topic 2🅱️ Flashcards
coordination number
number of atoms or ions immediately surrounding a central atom in a complex or crystal
coordination number of ccp or fcc and hcp structures
12!!
3 above, 3 below, 6 on the same level
bcc coordination number
8
not closed packed
cubic geometry
primitive cubic structure coordination number
6
octahedral geometry.
the atom is part of a few unit cells
what’s an interstitial site
gaps between closed packed structures
atoms,, even when closely packed,, have gaps between them,, they aren’t packed with 100% efficacy
can interstitial sites be occupied by other atoms
yes!!!
most efficient way of packing
being closely packed
reduces the interstitial sites between them.
how can interstitial sites be categorised
categorised by their geometry
2 close packed type of interstitial site
HCP + CCP can have which interstitial sites
- octahedral site
- tetrahedral site
octahedral interstitial site
between 2 triangles above + below.
between 6 atoms
can see all the way through the structure
tetrahedral interstitial site
- between a triangle above + a single atom below
(can’t see all the way through the structure)
between 4 atoms
amount of octahedral sites in a close packed structure issss
‘N’
where N is the amount of atoms in host
number of tetrahedral interstitial sites in a close packed structure
2N
N is the number of atoms in a host
tetrahedral: between 4 atoms
double the amount of octahedral sites
how can we draw a unit cell diagram
- space filling diagram
- ball and stick diagram
- cell projection diagram
what is a cell projection diagram
a 2D diagram of the unit cell,, viewed from above
what is lost when drawing a cell projection diagram
info on the Z axis!! aka how tall the unit cell is + where the diff atoms are placed on the z axis
how can we show where the atoms are in a cell projection diagram
draw the atoms in diff environments :: code them with either 0,1 or 1/2 to show where they’re located
when drawing a cell projection diagram,, what must we do
look at the diff atom environments
code each different environment
give them a number to show where they are on the Z axis
are close packing structures 100% efficient
no!! they have interstitial sites aka gaps between atoms in a close packed structure
how can we measure how efficient a close packed structure is in terms of packing
find the packing efficiency
what is the packing efficiency
the percent of the structure that is filled by the atoms // ions
packing efficiency equation
volume of atoms in a unit cell // total volume of the unit cell
x100
what must we find to figure out the packing efficiency
we must know the volume of the atoms + the volume of the unit cell
how do we figure out the total number of atoms in the unit cell
- find how many atoms there are + if they’re on a vertices or a face
- find their contribution eg: 1/ how many other unit cells they’re present in
- contribution x total amount of them in ONE unit cell
how do we find the total volume of atoms in a unit cell
- u have the total amount of atoms
- number of atoms x volume of one atom
what is the equation for the volume of one atom assuming it has hard sphere behaviour
V = 4/3 nr3
n = pi
r = atomic radius
how do we find the total volume of the unit cell cell
length = 4 radii
use Pythagoras
to find a side (if it’s cubic : a=b=c)
so volume is a3
pythag will give one a 🫶
what’s an intensive property
a bulk property
they’re independent on the size of the system
density is an example 🫶
equation for density
density = mass / volume
to find the density of the unit cell what to we need
the volume of the unit cell
total number of atoms so we can find the total mass of unit cell.
what do we multiply the mass by to find the mass of the unit cell
not the total amount of atoms.
but the total amount found by their contributions.
converting pm into cm
x 10-10
to convert amu to grams
amu / avogadros number
unit for density
g/cm3
or kg/m3
amu to grams
divide ➗ by avogadro
pm to m
x10 ^ -12
common density units
g/cm3
kg/m3
density of unit cell steps
density = mass // vol
(mass in amu / avo) x number of atoms in unit cell
vol = volume of unit cell
grams and cm3
kg and m3
mass/volume
