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good afternoon everyone this is Eric
Paton introduction to materials
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engineering chapter 12 ceramics and
properties structure and properties of
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ceramics. issues to address today are how
do crystal structures of ceramic
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materials differ from those of metals?
how to point defects in ceramics differ
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from those point defects found in metals?
How are impurities accommodated in the
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crystal and the ceramic lattice? and in
what ways are ceramic phase diagrams
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different from these diagrams of metals?
how are the mechanical properties
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ceramics measured and how does that
differ from metals
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but here is the periodic table again you
remember this early on chapter where we
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were identifying characteristics for
ionic and covalent bonding as you might
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remember if there's a large difference
in the electronegativity between atoms
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then they will be more ionic
characteristics. if the electronegativities
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are very close then that
would be more of a covalent structure so
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as an example here calcium fluorite the
electronegativities of 1.1 and 4.1 are
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relatively large so that would be mostly
an ionic bond and some carbide which is
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also a ceramic has electronegativities
that are very close to each other
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of 2.5 and 1.8
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so we're gonna look at two factors that
can determine the crystal structure of
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ceramics first is the relative
size of the ions and secondly is the
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importance to have charge neutrality so
as far as the distance between the atoms
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that you remember early on in in the
subject be showed a energy versus atomic
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distance between the atoms
and there is a minimum energy where the
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distance between the atoms is stable
if they start to get too close to each
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other then there is a very large
repulsive force and energy is very high
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those atoms separated and also if you
get further apart from the atoms then
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the energy goes up as well so the
minimum bonding energy is a stable point
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the
structure on the left here where there
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is a gaps between the cations and the
anions
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is not stable and the right two
structures you do have a stable
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structure in there
the second is the maintenance of charge
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neutrality
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so just to back up for a minute I didn't
mention the introduction of cations the
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cations are positive I typically
remember that by just um seeing that
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there's a T and the cation and the T
looks like a positive charge so that's
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how I remember that the cations are
positive and anions then must be
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negative and the cations are also small
ways smaller than the anions and the
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reason why is the cations give up
electrons and when it becomes ionized so
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the relative or so the remaining
electrons are held more closely and that
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results in a smaller radius so back to
the maintenance of charge neutrality the
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net charge on ceramic should always be
zero so if say the cation normally has a
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+2 charge then if it combines with two
fluorines that only have a negative one
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charge then there must be two of them
for the charge neutrality
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so this is reflected in this chemical
formula here a which is a cation X which
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is the anion then M and P are just the
relative number of atoms for each to
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maintain charge neutrality all right now
we're going to look at two the
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coordination number and atomic radius or
five different types of crystal
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structures and ceramics most importantly
we want to look at the cation to anion
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ratio and that's going to determine then
how they are going to arrange themselves
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so to form a stable structure
how many anions can surround the cations
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so for the when the ratio when the ratio
of the cation to anion radiuses is less
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than 0.155 that has a coordination
number of 2 and the type of crystal
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structure is linear there is a picture
of just two two anions surrounding one
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cation so that has remember coordination
number is the number of nearest
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neighbors the nearest number of
neighbors is two here in that case
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moving on we can see the triangular
structure has three nearest neighbors
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that has coordination number three and
the range in the ionic radii ratios is
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0.155 to 0.225 and then the
ratio just goes up the range goes up with
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the more and more anions surrounding the
cations so the coordination number of
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four or the tetrahedral that's very
