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visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: So I got much
more than one request to do some stuff on
nuclear materials, and I think it's just
about the right time. That you guys know
enough about radiation interacting with
matter and everything, and stopping power,
and processing, to actually make sense of
nuclear materials and radiation damage. And this is my whole
theme, so happy to come talk to
you guys about this and show you why I
think it's interesting. Because it all goes-- this slide kind of gets onto it. It starts off with the
single-atom atomic defects that make up the basic
building blocks of damage and ends up with things that
break in nuclear reactors under radiation. And so to understand
the whole thing, you've got to know everything
from the single atoms on the sort of
femtosecond scale, all the way up to
the engineering scale where things evolve over
years or even decades. So we'll be talking-- first, probably
today, we're going to go over a material
science primer. So who here has had any
courses in material science? No one. That's good because I'm
assuming that there is a-- see, no one knows anything here. I know there's a couple material
scientists in the class, and I'll apologize ahead of
time if it's a bit of a review. But we'll be going mostly
through what are materials and what are the defects
that change their material properties, and
how do they behave. That'll take us
through about today. So then tomorrow, we can see how
radiation causes those defects and actually changes
material properties. So there's a whole laundry
list of different ways that materials
fail, and most folks are concerned with
all of these-- everything from simple
overload, which means you stress something too
much and it just breaks, to all the different
forms of corrosion. That's a whole field in itself. And then there's
the things that just we have to worry about
because they're only activated with radiation damage. And in this case, this isn't
quite ionization by radiation, but it's actual radiation
slamming into nuclei and moving atoms
out of their place. And we've got one figure
that we had recently in a paper that sums up the
entire multi-scale picture of radiation damage, from the
femtosecond to, let's say, the megasecond scale. Or I think it's more than that. Maybe gigasecond would be
the right word for that. And all the way down from the
angstrom to the meter scale. And I want to walk you
through sort of a lens scale by lens scale depiction
of radiation damage. It all starts with knocking
atoms out of place. We've mentioned
this a little bit when we talked about
nuclear stopping power, and this is where it
actually comes into play. Sometimes an incoming
neutron or photon or ion can displace an atom
from its original site, and we call that a physical--
it's a displacement. And then that atom comes
off with quite a bit of kinetic energy and can
knock into a whole bunch of other atoms. Now this loss of the solid
crystalline structure, you can't really tell what the
original structure looked like, right? It actually comprises a
very small, localized zone of melting called
a thermal spike. If you think about,
all these atoms are vibrating at
fractions of an eV-- at thermal energies,
like the thermal neutrons we talked about in the reactor. Then you hit them
with an MeV neutron. They might transfer
100 keV of energy. And a bunch of these
atoms will then be moving about at, let's
say, a few hundred eV. That's way beyond
liquid temperature. So actually, it's been
theorized that there's a little pocket of atoms around
three to five nanometers wide that reaches, like, 10,000
Kelvin for a very, very short amount of time-- less than a picosecond. Because almost
instantly, those atoms knock into the ones
around them, and this is how the process of
heat transfer occurs. And so, very quickly,
you get what's called the quench, where
most of those atoms very quickly knock
into other ones, slowing down, finding their
equilibrium positions again, but not every one. You can see there's a few
places where the atoms are still out of their original location. And it's those residual
defects that actually comprise radiation damage. And as those defects build
up, they start to move. They can diffuse. They can be transported
ballistically by more radiation damage. They can move by all sorts
of different mechanisms and eventually find each other,
forming what's called clusters. So a bunch of those missing
atoms could find each other and make a hole,
which we call a void. A bunch of the extra
atoms shoved in between the other
ones can form things called interstitial clusters. We say interstitial because
it's like in the space in between where you'd
normally find some atoms. So let's say you had a whole
bunch of those missing atoms come together, forming a void. This is an actual Transmission
Electron Microscope, or TEM, image of a void-- pockets of vacuum in materials. Notice anything interesting
about its shape? AUDIENCE: It's, like, rounded. PROFESSOR: It's rounded, but
what's most striking to me is it isn't actually round. So you would expect a void or a
bubble to be kind of spherical, right? That's the minimum energy
configuration of most things. Not so when you have a
little pocket of vacuum. It's where crystallinity
comes into play. And these voids can end up
forming superstructures. What curious thing
do you notice here? For this whole
ensemble of voids. Yeah? AUDIENCE: It seems like
they're all in line. PROFESSOR: They are all
in the same direction. Kind of funny. That's definitely not
an accident, right? That's not like they're
randomly aligned. There's a reason
for this, that we'll go into in a couple slides. Yeah? AUDIENCE: What's
the size scale here? PROFESSOR: The size scale? I think these are on the
order of 20 nanometers or so. Yeah, I cropped these images
just to get points across. Let's see if it says
in the older one. Not quite. Yeah, but these voids can get
