We have discussed the sio2 structure. Now what I would like to do is to answer the question, is it possible to decide ahead of time whether a particular material, an oxide material, is going to produce a glassy structure? Well, it was ultimately described by Zachariason who put together a series of rules that would help explain what particular systems and what are the requirements that must exist in the structure before a glassy structure can form. Now when we first begin to look at Zachariasen's rules, what we'll use is the structure B203. As it turns out, B203 happens to be one of those oxides that will in fact form a glassy network. So we'll look at it for the particular reason, that when we describe the structure of B2O3, what we're looking at is a particular polyhedron that looks like a equilateral triangle. Because of the fact that we have a plus 3 charge for the boron and a minus 2 charge for the oxygen, the structural formula is B2O3. Unlike when we were talking about silica, we had the plus 4 for the silica inside, and as a result what we had was the particular geometry of a tetrahedron. But in the case of the B2O3, which is relatively simple and easy for us to consider, we'll just look at these triangular units. So we have the oxygens in blue, and the boron that sits in the middle of the equilateral triangle. Now the question is, how do these wind up coming together and forming a structure? In the case of B203, what happens is, in order to develop the B2O3 structure from that primitive triangular structure we have, and in order to be able to balance the borons and the oxygens, all of these units are connected together with, again, what we refer to as the bridging oxygen. And generally we're going to have an angle between the borons of somewhere on the order of about 180 degrees. So it'll be less than 180 degrees, but because of the large positive charge associated with the boron, boron plus 3 and boron plus 3, there's going to be a steric hindrance to prevent those borons getting too close to one another. And as a result, what we're going to do is to develop a random three dimensional network. So, the oxide glasses, the ones that are the materials that form the glass, are composed of these, what we refer to as oxygen polyhedra. In the case of the B2O3, it's triangle, and the case of the SIO2, what we're going to have there is a tetrahedron. So we form a polyhedron, and, when we look at the polyhedron, what we're going to consider is the coordination number associated with the cations and the anions. When we first look at the oxygens, what we see is in this particular case, each oxygen is going to be surrounded by two cations, a boron 3 plus and another boron 3 plus, and you can see that in the illustration. Now when we take a look at the cation and see what its coordination number is, What we see is, that black circle is surrounded by a total of three oxygens in this case. But if we think about the SiO tetrahedral units, what we have there is each one is surrounded by four. So, when Zachariasen put these rules together, what we find is in the case of the cat ions the coordination number will be either three our four. Now as we continue on looking at the B2O3 system what we're going to come up with is the fact that the oxygens that cause the bridging are the ones that occur as a result of connecting the corners of the triangle. What we could also have happen is, rather than the corners of the triangle connecting, it would be possible to put together the two triangles having a common edge between them. Now the problem with that is once again, if you look at the boron 3 plus and the boron 3 plus in the other unit, what you see is a location where those two borons are going to want to repel one another. So this concept of steric hindrance is going to prevent this particular structure from forming. So, what Zachariasen did was to say, okay, let's see how these polyhedra all wind up connecting. So, what we're going to see is from this particular picture the polyhedron cannot connect at edges. And if we move out of B2O3 and move into silica, what we see is they can't connect across the faces. So we can't have edges, we can't have faces, and so the oxygens therefore must be connected through the bridging oxygen at the corners. And each of those polyhedron need to be shared with at least three corners. And this, then gives you the picture that we get for the development of these oxide structures. So Zachariasen put together these very simple rules in order to come up with the picture that describes the materials and the requirements on these oxide glass systems. Thank you.