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visit MIT OpenCourseWare at ocw.mit.edu. MICHAEL SHORT:
Anyway, today is going to be a lot lighter than the
past few days, which have been heavy on theory and new stuff. And I want to focus
today on what can you do with the photon and ion
interactions with matter. So we're going to go
through a whole bunch of different analytical
and materials characterization techniques
that use the stuff that we've been learning and see
what you can actually do. And I'll be drawing
from examples from the open literature,
from textbooks, and from my own work. So stuff I was doing
here on my PhD thesis is actually a direct result of
what do we do here in 22.01. So a quick review just to get
it all on the board of what we've been looking at. So I don't hit
anyone on the way in. We talked about different photon
interactions, which include the photoelectric effect. Let's say this
will be the energy of the scattered whatever, and
this will be its cross section. We talked about
Compton scattering. We talked about pair production. For the photoelectric effect,
the energy of the photoelectron comes off like the
energy of the gamma ray minus some very small
difference, the binding energy of the electron. Let's just call it Eb. And this effect starts
when you hit what's called the work function. I'm just going to put
this all up there, so when we explain the
analytical techniques, we can point to
different bits of this and explain why we use
these different things. The cross-section, I made
sure to keep this handy, so I don't want to lose it. Strongly proportional with z. So the cross-section
comes out of another line. What was it proportional to? Oh yeah, this is nuts. It's like z to the fifth
over energy to the 7/2, which says that for
higher z materials, the photoelectron yield
is much, much stronger, and it's way more likely
that way lower energy. So you can imagine
if you wanted to use this in an analytical
technique, and you want to study which
photoelectrons come from which elements, you might think to use
a low energy photon to excite them, not a high energy photon,
because like we had done a couple of times
before, if we draw our energy versus major
cross-section range, we had a graph that looks
something like this, where this was the photoelectric effect. This was Compton scattering. This is pair production. And so by knowing what energy-- oh, I'm sorry. That's supposed to be z. And this would give you
the dominant process that each the combination
of energy and z. So if you know what
energy photons you've got and what you're looking
for, well, there you go. Let's see. What was the energy of
the Compton electron? Remember the wavelength formula. It was like alpha 1
minus cosine theta over-- let's see. Another 1 minus cosine theta. In came the gamma ray energy. What was the part
that came beforehand? That's why I have this
here because I don't want to write anything wrong. It's good to have it
all up there at once. 1. Yeah. That's all I was missing. Cool. And the cross-section
for Compton scattering scaled something like z over
energy, something pretty simple, not nearly as
strong as pair production or photoelectric
effect, so you can think Compton scattering
happens much more dominantly at low
z or the other two don't really happen
that much at low z, whichever way you
want to think of it. And for pair production, you
get a whole mess of stuff. You get positrons coming out. You get a bunch of
511 keV gamma rays and all sorts of other
things you can detect. And the cross-section,
this one's got the funny scaling term. This one, yeah. It's like z squared log. Energy over mec squared, so some
z squared kind of dependence. So let's keep those up for now. Let's get the electron ones in. AUDIENCE: [INAUDIBLE]
mez squared? MICHAEL SHORT: Was it z squared? Let me check. No, that's a c. AUDIENCE: [INAUDIBLE] MICHAEL SHORT: Yeah. Yeah, just make sure
that's clearly a c squared. So now let's call
it charged particle, or just more generally
ion electron interactions. Since these are more
fresh in our head, what are the three
ways in which charged particles can interact with
matter that we talked about? Just rattle off any one of them. AUDIENCE: Bremsstrahlung? MICHAEL SHORT: Yeah,
Bremsstrahlung or radiative. What else? AUDIENCE: [INAUDIBLE] MICHAEL SHORT: Is what? AUDIENCE: Ionization. MICHAEL SHORT: Ionization. Which we'll call
inelastic collisions. And? AUDIENCE: Rutherford scattering. MICHAEL SHORT: Yep,
Rutherford scattering. Which are kind of elastic
or hard sphere collisions. And if we had to make
kind of a table of when do we care about
which effect, let's say this was an ion or
electron, scattering off of either electrons or nuclei,