upwards of tens of nanometers. As small as single atoms. Yeah? AUDIENCE: Sorry, what is this? PROFESSOR: This is
the accumulation of radiation defects
into what's called voids. Yeah. Don't worry, we'll go over
it in more detail again. And if you get little pockets
of vacuum in your material, you're not creating
or destroying mass. You're just moving it. So those voids, where that mass
was has to go somewhere else, and you actually get
things that swell in the reactor on their own. They don't change mass
but they change volume. They just kind of puff up
like Swiss cheese, sometimes upwards of 20% or 30% changes
in diameter and length for some tubing. Now if you're depending
on these fuel rods being a certain space
apart in a reactor and they start to swell,
squeezing out the coolant, you lose the ability
to cool the reactor. Because then how can you
get water around something where the tubes have
then swelled together? There's lots of other bad
things that can happen, which we'll get into. And so then that's the
origin of void swelling. From single missing
atoms called vacancies, they can cluster
into voids which then cause physical dimensional
changes of materials on the scale of
centimeters to meters. And that's why we say it's
this full multi-scale picture of radiation damage. But to understand,
what is damage, you have to know what is
an undamaged structure to begin with. So it doesn't make sense to say,
how does a structure change, if you don't know
how it behaves. So I want to give a very quick
primer to material science. And apologies to any material
scientists in the room because this is going
to seem really basic, but this is a very quick
intro to this whole field. I want to go over quickly,
what is a crystalline solid? A perfectly undamaged
material would be a set of atoms lined up
in a very regular lattice and of regular array, where you
move over a certain distance and you find another atom. And this extends forever
and ever and ever, all the way out to when
you reach the free surface. And so this is what we would
call an undamaged material. A pristine, perfect,
single crystal. By crystal, I mean
an arrangement of atoms in a certain direction. So notice here, all of the atoms
are lined up in, let's say, some cubic xyz way. That's what we would call
one crystal or one grain. You'll hear both of those. And you'll notice also that
the arrangement of the atoms tends to determine what the
physical objects look like. Or we like to say
that form follows structure in material science. So for materials
like pyrite, which follows a simple cubic
structure, that's the crystals you pull out of the ground. They mimic their
atomic configurations in physical
centimeter-sized space. For gold atoms, they adopt a
slightly different structure. It's still cubic
but there is atoms shoved into the cube faces. It's what we call
Face-Centered Cubic, or FCC. And you start to see
cube-looking structures all over single
crystals of gold. Another one, gypsum. It's got a very different type
of structure called monoclinic, where none of the sides of
this parallelogram are the same and there are some funny angles. But if you look at the
arrangement of the atoms and the actual crystals
of gypsum that grow, you see a striking similarity,
which I find pretty neat. I also want to mention, what
is the absence of structure in material science? We call that something
that's amorphous. Amorphous means without form. So for example, crystalline
indium phosphide would have this regular
structure like this. You move over a
certain distance, you see another green atom,
and so on and so on and so on. In an amorphous material,
it can still be a solid, but there is no fixed distance
between any certain types of atoms. And radiation can cause a
lot of this amorphization by knocking the atoms about
and having them freeze in random configurations. This is one of the ways
that radiation damage can embrittle materials because-- well, we'll get into that. So now let's talk
about the defects that can be created
in a perfect crystal. The simplest ones, we
call point defects. They're zero-dimensional
because they're just single atoms out of place. You can have what's called
a vacancy, where if you had, let's say, a face-centered
cubic lattice of atoms, where you have atoms on every
cube corner and every face, if you just pull
one out somewhere, we refer to that as a vacancy. A missing atom. It had to go somewhere,
though, and we'll get to where it is
in just a second. So it might be kind of hard
to conceptualize, how do we know that there are missing
atoms in all these little cubes or lattices? We do have direct evidence. They're what's called
quenching studies, where you can measure the
resistance or resistivity of a piece of material
after heating it to a certain temperature. Because it turns out that the
hotter you make something, the more of those vacancies
just naturally occur. You won't actually ever
find an absolutely perfect single crystal
anywhere in nature, unless you go to zero
Kelvin for infinite time, then the atoms arrange
themselves thusly. There's always some amount
of atomic vibration going on. And there's actually some
thermodynamic energy gain to having a few defects
in your structure. And that number of
defects increases with increasing temperature. Once you get to the melting
point of a material, or like right before something
melts, you can have up to 1 in 10,000 atoms just missing. Moved somewhere else. We call that the
thermal equilibrium vacancy concentration. And we can measure that using
these resistivity measurements, where you heat materials up to
higher and higher temperatures, cool them down suddenly
in, like, liquid nitrogen or liquid helium, and measure
the change in resistivity. The more defects there are,
the harder it is for electrons to flow through. And the only thing that could
really be responsible there in a single element
would be vacancies. So we do know that
these really exist. They can also cluster up. It turns out that
every time you have a vacancy in a material,
