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.

Levels of Atomic Levels of Atomic ArrangementArrangement

Definitions

Amorphous

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

Crystalline

• Long range order of atoms

Unit Cell

• Basic building block of Crystal Structure

• Repeated through space

• Like a Lego piece in a Lego building

Describing the Crystal Describing the Crystal LatticeLattice

• Lattice Points

• Lattice Parameters– a, b, c, describe length of

sides– describe angles

between sides

Bravais LatticesBravais Lattices

Common Crystal Structures of MetalsCommon Crystal Structures of Metals

Body Centered CubicBody Centered Cubic

Example - Steel

Common Crystal Structures of MetalsCommon Crystal Structures of Metals

Face Centered CubicFace Centered Cubic

Example – aluminum and steel

Common Crystal Structures of MetalsCommon Crystal Structures of Metals

Hexagonal Close PackedHexagonal Close Packed

Example – titanium, some ceramics

Coordinates of PointsCoordinates of Points

Miller Indices - DirectionsMiller Indices - Directions

1 – Identify the location (coordinates of points) for the arrow head and tail.2- Subtract the head from the tail3- Clear any fractions4- Put a line over any negative values5- Enclose in “[ ]”

Group work

• Use Miller Indices to identify the following directions

(011)

(100)

(101)

(110)

(001)

(010)

• 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?

(011)

(100)

(101)

(110)

(001)

(010)

Directions of Form

• Generic directions – ex diagonal of the face

Directions of Form

• Generic directions can be noted using < > instead of [ ];

Close packed direction

• Direction on a unit cell in a crystal where all of the atoms are touching!

• For FCC this is the <101>

• For BCC this is <111>

Miller Indices - PlanesMiller 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.

Group Work• Determine the Miller Indices for

the following plane

1/31/3

• 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

• 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

• 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

Planes of FormPlanes of Form

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?)

Close packed plane is of the form {111} see previous example

This

Looks like this….

Close Packed PlanesClose Packed Planes

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 => easier to plastic deform…think of Aluminum and Steel…does this make sense?

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?

Unit Cell 1

Unit Cell 2 Unit Cell 4

Unit Cell 3

Atom 1

Repeat Distance – Distance between two atoms

Repeat distance = ½ diagonal of

face

Repeat distance =

lattice parameter

Describing the Packing Describing the Packing Efficiency of aCrystal Efficiency of aCrystal

LatticeLattice• Coordination Number – number of

nearest neighbors – speaks to how efficiently packed a unit cell is

• Packing Fraction– Linear – Planar

• Density– Linear– Planar– Material

Miller-Bravais IndicesMiller-Bravais Indices

Development of a Grain Development of a Grain StructureStructure

• 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 => small grains

– fast growth rate => large grains

– grain structure affects mechanical properties