in either elastic or inelastic ways. First of all, when
do we actually care about elastic
scattering off of electrons, which would be
hard sphere collisions off of electrons? To help get you going,
in an elastic collision, the maximum energy transfer
can be this formula gamma times the incoming
energy, where gamma is 4 times the incoming mass
times the mass of whatever you're hitting over
n plus big m squared. Let's say if one of these
masses was mass of an electron. What is gamma approximately
equal for most cases? Well, let's say this was
like electrons scattering off of protons or vice versa. How much energy
could an electron transfer to a proton in
an elastic collision? Basically zero. The only time which
this actually matters is if it's an electron hitting
another electron, in which case you can have pretty
significant energy transfer. So I'd say for elastic
collisions off of electrons, you only care about those
for other electrons. And I'm going to put in
low energy electrons. Why do we only care about
them for low energy electrons? Or in other words, what are the
other methods of stopping power or interaction-- yeah, Chris. AUDIENCE: [INAUDIBLE] MICHAEL SHORT: Exactly. Yep. We already saw
that Bremsstrahlung the radiated power scales
with something like z squared over m squared. So with a really small
mass and a really high z and also a higher
energy, you end up radiating most of that power
away as Bremsstrahlung. And there's not much of a
chance of elastic collision. So we only care about
low energy electrons when it comes to elastic
collisions with electrons. For inelastic collisions
with electrons, well, that's the hollow
cylinder derivation that we had done
from before where you have some particle with a
mass m and a charge little ze, getting slightly deflected
by feeling the pull-- depending on what charge it is,
it could be towards or away-- of that electron away from
some impact parameter B. So we care about this
pretty much all the time. Electrons and ions or
stripped bare nuclei actually matter in this case. For elastic collisions
off of nuclei, this is what Rutherford
scattering is. It's a simple hard simple
hard sphere collisions, so this matters pretty
much all the time. What about inelastic
collisions with nuclei? What does an inelastic collision
actually mean with a nucleus? So fusion could be one of them,
but let's go more generally. We have some nuclear reaction,
where it's the old thing that I keep drawing all the time
of some little nucleus striking a large nucleus. In an inelastic
collision, this is the case we haven't
considered yet, but I want to show you
what actually happens. In an inelastic collision,
these two nuclei join together to
form what's called a compound nucleus
or CN, at which point it breaks apart
in some other way. So there might be some
different small particle and some different large
particle coming off. But in an inelastic
collision, it's almost like the incoming
particle is absorbed and something else
is readmitted. It could be that same particle
at a different energy, and it could be a different
energy altogether. So yeah, I'd say
fusion is an example. It's kicked off by an
inelastic collision, because you've got to have
some sort of absorption event of the small nucleus
by the big nucleus. And then, maybe if it fuses
and just stays that way, it releases a ton of
its binding energy, well, that's pretty cool. So these actually
do matter, but not for all energies in all cases. So let's go back to the Janis
database of cross-sections to see when inelastic
scattering actually matters. Bring us back to normal size. And we'll look at some
of the cross-sections to see when do we actually care
about inelastic scattering? So we haven't selected
a database yet. Let's say we're firing
protons at things. And pick a database
that actually has some elements listed. Not a lot. But iron, that works. So we can look at the difference
between the elastic scattering cross-section and the
anything cross-section. So the red curve here-- can I make it thicker easily? Probably. Yeah, I can make it
thicker pretty easily. Easier to see. Plots. Wait. That's not what I wanted. I'm not going to mess
around with this anymore. Do you guys see the two lines? OK, so this is the elastic
scattering cross-section. Kind of funny to
see it negative. But then there's the
anything cross-section which picks up at around 3 MeV or so. And it usually takes
somewhere between 1 and 10 MeV for inelastic scattering
to quote unquote turn on, and that's because
you have to be able to excite the nucleus
to some next energy level. So sending in a proton
at like 0.01 MeV is not going to excite any
of the internal particles to a higher energy level. So if you want to see some