common crystal structure and that's also
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called the zinc blende or zinc sulfide
crystal structure we're gonna go into
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each of these a little bit more on the
following slides so then
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the octahedral has coordination number
of six as you can see here there's the
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four surrounding plus one on top one on
bottom and that is sodium chloride
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crystal structure and finally the cubic
crystal structure also called the cesium
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chloride structure looks like the one
here to the right
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so as the cation gets bigger a point
occurs when they can be surrounded by
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another anion and so that's what it's
going to happen there so going up here
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we have larger and larger at ion
radiuses going from top to bottom
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so it's geometry here determines what
the cation to anion ratio is for each
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of the types of crystal structures so
let's look at as an example the
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octahedral structure which is the
coordination number of six so that's
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that this one right here so that um you
can see it has the four surrounding plus
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one on top one on bottom so this is a
slice looking sorry this is a slice
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looking straight down at those four
anions surrounding the one cation here
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which is the red one in the middle then
the dotted line is the anion that is
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directly above another anion that's
directly below so
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- to determine the ratio of the cation to anion
we have to first look at the
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relationship to a which is the unit cell
length for this octahedral and the unit
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cell length is just a here so that is
also equal to two of the anion radiuses
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at one radius here and one right here
additionally we can determine the length
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of the diagonal of this 45-45-90
triangle which is this a then the
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diagnosed is root 2a and that's also
equal to two of the anion radiuses we
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got one here one here plus two of the
cation ratios are radiuses so there's
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two of em ions two of the cations add
those together that's equal in
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relationship to the unit cell length a so
that's equal to root 2 a so plugging
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then in the root 2 a so are you plugging
in this into this equation here then we
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get to root 2 times the radius of the anion
so simplifying this then we just divide
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through by 2 then this equation then we
isolate the radius of the cation by
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subtracting these two the anion by both
sides and then factoring out the r anion
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gives you then this equation here
then just dividing through again by the
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radius of the anion both sides here that
then is equal to the root 2 minus 1. or 0.414
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so that number then is the
minimum in the range for the octahedral
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so if you go back look at
point 0.414 you go back here
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again the octahedral the minimum for
that range is 0.414 so then it can
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then grow and grow until it can finally
accommodate more of the anions and so if
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you go back to this slide that's kind of
what's going on here where the minimum
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is the center image here and then as
the cation grows and grows grows
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eventually it will be able to
accommodate another of anions that's
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when you would jump up to the next type
of crystal structure here which is the
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cube.
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you might be asked and on homework or
final to derive the cation to anion
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ratios for some other crystal structure
so here's an example problem where we're
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predicting the crystal structure for
iron oxides let's say we know nothing
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about iron oxide other than the atomic
radius of the iron and oxygen so we can
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get those as given from the table and we
need to select the iron two-plus because
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of charge neutrality oxygen is always a
to minus so because iron can take on a 2
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plus 1 for it 3 plus we're gonna select
the two plots because that's what we are
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charging neutrality and so the ratios of
those 2 is then 0.55 so going back to
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our table right is 0.55 lines well it
lies right in between this range here so
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it would be a octahedral type or a
sodium fluoride type of crystal
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structure but a coordination number of 6
and that's exactly what we have here
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coordination number of 6 and so it has
the sodium chloride crystal structure so
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you might be asking um why do we call it
a sodium chloride crystals when it's an
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actually an iron oxide well that is
because I think it was because they
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first determined this type of octahedral
structure with sodium chloride and so
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just to give it a name the all of the