the other atoms move in a little bit towards
it, relaxing the pressure they feel from the atoms nearby. And one way for a whole
bunch of vacancies to lower the stress of the
whole atomic configuration is to cluster together. So if you have a whole
bunch of vacancies, they may not allow as
much stress accommodation as if they were separate,
when they're together. Now you might ask, what
happened to the original atoms? You can't just take atoms
away and then go nowhere because you can't just
destroy matter, right? Unless you turn it
into energy, which is what we do in
nuclear engineering. So in the material
science world, they end up as what's
called interstitials, where you kind of have a
vacancy created from somewhere that knocks that
atom out, and it gets stuck in the next biggest
space between some other atoms. And we refer to those
as interstitials. And those can cluster up, too,
to reduce their total stress in the lattice. They can cluster up into
what's called split dumbbell interstitials. Instead of having one
extra atom shoved in here, you might rearrange
a couple so there's two atoms in the center
of a cube instead of one. And that tends to be a lower
energy or a more stable configuration. So let's look a little bit at
the energetics of these point defects because
understanding how they move and why will tell us a lot about
how radiation damage happens. So it turns out
that interstitials are very hard to make. It's really hard
to shove an atom where it doesn't want to be. But once you get it there,
it moves very easily. Let's draw a quick,
simple cubic lattice to do a little
thought experiment and explore why that might be. Let's say I want to shove
an interstitial atom in here between these other atoms. Well their electron
clouds are going to repel, and it's going to push
all the nearby atoms away by just a little bit. And these ones might
push the other atoms away by just a little bit,
stretching out the lattice, or adding some
compressive stress wherever that interstitial is. But then how would it move? What's the biggest
barrier it has to overcome to get to the
next adjacent location? Well, which direction
would it go? Would it go this way? Probably not. There's an atom in the way. So it's going to find the
path of least resistance to try to get over here,
because like we've talked about before, all atoms
are always in motion. Vibrating. Some of them will
be energetic enough to squeeze through
these two atoms and get over to the next site. And that turns out to be
a pretty easy process. We can look at the energy
required for an interstitial to move. We notice it's really small
fractions of an electron volt, whereas creating them takes
two or three electron volts. In atomic land, that's a
very high energy penalty. Now let's look at vacancies. They're quite the opposite. They're rather easy
to make but they're very hard to move,
compared to interstitials. Notice that the
energy of movement is about the same as the energy
of formation for vacancies. To take an atom out
or to pluck it out, you have to break every
bond between nearby atoms. So you actually have to put
energy in to break those bonds and then remove the
atoms somewhere else. Now these things are
usually made in pairs, so if you think about
how much energy would it take to cause a single radiation
damage event where you have one vacancy, which let's say
would have been right here, and one interstitial, it takes
the sum of these two energies-- usually about four
electron volts. That's not something
that tends to happen chemically or from stress
or from something like that. But radiation coming
in with hundreds of keV or even MeV neutrons,
anything's on the table because it's high enough energy. Yeah? AUDIENCE: What would take
about three or four eV? PROFESSOR: So it would
take about three or four eV to make a pair of a
vacancy and an interstitial. If you just add these two up. It comes usually to about three
or four eV, or electron volts. And that's a very
difficult thing to do in sort of chemical world,
where reactions might proceed with fractions of
an electron volt. But when you have MeV
neutrons coming in, they do whatever they want. They'll do whatever they will. So someone actually
asked me yesterday, what sort of materials can
you put in the way of neutrons to stop them from doing damage? And the answer is,
pretty much nothing. Fast neutrons tend to travel
about 10 centimeters, even in things like steel
or water, and they're going to hit what
they're going to hit. There's not much you can do
but put more things in the way. And we can only get to a certain
density with regular matter. And I think osmium has
upwards of, like, 22 grams per cubic centimeter density. That's not enough
to stop neutrons, even over a
considerable distance. Unless you had, like,
liquid neutron star, that you could pack nuclei in
at a way higher number density, not much you can do. So moving up in the
dimensions, there's another type of defect
called a dislocation, where it's actually energetically
favorable to slide an extra half-plane of atoms
in between two sets in here in the crystal lattice, creating
a sort of bulged-out structure like you see right here. And dislocations are one of
the most important defects in material science
and radiation damage. They're what I like to call
the agents of plasticity. If you deform a material
enough that it doesn't just spring back, then most likely,
you were creating and moving dislocations in the material. If you think about a
couple of different ways to cause deformation-- let's bring our
perfect lattice back without all these
extra notations. If you want to slide or shear
two planes of atoms across, and they're all
bonded to each other, what do you
physically have to do? How can you get these atoms
to slide across each other? What sort of energy do
you have to put into it? Yeah? AUDIENCE: [INAUDIBLE] energy. PROFESSOR: Yep. Because all these atoms
are bonded to each other, if you want them
to move, you have to break every
