Then we'll start with that. So let's just start with vacancies, because they're really important. The I'm not going to go into this in too much detail, but you know that they're very important, for instance,

for diffusion. And they're also the predominant point effects in thermal equilibrium in any crystalline material, certainly in steel. And you can basically compute, if you

know the formation enthalpy of a vacancy, you can compute the concentration of vacancies. That's the ratio of vacant lattice places to total lattice positions.

And it's basically this exponential function. And you can plug in values for the vacancy formation enthalpy, and for the Boltzmann constant, and for the temperature. Say, for instance, we choose the reheating temperature

of steel in many industrial processes around 1250. You get 1523k. You obtain 10 to the minus 7. So that's all very well. So there are our predominant point defects.

But in our case, we're interested in vacancies, not at equilibrium, but in non-equilibrium state situation. So when you process steels, we very often do things like clenching or plastic deformation.

And when you do this, you always generate, or you end up with many more vacancies than at room temperature, for instance, than you anticipate. So you have an excess density of vacancies.

And I also said that, for instance, when you have these dipoles, you can have interstitial dipoles. And that's a way of creating interstitials in your material. But the amount of vacancies you make by plastic different, oh, it's very much larger than interstitials.

Right. Of course, diffusion, self-diffusion in substitutional diffusion in steels is related to concentration and mobility of these vacancies. And so if you have an excess vacancies, it will impact, for instance, diffusion, but also

the mechanical properties. So another thing that's important is looking at the ratio of migration to formation enthalpy of a point defect. You have an idea of its mobility.

So the enthalpy of vacancy formation in BCC metals is about the melting temperature divided by 1,000. This is the order of 1.8 eV. The migration enthalpy is related to elastic properties. And so there are formulas for that shown here.

And that gives you about 0.57 eV. So if you make the ratio of 0.57 and 1.8, you get a value that's 0.3. Well, it turns out that that's a really low value. And it's a good indication to tell you

that vacancies are very mobile in alpha iron. And that means that, for instance, when you reheat, you do a recrystallization annealing of steel, and you need to quench the material,

you will have a large amount of excess vacancies at room temperatures. We call them mono-vacancies, isolated vacancies. But that doesn't stay very long like that. They will quickly form complexes. They will attach themselves to substitutional atoms

or interstitial atoms. Or they will attach to each other. They will form vacancy clusters, basically little empty spaces in your crystal

by clustering with about typically 100 vacancies. And you can observe these things. For instance, take a steel, and you heat it up.

And then you quench it really rapidly. You can observe that your structure is full of these blobs, let's say.

And if you manage to orient your crystal correctly, if you will, in certain directions, these blobs will actually look like very crystallographic, have very crystallographic directions.

They will actually be lying on 100 planes. What are these is basically clusters of vacancies. So what you're actually seeing here is the vacancy. So this is a lattice, the pure lattice.

And you've got all these vacancies in the lattice that come together and they coagulate. So when a vacancy comes here, that

means that an iron atom has replaced it. And so when all these vacancies come together on a plane, they form a little platelet of vacancies. And so if I redraw this, but now using a dislocation

picture, this is what it looks like. It's as if I have an extra half plane coming this way, an extra half plane coming that way, and in between nothing. So it's as if I had put in vacancies.

And so you form a little circular loop. And these are these circular loops. These are these circles that you see everywhere here in this structure. So they're there. They're real.

And if you have excess vacancies, they will tend to, certainly if the concentration is high, to form dislocation loops. In addition, there's some interesting effects. This is a rather high energy situation.

And what you often see is that these vacancy loops will form on screw dislocations. And there will be a number of process steps. I will not talk about these processes.

But that will end up giving you a screw dislocation that goes like this, that form a helical dislocation. And you can see them. For instance, here is a very nice one. Looped a couple over there.

So you form helical dislocation structures as a consequence of the absorption of many vacancies on a screw dislocation. It's almost weekend, Elisa.

She's like, ah. Right. So that's for the vacancies, one type of point effect. Other types of point defects are interstitials, yes, obviously.

