recall engineering properties are a direct result of the structure of that material. microstructure:...
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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.
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Levels of Atomic Levels of Atomic ArrangementArrangement
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Definitions
Amorphous
• No long range order, short range atomic order (1 -2 atomic diameters)
Crystalline
• Long range order of atoms
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Unit Cell
• Basic building block of Crystal Structure
• Repeated through space
• Like a Lego piece in a Lego building
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Describing the Crystal Describing the Crystal LatticeLattice
• Lattice Points
• Lattice Parameters– a, b, c, describe length of
sides– describe angles
between sides
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Bravais LatticesBravais Lattices
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Common Crystal Structures of MetalsCommon Crystal Structures of Metals
Body Centered CubicBody Centered Cubic
Example - Steel
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Common Crystal Structures of MetalsCommon Crystal Structures of Metals
Face Centered CubicFace Centered Cubic
Example – aluminum and steel
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Common Crystal Structures of MetalsCommon Crystal Structures of Metals
Hexagonal Close PackedHexagonal Close Packed
Example – titanium, some ceramics
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Coordinates of PointsCoordinates of Points
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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 “[ ]”
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Group work
• Use Miller Indices to identify the following directions
(011)
(100)
(101)
(110)
(001)
(010)
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• 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)
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Directions of Form
• Generic directions – ex diagonal of the face
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Directions of Form
• Generic directions can be noted using < > instead of [ ];
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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>
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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.
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Group Work• Determine the Miller Indices for
the following plane
1/31/3
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• 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
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• 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
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• 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
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Planes of FormPlanes of Form
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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?)
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Close packed plane is of the form {111} see previous example
This
Looks like this….
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Close Packed PlanesClose Packed Planes
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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?
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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
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Repeat Distance – Distance between two atoms
Repeat distance = ½ diagonal of
face
Repeat distance =
lattice parameter
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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
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Miller-Bravais IndicesMiller-Bravais Indices
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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