mixture of different structures within a
  material
• has a great affect on mechanical properties.

2
Levels of Atomic Arrangement
3
Definitions

• Amorphous

• Crystalline

• No long range order, short range atomic order (1
  -2 atomic diameters)

• Long range order of atoms

4
Unit Cell

• Basic building block of Crystal Structure
• Repeated through space
• Like a Lego piece in a Lego building

5
Describing the Crystal Lattice

• Lattice Points
• Lattice Parameters
• a, b, c, describe length of sides
• a. b. g, describe angles between sides

6
(No Transcript)
7
Bravais Lattices
8
Common Crystal Structures of Metals
Body Centered Cubic
Example - Steel
9
(No Transcript)
10
Common Crystal Structures of Metals
Face Centered Cubic
Example aluminum and steel
11
Common Crystal Structures of Metals
Hexagonal Close Packed
Example titanium, some ceramics
12
(No Transcript)
13
Coordinates of Points
14
Miller Indices - Directions
1 Identify the location (coordinates of points)
for the arrow head and tail. 2- Subtract the
head from the tail 3- Clear any fractions 4- Put
a line over any negative values 5- Enclose in

15
Group work

• Use Miller Indices to identify the following
  directions

16

• 1 0 ½ - 0 ½ 1 1 -1/2 -1/2 2-1-1 (place
  line over neg values)
• 011 100 -111
• ½ 00 010 1/2 -1 0 1-20
• How did you do?

17
Directions of Form

• Generic directions ex diagonal of the face

18
Directions of Form

• Generic directions can be noted using lt gt instead
  of

19
(No Transcript)
20
Close packed direction

• Direction on a unit cell in a crystal where all
  of the atoms are touching!
• For FCC this is the lt101gt
• For BCC this is lt111gt

21
Miller Indices - Planes

•  
• Determine the intercepts of the plane on the
  crystallographic axes If the plane intercepts
  the axis at the origin, then the origin must be
  moved to another location, If the plane does not
  intersect a particular axes then the intercept is
  considered to be infinity.
• Take the reciprocal of the intercepts.
• Clear any fractions
• Enclose values of h, k and l in parenthesis,
  indicate negative values by placing a bar over
  that value.

22
Group Work

• Determine the Miller Indices for the following
  plane

1/3
1/3
23

• Example 1
• X infinity
• Y 1/3
• Z infinity
• Reciprocal
• X 0
• Y 3
• Z 0
• No fractions to clear, no negative values
• (030) planes parenthesis

24

• Example 2 (move origin to 001)
• X 1
• Y infinity
• Z - 1/3
• Reciprocal
• X 1
• Y 0
• Z -3
• No fractions to clear, negative values , put line
  over number
• (10-3) planes parenthesis

25

• Example 3 (move origin to 010)
• X 1
• Y -1
• Z 1
• Reciprocal
• X 1
• Y -1
• Z 1
• No fractions to clear, negative values , put line
  over number
• (1 -1 1) planes parenthesis

26
Planes of Form
27
Group Work

• Determine the Close Packed Plane for an FCC unit
  cell (draw it and use Miller indices to define)
• Determine the close packed plane for a BCC (hint
  this is a trick question, why?)

28
Looks like this.
This
Close packed plane is of the form 111 see
previous example
29
Close Packed Planes
30
Who Cares?

• The mechanism for plastic deformation most often
  occurs on close packed planes in close packed
  directions and that is why we care!!!
• More close packed planes and directions gt easier
  to plastic deformthink of Aluminum and
  Steeldoes this make sense?

31
Atoms per Unit Cell

• Atoms are shared between unit cells
• How many atoms/unit cell does a BCC crystal
  structure have?
• How many atoms/unit cell does an FCC crystal
  structure have?

32
Repeat Distance Distance between two atoms
33
Describing the Packing Efficiency of aCrystal
Lattice

• Coordination Number number of nearest neighbors
  speaks to how efficiently packed a unit cell is
• Packing Fraction
• Linear
• Planar
• Density
• Linear
• Planar
• Material

34
Miller-Bravais Indices
35
Development of a Grain Structure

• Crystals or grains small continuous volumes of
  solid
• Nucleus
• Basic lattice is repeated through space
• Grain boundaries
• Nucleation and growth
• Number and size of grains
• fast nucleation rate gt small grains
• fast growth rate gt large grains
• grain structure affects mechanical properties