On occasion, we're interested in predicting the behavior of materials.
And in this lesson, what I would like to do is to introduce the concept of
a phenomenon that is related to adding certain elements to a material.
And there is a law that describes what happens
during the additions of these materials to the structure of the material.
I'm going to first give an example by looking at a simple raft of bubbles,
and so that's what's up here on the slide right now.
This is the result of an extensive investigation by Bragg and
his co-workers early in the 1900s, in 1947.
What they did was to take a solution that contains soap.
And they bubbled air through that solution.
And if they controlled the pressure of the air, and
the diameter of the capillary that was blowing the bubbles.
They could make a nice uniformed distribution of bubble sizes.
And when those sizes were packed together,
what you found was the high packing factor that you normally see in either FCC or
BCC, so we've seen this packing structure before.
We're going to make use of these bubble solutions to illustrate a number
of very important points, not just in this module, but in a subsequent module.
What I want to point out here is that if we look at various locations
in this bubble raft, and what I've done is I've illustrated these regions using
an equilateral triangle and what you can see is that this raft is perfect.
And what we have is no missing sites, and
in addition to having no missing sites, we have perfect alignment.
So then what we're looking at is in effect a two dimensional single crystal.
Now suppose we take a bubble raft, and this time we control the size so
that we can produce a uniform raft of spheres of the same dimension.
And then, on occasion, what is introduced is a sphere
of larger diameter, using a different diameter capillary.
And as a result of that, what we've done is to produce a solid
solution with all the radii being the same
surrounding one of these bubbles that is slightly larger.
And what you can see here is what we've described in previous discussions in this
module is the fact that we wind up distorting the structure in the vicinity
of this slightly larger radius soap bubble.