So, when we look at the beginning of the JMA curve,

what we see is a part that we refer to as nucleation.

To there's a certain period of time for the grains to nucleate, for

the grains to begin to form, and then we have a particular point that we say start.

The reason we fix a start point on here, as opposed to trying to draw the line so

that the nucleation goes to zero,

is the fact that the function is behaving in asymptotic way.

So what we want to do is start when we can see a notable change in the structure.

And then what we have is at the end, the finish time, and

what's happening at that particular point

is that again we have an asymptotic behavior of the transform function.

And what we want to do is be able to terminate that reasonably, so

we'll call the termination the finish.

Now, a lot of times the start and

finish will be basically determined by how easy it is for

you to identify while you're making measurements, the start and the finish.

Okay, but once you've done that then you can go ahead and

you can assign the values for the start and the finish on the diagram.

When you look at the curve, the other thing that happens is,

the curve is beginning to slow down at longer periods of time.

And I've written up there the word impingement.

And basically what that means is, as the crystallization

amount increases, we're beginning to slowly run out of space.

And the growing grains begin to physically impinge on one another.

So the process does begin to slow down.

So now we look at the Johnson Mehl Avrami equation.

And I've just reorganized it.

And so now what I have is, I take that function,

take the log of both sides of the equation.

And I get the log of the quantity one minus x.

And that's equal to minus kt raised to the n power.

Now what I'm going to do is in effect multiply that equation by n minus one,

and this is what I get.

So i take the reciprocal of the one minus x, and

that's going to be one over one minus x, and that's going to be equal to kt.

Now if we take the logarithm one more time,

what we're going to wind up with is this function will ultimately become linear,

and it's linear as a result of that second logarithm that we're taking.

So if we plot the log of the log of one over the fraction

transformed subtracted from one.

What I'm going to get is the behavior that I'm looking for.

And that's going to be a linear behavior.

And I'm going to be able to extract based upon

the plot of the log log of one over one minus x.

I'll be able to determine what the value of n is.

If we look at a variety of different temperatures, for example,

I've given T2 and T1.

So we do the transformations, we define the start, and we define

the finish points of the transformation at the two different temperatures.

Then what we do is, we go to the second temperature, and

we do essentially the same thing.

Determine the start and the finish.

Then what we wind up doing, is to take those points that we determine

using the JMA equation, and we identify

what we refer to as the start point and we refer to it as the finish point.

And we have for the second set of data at temperature T2, we have the blue points.

And this curve, this full black curve, for the start and

the finish or in this case, 1% and 99%,

those curves are determined by running a whole series of different temperatures.

So we can fill in the data between what we have at T1 and

above T1, and what we have at T2 and below T2.

So consequently, we're able to produce the curve, and

the curve appears as it does in the visual.

Thus, the bottom curve represents

something that we refer to as an isothermal transformation curve.

We do experiments at constant temperature, and we plot those.

And that plot tells us the progression of the transformation

as a function of temperature.

So we're going to be using these isothermal transformation curves in

subsequent lessons where we can begin to talk about the different

types of phase transformations that are important to the material scientist.

Thank you.