sodium chloride crystal structure and so
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there are many other types of ceramics
though that take on that rock salt
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structure and for example magnesium
oxide or iron oxide and if you're
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looking a little bit more closely here
it's actually two interlocking FCC
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structures if you just ignore the red
cations here just look at the fluorines
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there's your familiar FCC where you have
four on the faces and then you have eight
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on the corners and then if you look at
the sodium then is just shifted down by
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a half a unit cell length so now these
Reds are the cornered atoms and then
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these red ones down here are the face
ones and then you would have another set
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of quarter sodium on the bottom
so that's your two interlocking FCC
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structures
again I said that other types of sodium chloride or
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rock salt structures are magnesium oxide or
iron oxide here you have magnesium oxide
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and identical to the previous one
it's just types of atoms and a slightly
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different ratio 0.5 1 4 however it still
falls in that range here in the rock
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salt or sodium chloride structure still
falls in that range or
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magnesium oxide
and again with six years neighbors now
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another type of crystal structure then
this is another AX so that means that
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there's one anion for every one cation
at 1:1 ratio just like the rock salt is
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ax so and this is called the cesium
chloride crystal structure and so with
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cesium chloride differences in the an
ion cation ratios is very is much higher
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so that means you can accommodate more
anions around the cation 0.939 for this
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one that falls in this range here with
coordination number 8 and so that's that
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cesium chloride crystal structure the
cesium chloride
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as that eight see how there's four nearest
neighbors on top four nearest neighbors
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at the bottom and it looks kind of like
BCC if you take both atoms together but
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because we have to look at each anions
separately it's more like a simple cubic
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for the other chlorine and that's why
it's called a cubic structure so and
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that's a cesium chloride so there are
other types of cesium chloride
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structures and but this one is the the
other type which is called the zinc
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sulfide or zinc blende kind of jumping
around from here remember okay so zinc
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blende is this one right here zinc
blende as a coordination number for it
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it's in the range in this range here so
going back over to the
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the zinc blende an example this is zinc
sulfide and if we look at other types of
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compounds semiconductor compounds like
gallium arsenide just a compound
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semiconductor Cadmium Telluride and these
are not technically ceramics but we
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borrow the structure the ceramic
structure need for these compound
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semiconductors so we do call those
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zincblende semiconductors so looking at
that Alright jumped forward alright so
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there is what it looks like
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Zinc atoms in a
lattice of tetrahedrons and so you
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have like you know four one one two
three four nearest anions for each of
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these
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so let's look at the the fluorite
structure this is the AX 2 crystal
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structure meaning there's two fluorines
for each of the calcium and this is a
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little bit harder to visualize so this
actually has eight cubic structures whoa
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eight cubic structures here one two
three four five six seven eight
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the cubix are the fluorine atoms so
there has to be twice as many chlorine
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atoms here as the as the calcium and the
calcium are going to try to be as far
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away from each other as possible so to
do that for the calcium's being in the
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interstitial sites this calcium then is
in the far left back cube and then the
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next one to get a spacing far away from
each other is going to be in the front
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right cube and in order for then that
the other two al seems to be as far away
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from the top two and they take the
alternating sites interstitial site so
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this calcium it's gonna be in the back
right and then this calcium is going to
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be in the front left but this one's in
the back this one's in the front this
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one's in front it's the back being as
far away from each other as possible and
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they're gonna occupy the center of the
cubes that interstitial sites
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all right so that's the fluoride
structure
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another type of crystal structure is the
perovskite structure this is actually a