The interstitials we care about are hydrogen, carbon, nitrogen, and boron. Boron is a little bit ambiguous as a point defect. But let's just say a few things about hydrogen. So hydrogen is very small atom.

It's very insoluble in alpha-iron, yes. But it's very mobile in alpha-iron. Actually creates a lot of problems. And we'll talk hopefully about this when we talk about hydrogen cracking in ferritic steels.

In gamma-iron, it's very different. We have a very high solubility for hydrogen and a very low mobility. So you can dissolve much more hydrogen in gamma-iron, but it doesn't diffuse very quickly.

And it's kind of surprising because hydrogen being such a small atom. In contrast to carbon and nitrogen, which are in the tetragonal lattice interstices,

the hydrogen is in so-called T sites or tetragonal sites. This is a hydrogen lying in tetragonal site. And it has a very low activation energy for diffusion. So 0.047. So that's the activation energy for carbon is 0.8.

So it's like 20 times less. It's extremely rapid diffusing element in alpha-iron. So hydrogen can be trapped at dislocations,

in particular screw dislocation. And once it's trapped in the dislocations, one of the things we know is that it's really trapped at dislocations. So it doesn't really diffuse rapidly along the core of the dislocation to give you something that's called pipe diffusion.

It doesn't happen with hydrogen. So that's just some information about important interstitial. Another important interstitial, we'll come back to carbon, is many times in course.

So some general things. The carbon is located in tetragonal interstices in both alpha-iron and gamma-iron. The solubility of carbon in alpha-iron is extremely low.

And the reason is that even in the octahedral sites, where you find a carbon, where the carbon is located, you will have considerable lattice distortion. And so when we put in a carbon atom

in an octahedral site, it pushes, it distorts the octahedron. It expands the octahedron in the z direction, and it contracts it in the plane of the octahedron.

Right. So although we, and nitrogen does the same. Although we, and certainly in introductory classes on steels,

people have a tendency to say, well, carbon and nitrogen, they behave the same way. That's not strictly true in terms of lattice distortions, in terms of diffusivity, yes. But nitrogen, in contrast to carbon,

will stay in solution much more easily than carbon. Carbon has a very high tendency to form carbides, things like cementite. Nitrogen's much more difficult to get it out of solution.

And that's important, because you probably know from undergraduate lectures that aging is a traditional problem for steels, but it's not carbon aging that's the big problem.

It's nitrogen aging. So you really need to stabilize the nitrogen. It's more difficult than carbon. The other thing is carbon has a really nice property is that because it's not very soluble in the lattice, it will go to grain boundaries.

And when it's in the grain boundaries as a solute, it strengthens the grain boundary cohesion. So that's good. So we don't mind a little bit of solute carbon in the lattice. Nitrogen doesn't do this. Nitrogen stays pretty much homogeneously distributed in the lattice.

So when carbon atom goes from one octahedral position to the next octahedral position, the one that's closest by is this one here

between these two atoms here. It has to go through a tetrahedral position. And that's a very high energy position, and that's what explains the activation energy of 0.8 electron volts, about 0.8 electron volts.

Boron is some special properties. It's low temperatures. It's substitutional, but it diffuses interstitially. It's kind of interesting. And at higher temperature, it becomes an interstitial solute with a very fast interstitial diffusion.

So if you do thermal treatments, you take your steel to high temperature, the boron goes interstitially. And then when you quench it, you get lots of interstitial boron rather than substitutional boron, which is the normal position

of boron at low temperatures. OK, so that's kind of interesting to know. OK, so we have point defects. Point defects interact with each other,

and point defects also interact with dislocations. So let's say a few things of this. So a steel, the atoms are not really distributed homogeneously. There is a lot of point defect associations going on.

So the solution is very often not perfectly random, because vacancies, interstitials, and substitutional atoms will form complex, will form pairs, or point defect complexes.

And so this type of interaction will have an impact, because it will, for instance, have an impact on solubility or precipitation kinetics. For instance, I was going to give you an example. If you have pure iron carbon alloys, the carbon that's in supersaturation will precipitate more rapidly than in the case

of an iron manganese carbon alloy, because the manganese, when it's present, will form dipoles. So it will combine. It will have a very strong attractive interaction with carbon.

