Chapter 3 - Crystalline Structure Flashcards
Crystalline materials are often structures found in…
metals, ceramics, and some polymers
What are noncrystalline materials?
atoms that have no periodic packing.
What is another term for Noncrystalline?
Amorphous
What is a unit cell?
the smallest repeat unit of a crystal structure
How many atoms make up a simple cubic, FCC and BCC?
simple → 1 (8 corners)
BCC → 2 (8 corners & one in the middle)
FCC → 4 (6 halves, 8 corners)
What is the Atomic packing factor?
The volume of atoms/volume of a unit cell
What is the atomic packing factor for simple cubic
π / 6
What is the atomic packing factor for BCC?
π / (3 root(3))
What is the atomic packing factor for FCC?
3π / 8root(3)
to find the a to r value in a simple cubic unit cell
one side length (a) is 2 r
to find the a to r value in a BCC unit cell
find the length from one corner, to the farthest corner away (note across the x & y axis is a root(2)
to find the a to r value in an FCC unit cell
use the two side lengths b across the face and calculate the hypotenuse using r and a
What does this formula mean? what do each of the variables represent?
𝜌 = 𝑛𝐴 / 𝑉 C 𝑁 A
n = number of atoms/unit cell
A = atomic weight
VC = Volume of unit cell = a3 for cubic
NA = Avogadro’s number
= 6.022 x 1023 atoms/mol
List the densities of metals, ceramics, and Polymers from highest to lowest density.
Metals > ceramics > polymers
What are single crystals?
When the periodic arrangement of atoms (crystal structure) extends without interruption throughout the entire specimen.
What are polycrystals
Composed of many small crystals
or grains
What are the four different steps in the solidification of a polycrystalline material?
- small crystalline nuclei develop
- growth of crystallites
- formation of grains of irregular shapes
- grain boundaries
define Anisotropy?
A given property value depends on the crystallographic direction of measurement.
Are polycrystals isotropic or anisotropic when the grains are randomly oriented or if they are textured (preferential crystallographic orientation)?
isotropic, and anisotropic respectively
What is Polymorphism?
a material that can have multiple different crystal structures depending on the
conditions it is in (temperature, pressure etc.).
What temperatures and crystal structures form in iorn in particular temperatures
> 1538 °C → liquid
1538 - 1394 °C → BCC (δ -Fe)
1394 - 912 °C → FCC (γ -Fe)
< 912 °C → BCC (α -Fe)
oya
How to solve a crystallographic Direction problem (5 steps)
- Determine the coordinates of the vector tail and vector head
- Take the head coordinates and subtract the tail from them
- Normalize coordinate differences in terms of lattice parameters a, b, and c:
- Reduce to integer answers
- Enclose in square brackets, no commas
What is the formula for Linear Density?
number of atoms/unit length of direction vector
What is the algorithm used to find the crystallographic planes?
- Read off intercepts (x, y, z) of plane
- Take reciprocals of intercepts
- Reduce to smallest integer values
- Enclose in parentheses, no commas i.e., (hkl)
What is the equation for Planar Density?
atoms centers in a 2D plane / area of a 2D repeat unit
What does directional equivalency mean?
that every equivalent direction and plane have the same planar and linear densities.
What is the unit cell edge length for a face-centered cubic in terms of R?
a = 4R / root(2)
What is the unit cell edge length for a body-centred cubic in terms of R?
a = 4R / Root(3)
What is this formula?
p = N A / (VC NA
What are the terms in it?
p = density
n = number of equivalent atoms in a unit cell
A - atomic wieght
VC = Volume of a unit cell (always a3)
NA = Avogadro’s number 6.022 * 1023
How can you tell if something is isotropic or anisotropic?
if they have particular grains that run across the structure in an organized way (anisotropic) or are made of just one material (anisotropic). If the grains are random, or there is a ton of different metals inside, it is more likely to be isotropic.
Would a polycrystal or single crystal have more isotropic properties? Why?
A polycrystal would have more isotropic properties because of the random orientation of the ton of anisotropic grains. Whereas different loads on the same unit cells (which are mostly not isotropic) in a single crystal would not balance out, but magnify instead.
How would a material being a polycrystal change its real density compared to its theoretical
density?
the theoretical density would be higher, as the crystals are not as closely packed together on the grain boundaries.
Rate the following structures from most to least ordered (Crystalline, polycrystalline, and Amorphous)
Crystalline, polycrystalline, and Amorphous.
Describe what type of notation is nessesary around the indices of these following terms: Point, direction, family of directions, plane, and family of planes
point → 123
direction → [123]
family of directions → <123>
plane (123)
family of planes {123}
When counting atoms centred in a plane which atoms do you count?
How many atoms are in the plane,
When counting equivalent atoms centred in a plane which atoms do you count?
The portion of the atom inside the plane, excluding the part that would be cut off at the edges
Define a maximally dense (or close-packed) plane/direction.
Plane/direction has no void space.
Does it matter what side you draw the arrow in a direction?
no, while they might have different directions their magnitudes are the same.
What is the Volume of a sphere?
4/3 π r^3