bond on that plane. That's a lot of
atomic bonds to break and it's extremely unlikely
that that would happen. In fact, if you broke
an entire plane of bonds in some material like this, what
would you physically do to it? You'd snap it in half. That would be fracture. So if you broke every
bond down this plane, you would then have two
pieces of this fuel rod. That's usually a pretty
high-energy thing to try to do. So instead, if you
shove an extra half plane of atoms in
there, and the bonds are kind of funny like so,
right at that extra half-plane location, then what you can
actually do is break one. Let's say you break this
one, form the next one, then break this one
and form the next one. And for a few
atoms to move over, you only have to break a
line of bonds, not a plane. So it's much less
energy-intensive to get a dislocation to move than to
just break something in half. Now you might ask, well, then
why do things actually break? Whether or not things
deform or break is a balance between this
process, which we call slip, and breaking an entire plane of
atoms, which we call fracture. So this one's called slip. The other mode is fracture. We would rather materials to
form in systems like reactors by slip, just
moving a little bit, then just breaking altogether. Unfortunately, when enough
radiation hits materials, you can fracture things
in a brutal manner, and we'll see what happens then. There's a couple
kinds of dislocations. One of them is called
a screw dislocation. So imagine you had a whole
bunch of sheets of atoms, and you made a cut
halfway through that sheet and then moved every
plane up by one position. You then got what's called
a screw dislocation-- kind of a spiral parking
garage of atoms surrounding that core right there. You can also have what's called
an edge dislocation, which is like the one I've
got here on the board right here, where you just have
an extra half plane of atoms shoved in right there. So there's two types, and they
move in two different ways. The edge dislocation behaves
like you may physically expect. If you kind of push like
this on two planes of atoms, it moves in the
direction you push it. Screw dislocations
are kind of screwy. If you push like this,
it moves perpendicular. Not going to get into
why, but just remember, screw dislocations are
fairly screwy in the way that they behave. Not quite intuitive. But that's OK. We don't have to
worry about those. And the way that
they actually move, like we showed right here, is
by what's called glide, or slip, where dislocations can slide
just by one plane of atoms or one atomic position
in a mechanism that looks something like this. Where, as that
dislocation moves, you only have to
break a line of bonds and then reform a
line of bonds, which is a much easier
process than breaking an entire plane at once. It's like you have to
break the square root of the same number of bonds. I'm going to skip ahead
through some of that. There's one other mechanism
of dislocation movement that's important to
us in radiation damage and that's called climb. This is when you
start to think about, what happens if you have
a dislocation, which we'll give this symbol right here,
and you also have a vacancy, let's say created
by radiation damage. If that vacancy can
move, it's going to find the most stressed-out
part of this lattice. Most likely, the
vacancy will move here. In other words, the atom
will move over there, leaving this vacancy over there. It's kind of funny to
think, like, what does it mean that a vacancy moves? Has anyone ever done
anything with semiconductors and talked about electron
and hole movement? OK, yeah. So what does it really mean
for a hole to move, right? A hole's not a thing. A vacancy's also not a thing. It's an absence of an atom. But here, we can say
that the vacancy moves in this direction when the
corresponding atom moves in the exact opposite direction. And then what
you've actually done is moved your dislocation up. Instead of moving in
the slip direction, you've now moved it in a
perpendicular direction. This is usually not
possible without things like radiation damage or
very high temperature. And then, to make
things even crazier, you can also have
what's called loops of dislocation, some videos
of which I'll actually get to show you. You can have a dislocation that
has part edge character, part screw character. If you look at how the
atoms are arranged here, you're looking from
sort of the top-down. You can see that
there's an extra half plane of these white atoms
shoved in in the black ones, and this right here would be
a completely edge dislocation. You can have a
gradual transition, where about 90 degrees
later, it looks like a spiral and that's a screw dislocation. And the net effect
of that is when you push in this direction
on an edge dislocation, it moves that way. When you push this direction
on a screw dislocation, it moves that way. So when you stress out
a dislocation loop, it just grows. You're not actually creating
or destroying matter, but what you're doing is causing
this small loop of extra half plane of atoms to grow further
and further until it actually reaches some obstacle or
the outside of a crystal. And these dislocations
can actually feel the force from each other. If I draw a clean one because I
think it'll be easier to see-- if I draw a small
lattice of atoms here and then a dislocation
core right there. So that's our dislocation core. This region of space right
here is compressively stressed. There's more atoms in that
space than there want to be and so it's kind of
crammed in there. While this region
right here is in what's called tensile stress. There's almost some space,
like right here, where there's too few atoms and they
kind of want there to be more. And these dislocations can
feel neighboring stress fields. Let's say there was
another one right over here that had its own
compressive stress field. They'll actually
repel each other because you don't want to add
even more compressive stress to anywhere in this
