Chapter 3 Flashcards
Is random packing dense? Is the typical bond length or bond energy greater?
non-dense
bond radius greater (longer on x-axis)– makes sense
Is ordered packing dense? Is the typical bond length or bond energy greater?
ordered
bond energy is greater (think, they are closer together and organized)
What are the two types of packing?
random and ordered
What are crystalline materials?
Atoms arranged in periodic; 3D arrays
What are crystalline materials typical of?
metals
many ceramics
some polymers
Are most materials crystalline or noncrystalline?
most materials are crystalline
What are Noncrystalline materials?
atoms that have no periodic arrangement
When do noncrystalline materials occur?
complex structures
rapid cooling– if you’re moving from liquid to solid too quickly, it doesn’t give the liquid enough time to arrange itself in an orderly way
What is a characteristic of metallic crystal structures? Why?
they are dense
Reasons for dense packing:
1. bonds are nondirectional
2. nearest neighbor distances tend to be small in order to lower bond energy (random packing?)
3. high degree of shielding (of ion cores) provided by free electron cloud
Which material has the most simple crystal structure?
Metals
What does a simple cubic (SC) Crystal Structure look like?
Centers of atoms located at the eight corners of a cube
What is the only atom that has a Simple Cubic structure?
Po
What are the close-packed directions in a simple cubic?
the cube edges– the atoms touch here
What is the coordination # for a Simple Cubic?
6
Why does it matter where the atoms touch in a crystal structure?
Properties depend on where atoms touch
What is a coordination number?
The number of nearest neighbors
What is the atomic packing factor (APF)? How do you calculate it?
Atomic packing factor is an indication of how efficiently the atoms are packed in the unit cell
APR= [(# atoms)(Volume of atoms in unit cell– 4/3pie R^3)]/ (Volume of unit cell)
** where R is in terms of a
What is the APF for a simple cubic?
0.52
What are the R to a ratios for the different cubic structures?
Simple: R=1/2a
BCC: 4R= sqrt(3)a
FCC: 4R= sqrt(2)a
What does a body-centric cubic structure look like?
Atoms located at 8 corners with a single atom at cube center
Which elements have Body centric cubic structure?
5 elements
Cr, W, Fe, Ta, Mo
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What is the coordination number for BCC structure?
8
What is the atomic packing factor for a body centric cubic?
0.68
How many atoms are in the unit cell of a BCC?
2
What is the structure of a face-centered cubic (FCC)?
atoms located at 8 cube corners and the centers of the 6 faces
How many atoms are in the unit cell for FCC?
4
What is the coordination # for FCC?
12
Which elements have FCC structure?
7 elements
Al, Cu, Au, Pb, Ni, Pt, Ag
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Peanut butter night is partially aggravating
What is the atomic packing factor for FCC?
0.74
What is the plane stacking sequence for FCC?
ABCABC…
What are some characteristics of atomic stacking sequences?
Atoms can’t stack directly on top of each other
What stacking sequence does a hexagonal close-packed structure (HPC) have?
ABAB
What is the coordination number for HCP?
12
What is the APF for HCP?
0.74
How many atoms are in the unit cell for HPC?
6
What are elements with HPC structure?
4 elements
Cd, Mg, Ti, Zn
How do you calculate the theoretical density for metals p?
Density= (mass of atoms in unit cell)/(total volume of unit cell)
= (nA/Na)/Vc
In general, what is the order of densities for the different material type?
p meal > p cermics > p polymers
Why do metals have the highest density?
- close-packing (metallic bonding)
- large atomic masses
Why do ceramics have lower density than metals?
They often have lighter elements
Why do polymers have low density?
- low packing density (often amorphous)
- lighter elements (C, H, O)
What is the density like of composites?
moderate to low densities
What is a single crystal?
When the periodic arrangements of atoms (crystal structure) extends without interruption throughout the entire specimen?
What are three examples of single crystals?
- diamond single crystals for abrasives
- single crystal for turbine blade
- quartz single crystal
What is another name for a noncrystalline structure?
amorphous
What are polycrystalline materials?
a material composed of many small, single crystals
What is the range of typical grain sizes for polycrystalline materials?
1nm to 2cm
What is anisotropy?
It’s a property value that depends on the direction of measurement (meaning properties change depending on which way you measure something)
When can you observe anisotropy?
single crystals (not single cubic– DIFFERENT)
What is an example of anisotropy?
The modulus of elasticity (E) in BCC iron
What is Isotropy?
uniformity in all directions
What kind of material has varying properties in regards to isotropy?
polycrystals
When will the grains of a polycrystal be isotropic? aniostropic?
Isotropic: If grains are randomly oriented– since they’re aligned randomly, there’s an average property
Anisotropic: grains are textured (they are deformed– elongated)
What is Polymorphism/allotropy?
Two or more district crystal structures for the same material
What is another word for allotropy?
polymorphism
What are two examples of polymorphism/allotropy?
- Titanium: α or β forms
- Diamond and graphite
Why does polymorphism/ allotropy happen?
There are different phases within the same solid
How does iron change crystal structure as temperature increases?
low temp: α-Fe BCC
medium temp: γ -Fe FCC
high temp: δ-Fe BCC
highest: liquid
What is a point coordinate?
A lattice position in a unit cell
How do you find the crystallographic direction for a point coordinate?
- determine the location of the head and tail
- head-tail
- normalize– make it an integer
- use SQUARE BRACKETS NO COMMAS
How do you write a point coordinate? plane?
Point: square brackets []
Plane: parentheses ()
NO COMMAS
What are a family of directions and how should you think about it?
Directions that are crystallographically equivalent
think about if you switch it, would it be the same but just with a different orientation
What’s an example of a family of directions? How do you write it?
<100> = [100],[010],[001],[-100], [0-10],[00-1]
What is the linear density of atoms (LD)?
(number of atoms centered on the direction vector)/ length of direction vector
What are the Miller Indices of a plane?
(###)
How do you determine the Miller Indices of a plane?
- Create a new origin if a plane passes through the select one (new unit cell)
- Create intercepts of the plans using a,b,c ratios
- take reciprocals
- normalize by multiplying by a,b,c
- make small integer values
- enclose resulting Miller Indices in parentheses (no commas)
What are the Miller Indices in letter names?
h k i
l (for HCP)
For HCP, how do you determine the Miller Indices?
use a1, a2, and z
i= -(h+k)
How do you find the Planar Density of Atoms (PD)?
PD= (# atoms centered on a plane)/(area of plane= a^2)
** area that it makes up on the coordinates
** a^2
What diffracts X-rays?
Crystallographic planes of atoms
To diffract light, what must be true ?
The diffraction grating spacing must be comparable to the light wavelength
What is interplanar spacing?
The distance between parallel planes of atoms
What can you compute for diffraction using wavelength and theta?
Interplanar spacing
What is the diffraction pattern for polycrystalline alpha ion BCC? planes (100), (200), and (211) have the highest diffraction angle?
planes (100), (200), and (211) have the highest diffraction angle?
lowest is 110, then 200, then 211
lowest diagonal, then flat on x, the triangle
What are the three things you need to be able to calculate the theoretical density of a metal?
Crystal structure, atomic weight, and unit cell lattice parameters
Are most single crystals isotropic or anisotropic?
anisotropic– properties vary with orientation
