Lecture 2: Atomic Bonding and Crystal Structure (cont.) Flashcards
What if a place does not intercept with any of the axes shown?
shift the plane parallelly so it can intercept with a&b
What qualifies an equivalent plane? what are different examples of equivalent planes in cubic structures that belong to the same family plane { 1 1 0 }
Equivalent planes can be transformed into each other (rotation reflection or inversion -)
What coordinate system is used for hexagonal crystals
four-axis (Miller-Bravais) coordinate system
What is the method for defining the coordinate system for hexagonal crystals (when component c is 0)?
- vector repositioned (if necessary) to pass through origin
- read off projections in terms of unit cel dimensions a1, a2, a3, ac
- adjust to smallest integer values (not inverting)
- enclose in square brackets, no commas [uvtw]
u + v + t = 0 must hold
How would you determine the miller-bravais indices for this crystal?
what is it called for a hexagonal crystals when c is 0?
it’s on the “basal plane”
How do you find the indices for a hexagonal crystal with an os vector NOT on the basal place (non-zero)? (os means origin to s vector)
How do you convert from 3-axis to 4-axis in hexagonal crystals?
’ - related to 3-axis, u v t w related to hexag
u = 1/3 (2u’-v’)
v = 1/3 (2 v’-u’)
t = -(u+v)
w = w ‘
How do you find the miler-bravais indices for this hexagonal ABCD plane?
intercepts –> reciprocals –> miller-bravais indices
How do you find the miller-bravais indices for this pyramidal plane?
BCC : atoms/unit cell? close-packed directions? CN? atomic packing factor? body diagonal direction/lattice constant formula?
2 atoms/unit cell
close packed <111> directions
CN = 8
APF: 0.68
4r = a*sqrt(3), body diagonal <111>
FCC : atoms/unit cell? close-packed directions/planes? CN? atomic packing factor? face diagonal direction/lattice constant formula?
4 atoms/unit cell
<110> close packed directions
close packed planes {111}
CN = 12
APF = 0.74
face diagonal <110>, 4r = a*sqrt(2)
HCP: atoms/unit cell? close-packed directions/planes? CN? atomic packing factor?
6 atoms/unit cell
close packed <11-20>
close packed planes {0001}
CN = 12
APF = 0.74
Which basic crystals are close-packed structures?
FCC and HCP
What are the close packed planes of FCC and HCP? their packing sequences?
FCC:
{111}
ABCABCABC (repeat every 3 layers)
HCP:
{0001}
ABABABAB (repeat every 2)
what is a stacking fault?
when a certain layer in the packing sequence does not follow
What structures do most pure metals form? Carbon? Give an example of allotropy.
BCC FCC or HCP
Carbon: graphite or diamond
Allotropy: Fe- BCC @910 °C, FCC@1400 °C, BCC@1535 °C
Give two examples of AB-type compounds. what do they look like?
Magnesia & Brass
MgO - 2 FCC lattices formed
CuZn - BCC with Cu @ corners and Zn @ body center