And that keeps the carbon in solution. So it prevents the precipitation formation of carbides. So for instance, a strong attractive interaction with manganese, nitrogen, and chrome. There can be attraction, but there can also be repulsion.

Weak repulsion between carbon and chrome, and a very strong repulsive interaction between carbon and silicon. One of the stable complexes in alpha-ara is our carbon vacancy complexes.

They have a high binding energy. And so several carbon atoms can be associated with a single vacancy. And the existence of these, and they are very highly mobile.

They can move very quickly to the lattice. And this association of carbon vacancy complexes has been used to explain enhancement of carbon diffusivity at higher temperatures. Things can change dramatically when

you go from ferritic to austenitic situation. So whereas carbon and vacancies form complexes in alpha-ara, they don't in gamma-ara. The interaction energy is negative. And so it's slightly repulsive.

So very complex things happen with point defects in steel. And it's not very much studied, except for people who worry about these things. If you are in the nuclear industry,

you generate a lot of point defects in your material. And you are worried about what these excess point defects do to your material. So this brings me to interstitials and self-interstitials in alpha-ara.

When you irradiate metals, you irradiate iron or iron alloys, ferritic alloys, martensitic alloys that are used in nuclear applications, you form vacancies and you form self-interstitial atoms, SIAs.

So the thing is, you have to imagine these nuclear reactors, they operate not for a few minutes, they operate for years and years. So there is this very slow but steady production

of point defects. And eventually, you get observable damage to the structure of your material. And of course, everybody is very concerned about this. And there's lots of work by the steel research

community in the nuclear industry on point defects. Yes, so these neutrons, when they interact with the solid, they create cascades of vacancies and interstitials.

And that is an unstable situation. You form clusters of interstitials. And these clusters, surprisingly enough, are extremely mobile. Yes, they are like plate-like clusters that can move very

quickly through the lattice. And these clusters will interact with dislocations with grain boundaries. And that can have quite serious effects. And we're talking about radiation damage. Now itself, when we have a single self-interstitial,

they tend to, the same way as interstitial carbon will, form specific crystalline structures. So if I push an iron atom into an interstitial position,

as in radiation damage, they will tend to form 110 dumbbells, or 111 dumbbells, which are also called crowdions. Because there should only be one atom here.

There are two atoms in that space. So they crowd each other up. And you can see that these substitutional defects, of course, are very high energetic defects. So how does this thing form?

So you have your high energy neutrons, for instance. They create displacement cascades. On the outside of this displacement cascade, I will form mainly interstitials. Inside here, I will form clusters of vacancies.

And this doesn't stay stable. You will get these excess vacancies. Excess interstitials will form voids, or will go to grain boundaries, or will be associated with dislocations.

And so as I said, one of the ways to easily get rid of vacancies or interstitials is just simply by annealing the material.

You just go to high temperature. Then you re-establish thermodynamic equilibrium, and you cool down slowly. Of course, you cannot do this with a nuclear reactor. And that is the big challenge, of course.

And I think we're done for this. So we have a few minutes. So we'll start. Just introduce the next chapter.

Why is this not crystal plasticity? Because some of the things are a little bit related to what we discussed.

And because I brought pencils today to illustrate pencil glide, and I will probably forget them next week. So we'll be talking a little bit more about crystal plasticity. And now we'll try to concentrate in that chapter

on really the detail of the motion of dislocations in ferritic steels and in austenitic steels. And how we can model their behavior.

So again, we have slip systems in austenite and ferrite. We have austenite, 1-1-1 planes, always 1-1-1 planes, no other one. And the Burgers factor for slip, A upon 2, 1-1-0. And they can dissociate.

In the case of BCC, we can have 1-1-0 planes or 1-1-2 planes. You'll see in a moment why I'm only interested in 1-1-0 planes and I pretty much forget about 1-1-2 planes as during the course.

