Welcome back.

We're beginning in this lesson to describe binary diagrams,

that is two component systems.

And the first one we're going to be looking at is what we refer to

as an isomorphous diagram.

An isomorphous diagram, as represented in this slide here,

is much like what we would consider an ideal diagram.

It's the simplest of all diagrams that we have in terms of two component systems.

And the terms that we want to describe on the isomorphous diagram

initially are up on the slide.

First, we want to describe the regions of single phase and two phase

equilibrium and some of the lines that separate these various phase boundaries.

In the first case,

what we want to do is we want to look at the line that we refer to as the liquidus.

The liquidus is the line that separates the single phase field

of the liquid from the liquid plus solid two phase region.

When we describe the solidus, again now the solidus represents the boundary that

separates the region between the liquid plus solid phase field and

the solid region.

We'll introduce, again, the phase rule, but

what you see in this particular case is a slight change in the phase rule.

In the previous lesson, when we were talking about the phase diagrams and

we introduced the Gibbs phase rule, we had it written down as F = C- P + 2.

In that particular case what we were doing is, we were looking at a system in

which both pressure and temperature were the thermodynamic variables of interest.

Now what we're going to do is modify it, and

we're doing that primarily because now we're looking at two components.

When we look at the phase diagram as it's written, we're fixing the pressure.

So we're now looking at sometimes referred to as the condensed phase rule,

where we become F = C- P + 1, and temperature is our thermodynamic variable.

Now in the single phase field what we want to do is go back and take a look at

what we mean by the degrees of freedom using this condensed phase rule.

And what we have here first is a region where we have F = 2.

In the F = 2, we're in a single phase field.

And what that means to us is that when we are trying to describe the system and

be very specific about the thermodynamics of the system,

we have to supply two pieces of information.

The information that we have to supply in this particular case is going to

be the composition of the phase,

which happens to be the composition of the alloy,

as well as the temperature at which this particular composition is being exposed.

So down in the single phase field we have a region that we refer as

the two degrees of freedom.

And, of course, we have something very similar

up in the region where we have only the liquid phase.

Now another point that I want to bring to your attention is at the bottom of

the phase diagram it says that we're looking at a solid solution.

What we mean here is that as we move from pure A to pure B,

we are allowed to have all mixtures of A and B.

And as it turns out, there's an important system that behaves this way, and

we're going to see more about it as we go into this module.

That's the copper nickel system.

And if you recall from the rules of Hume-Rothery,

if we are to have extensive solubility of one material in another and,

in particular, when we look at a system like we're describing here with this

phase diagram, the two phases, or the two components that we're looking at,

have to both have exactly the same crystal structure.

So that way we would have a continuous solid solution from A to B.

And in the case of copper and nickel, both of those elements are face-centered cubic.

So in the two phase field, now something is a little bit different.

With respect to the two phase field,

we're in a region where we have one degree of freedom.

And what that means in terms of this behavior is that we choose a temperature.

And when we choose the temperature, we automatically wind up fixing

the compositions of the two phases that are in equilibrium.

And when we wind up dropping our lines between

the location of the phase boundary with respect to both the solid and the liquid,

what we're then able to do is to determine what the composition of the phases are.

Now, what's important here is

that it is the composition of the phase that is important.

Now when we get into a two phase field we may have an overall

average composition which lies between these two phases.

But the phase that we really need to identify

is one of the single phases that define the two phase field.

So for example, when we choose the composition of B in the solid,

it is uniquely fixed at that temperature.

And, of course, we know because we have to have thermal

equilibrium between the two phases, we have to be at the same temperature.

So we have to specify either the temperature or

the composition of one of the phases.

Now when we start talking about some additional issues with respect to

the isomorphous phase diagram, again our continuous solid solution.

And now what we can do is we're going to drop a line

which takes us from some elevated temperature below the liquidus and

it's going to drop us down to a temperature below the solidus so

that we're in a single phase field, beginning and ending.

And as a consequence of being in that single phase field,

we know that the composition of the phase is the composition of the alloy.

Now when we come down into the two phase field,

once again we have a fixed temperature.

And because we have a fixed temperature, we know the compositions of one of

the phases and then immediately we know the composition of the other phase.

Then when we get down to a lower temperature where we're in the single

phase field, then what we have is a uniform composition of a single phase

material and the composition of the alloy, again, is the composition of the phase.

Now let's continue on with our analysis of the binary diagram.

And this time we're going to look at the situation when

we have equilibrium cooling.

When we cool down from some elevated temperature and we reach the liquidus

boundary, what happens as soon as we reach the liquidus boundary?

We find that we get the composition of the solid,

which is the composition of the first solid that forms.

And again, we have a horizontal line between the composition of our alloy

at where it hits the phase boundary, namely the liquidus boundary.

And then we draw the horizontal line over

to give us the composition of our solid phase.

And we drop it down to the x axis, and

now what we have is the composition of B that is in our solid phase.

Now if we go in the other direction,

that is, we start out with a homogenous alloy, we increase the temperature.

The first boundary we hit is the solidus boundary, and

that boundary gives us the composition of the solid that happens to be in

equilibrium with the composition of liquid, which is given over to the right.

And then what we can do is to drop a line vertically to

the x axis to determine the composition of B that's in that liquid phase.

Now when we look at this material, what we´re looking at for

this particular alloy composition, the difference between the liquidus and

the solidus temperature is given as those difference between the dotted lines.

And what we refer to then is that we are dealing with now

the freezing range of the alloy.

So, as we change the alloy composition, you can see because there is a difference

in the distances between the liquidus and the solidus for each composition,

we´re going to have a different freezing range for the alloys of interest.

Thank you.

1.5 Binary Isomorphous Phase Diagrams

Material Processing

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