pretty interesting cases, let's go to incident
neutron data where we have a
ton of this data. And I'll show you some examples. We've got lots more
data for neutrons. So now we can look at some
of these cross-sections. Like this z n prime. Let's take a look at
what that looks like. That means a neutron comes in. Different neutron comes out. Notice that the scale
only starts at 862 keV. So let's make it something else. Oh my. Look at that. Nothing going on until you
reach almost 1 MeV, which means, hey, inelastic
scattering doesn't really turn on until that. So I would say that
this can matter, but for higher
energy collisions. So yeah, it matters
pretty much all the time. But higher energy collisions. And there's actually-- yeah. AUDIENCE: What does it
say in the top left box? MICHAEL SHORT: Only for
low energy electrons. That's the sort of compound
reason that I and Chris said, one, is that you can't
transfer much mass in an elastic
collision, or I'm sorry, much energy in an
elastic collision unless the masses are
close enough to each other. And two, at higher
energies, the electron radiates Bremsstrahlung
much, much, much faster. As we saw at around
10 MeV, Bremsstrahlung and inelastic scattering give
about equal contributions to the stopping power for
high z materials like lead. So once you're down and
let's say like the keV range, yeah, electron elastic
collisions might matter. So we talked about those three. Now I think we can launch
into the analytical technique. So for the rest of the lecture
today, it's all going to be what can you do with the
stuff that we've been learning since the first exam. I know it hasn't
been long since, but we've actually
learned a ton. And I want to show you
what's actually possible. And this is not going
to be with slides. It's all live from
websites that I'd love for you guys to be able to
follow along with or check out at home. So I'm going to show
you an awesome resource through the MIT libraries
and how to get there. If you go to
vera.mit.edu, there's a great tool called
the ASM Handbook. You can see I've
been there before. There's the ASM
handbooks online, and this is kind of
that's everything to know about material
science, metallurgy, and analytical techniques,
absolutely everything from corrosion to fractography,
to characterization, to structure of materials
to where you can find every single alloy, to
binary phase diagrams of how things mix, and we're going to
head to one of these handbooks. Number nine or 10,
materials characterization, because with the stuff
that's on this board, you can understand how most
materials characterization techniques work. And I want to show
you a few of them. One of which-- no, two of
which, we're going to demo out next Friday's recitation. So I think I told you
guys in the syllabus and probably in
person that we're going to try out some
scanning electron microscopy and some energy
dispersive X-ray or EDC analysis. So with the X-ray transition
stuff you've learned, you actually know how
to elementally analyze different materials. And with scanning
electron microscope, you can get some idea about how
electrons can make images much better than optical images. So let's head to electron
optical methods, scanning electron microscopy, and show
you what one of these things actually looks like. Let's take a look at an SEM, or
scanning electron microscope. So up at the top, there is a
device called the electron gun. For now, just imagine it's
a source of electrons, but in a few minutes,
we'll actually explain how it works
using the principle of thermionic emission, which
we talked about last Friday. You've got some
electronic lenses, some focusing coils, that
caused this beam to get focused further and further. So let's say you had this
electron filament giving off electrons in all directions. When you see boxes with x's
like this on an electron optics diagram, it usually means
this is like a focusing coil of some sort. So that will cause the electrons
to get bent and focused. There'll be another set of
coils that focuses them further and some scanning coils
that actually raster or xy scan this beam across the
surface of a material. And so in this way,
what you're actually doing is putting the
electron beam at one part of your material and
then with another detector, let's call it a secondary
electron detector. Looking at the electrons
produced from collisions with those other electrons
that then get detected here, and the number of electrons
produced at a point gives you the
brightness of the image. That's kind of as simple
as it is despite how complicated this diagram looks. There's an electron source. There's coils that
scan it back and forth. Like has anyone ever seen
