In this lesson,

we're going to be talking about how we can apply some of these abstract concepts

of packing factors in face-centered cubic and body-centered cubic materials.

We'll begin with our calculation in the following way.

First we know that the density is mass per unit volume.

And in this particular case, when we think about mass per unit volume,

it defines a quantity that we've described previously as an intensive quantity.

That is, it doesn't depend upon the amount of material that we have.

So, in order for us to begin the calculation,

we have to come up with the description of the mass.

So, for example, let's consider the possibility of calculating a material

that is in the hearts sphere packing arrangement, either BCC or FCC.

So in this case we need to know, how many atoms do we have in the unit cell?

We need to know what the mass of each of those atoms are in that unit.

For example, if we want to calculate a body-centered hard sphere cubic packing.

What we know is that we have a total of two atoms in the unit cell,

we know the relationship between the volume and the edge of the unit cell, and

we also know what the relationship between the edge of the unit cell is and

the radius in the packing of that hard sphere BCC structure.

Alternatively if we look at the FCC material,

here's the picture of our FCC unit again.

And we have a total of four atoms in the unit cell, and

we know what the relationship between the volume of the unit cell is, and

the dimensions of the edge of the unit cell.

And we know then the relationship between the edge of the unit cell and

the radius of the hard sphere.

So this provides us all the information that we need to know

to do a calculation of density.

So let's take a look at a couple of problems.

First of all,

we'll take a look at calculating the density of a material like iron.

Iron can be, can exist in the form of material which is body-centered cubic.

So we need to return to the body center cubic lattice that we've been describing.

We know that there are, in the case of the BCC hard sphere,

there are two atoms and those two atoms lie in the BCC unit cell.

We know that the atomic mass of iron is going to be 55.85 grams per mole.