In this lecture, we're going to start talking about directions. Now, previously, I did mention when we were talking about lattice structure, distances from the origin or the lattice point in reference to 000 or, 1/2, 1/2, 1/2. Now we're going to clarify those by looking at how do we identify positions in the unit cell, and how do we make notations about a specific direction and a family of direction. A family of direction means they have the same linear density, they have the same symmetry. When we talk about individual directions, we're going to use this square bracket, we can enclose it with integers or fractions. Now notice there are no commas in here. With our notation, we just have them separate, no commas. Then we're going to look later at a family of direction. Again, those things are going to be based on the carrot brackets. Those mean those directions that have the same linear density, same symmetry. Now, we saw earlier that the direction of the BCC materials, for the case of iron, that is when we grow out the single crystal, we want to grow it along the [111] direction because that gave us the highest modulus of elasticity. Now, that's BCC. Nickel is FCC so we want to grow that one in the close packed direction. That's going to be along the [110]. For different crystal structures, we can have the flexibility to grow along specific crystallographic direction to give us the maximum strength or whatever. Now we look here is silicon ingot, which has a diamond structure, which is FCC lattice with a two atom basis as 000, and the other at 1/4, 1/4, 1/4, that gives us the diamond structure. In this particular case, we're going to grow along the [100] type direction. That means once I cut the wafer, correct. If I cut it perpendicular to that growth direction, that means all those atoms on that surface for that single crystal will have the same properties. Here, I can do the same thing with gallium arsenide semiconductor here, I'm using it to play my DVD. It's grown along the [001] direction, and notice here it has the gallium arsenide structure or the zinc blende structure as FCC lattice two atom basis. But as opposed to being the same atom, I have gallium at 000 and arsenic at 1/2, 1/2, 1/2. Because of the symmetry, I can do it the other way. I could say arsenic at 000 gallium at 1/4, 1/4, 1/4. I got to give you the FCC lattice plus two atom basis. For the diamond structure I got a FCC lattice, two atom basis. I got silicon at 000, silicon at 1/4, 1/4, 1/4.