the old cathode ray tube, CRT televisions? There's going to come a
day when that answer is no. And I'm kind of
worried for that, because that's the day
I'll officially become old. But for now,
everyone's seen a CRT, and the way that
actually works is there's an electron gun that
fires and scans left to right and up to down our rasters and
produces that electron image. In an SEM, you use an electron
gun, kind of similar, and then collect the electrons generated
in the specimen, what's called secondary electrons. And the number that
you see gives you the brightness of the image. The cool thing is
this actually allows you to look at both
secondary electron contrast and topology of a sample. So let's say this was your
secondary electron detector. And you had an electron beam
scanning across your sample to some of those
peaks and valleys. And I'll probably draw one
right here for a good reason. Let's say the electrons
hit right here, and you send out a wave
of secondary electrons. The material partly determines
how many electrons come off, but also, so does the geometry. There will usually
be a little cage with some sort of a
positive voltage on it to attract those
secondary electrons. And some of them will curve into
the detector and become part of your signal, but
some of them won't. Meanwhile, if you have this
beam right here producing secondary electrons,
pretty much all of them go slamming into your detector. And that's what actually
allows the electron microscope to get topology. That's why images in
the SEM look fairly 3D. So I want to show you a few
examples from my own boredom when I was doing
a lot of science. There we go. I have a whole
gallery of SEM images when I was supposed to be
doing something better. Oh no. 404. My website's broken. Oh yeah. This is also what you do
when you're bored, right? Make your own 404 page. My SEM galleries are dead. Well, that's OK. I have other images
ready to show you guys. So this is a neat-- this is
a paper that I published out of my PhD work that
shows the real difference between optical and
electron microscopy. Part of it is the limit
of your resolution depends on the wavelength or de
Broglie wavelength of the thing you're using to make the image. So an optical
microscope, in this case, you can't get better resolution
than about half a micron, because even the blue
wavelengths of light are getting down into about
the 450 nanometer regime. And it's very difficult
without interference techniques or other fancy things to
beat that diffraction limit, to beat the sort of wavelength
limit of optical microscopy. So this is a 500x
optical microscope image, and you can see these
little fingers-- in this case, it's
liquid lead bismuth penetrating into
a stainless steel that we were doing
corrosion experiments on. And that's as good
as the image can get in an optical microscope. Switch down to an SEM,
and then all of a sudden the picture becomes much,
much, much more clear. You can start to see things--
the best SEM we have in our lab has an ultimate resolution
of about 1 nanometer. Now, resolution is
kind of a funny thing. It's neat to tell
you what that means. It doesn't mean that if
you have a pattern of lines that are exactly one nanometer
thick, that you will see them as lines 1 nanometer thick. It means that if
you then plot, let's say, your signal or your
brightness versus x, you'll have some barely
distinguishable and fuzzy lines, just enough for you to
say those are two optically distinct features. So what you'll actually see
in a 1 nanometer microscope is maybe something like this. That's technically resolved
at the level of 1 nanometer. So the best you can do for
crisp objects in this thing is about 20 nanometers. Not bad. It's like something that's a
few thousand atoms on a side. Pretty cool. And so what you can see in
here is liquid lead bismuth penetrating into
this stainless steel, and you notice a few
different things. This image was taken in
backscatter electron mode. Back scattering is-- we've
talked about this before. When you have a scattering
event where theta equals pi, we call that backscatter. Let's kind of split this
into regular and backscatter. For a backscattering, the
cross-section for this is proportional to z
squared, another one of those extremely z dependent
cross-sections, which means that the larger the z,
the higher the atomic number the more backscatter
contrast you get, so if you want to figure out
where the little lead whiskers are penetrating into
the stainless steel, since lead has a z of like 82,
and iron has a z of like 26, it shows up like night and day. Do you have a question, Julia? OK. Yeah, so this is something
we'll actually be able to do. So for the two folks I
