Compare long range and short range order:
Noble Gas: No regular ordering
Water/Silica: Some short range ordering
Metals: Crystaline, lattice structure that repeats 100’s or 1000’s of times
What is a lattice?
A lattice refers to a repeating, three-dimensional (3D) structure where atoms are arranged in a periodic pattern.
This differs from a polymer chain, as they are not periodic in nature
What is a unit cell?
The single basis lattice pattern, that when duplicated and translated, produces the entire crystal structure
What is a lattice parameter?
axial lengths: a, b, c
angles between axis: α, β, γ
What defines allotropic?
refers to pure elements that can have more than
one crystal structure.
What defines polymorphic?
refers to compounds that can have more than
one crystal structure.
What are polymorphic transformations?
Same material that have different atomic structures.
Example:
Iron is BCC at lower temps and FCC at higher temps
What is coordination number?
How many atoms are in
contact with a particular atom
What is the Procedure for Finding Miller Indices for
Directions?
- Determine the indices for two points lying in the direction of interest.
- Subtract the “tail” coordinates from the “head” coordinates.
- Clear fractions and/or reduce to lowest integers.
- Enclose the numbers in square brackets [], negative signs on top
What are Directions of a Form?
implies that what is seen in each of these directions is identical.
“Directions of a form” are indicated by <chevrons></chevrons>
Example:
< 1 0 0 > === [1 0 0] => [0 1 0] => [0 0 1] => negative variants
What is Repeat Distance?
Distance between lattice points along a
certain direction
What is Linear Density?
lattice points / unit length along a direction.
What is Packing Fraction?
Fraction of direction covered by atoms
(linear density * 2r)
What is the Procedure for Finding Miller Indices for Planes in Cubic Systems?
- Determine the points at which the plane intercepts the x, y, and z axes. If it intersects the origin, move the origin.
- Take reciprocals of these intercepts.
- Clear fractions but do NOT reduce to lowest integers.
- Enclose the numbers in parentheses () with negative signs on top
- Planes and their negatives are identical.
- Planes and their multiples are not identical.
- Planes and directions with identical Miller Indices are perpendicular to each other.
- Planes of a Form are indicated by curly brackets {}
What is the Procedure for finding Miller Indices for Directions using a 3-axis system in HCP?
- Determine the indices for two points lying in the direction of interest.
- Subtract the “tail” coordinates from the “head” coordinates.
- Clear fractions and/or reduce to lowest integers.
- Enclose the numbers in square brackets [] with negative signs on top
What is the Procedure for finding Miller Indices for Directions using a 4-axis system?
- Determine how many lattice parameters you must move in 2 of
the 3 in-plane directions to get from the tail to the head of the vector.
(Hint: choose the two axes not aligned with the direction of interest). - Designate these as (h,k,i,l).
- Calculate that h+k = -i.
- Clear fractions and/or reduce to lowest integers.
- Enclose the numbers in square brackets [], with negative signs appearing on top of the numbers.
What is Procedure for finding Miller Indices for directions using a 4-axis system OUT-OF-PLANE directions?
- Follow the previous procedure for finding the direction of the in-plane component of the direction.
- See how much you overshot with inplane direction, divide by magnitude.
- Add the distance in the c direction.
- Clear fractions and/or reduce to lowest integers.
- Enclose the numbers in square brackets [], with negative signs on top
What is the Procedure for finding Miller Indices for Planes using a 4-axis system?
- Find the intercepts of the plane with all three of the basal plane axes as well as the intercept with the c axes.
- Take the reciprocals.
- Clear fractions.
- Check the relation i = - (h+k)
where h is associated with a1,
k with a2, i with a3, and l with c. - Enclose 4-indices in parenthesis: (h k i l) .
What’s the deal with ABABAB vs ABCABC stacking?
One almost can do magic. Abacadaba!