But these are the slip systems. And the Burgers factors are along 1-1-1. So the Burgers factor in both structures is well defined. The slip plane is a little bit less defined here

because we get so frequent cross slip. So the dislocations will give us, macroscopically, the impression that the slip plane is not well defined.

Let me tell you what I mean. Right. Well, before I say this, let's just say something about the slip planes in alpha iron. So first of all, in pure alpha iron, I'm not talking about steels.

So don't say that I said something about steel, yes? But in alpha iron, if you take pure single crystal of alpha iron, this slip plane is actually temperature dependent. And at low temperature, in single crystals of alpha iron,

you get 1-1-1-0 slip. When you increase the temperature, yes, it's 1-1-2 slip, not 1-1-0 slip, 1-1-2 in alpha iron. However, and of course, there is a domain

where both 1-1-0 and 1-1-2 slip occurs. So you can get frequent cross slip on all these planes. However, in alloys, in ferritic steels,

the low temperature slip on 1-1-0 planes is extended. So we get slip on 1-1-0 planes in steels.

Now, the fact that you get so much frequent cross slip in the case of BCC means that when you look at deformed steels, you look at the grains, you never see slip lines.

You never see slip lines. And the reason is not because you don't have a well-defined slip plane. It's simply because the dislocation cross slip so often. And this process is described as pencil gliding. So now you know why I brought this with me.

So what I have here is pencils. So now I'm going to glide them. I'm going to glide them. So from your perspective, all the pens have gone this way.

Very, very clearly this way. And they didn't go a little bit upward. They just went like this, all of them. However, if I now make you look in this direction and ask you, where was the slip plane? Well, you say, well, it depends. I would have to this here and then this.

So you'd have a crooked slip plane when you would actually look at the slip plane. On the macroscopic level, where you're sitting. But if I now give you the pens, you will see that they're all hexagonal. And that actually, they were all gliding on a similar type of 110 plane,

except not a single one. So this happens in ferritic steels and BCC iron. In gamma iron, it doesn't happen like this. And the reason why it can do this in BCC

is because the dislocations can move up and down. So change glide planes. In FCC, there is no cross slip. And this is what happens. The dislocation stays on its slip plane. And so at the microscopic level, the slip plane

is very visible. But even where you stand there, you can see a line, which you didn't see just a moment ago. You can play around with this, just give it a round so you get a good feeling of the difference. But if you ever get a chance to, for instance,

if you take a hardness test, very simple hardness test on a ferritic steel and on an austenitic steel, you will see exactly that.

You will be hard pressed to find straight lines in the grains next to the hardness indentation when it's a ferritic steel. However, the austenitic steel will be full of very sharp, and very long lines.

And what basically is a very clear expression of the fact that if you have dissociated dislocations, as in most austenitic steels, you have limited cross slip,

and you have planar glide rather than wavy glide, which is the case for ferrite. And most ferritic steels will give you this. And this is this picture. So the slip direction in BCC is very well defined.

It's a 1-1-1 direction. The slip planes are also very well defined. They're 1-1-0 planes. However, the dislocation can cross slip so often that macroscopically, the slip plane appears not to be well defined.

So let me just put my pen. So it's appearance, OK? Because in the past, people would all say, oh, the slip is not chrysalographic,

right, which is really a very unfortunate choice of words. And OK, so what we will do, I'm going to stop here,

but just for the last minute, so what we'll do now, we'll try to understand how much force it takes us to move dislocations. And as we go, we'll see that there

are thermal effects in motion of dislocations, thermal effects. And that in ferrite, and so in ferritic steels, these thermal effects are very pronounced, very, very

pronounced. Consequence is that in ferritic steels, as we decrease the temperature, the stress needed to make dislocations move increase very strongly, very strongly. And that has impact on many mechanical properties of steel.

The interesting thing for us is that the start, this initiation of the increase in the stress needed to move dislocations in ferrite happens actually at around room temperature, right? So there are many applications which

are impacted by this thermal dependence of the stress needed to move dislocations in alpha iron and ferrite steels. OK, well, thank you for your patience. Thank you also for coming on Friday afternoon.

And so next week, I'll be out of town till Wednesday. And the class will be on Thursday as usual.