asked to bring in samples, if you want to bring
in something with very different elements
in it, we should be able to see it in backscatter
contrast very, very clearly. And in the image of the
SEM, I'll go back to that-- which one of these pages is it? Notice here that there is
a backscatter detector. So it will detect which
of those electrons scatter back at
almost 180 degrees. And that's at about z squared
proportionality, super useful tool, because if you want
to see, for example, where the circuit board
traces are, and you want to look at aluminum
versus oxygen contrast, that'll help you really well. If you want to see where
is lead penetrating into stainless steel, it
shines up clear as day, which is pretty fun. The other thing
the electrons will do when they enter
into a material is excite lots of things. So anything from X-rays
to Auger electrons. So now I'd like to bring up
Auger electron spectroscopy. Electron or X-ray
spectroscopic methods. Auger electron
spectroscopy, it's not just a thing to
trip you up on the exam or a little minutia
from radioactive decay. It's actually incredibly
useful, because of where the Auger
electrons are generated and what they tell you
about the material. So as a quick refresher,
normally you could have, let's say, if a photon comes
in and injects a photo electron as another electron
comes to fill that hole, either an X-ray will be
emitted or an Auger electron will be emitted. And it's those Auger
electrons, they're outer binding energy electrons. They have very low binding
energy, which means-- let's see. I keep running out of room. You know, I'm not
going to draw it. I'm going to show you, because I
know there is a diagram of what I want to show you here. If you want to see where the
Auger electrons are actually produced in the material-- here we go. Since they're such low energy,
the only Auger electrons that actually get out would be
in this outer few mono layers. In fact, there's some
Auger electron energies that can only get out
one or two atomic mono layers from a material. So it's one of the
best surface analysis techniques that we have. You can both use Auger electrons
to make an electron image, like any other SEM. And you can collect them
and measure their energy to figure out which
elements they came from. And this kind of
teardrop shape is a-- one, it's a great synthesis
of all the information you need to know in the SEM
that we'll see on Friday. And two, its why people
screw up SEM analysis a lot. A lot of the X-ray
excitation happens down here. Why do you think that the
X-ray exaltation would happen near the end of the path
of the electron beam from what you know
about stopping power? Or, if I asked you to
draw a graph of let's say energy versus stopping power
for ionization, what would it look like? Yeah. AUDIENCE: It comes up
like a peak at low energy. MICHAEL SHORT: Yeah. AUDIENCE: And then
drops back down. MICHAEL SHORT: Yeah. AUDIENCE: And as the energy goes
out, it sort of flattens out. MICHAEL SHORT: Yep,
sort of flattens out, and then eventually starts
picking up again but not very much. So as the energy of
whatever you're going into-- I'm sorry, whatever
particle you're sending in it gets lower,
it's stopping power increases, and you have a much higher
chance of this ionization happening, especially in
the case of electrons. They usually come in at
between 10 and 40 kV. And so near the
end of their range is where they produce
a lot of the X-rays. Now there's a lot
of other nuances to say, well, which
X-rays were produced here and what elements are they from. Let's say you had the same
material here or here. Fewer X-rays will get
out of the bottom region than they will from
the top region. So if you happen to
be analyzing something that has a gradient
in composition or a change in composition
from the top to the bottom, you might be like, oh, well,
I have a few nanometers of oxygen on silicon. Why aren't I seeing
any oxygen X-rays? Because you're probably
generating them down here. That's one of those
things to note. So sometimes you'll
see and elect an elemental map of
things that shows X-rays of certain element
coming from somewhere, and you can't see it
at all in the image. That's because they
might be underneath what you can see in the image. It's kind of tricky like that. I'll show you some examples
of what those maps look like also from this paper. So from the electron
image, we sort of concluded, all right, lead
is probably penetrating into the stainless steel. How do we know for sure? You can make EDX or
elemental dispersive-- I'm sorry, energy
dispersive X-ray maps by focusing the electron
beam at one point, collecting all the
different X-rays and then moving from
one point to another to see when do you get
