 is it clear principle? Face center atom, so what you have to keep in mind is very important I will discuss other things also into this with reference of this you know result only that in FCC unit cell, in FCC unit cell the face center atom is in touch with adjacent face center atom, coordinate flux carrier atom but adjacent face center atom also right. Opposite value you let it be this face center is in touch with 1, 2, 3 and 4 plus 4 coordinate 8 and when you extend this the upper cube right there also the face center atom I will touch adjacent face center, so the coordination number is what? Coordination number is 10, Coordination number also you can do but this one is easier I will do it clear it. Rank is 4, Coordination number is 12, so what is the packing fraction? That will be 4 into 4 by 3 pi R cube by A cube and this will be what R over A correlation we already have this is 0.74 you will get 0.74 which is 74 percent and percent is void is what? 26 percent you will see the packing fraction here also it is more than BCC because number of effective atom is also more hence it should occupy more volume sorry more volume of the cube than the other 2 right. Now other thing you see here like I said FCC is the most important one for this chapter mostly you will get questions from this only because it is speaking of tetrahedron octahedron sorry void form of this okay now you see what I said this coordinate atom so two things I have told you just now face center is in touch with adjacent face center atom and coordinate atoms are also in touch with 4 face and 3 face center this coordinate atom is in touch with this face center this face center and over all the face center okay so imagine like this this here is in touch with or here what I mean is this is in touch with okay you have so you are in touch with here you will have a void because shape is spherical okay go ahead here you will have a void this void forms by the combination of 1 2 3 4 so this void is a tetrahedron see does it look like a tetrahedron yeah another thing you already know that this face center is in touch with that face center and this face center okay so overall we will have a void over here okay so we will have a tetrahedron void because 4 atoms will have a tetrahedron void here also okay one body type will pay you have 2 tetrahedron one here you have to do 1 2 tetrahedron void 1 1 body type up you see this one You can see the yellow one, you can float it. This is the square, okay? And this attempt, which is the sentence of the front face, it will be a little outwards, okay? Okay, leave it. This one, the one above and the one below, leave it. This four are in touch, right? Yes. Okay? You put one on top of this, and look from below. So, you'll have this void here, okay? What is the interface? Okay? That's what I'm saying, square by pyramid. This is one, this is one. So, square by pyramid is not forming. One square is formed from this square, one above and one below. Okay? Look at this square, this square is formed like this. Okay? One, two, three, four. One, two, three, four. And this one, the center of the face, that will be this. And one below will be the center of the face. So, there will be a void at the center of the face. Okay? The one that will come here, that void is octahedral void. Six here. Six here. Six here. Yes. Six here. Octahedral is six. Eight is also going to come here. Don't get confused with that. I have been actually, when steric number is six, it is octahedral. Square by pyramid, it's not eight. Okay? Is it clear? So, void together? Void with a gap. Okay? So, FCC unit cell may have two voids, two types of voids possible. One is tetrahedral and octahedral. Okay? Now, the position of this void is very important. Okay? Void present. That is very important. So, on one body diagonal, we have two tetrahedral void present. Write down. So, you can watch this. In FCC unit cell, on one body diagonal, we have two tetrahedral void present. Okay? So, total number of tetrahedral void is what? Number of? Six. What is six? How is it over? How many void diagonals are there? Four. Four. Four. That is, two corners are there. There are eight corners. So, four voids diagonals are there. Okay? A Q. A Q. A Q. Right? So, four void diagonal. So, four void diagonal gives you total eight tetrahedral voids. There are eight tetrahedral voids present within the unit cell. So, contribution of all these tetrahedral voids, which are atoms or ions, tetrahedral voids to present, what will be the contribution? One void. Because, in the unit cell, it is here. Okay? It is here. So, contribution will be one. Even for octahedral void also, the contribution will be one void. Correct? How many octahedral voids present? One. One at the body center. And at all edge center also, octahedral void is present. Edge center, you have to imagine the entire crystal lattice. No. No. What? No. No. The point is, you will have an octahedral void here. You have to imagine octahedral void. And at all fifths, edge center, you will have an octahedral void. You have to imagine the entire crystal lattice. Okay? But I will select you to memorize this. Okay? Edge center will have octahedral void. Body center will have octahedral void. So, if I ask you, how many octahedral voids are present? So, what will write? Four. One for this, contribution is one. In center, what will be the contribution? One by four. So, one by four into? Eight. Twelve. So, that is three. Three plus one? Four. Is it clear? Position of octahedral void, you should know. It's very important, okay? Edge center will have an octahedral void. Do I have to go wrong? Just go. What? Solution number. No, it's not. You are taking the corner atoms. Can you answer one thing? I don't know what are you talking about. I will ask you only one thing. With one corner, how many faces we can draw in the crystal atoms? This