All right.
So we know that plastic deformation in metals
occurs by the movement of dislocations.
And that's the stepwise breaking and reforming of bonds.
And we, in fact, know that dislocation
is as a one-dimensional imperfection in the crystal.
Let's take a look at ways that we
can prevent a dislocation from moving
or present an obstacle to a dislocation moving.
And first, well, what we'll do is we'll go from one dimension
down to zero dimensions.
And so what's zero-- what has zero dimensions to it?
Well, something that exists-- or if I draw x, y, and z for you
here, something has zero dimensions
but only exists in one point in space, one point.
So sometimes we actually call these things point defects,
point defects, because they only have a zero dimension to them.
A line has one dimension, right?
That's a linear defect.
So we're going to look at some point defects.
And what type of a point defect could you have in a material?
And particularly, let's focus on crystalline or organized
or ordered solids.
So we have a number of atoms arranged somehow in a solid.
And I'm being very general here with my atoms.
I'm drawing them as little circles.
We're treating them as little circles.
If you want to think in three dimensions,
these would be spheres.
But here's a crystal of some atoms that are arranged.
And what if I had, say, instead of these atoms,
I had some other atom that was similar in size and properties
but maybe just a little bit bigger, something like that?
So what would be the result?
The result would be that the atoms that
are kind of close to that one-- I'm being general here--
but the atoms in the vicinity of this atom might be pushed away.
And what's this atom actually really doing right here?
This atom here is taking a spot of another.
It's substituting for one of these host
atoms, the white atoms.
So this green one is substituting for a white one.
So this is called a substitutional atom.
And because it's not the same as the ones around it,
it's called a substitutional impurity.
And what it's doing is it's a point in space.
It's not a collection of atoms.
It's not like a particle.
It's not a piece of sand in your coffee or something like that.
It's a molecule of sugar dissolved in your coffee.
In the solid case that we're talking about here,
it's a solid atom, a single atom of some other element dissolved
in this solid.
So it's actually forming what we call a solid solution.
So it's a solution in the same sense
that you would discuss a solution or a liquid solution.
But now it's in the solid state of matter.
So you could have an atom like that
that's a little bit bigger.
You could have one, of course, that's a bit smaller.
And you'd create some-- the arrows,
these red arrows would be reversed.
But you can also have an atom that's much, much smaller.
Like this green atom was roughly the same size
as that white one.
But what if it's a tiny, little atom that just fits in,
nestles into the space between some other atoms?
Well, going into the space between other things,
we have fancy word for that.
So this in space between, in the space between.
So the space between other atoms is called an interstitial site,
interstitial.
So that's an interstitial impurity.
An example of an interstitial impurity
would be carbon in iron.
An example of a substitutional impurity
would be perhaps copper in nickel.
They're both the same size.
They actually have the same crystal structure
so they can substitute in for one another.
And there you go.
There's a couple of impurities, point defects that we have.
When we have a solid solution in a metal,
we call this-- in a metal we have
another name that I'm sure many of you are familiar with.
In a metal, what do we do?
We call that an alloy.
It forms an alloy.
When we're mixing two elements together, it forms an alloy.
All right.
So that's fantastic.
The last thing I want to look at then
is, how can we use that, the presence
of some kind of impurity, to make
it more difficult for a dislocation to move?
So let me draw a dislocation here,
and I'll speed up time for you here.
OK.
Look at that.
So through the miracles of science,
I created a dislocation and really quickly.
I saved you the agony of watching me draw circles.
And we know that to get this dislocation
to move through the application of a shear stress,
we've got to have this bond or row of bonds break
and then reform, and it's going to move.
So we want to present some kind of an obstacle to that.
Well, oftentimes, what can happen
is these little impurity atoms can cluster themselves
around the dislocation line.
And they do that because that actually
creates a lower energy.
It's an easier place for them to exist.
So I'd like you to consider, say,
this scenario of the impurity atom existing
at the bottom of the dislocation versus another scenario, which
would be-- let me draw it for you.
So what if we had this scenario, where
we've got an edge dislocation existing separately from-- sort
of this thing became detached here somehow, separate
in the same material but separately
existing far away from it was this interstitial.
So you have to remember that this interstitial is disturbing
these atoms, and there's strain in the lattice.
And then this dislocation here is, [? wow, ?]
creating some strain.
There's tension below the dislocation line.
There's some compression up here.
So we can have the two exist separately,
or through random movement, just random diffusion,
this interstitial could move over and exist here
at the dislocation line.
So which one of those is at a higher energy?
Well, when they exist separately,
there's actually a higher energy.
There's more lattice strain total
when they exist separately.
An analogy-- I mean, sort of a mechanical analogy
that you could think of, I suppose,
is say you've got a bookshelf.
And maybe you've done this.
And you've got-- on your bookshelf
you've got a set of books.
OK.
Here's some books, make that.
There you go.
And you know this scenario.
You've just got this much space here to fill in another book.
And you've got to position-- what do you need to do?
You need to position this big, thick book in there.
OK?
I'm going to make it yellow.
There's your new book, and you want
to put that into the bookshelf.
So what do you do?
Well, you've got two options.
The first thing you could do is you could squeeze the book
in to that spot right there.
So you could take this book right here and squeeze it in.
But I mean, you get a sense for the fact that's not really
going to go.
And so what's going to happen is you're
going to have to squeeze it in.
It's going to deform.
You squeeze your book in.
It's hard to do.
And you get that book in there.
That's one option.
The other option that you've got, option two, is this.
Well, you realize that you have some space over the books.
Now really, I should have done this more carefully
and actually drawn the space above the books
in all the cases.
So let's just quickly fix that.
All right?
I didn't think ahead, see?
I didn't think ahead.
Bad prof.
So there you go.
OK, look, now we've got that space there
over the top of the books.
In this case here, [? this scenario, ?]
when we squeeze the book into that spot.
So scenario two, what we're going to do
is we're going to just pop the book in that space on the top.
How times have you done that?
You've probably done that before if you have a bookshelf,
and it just fits in easy.
Which one has more energy overall, when you squeeze it in
or you fit it into the space that already exists?
So this one here is in the space already existing.
All right?
Now, I don't know if this is a perfect analogy.
But the book is squeezed into the space that already existed,
and this makes for a lower energy.
That's what we're after.
So which scenario here has the book
squeezed into the space that already existed?
Well, the book, the interstitial site,
is squeezed into the place, the dislocation line,
that already existed.
There's already some space in the lattice
that you can put this impurity.
So why not put it there?
And it'll create less strain overall.
If you have them exist separately,
you have this empty space exists separate from this book that's
squeezed in, it's a higher energy.
There's higher strain energy.
Lower energy when it fills a space that's already there.
So when our interstitial filled the space that's already there,
it creates a lower energy overall.
And so it's harder than-- if we imagine this dislocation moving
through the application of a shear
stress-- for this dislocation to break away from this impurity
because it's pinned in place by the impurity.
The impurity has pinned the dislocation.
It has to go to a higher energy state of them existing
separately for the dislocation to move away from the impurity.
So the impurity pinned the dislocation.
All right?
Now, that's not the entire story,
but it's pretty good for describing strengthening
of a metal through a solid solution
strengthening, the formation of an alloy or a solid solution.