characteristic X-rays from each of those elements. So you can actually
prove to say, yes, those little fingers
are indeed bismuth and lead, and you can see that, in this
case, where the lead in bismuth is, the iron is not. But the curious
thing we found is that in this whole band right
here, most of the chromium disappeared. So it turns out that
the corrosion mechanism was chromium dissolution. And we would not have been able
to know that without this EDX mapping, and without
understanding how the EDX maps are made from the electrons
interacting with matter and producing
characteristic X-rays, wouldn't have been
able to prove this. Yet another example
where the basic stuff you're learning in 22.01 is
the theoretical underpinning of the techniques that
we use all the time in material science, which
I thought was pretty cool. I've got more
examples of that that are even more
striking, because I let it collect for a little longer. You can actually see right
here that where the bismuth is, the iron isn't, but the
iron's not dissolving. The chromium is. It's just the lead
and bismuth are kind of sucking the chromium
out of the metal right there, and that's what making the
stainless steel less stainless. It's pretty neat. Then on to EDX analysis,
what sort of information are we looking at every
one of these pixels? I have a couple of other
example X-ray spectra. So now we're in a
position to understand why one of these X-ray
spectra looks the way it does. In this case, we're firing
electrons at a material. Let's see. Where is our material
we're firing at? Right here. So we're firing in electrons. And in some cases, let's
say we had an iron atom. That electron can
eject another electron. And then one of
those other electrons will fall down in
that shell, giving off a characteristic X-ray. In this case, since it's from
the third to the second shell, that would be what we call
an L X-ray or a something to level two transition. And every element has got
its characteristic X-ray transitions, like we saw on the
NIST X-ray transition database. And since we know
what all of those are, we know where to expect them. So we know where we expect
to see chromium's X-rays and iron's X-rays. Gold's kind of an
interesting one. There's two things about
doing analysis with gold. A lot of times you have to
coat your materials in gold to boost their secondary
electron contrast. But also gold, I think
it's its L line or M line, I forget which one, is the
same as argon's K line. And we have an expression
in the electron microscopy world, the probability of
finding argon in your sample decreases with experience. Takes a second to parse that. Chances are, if you're
looking at a solid material. You don't have argon in it. But there are extra lines
that overlap with each other, like the L line for gold
and the K line for argon are at pretty much the
same energy, certainly similar enough that it's
within the resolution or like full width of half
maximum of these two peaks. So remember how we were
analyzing the uncertainty of our banana spectra with
the FWHM or full width at half maximum? Same thing here,
and you can really see that the energy
resolution of this detector is not the best. So if you see a
peak, it might be due to two or more peaks
crowding in that right there. And with a lot of correction
factors that I won't get into, you can then use
this information to integrate the area
under these peaks and get elemental analysis. You can say how much chromium
or how much iron and silicon is in one of these samples. What's this stuff
here on the bottom? Anyone tell me? That continuum of
observed X-ray energies? AUDIENCE: Compton. MICHAEL SHORT: Compton
scattering is a photon effect, so that would be-- if this were a photon
analysis spectrum, then you would see something like
this but of a different shape. You'd have that Compton
bowl with an edge. But this is, in
this case, electrons interacting with material. What do you think is causing
that broad background? Well, what are the different
ways in which electrons can interact with matter? You're seeing the
ionizations here. We're not really seeing
Rutherford scattering. What's left? AUDIENCE: Bremsstrahlung? MICHAEL SHORT: Bremsstrahlung. Yep, that's exactly it. So the observed
Bremsstrahlung spectrum follows this sort of
characteristic peak early and then tail off curve. What's the actual
Bremsstrahlung spectrum that we're not sensing? What would it look like? Always running out of room. If this is what we're
actually observing, let's say we have a few peeks,
that would be intensity, and that would be energy, what's
really going on physically that we're not seeing? Yeah. AUDIENCE: Isn't it sort of like
