We're going to continue with the analysis using the JMA equation.

We'll use some data and we'll take a look at the data and see how we can,

from the data that we have, we can determine the values of k and m.

Now, let's focus our attention on calculating the parameters in

the Johnson-Mehl-Avrami equation.

In order for us to do that, we need some experimental data.

And what we are provided here is the experimental data where a certain phase,

alpha, is transforming to a second phase, beta.

The process is over when all the alpha is replaced by beta.

And this, for the first set,

we're looking at one particular temperature, at 415 degrees.

So what we want to do is, we'll plot the data, then we'll indicate on the data

plot what the start and the finish of the transformation are.

And then, ultimately, we would like to be able to derive a rate constant to

describe the transformation behavior.

In order for us to do the third part of this, we're actually going to have to have

another set of data taken at an additional temperature.

Okay, so let's answer the parts A and B first.

We're looking at this isothermal transformation and

here are the data that are now plotted.

And I"m plotting the data,

fraction transformed, as a function of the log of the time.

So there's my data.

Now what I do is to, I fit a curve through that data set.

And what I will identify is the start of the transformation and

I'm going to identify the end of the transformation.

Now, in terms of part C, what I'm going to do is to take a look at

my JMA equation again, and I'm interested in determining what the rate constant is.

The way that I'm going to determine the rate constant is I'm going to

determine it at a particular time.

And when I put in a particular time, then I will calculate or determine

what the value of the rate constant is at that particular fraction transformed.

So the easiest way, because of the way that I have written the JMA equation,

I'm going to determine the rate constant at 1 over the temperature.

So when I insert 1/t for my rate constant, I get the expression that has

the minus exponential of -1 raised to the n power.

And what you see here is, by doing that, I can evaluate the exponential.

And I come up with a value of the fraction transformed of 0.6321.

So at the value of k equal to the reciprocal of temperature,

this is the value of fraction transform that I'm going to use.

What I do then is to take that plotted data and

identify where I am taking my rate constant.

So here are the data set and here's how I have identified the data.

And what I've done here is to identify the fraction transform 0.6321.

And once I've identified that,

I'm going to determine based upon the fact that k is equal to 1 over t at that point.

And thus, what I'm able to do is to calculate based upon what the time is for

that material to transform to 63% of the total fraction

of the alpha phase going to the beta phase.