face? No, diagonal. Diagonal. Diagonal. Why are you considering? It's diagonal. It's not a face of unit cell. Face of unit cell. I am talking about. For this corner, you see you have three faces. Here are the four faces. So, I think they are. Okay? So, position of octahedral void is at the body center and all instead. Number of octahedral void is what? Four. Four. Number of tetrahedral void is what? Eight. Eight. Rank is what? Four. Four. So, if the effective number of atoms of unit cell is n, then the number of tetrahedral void is 2n and number of octahedral void is n. Position is very important. So, it comes in the other way. Because sometimes you will get questions about the number of atoms that are removed. Okay? So, you should know where are they removed? Where are the corners removed? Tetrahedral removed? Octahedral removed? And what is the formula of the crystal? Position you must remember. We will do that question. How many atoms were initially purchased by cubic? Cubic, cubic. So, tetrahedral void is n? Yes. Tetrahedral is 8, no? So, it is 2 into n. Number of octahedral void is n. Yes. Okay? So, simplest way of telling you, cornered cube, imagine. So, we can use. No, taking another cube in a cube. So, that's what happens. So, whatever you have done, that's what I want to tell you. What I am suggesting is you don't take cornered atoms. You get confused. The best way is to take this space center. This is 4 iron touch, 4 corners and 4 on the top. Okay? Now, there are two, three things we need to again find out here. Can you tell me, we'll have an octahedral void here at the body center and at that edge center. What is this distance? Which is the same thing? This face center here. Okay? Sorry. This body center octahedral void and one octahedral void here. Root 3 by 2. Root 3 by 2. Root 3 by 2. Let's just see. No, first understand. This edge center and this body center. What is this distance? A by 2. Yeah, A by 2. This is A by 2. The entire thing is A. This is A by 2. A by 2 and what is this? A by 2. A by 2. So what is this? A by 2. A by 2 is square root. A by 2. A by 2 and this is the hypotenuse. A by 2 whole square plus A by 2 whole square root under root. Okay? That is A by root 2. A by root 2. Correct? What happened? It was simple. A by root 2. A by root 2. A by root 2. A by root 2. A distance. This is the distance between the two octahedral void. We are trying to find out the distance between the two octahedral void. Minion is the distance between the two octahedral void. Question is asked. This is the minimum distance of the two octahedral void and what is the edge length of the unit. It's just a geometry. So this distance is what you are getting? A by root 2. This octahedral and this octahedral void. Both are H-centered linear. This is the distance. This is A by root 2. A by root 2 means the distance between the two octahedral voids is what? A by root 2, right on this, distance between the two octahedral voids is A by root 2. What is the distance between the two octahedral voids? Where is the betahedral voids? Here. Leave this here, in the classroom, imagine for the end of the week. Here, a tetrahedral void is on the top of the garland, okay? And the center is here. So what is the center's shear distance? Totally, it's root 3 by 2, because the bird angle is root 3. This half is root 3 by 2. What is the half of that? Root 3 by 4. What is the other half? Root 3 by 4, the two are added. Root 3 by 2. Where is the distance between this tetrahedral void and this tetrahedral void? Root 3 by 2. Which is on the same void angle. The distance between the two octahedral voids is root 3 by 2. Root 3 by 4, root 3 by 4, add it. Root 3 by 2, okay? But the distance between the void angle is also root 3 by 2. It's root 3A, not root 3 by 2. Okay? So root 3 by 2 is the distance. Root 3 by 2 is the distance between the two tetrahedral voids on the same void angle. Now, we are trying to find out this tetrahedral void and this tetrahedral void. Okay? What will be the distance between the two? Now, how do I say it? Let's call it AB. Okay? AB, we need to find out. Questions on where we are at? Okay? We need to find out AB. Body central where O is written. O, E again AB. E again body center O. Or, what are you doing? This edge length is CD. Okay? This edge length is CD. Okay? This is AB. And this is the body center O. We need to find out the distance. Can you take it out? Can you take it out? Yes. So this is A. So what is this? 3 by 2. Over a similarity we can leave it. Okay? What do you say? Decrease. It's clear. Yes, whatever. Okay? Okay? Okay? Yes. So this distance is about 3 by 2. On the same bird eye. And this distance is A by 2. This is the smaller one. So minimum distance between the two tetrahedral voids is A by 2. And this is the minimum distance. 3 by 2, 3 times more than this. 3 times more than this. So, a question directly pushed there. What the minimum distance between the two tetrahedral voids is this? What is the edge length? You know the formula you can write on A by 2 is this. The price of that will be the answer. Or suppose A is the edge length. They'll ask you what is the minimum distance between the two tetrahedral voids? Or you can say what is the distance between the tetrahedral voids at the same bird eye? That will be root 3 times A by 2. So for the minimum distance it's a different range. Yes, yes. This is for the bird eye and this for the bird eye. Because this distance is coming, this distance is coming lesser than this. So obviously A by 2 is root 3 times more than this. This will be the minimum distance. And for the rest it will be this. Change to 1. Sorry about this. So minimum distance between the two tetrahedral voids is what? A by root 2. A by root 2 is for tetrahedral voids at two different bird eye. The distance between the two tetrahedral voids at the same bird eye is what? Root 3 by root 2. Okay?