almost like exponential decay. So it starts out with very
high intensity and goes down. MICHAEL SHORT: That's right. You actually should get more
low energy Bremsstrahlung. One of some of the
reasons you don't is that the lower energy,
those X-rays come out, the more they get self-absorbed
in the material in the few gas molecules in the SEM and in
the window of the detector. So just because
this is what you see doesn't mean this
is what's actually going on in your material. If we think back then to where
the electrons and X-rays are generated, the X-rays that
are generated down here, the lower energy ones are
going to be shielded more. And this kind of messes up
your elemental analysis, because if the
X-rays produced here, proportionally more
of the low energy ones will get out than
the ones produced here. So as you change your-- as you change your
electron beam energy, you might see your elemental
composition appear to change when you know it's really not. And that's because where the
X-rays are being generated change, and proportionately,
more of the low energy ones get self shielded
by your material. So you actually have
to correct for that and input your beam energy
into the EDX analyzer so it knows how to
correct for this. But with the understanding
I've been giving you guys in this class you
can understand like well, why can you get screwed up? Why do we have to have all
these correction factors? I think it's pretty neat. Then let's get on to some of the
other methods, like X-ray photo electron spectroscopy or XPS. This is something I
hinted to a little bit earlier that actually uses
the photoelectric effect, because it's a photo
electron spectroscopy method. This one's incredibly useful
because not only does it tell you what
elements are there, but in what binding
state they are, because photo
electron spectrometers can be incredibly precise. The energy equation should
look pretty familiar to you it's whatever photo
electron you get is the gamma ray
energy that comes in minus the binding
energy of that electron and the work function. And so you can very,
very simply figure out for a given element
and a given electron shell what photo electron
energy's do you expect. So you can collect them. So I'll show you another
example from this paper, where we started to do that. We wanted to answer
the question, what are the oxides forming
on the stainless steel when lead corrodes it? And just telling
you which elements are there and in what
proportion doesn't give the answer, because
what if there's multiple phases of each oxide? Like, for example, iron can take
forms like FeO, Fe2O3, Fe3O4, and this FeO can actually have
a range of stoichiometries. So how do you know? You don't know. There could be like scores
of phases of this iron oxide. The question is how you
know which ones are there. The photo electrons
will tell you. So what you can do first is fire
monochromatic X-rays, so single energy X-rays, in this case
from aluminum at your material and see which photo electrons
of which energy come off. And you can tell
which atomic shell they're from and which
elements they should be to a very high precision. In this case, this is done
to 100 milli MeV or 0.1 MeV precision, 0.1 eV precision. So we can tell not only
what elements are there, but what shells they came from. Then you can get even crazier. You can scan very
slowly over one of these peaks with
0.001 eV precision and start to see
something pretty cool. If you look at the
carbon 1s electrons, you can see that there
are actually three of them only a couple eV apart,
and this corresponds to different binding states
of molecules with that carbon. For an even more subtle
example, but ended up being incredibly
important for us, here's one of the
chromium 2p shell peaks. You can actually
see there's three of them superimposed
give that funny looking peak shape right there. What that actually
tells us is that there's chromium in three different
binding states in that oxide. And the ones we figured
out must be there, we saw the ones corresponding
to Cr2O3, FeCr2O4, and I forget which other one,
but we have them tabulated. There we go. Oh wow. Fe 2.4 Cr 0.64, known
crystallographic phases of these oxides. So you can look
at the peaks found to have resolution of like
100th of an electron volt, compared to reference values
taken on pure compounds and materials to figure out
what actual oxides do you have. That can help tell you things
like how protective are they, how fast are they going
to grow, and are they going to be a
problem if you want to use this new stainless
steel that we developed in a lead bismuth reactor. The biggest problem with
lead bismuth reactors is lead corrodes
like everything. And so the whole point