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type of ceramic that's really increasing
in popularity now after spending so much
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time in the research labs and this one
is asked a strong material for me
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because I studied it as a graduate
student use in non-volatile memory
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applications and what you have here is
titanium which is this small and that's
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in the center and then you have the
barium which on the corners and the
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oxygens with from the faces and this
this titanium doesn't always want to be
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right at center either is offset above
or offset below a little bit that's
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where it it maintains the furthest
separation from the other atoms in this cube
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so that's why it's considered a
ferroelectric and it's also increasing
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popularity now as a high-efficiency
solar cell material
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so in summary of a common crystal
structures we have the rock salt so you
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or I structure type is ax cesium
chloride also ax and the zinc blende
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it's also ax and the fluorite ax 2 and
frogs guide a B X 3 and here are some
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examples of each of those here and their
coordination numbers
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so skipping gears a little bit now we're
gonna jump into silicate ceramics so
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silicon-oxygen
are the most common elements on earth so
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here is the sio2 which is also called
silica it's polymorphic polymorphic form
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can be either quartz cristobalite or
tridymite and the strong silicon oxygen
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bonds lead to the high melting
temperatures or sio2 so the image on the
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right is that of the crystobalize items
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you
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okie-doke so last structures the basic
unit of the silicate is sio4 with a
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negative charge of four on that and
because there is you know there's a four
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of the oxygens and only one silicon so
the glass is considered a non
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crystalline its amorphous however
crystalline is why quartz is crystalline
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and it has this octahedral type
arrangement here of silicon and oxygen
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but because of the the addition of
sodium here we don't have that perfect
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arrangement and we can still have charge
neutrality with all of these broken
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bonds in there
as of the smaller ion charge of sodium
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as compared to the silicon so we can
have all these broken bonds and so often
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atom purities to change the properties
of glasses
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there's also something called layered
silicates and for example clays mica
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talc these have these like layered
structures of the octahedral they
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octahedral arrangements here and these
are just connected together in 2d planes
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and then they are bonded adjacent planes
are bonded together through weak like
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Vander Waal charging between these
negative charges that are that are you
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know out of plane for here and so you
get negative charging which is balanced
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by these charged cations so polymorphic
forms of carbon we're gonna jump into
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diamond diamond does it really fit into
ceramics but it's such a unique material
00:26:13
that you figure the only place to put it
here was in the ceramics chapter so
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let's just talk a little bit about it
because it's so important polymorphic
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forms of carbon are the tetrahedral
bonding carbon there are four four
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neighboring carbon atoms and one two
three and four you just look at this one
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here you have four surrounding it that
are bonded to it it has a large .. you
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can have large single crystals of
diamond like gemstones the small
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crystals are used for grinding and
cutting and you can have diamond thin
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films that are deposited that are hard
surface coatings and those are cutting
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tools and medical devices
Oh carbon is also in can also be in
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layers instead of crystalline form and
when carbon is layered
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we call that graphite so graphite is
what's used in pencil lead it's just
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layers of carbon atoms that are weakly
bonded together by these Vander Waal
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forces and so graphite is actually a
very good lubricant item see graphite
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sprays or other things it's also a
constituent in cast iron and the
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graphite flakes make cast iron very
machinable because of the lubricating
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property of graphite
so and that's again it's because these
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graphite plates and slide past each
other
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but the week Vanderwall bonds
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now we're going to jump into point
defects and ceramics so ceramics can
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either have vacancies or they can have
interstitials vacancies exist in
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ceramics for both cations or anions so
here is an example of a cation vacancy