group of atoms. So they'll actually repel
each other to the point where, if you get
two dislocations too close to each other, they'll
what's called pile-up, or they'll refuse to move a bit. So I want to show
you some videos. We can actually see
these dislocations. In this one, you see that faint
line right there originating from this area? That's actually a
dislocation loop under stress and that's actually growing. So what you're seeing
here is an image of electrons passing
through material and looking at regions
of different contrast. So wherever there is more
atoms or fewer atoms, it looks darker or lighter,
and that can tell you what sort of defects there are. You guys all see that
faint line right there? Notice how the
loop's just growing. It's not like you're
moving a line, but you're literally
growing a line out of what looks like nothing. There's another one we
call a Frank-Read source. It's a source of
dislocation loop. So what you're seeing
here, each of these lines is a single dislocation. And then right there, you
see that loop suddenly form? Let's show you that one again. I'll point on where to look. By stressing out
materials, you can actually create additional dislocation
loops, right around here. And there it is. You guys see that one? Yeah. Out of what looks like
nothing but is actually just a couple of
atomic defects, you can create a dislocation
loop and allow more plastic deformation to take place,
which I think is awesome. Look at this one. Another dislocation
source in germanium. It's a little
easier to see, also because it's making this sort
of spiral set of dislocations a little slower. So you can track its
motion a little easier. Notice how they all kind of line
up on certain atomic planes. Yeah? AUDIENCE: Does the topology
of these things ever change, or is it always just
a slow [INAUDIBLE] PROFESSOR: The
topology will change. Let's say, if it
hits another obstacle or another
dislocation, yeah, they can slam into each other
and change topology. AUDIENCE: Breaking
too [INAUDIBLE] PROFESSOR: All sorts
of things, yeah. That's a subject for a
whole other class, I'd say. I want to skip
ahead to the pile-up because I think this kind
of gets the point across. But actually, we can
see direct evidence that dislocations feel
each other's stress fields. When you get enough of them
lined up, they won't overlap. They actually push each other
in a kind of dislocation traffic jam. Because what's happening
on the atomic level is, they feel each
other's stress fields. There might be a source of
dislocations further away, but when they get too
close to each other, it literally is a
dislocation traffic jam. I mean, if you try and hit
the car in front of you, the repulsion of the electrons
between your and their bumper will prevent the cars from
getting a certain distance closer to each other. Same kind of thing here. Moving onto grain boundaries,
a two-dimensional defect. Any time you have
a perfect crystal of atoms that meets
another perfect crystal at a different orientation,
or where the atoms are arranged in a
different direction, you end up with a
boundary between them that we refer to as
a grain boundary. So you can actually see, this
is a direct physical image of atoms of two different
crystals meaning at the grain boundary. Again, taken in the transmission
electron microscope. So for those who
didn't know, yes, we can see individual atoms
and the defects between them. I definitely didn't know
that in high school. They didn't even
mention that whatsoever. Did you guys ever
see images like this? Anyone? Yes? Raise your hand. Just one, OK. So yeah. It's important for
you guys to know that we can have direct evidence
for all this blackboard stuff because you can see atoms
in the transmission electron microscope and see what happens
when the two of them meet. You see this kind of regular
structure of empty space where this grain
boundary meets, right? You can actually model it as
a line of 1-D dislocations, because if you take
a line of 1-D lines, you end up with a
2-D boundary, which you can see very clearly here. It's almost like there's an
extra half plane right there. Another one there, another one
there, and another one there. And we call that a
tilt grain boundary. Grain boundaries are nice in
that they can accommodate lots of these little
zero-dimensional defects, moving to them without
getting destroyed. So grain boundaries
are one of those ways that radiation damage
can be removed. And that's one of the reasons
why most small-grain materials are really-- nano-grain materials are more
resistant to radiation damage than large-grain
ones because they act as what's called sinks or
destroyers of radiation damage. There's another kind of 2-D
defect called a twin, where you can actually get a little
chunk of atoms sort of switch orientation. And you can see these very
clearly in, again, TEM micrographs, and the evidence
actually that the twin actually is a different physical
arrangement of atoms, even though you can't see
the atoms in this little band right there. Look at the way the
dislocations line up. Those dislocations
tend to line up in energetically-favorable
directions, and in this grain, they're all this
way, and in the twin, they're all lined up like that. And then finally, there's
the most intuitive defect, inclusions. A 3-D piece of some other
material inside what would otherwise be
a pure material. This one, I actually pulled
out of the rotor that powers the Alcator fusion reactor. I was asked to do some
analysis to find out, is the structure of
that rotor changing, because General Electric who
was insuring this rotor said, we don't want to
insure it anymore. Thanks for the premiums, but
we're not insuring it anymore. And we said, why? And they said, oh, it's
structurally unsound. So we said, oh yeah? We'll be back in a year
and we'll talk about it. And we did a lot of
this work to find out that, actually, the structure
hadn't really changed since 1954 when it was made. But what we did also
see is we could pop out little precipitates
