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 Arrangement

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 Lattice Lattice Points Lattice Parameters –a, b, c, describe length of sides –  describe angles between sides

Bravais Lattices

Common Crystal Structures of Metals Body Centered Cubic Example - Steel

Common Crystal Structures of Metals Face Centered Cubic Example – aluminum and steel

Common Crystal Structures of Metals Hexagonal Close Packed Example – titanium, some ceramics

Coordinates of Points

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 “[ ]”

Group work Use Miller Indices to identify the following directions

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?

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 For BCC this is

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.

Group Work Determine the Miller Indices for the following plane 1/3

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 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 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 2Unit Cell 4 Unit Cell 3 Atom 1

Repeat Distance – Distance between two atoms Repeat distance = ½ diagonal of face

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

Miller-Bravais Indices

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 => small grains –fast growth rate => large grains –grain structure affects mechanical properties