What we find is as a result of the way the atoms on the lattice or

the crystal are organized,

the structure has something we refer to as free electrons.

And free electrons is a theory that's been around for a long time, but

the interesting part about it is it goes a very long way to be able to understand

the characteristics of metallic materials when it comes to electrical conductivity.

This slide represents two important points.

The first is it shows a collection of circles,

each of which represents the core of a particular atom.

And I've organized them in such a way that each one of those is periodic so

that I could choose a small unit in which I have, for

example, four atoms that I have together.

And those four atoms can be translated either up or down, and what I can

then do is to produce that structure in either two or three dimensional space.

So, this is what we mean by the notion of a crystal and its regular periodic array.

When we take a look at a metallic material, the way the metallic

material operates is that we have positively charged cores.

And the reason that those cores are positively charged is the electrons

are able to move through the structure when a voltage is applied to the metal.

As the electron moves through the structure,

it's accelerated, it's decelerated.

And what happens is its mean free path, or the distance between the inner spacings of

those circles, wind up controlling what we refer to as the mobility of the electron.

As the mobility begins to drop,

what we find is the electrical conductivity will drop.

What we're going to be looking at are two parameters here.

The first one is we know about conductivity, and

conductivity is really the reciprocal of a property that we refer to as resistivity.

And resistivity is a property that we sometimes called an intensive property.

Mainly, if you look at the expression on the right-hand side,

where we have rows equal to A over L times big R, what we're talking about here is

the geometrical factor A over L, and it factors out the geometry of

the particular device that's conducting the electrical current.

And again, R represents the resistance.

So if we look at the left-hand side of the equation,

Ro represents what we call the intensive property that's geometry independent.

And on the right-hand side, we have the extensive property, and

that extensive property happens to be dependent on the particular geometry.

We like to be able to use intensive properties as opposed

to the extensive properties simply because we'd like to

have geometry not part of our behavior of the material.

So we're going to be talking about, from time to time,

properties that are intensive as opposed to properties that are extensive.

When you look at this very simple model, two things can ultimately emerge as

a result of the model that we refer to as the free electron model.

One of the things is that as we increase the temperature,

I've distorted these structures by making a little ellipses,

and what I've done is I put arrows inside of those ellipses.

The idea here is to indicate that as a consequence of changing the temperature

and increasing the temperature, what happens is these atoms begin to vibrate

around their equilibrium rest position.

Now what happens as a consequence of those thermal agitations is that as

the electron tries to move, it's scattered much more readily by those positively

charged cores that have been vibrating around their equilibrium positions.

And as a consequence of that, what happens is that with increasing temperature,

there is a decrease in the mobility of the electrons.

So characteristic of all metals, as the temperature goes up, the resistivity

winds up increasing, or alternatively, the conductivity begins to dry.

If we consider now the same collection of atoms, but this time,

we've introduced either another atom that makes up what we

refer to as a solution, or we wind up creating a vacancy,

that is one of the atoms happens to be missing in this periodic array.

Whenever we do that, once again, what we do is to change the mean free path of

the electron, and therefore, the mobility.

And what you can see by the mathematical expression on the right

is as you change the number of these defects that are in the lattice,

what you wind up doing is to decrease the electrical conductivity and

increase the electrical resistivity.

So the presence of these impurities will have

an adverse effect on the conductivity of the material.

What we're going to focus on here is that, in general, metals tend to be more

dense than some of the other materials that we're going to be looking at.

And density plays into our understanding and

how we can apply certain materials to specific engineering structures.