Lecture 2 Flashcards
What did Robert Hooke suggest the different shapes of crystals was due to?
The packing together of spheres
What is the difference in hexagonal versus square atomic layers
hexagonal have the spheres sitting in the diagonal space and squares are parallel with each other
What is an interstice
the space between the spheres
What does the atomic packing diagram of close-packed hexagonal layers look like?
What is the simplest way of stacking layers of atoms for close-packed hexagonal? What is the result?
place the atoms center directly above one another.
The result of this is the simple hexagonal structure (SH)
Are there pure elements in simple hexagonal structure? why?
no because the atoms in the second layer occupy the “hollows” or interstices between the atoms from the layer below.
This minimizes the total energy of the system (so it’s the most stable configuration)
where do atoms in the second layer of the close-packed hexagonal layer of atoms exist?
the interstices between the atoms from the layer below to minimize the total energy of the system to the most stable configuration
For close-packed hexagonal (not SH) layers of atoms, where are the options for the 3rd layer?
“A” position, or ABABABAB…
“C” position, or ABCABCABC…
If the atoms on the 3rd layer of a hexagonal-close packed go directly above the atoms on the first layer, what are the characteristics of this crystal?
hexagonal-close packed
ABABAB stacking
2-layer repeat
open channels
if the atoms in the 3rd layer of a hexagonal close packed go directly above the unoccupied interstices (C sites), what are the characteristics of this crystal?
cubic close-packed (CCP)
ABCABCABC
3-layer repeat
no open channels
What is the difference between the top view versus side view of 2nd layer HCP and CCP
the same
What is the difference between the top view versus the side view of the 3rd layer of HCP and CCP
HCP– above A
CCP- interstices
Why is a structure made of a three-layer stacking sequence of hexagonal layers called cubic-close packed
the shape and symmetry of the unit cell
What is a unit cell
the smallest group of atoms that can be repeated in three dimensions to form the entire crystal lattice
what’s another name for CCP
FCC
Describe the unit cell with CCP structure
close-packed layers lie perpendicular to the body diagonal of the cube (ABC in figure)
how many close-packed layers are there in CCP
4 different body diagonals in a cube
atoms in contact along the diagonals
**think the ABC is close-packed in the diagonals on 2 different plane directions
how many atoms are in the CCP unit cell
4 atoms
how do you take into account half atoms in calculating atoms per unit cell
count half to this atom, because the other half goes to a different atom
What is the coordination number of CCP
12
what is a coordination number
number of nearest neighbors
what is the relationship between a (lattice parameter) and atomic radius r in CCP
what does the variable “a” stand for
the lattice parameter, proportional to the distance between atoms
what is the atomic radius r
the radius of an atom within the unit cell, usually in relation to the lattice parameter a
what are the different unit cells of the ccp structure
cubic (conventional) cell
rhombohedral cell
how is the rhombohedral unit cell of ccp built
stacking triangular layers of three atoms instead of six
why is the rhombohedral unit cell for ccp less useful
it doesn’t show symmetry
for the unit cell of the HCP structure, how are atoms in contact?
atoms are in contact along the side faces of hexagon and in between the A and B atoms
how do HCP, CCP, and rhombohedral relate
same AB layers,
HCP and CCP change from the position of the 3rd layer
HCP ABABA, CCP ABCABC
rhombohedral is another version of the ABCABCABC (CCP) pattern but built by stacking layers of three atoms not 6
how many atoms are in the HCP unit cell
6
what is the HCP coordination number
12
what is the relation between the a and r in HCP
a = 2r
What are the differences between HCP and CCP unit cells
HCP
coordination number = 12
atoms/unit cell = 6
a = 2r
CCP
coordination number = 12
atoms/unit cell = 4
a = 2sqrt(2) * r
why is it important to identify the close-packed planes/directions?
close packed planes have high catalytic activity
deformation in crystalline materials happen primarily via sip on close-packed planes along close-packed direction
why are close packed planes importan
highest catalytic activity
where does deformation in crystalline materials happen primarily
via slip on close-packed planes along close-packed directions
what does close-packed mean
most tightly packed (high density of spheres), most efficient packing
are there gaps in between atoms in close-packed HCP and CCP?
yes, called interstices
what is another name for packing density
atomic packing factor
how do you calculate the packing density
PD = (vol occupied by atoms)/(total volume of unit cell)
vol of atom = 4/3 pi r^3
# atoms inside unit cell
example for FCC
what is the packing efficiency of close-packed structures?
74%
what is the packing density of CCP/FCC
0.74
what is planar density
density of atoms on a particular crystal plane
how do you calculate planar density
PD = (# atoms on a plane * area occupied) / (area of the plane)
do the different crystallographic planes of a unit cell have the same or different surface areas
different
what are three examples of properties that might be different depending on the direction a plane of a unit cell is measured in
hardness, resistivity, catalytic activity
What do the (100) (110) and (111) planes look like