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right here here's an example of an
anion vacancy so you have to have these
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in pairs for charge neutrality if you
have a cation vacancy
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alternatively you can have an
interstitial
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and an interstitial is just shoved in
the lattices extra cations as normally
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doesn't exist for anions because the
anions are much larger and to get in and
00:29:07
I had an interstitial difficult to cram
into that lattice
00:29:11
so as far as charge neutrality for these
defects there are two types of ceramic
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defects there's what we call that the
Frenkel defect and a Schottky Frenkel
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defect it's just a cation vacancy
cation interstitial pair
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so if you look at what's going on down
here to maintain charge neutrality and
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crystal if you're going to have
00:29:40
a yeah if you're going to have actually
let me talk first about the Schottky
00:29:47
defect you're gonna have charge
neutrality here if you're gonna have to
00:29:51
remove a cation you also after do the
you have removed the cation here you
00:30:01
also have to remove the anion here
maintain charge neutrality so the
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Schottky defect here is charge neutral a
Frenkel defect on the other hand is just
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one of the interstitials that's moved
out of its site here and it's been
00:30:17
rammed into this other site not really
an energy preferred situation much
00:30:23
rather be here but did any pace
sometimes that interstitial can end up
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in the wrong place and that's called a
Frankel
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a Frankel defect I like to remember
the Schottky defect because I think of
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like you're shooting out atoms from the
matrix and so like you know these guys
00:30:47
are being removed however the Schottky
nothing's being removed it's just a
00:30:52
reposition of an interstitial so that's
the Frenkel defect and the equilibrium
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concentration of these defects is
related to the Arrhenius relationship which we've
00:31:05
brought up before and so the higher the
temperature here the greater
00:31:10
concentration of these defects
of imperfections in ceramics and what we
00:31:19
can do to maintain charge neutrality
00:31:24
let's take as an example the rock salt
or sodium chloride ceramic here and we
00:31:35
added an impurity of calcium inside so
in order to maintain charge neutrality
00:31:43
since calcium has a +2 charge then we
have to remove not just the one that
00:31:51
being replaced but an extra one out of
the lattice and because sodium is
00:32:00
charged as a plus one charge on it
that's why we have to remove two
00:32:07
sodium's for one else 'i'm so we're left
with a cation vacancy in the
00:32:15
substitutional cation impurity so for a
substitutional anion impurity let's say
00:32:23
we're going to place we're gonna put an
oxygen impurity into the lattice now
00:32:30
but because that has a plus i'm sorry a
negative two charge and we have to
00:32:36
remove not one of the fluorines but two
of the pull means maintain charge
00:32:43
neutrality and so that means we're going
to be left with an anion vacancy with a
00:32:51
substitutional anion purity
00:32:56
now let's look at mechanical properties
of ceramics so let's consider what would
00:33:04
happen if we tried to just do a regular
old tensile test of a ceramic bar well
00:33:12
it would kind of just shatter everywhere
and it would be pretty dangerous so when
00:33:19
we look at mechanical properties
ceramics we don't do tensile tests do
00:33:23
you bend tests and let's consider the
mechanisms of deformation so we know
00:33:31
that ceramics are very brittle and when
they're in crystalline form they move by
00:33:39
a dislocation motion
and there there you know those
00:33:46
dislocations are very difficult to move
as the ionic nature know that there is
00:33:54
very few
slip systems and there's a resistance to
00:33:58
the motion because the ions have to
slide past each other and sometimes they
00:34:05
have to get very close to ions of
their same charge so they do not like to
00:34:14
get very close to each other as you saw
they bonding energy spikes dramatically
00:34:21
when you try to get these atoms close to
each other
00:34:26
all right so so instead we do these flex
tests and kind of like you did flex
00:34:36
tests on our aluminum bars earlier in
the quarter we do these three point Bend
00:34:43
tests and we can calculate the elastic
modulus through these equations here the
00:34:52
first one is when there's a rectangular
cross section and then the one down here
00:34:56
is when you have a cylindrical cross
section we can get the elastic modulus
00:35:03
by knowing the which is just you know
force over the Delta which is the
00:35:13
deflection distance
00:35:19
all right so
00:35:23
here is a example here
um typical values for some of these
00:35:35
values or elastic modulus of silicon
nitride silicon carbide aluminum oxide
00:35:42
and glass they're all very very high
much higher than metals except for this
00:35:47
one and the flexure strength and
calculated using slightly different
00:35:57
equations for rectangular cross-section
and radius so we have elastic modulus
00:36:03
and the flexural strength which is Sigma
sub F pass alright so in summary we
00:36:14
looked into the inter atomic
bonding in ceramics and that bonding is
00:36:20
typically either ionic or covalent or a
combination of the two and the crystal
00:36:28
structure is going to be dictated on
maintaining charge neutrality and the
00:36:35
cation to anion radii ratios talking
about imperfections we looked at several
00:36:44
different types of imperfections or
defects there's vacancies there's
00:36:50
interstitial which are normally cation
interstitials looked at in Frankel which
00:36:56
is just a shifting of the anion into
another location and a Schottky which is
00:37:02
the removal of both the cation and an
anion from lattice we also looked at
00:37:08
impurities though by substituting either
an anion or cation we can go into an
00:37:18
interstitial sites or substitutional
sites and B are always maintaining
00:37:25
charge neutrality number these
impurities are atom are the purities are
00:37:31
added
Oh room temperature we can do room
00:37:35
temperature mechanical tests with
ceramics not tensile test but flex your
00:37:40
tests and we can measure you can get
measurements of elastic modulus and also
00:37:47
the flexure modulus which is the flexure
strength or Sigma is all right well that
00:38:00
summarizes the chapter twelve ceramics
discussion and I'll see you in class
00:38:07
have any questions