of manganese sulfide. So there's always
sulfur in iron, and sulfur tends to
be a bad actor when it comes to material properties. You throw manganese
into iron to scoop up that sulfur in the form of
these little precipitates or inclusions, which we
were able to see perfectly when we did an x-ray
map, just like the one we did after the first exam. It's like we were looking at
Chris' copper silver alloy, mapping out where is
the copper and silver. I made this image the
same way, mapping out, where is there iron,
manganese and sulfur. That's how you can
tell what it is. And so dislocations and
defects can actually interact. Let's say this is
the interaction of a 1-D defect, a dislocation,
with a 3-D defect, a void. If you have a material
that's deforming plastically, very smoothly, and isn't
going to undergo fracture, you want the dislocations
to be able to move. If you put anything in their
way, they tend to get stuck. It's not easy for
that dislocation to shear through a whole
bunch of extra atoms. And in some cases, you can
stop that motion and favor fracture over slip. So any time you
make slip harder, it means that you're making
fracture more likely. I didn't say you're
making it easier, but you're making
it more likely. And you would
prefer for materials to deform a little bit by a slip
than just break by fracture. So I think now is a good point
to go over a few key material properties. All of these are sometimes
used to describe the same thing in colloquial speech. That is wrong. Has anyone here thought
that, let's say, stiffness or toughness or
strength meant the same thing? No. OK. A few people. It's OK. Because it's used wrong all
the time in colloquial speech. These actually refer to
different material properties with different units. And we're going to go into
a little bit about what they are and then show
you a few videos to test your intuition about
the differences between them. So first, I want to mention
what you're seeing right here. It's called a
stress-strain curve. Stress is simple. Stress is just a force
divided by an area. And usually, the
criterion for will a material deform
or will it break is does it reach
a certain stress. It doesn't matter just how
much force you put on it, but it's like, how
much force per atom or how much force per area
determines whether bonds are going to break. And so on the y-axis is stress. Let's say the amount of force
per area we're putting in. And strain is the
amount of deformation. So that's stress. And strain is, let's
say, the change in length over the original length
of some material in what's called the engineering
or simplified notation. And so something
that is stiff means you can put a lot
of force into it but it won't deform very much. That's kind of the easiest
property to understand. Is something that's
very stiff will have what's called a
high Young's modulus, or a high slope right here. Something that's super
stiff, like a ceramic, you could really push
on it quite a bit, but you won't get it to deform
like you would this metal. So the opposite of stiff,
I would call compliant. Not soft. This is one of those
tricky things right there. Something that's stiff, you try
and flex it and it won't flex. Something that's compliant,
you put a little bit of force into it and it undergoes
some amount of strain. And that slope right
there between the stress and the strain, we call
the Young's modulus. We also note that
this part right here is what's called the elastic
region of deformation. By elastic, we mean reversible,
or it snaps right back. So right here, when I bend this
bar and it snaps right back, that's called
elastic deformation. And it's reversible,
because you can bend one way and it snaps right back. If I bent it more,
which I don't want to do because this is a nice
zirconium fuel cladding rod, you would deform
it irreversibly. You'd bend it permanently. And to undergo what's called
plastic deformation, when you deviate from the slope, and
then a little bit more stress can cause a lot
more deformation. Have any of you guys ever
tried pulling copper wire apart before? That's something I'd recommend
you try, for thin wire so you don't cut your hands. What you may notice is that
it's awfully hard to get the copper deforming
in the first place, but as soon as it starts to
stretch, it gets really easy. So this is something
I recommend. Go to the electronics
shop or wherever and try it out on some
really thin copper wire. If it's thick, you'll
slice through your fingers and you don't want to do that. Strength, however, that's
a different metric. Whereas stiffness
describes the slope here, strength describes the height,
or the stress at which you start to plastically deform. They're in different units. Stiffness is in
stress over strain, whereas strength is
given as a stress. So when you hear
things like the yield stress or the ultimate
tensile strength, that's referring to how
strong something is, which may have nothing to
do with how stiff it is. Toughness is another property. Toughness is actually kind of
like the area under this curve, because if you do a force
and apply it over a distance, that's like putting
work into the material and it ends up being
a unit of energy. So toughness will tell
you how much energy you have to put into
something before creating a new free surface,
otherwise known as fracture. And ductility is how much can
you deform it before it breaks. So it would be like this point
right here on the strain axis. So I'll give a little
bit more examples of what this is all about. Toughness, again,
is actually measured as an energy required
to form a free surface, or propagate a crack, let's say. Whereas something
that's ductile, it doesn't necessarily
mean that it's tough. Like, if you have a piece
of chewed chewing gum, you can stretch it quite a
lot with very little energy. And then you can say it's
extremely ductile but not very strong. A piece of copper
wire, you can also stretch it an
extremely far distance, but it takes more