of my graduate studies was design an alloy that
doesn't corrode and lead and make ab alloy
composite out of it. But you can't prove that it
works unless you not only know how fast it corrodes, but how
it corrodes, which oxides form, and in what order. That's the last
part I haven't told you about yet is what order. So I want to switch to another
technique called secondary ion mass spectroscopy or SIMS. In this case, you start
off with firing ions at a material, which will
then eject or sputter away secondary ions. In this case, this
process of sputtering-- let's say this is
your material here. You send in something
like oxygen ions, which might be like O2 minus
with a mass of 32, and then you blast
off or sputter away. A few atoms at a time
from that surface, and they'll come off the
various masses and charges, and in this case,
the sputtering could be due to Rutherford scattering,
because you might directly ballistically slam and
ion out of the surface. Then every one of these
ions has a different mass and a different charge. And by sending it through
a mass spectrometer, something that separates
these materials by their mass to charge ratio, because
the higher the charge, the more deflected
an ion will be. But the higher the mass, the
less deflected it will be. That should sound
really familiar. In our idea here where how these
ionization collisions happen, if you remember the
higher the charge, the stronger the Coulomb force-- that q1, q2 over r squared. I think there was a
constant in there. So the higher the charge,
the higher those q's, and the stronger
the Coulomb forces. But the larger the masses, the
less momentum it can impart. And so the deflection
will be weaker. Exact same thing's
happening here. And you can separate
out atoms not only by their charge and their
mass, but specifically by their isotope. So this is one of
those ways that you can figure out and make an
isotopic map of a material in three dimensions. You can scan your ion
beam across the material and collect the
ions at every point. And as you sputter,
you slowly wear away layers of this material. And so you can actually
reconstruct a 3D map with almost nanometer precision
of every single isotope that was at every location,
which is quite cool. As you can see, these
master charge ratios can depend on which isotope
of silicon you have, what sort of cluster, what
molecule, what charge you have. And you can do some pretty
crazy analysis of things to even figure out
what sort of compounds exist on surfaces, because
sometimes you sputter off whole molecules. They're going to have their
own mass to charge ratio. And that's what we did for
this lead bismuth work. Lots of XPS spectra
to jump through. We wanted to find out
which oxides were forming and in what order. Which one's the best
one I want to show? Think it's this one. So in this case, we
used ion sputtering to sputter away surface layers
to a depth of a few hundred nanometers, and we're actually
able to show that the chromium oxide, right here, was on
the outside of the sample, followed by silicon oxide,
followed by iron metal. So in this way, we
were able to figure out using XPS, the
nature of the oxides and using SIMS, the
order of the oxides, so not only how fast were they
growing to nanometer precision, but in what order did they form. And that helped us
figure out this sort of synergistic chromium and
silicon oxidation mechanism that helps really protect the
layers of the stainless steel and explain why it's corrosion
resistant lead bismuth, all using principles from 22.01. So it's about two of five of. So I wanted to stop and
see if you guys have any questions on these
analytical techniques, knowing that we're
actually going to go do a couple of these next Friday. Has anyone used any
of these before? Yeah, which ones have you used? AUDIENCE: SEM and
XPS, XPS [INAUDIBLE] MICHAEL SHORT: SEM and XPS? OK, cool. Yeah, we've got all
these instruments I think except for
SIMS here at MIT. Yeah. Yeah. AUDIENCE: Sorry, what
is that second equation on the energy for
Compton scattering? MICHAEL SHORT: This would be the
energy of the Compton electron that comes out when a
photon scatters off of it. So the photon will end
up losing some energy, and the Compton electron
will pick up that energy. AUDIENCE: [INAUDIBLE] MICHAEL SHORT: Sorry? AUDIENCE: What's the
denominator of that? MICHAEL SHORT: It's a
1 plus alpha times 1 minus cosine theta,
where alpha-- I'll mention what alpha is. It's a ratio of the photon
energy to the electron rest mass energy. This is kind of a nice-- on
these two boards right here, it's kind of a nice
summary of the stuff we've been doing over the
last three weeks or so, and then all the stuff
I showed you today is what you can do with it.