energy to do so. So that's both
ductile and strong. And then if you apply that
force over a certain distance, stretching out the
wire, you can also reveal some of its toughness
and how much energy it takes to stretch that
wire before it breaks. Hardness is the last material
property I want to mention, which is not any of
the ones that I showed on the stress-strain curve. Hardness is the
resistance to a little bit of plastic deformation. So assuming that
you're already here, how much more energy
do you have to put in to get the material
to deform plastic? So very different
material properties. I'll try and mention
all what they are. So if we have a
stress-strain curve like so, and it follows
the elastic region and then deforms
plastically, this point here is what we call
the yield strength. Whatever that point
on the stress axis is. This point right here,
our strain to failure, we can use as a
measure of ductility. This slope right here
refers to the stiffness. And finally, this
energy right here is something like the toughness. And the hardness isn't
quite on this plot. So I want to see if
you guys intuitively understand this, because
the next lecture, I'm going to be throwing around
the words like stiffness, toughness, ductility,
hardness, compliance, hard, soft, whatever,
and I want to make sure that you just at least
intuitively understand. There's a few videos you
may have seen before. Anyone here watch the
hydraulic press channel? There we go. Finally, something that
half the class does. We're going to
predict what's going to happen in each of these
cases based on these material properties. So in this case, this is a
pressurized cylinder of CO2. It's made of aluminum, which
is a very ductile material. It's also a very tough material. How do you think it will
deform when smashed? Anyone ever tried this? Squishing aluminum stuff. What happens? AUDIENCE: You compress it. PROFESSOR: You compress it. And then what happens? AUDIENCE: Fracture? PROFESSOR: Will it fracture? AUDIENCE: After a while. PROFESSOR: After a while, OK. If you put a lot of energy
into it, eventually, when you reach this strain to
failure, it should fracture. But in your personal
hands-on experience, does aluminum tend to fracture
when you bend it a little bit? AUDIENCE: No. PROFESSOR: So then what words
would you use to describe it? Based on this curve right here. Yep? AUDIENCE: Ductile. PROFESSOR: Ductile. I would say ductile
and not brittle because you can bend it quite
a bit or stretch it quite a bit before it fractures. How about stiffness? Is it really hard or really
easy to get aluminum bending? AUDIENCE: It's pretty easy. PROFESSOR: It's fairly easy. So would you call that
stiff or compliant? AUDIENCE: Compliant. PROFESSOR: Compliant. OK. What about strength? How hard is it to start
deforming aluminum irreversibly, compared
to something like steel? AUDIENCE: Not very. PROFESSOR: Not very. Especially pure aluminum. You can chew through it. If you guys ever got a
one yen coin from Japan, you can chew through it. Not very strong. Then again, your bite force
is also incredibly strong. But anyway, let's
see what actually happens when you compress a
rather ductile, compliant, and not that strong
aluminum canister. Is it actually going? Oh, it actually skipped ahead. That's what I wanted,
was their sound. It was also
pressurized with CO2. But notice what's left. So actually watch in slow-mo. Look how much you can compress
that, even after the explosion. No fracture. If you had done that with,
let's say, a glass canister, what do you guys think
would have happened? AUDIENCE: It would
have shattered. PROFESSOR: It would
have shattered. Yeah, we'll see that in
a bit with a material that may surprise you. AUDIENCE: So it basically
doesn't fracture, right? PROFESSOR: It will
fracture eventually, but the hydraulic press can't
get it that far in compression. So that would be something
that's extremely ductile, not that strong-- so it wasn't that
hard to deform. Certainly we know it wasn't
stronger than the steel base plate that they used
to do the smashing. Because whatever's
the softer material is going to deform more. So here he's going to have--
well I'll let him describe it, and then I'll let you guess
what's going to happen. What do you guys think
is going to happen? You've got what looks like
brass and copper coins on a steel base plate. Anyone have any idea? AUDIENCE: [INAUDIBLE] PROFESSOR: Yeah. Everyone's making
this motion, which means everything's going
to flatten out, right? Let's find out. Not nearly as much as
you might have expected. Is anyone surprised by this? What happened there? What actually happened there
was already described up here. When you get enough dislocations
piling up against each other during plastic deformation,
you can undergo a process called work hardening. That process can be
physically described by a lot of those dislocations
piling up and making it more and more difficult
to continue that deformation. So what happened here is
the brass and the copper, which started out quite soft,
not that hard, quite ductile, as you can see, and not that
strong actually got stronger as they were deformed. Interesting, huh? Did anyone expect
this to happen? OK. Let's go to one that I think
everyone can guess what's going to happen, a lead ball. So has anyone ever tried
playing with lead before? Hopefully not. I have quite a-- OK good, I'm not alone. How would you describe lead
in terms of the material properties here? AUDIENCE: [INAUDIBLE] PROFESSOR: Yep. It's not very stiff. It doesn't take much energy
to start deforming it. How else? Was it hard or soft? AUDIENCE: Soft. PROFESSOR: OK. Do you think it's
ductile or brittle? Yeah? AUDIENCE: It's brittle. PROFESSOR: You
think it's brittle. So by that, you mean it's just
going to break apart, right? If you deform it? OK, cool. And would you say it
is tough or not tough? Not a lot of folks have
hands-on experience with lead. It's probably good
for your brains. Let's find out. Lead pancake. So what words would you use to
describe what just happened? AUDIENCE: It's ductile. PROFESSOR: Ductile indeed. I don't know what
sort of brittle lead-- was it an alloy that you had
been playing with, maybe? AUDIENCE: It was
like a little sheet. It was just easy to snap. PROFESSOR: Aha, OK. So it was a sheet of lead
that was easy to snap. So I would not call lead
as a very tough material because you didn't have to
put a lot of energy into it, but did it deform quite a bit
before you snapped it or did it just crumble apart? AUDIENCE: Oh, it deformed. PROFESSOR: OK. So in that case, I would call
it ductile because it deformed a lot before breaking,
but I would not call it tough because it took
very little energy to get it to that breaking point. And it wasn't that stiff because
it was quite easy to get it-- let's say it's the
amount of stress you put in versus the strain. It could be quite low. And it would not be
very strong because it didn't take a lot of energy
or stress to get it moving. Let's look at another ball. In this case, a
steel ball bearing. What do you guys think
is going to happen here? AUDIENCE: It's going to shatter. PROFESSOR: It's
going to shatter. So you're guessing that the
steel is brittle, right? What else? AUDIENCE: Probably
pretty stiff and strong. PROFESSOR: Probably quite
stiff and strong, yeah. I think so, too, but
I don't think the guy that did this expected that. [INTERPOSING VOICES] PROFESSOR: Yeah. Did that surprise anybody? Yeah. Quite a surprise, right? So in this case, materials
like hardened steel aren't necessarily that brittle. In fact, you wouldn't want a
ball bearing to be brittle. If you get some small chip in it
or a little bit of grit or sand in the bearings, you would
shatter the ball bearing and cause instantaneous failure
of the rotating component. So what you actually want out
of a high-strength ball bearing is something that's
extremely hard. Resists deformation
so it doesn't undergo, let's say, change of shape
that would prevent it from rolling without friction
or with very little friction. You want it to be quite
stiff because you don't want the load of whatever you're
loading onto it to deform it, but you also don't
want it to be brittle. So it's got to be somewhat
tough and ductile to prevent sudden failure. You'd rather it compress a tiny
bit than just cracking in half. So you can make things like
ceramic ball bearings, which are very brittle, very stiff,
not that tough, but also very strong, and you just
have to make sure that whatever part
you make is not going to reach any sort of yield
strength criterion or crack or anything. Now the last one that's
probably the most surprising. They bought a $4,000 diamond. It's a diamond like that big. What do you know about
diamonds as a material in terms of these properties? AUDIENCE: They're hard. PROFESSOR: Yep, both is right. They're extremely stiff. It's the hardest material
that we know of, almost. We've made slightly
harder ones artificially. It's the hardest natural
material we know of. What else? Do you know whether
they're strong or tough? AUDIENCE: They're not tough. PROFESSOR: They're not tough. Why do you say that? AUDIENCE: Because
it will shatter. PROFESSOR: Have
you seen the video? AUDIENCE: [INAUDIBLE] PROFESSOR: Oh wow. OK. What else do we have? Yeah. So you're saying it's not tough. AUDIENCE: You can
cut diamonds, right? PROFESSOR: You can cut
diamonds with other diamonds. So the cutting action
usually depends on the relative hardness
of the material. So if you want to polish or
cut something abrasively, you need to use
a harder material because then the grit
itself won't wear away before the material
it's trying to cut. But what's going to happen here
is we're going to put a diamond and try compressing
it, and we'll see what its stress-strain
curve looks like. So votes on what's
going to happen. Who says, like Monica,
it's going to shatter? Who thinks it's going
to break the tools? Who thinks it's going
to deform plastically? Yeah, I've never seen a
diamond deform plastically. AUDIENCE: They still have
pretty big chunks, though. PROFESSOR: Oh yeah, they could
probably still sell those. Absolutely no deformation. It just rotates and explodes. Yeah. This would be a
material that we would say has almost zero ductility. Despite being
extremely hard, I don't know if there would
even been enough deformation to have a slight
dent in the tool itself. There's probably a little hole
where the point of the diamond poked in, but once there was
enough stress on that diamond, its stress-strain curve would
look something like that. Maybe like that. Yeah. So it's important
that you intuitively understand the differences
between strength, ductility, hardness, toughness, and
stiffness, because then next class, we can explain
how radiation changes them. So any questions on the
materials and properties from today? Yeah? AUDIENCE: Can you clarify why
something is, for example, ductile versus brittle? PROFESSOR: Mhm. So the reason something
would be ductile versus brittle is whether or not
you can plastically deform it, and that means whether or
not it's more energetically favorable for dislocations
to keep moving versus just breaking a plane
of atoms in any irregular direction and causing fracture. So again, ductility
versus embrittlement is the interplay between
slip and fracture. Slip is normally done
by dislocation movement. Any defects created by anything,
especially radiation damage, will make slip harder so that
any continued energy you put in will not move dislocations
but move towards fracture. If there's no other
questions, we'll look at the
stress-strain curves of some other familiar materials. It is 10:00, in case you guys
have to go to other classes. AUDIENCE: Are you taking any
nuclear activation stuff today? PROFESSOR: Yes. If you guys have things for a
nuclear activation analysis, hand it in. You guys bring stuff in? We're running out of
opportunities to do this. All right. In that case, the
entry fee for the quiz will be your nuclear
activation analysis sample.
