 types of unit cell types of unit cell this classification is based on the arrangement of atoms ions or molecules ok classification this classification is based on arrangement of atoms ions or molecules mainly we have two types the first one is primitive unit cell primitive or we also call it as simple unit cell primitive or simple unit cell the second type we have centered unit cell centered unit cell see the first part of this chapter like I said all those concepts of void unit cell geometry and all this concept should ok you have to imagine the structure also I will make you understand but if you think like and memorize simply and do the questions is very difficult ok the concept you have to understand that is in the first part of the chapter second part you have to memorize ok so for reference will be this classroom to understand the structure of the crystal that we discussed ok centered unit cell further classified into three categories ok the one the first one is BCC body centered cubic unit cell BCC is body centered cubic unit cell FCC is face centered cubic unit cell and in centered cubic unit cell ECC in centered cubic unit cell the most important one for this chapter is FCC FCC is the most important one BCC then the next important ok in center is not that important ok in centered cubic unit cell and centered cubic unit cell ok one will discuss this see I have been BCC body centered cubic unit cell cubic unit cell is unit cell the cube ok so you can draw a unit cell like this will have hexagonal unit cell also possible and when we say hexagonal unit cell it is a hexagon ok not a cube you have a cube in this right unit cell is this ok now like I said unit cell is this now when this unit cell you repeat in three dimensional or in all these three directions ok it is like a matchbox thousand matchbox if you are inside by side top and bottom you will get the entire lattice ok yeah if you have this what we say any structure suppose if you have an entire structure like diamond what is the basic structure of a diamond tetrahedral and you have an arrangement of tetrahedral carbon 4 carbons right now this 4 carbons the tetrahedral arrangement is actually there in the if you arrange this pattern in three dimensional space you get the entire structure of what diamond ok now when you take this particular structure out now what we say we have a repeating unit of tetrahedral carbon chain in diamond structure if you want to study the property of diamond you take the unit cell out you study the property of this that will be the property of the entire crystal ok so crystal is made up of a basic repetitive unit and that basically repetitive unit is what unit cell right mainly we will discuss about cubic unit cell ok that is the most important one excellent also possible only one thing is there we will discuss that ok but we will have this one only in the chapter cubic unit cell now this cubic unit cell like I said what is the lattice point lattice point is what where the atoms molecules are ions are placed ok so here you see if I place the atoms only at the corner these are the corners how many corners are there in a cube 8 corners right if atoms are placed only at the corner do not draw this a still simply we will do this one by one so these are the lattice point ok there are 8 corners so lattice points are this when the atoms are placed here ok now in a cube we will have 8 corners how many faces 6 faces you should know this 8 corners 6 faces how many edges are there 12 edges right 6 faces so we will have 6 face centre also 12 edges and 12 edge centre also so when the atoms are placed only at the corners that is simple unit cell or primitive unit cell correct this is one thing in the centre unit cell is what apart from the atoms at the corner the atoms are other position also into the unit cell like if you want to define this bcc we will have atoms at the corner and atoms at the body centre that is what is body centered cubic unit cell bcc if you want to define along apart from this atoms at the corner one atom at the body centre body centre means suppose this is a cube right so we will have atoms at all corners on the top four corners on the bottom right so we will have atoms here also at the body centre this is body centre unit cell ok face center is what we will have atom centre corner along with the atoms at the face centre right this is one face centre another face centre is this this face centre this all the face centre right so when the atoms are placed at all face centre it is known as face centered cubic unit cell ok in the centre means what atoms at the corner plus atoms at the opposite phase, any two opposite phase like the center and the center or this center and this center or this center and this center and see a front wall. There are three different units here, we have centered units here, we will discuss this like there are many things we have to find out into this like suppose if I ask you what is the effective number of atoms present in primitive unit cell, what is the effective number of atoms means what in a unit cell how many atoms are present, see actually you see 2 2, primitive unit cells what what did I ask you how many atoms are present in the unit cell, so effective you need to find out, so when the atoms are at this corner okay the entire atoms is not within the unit cell suppose me is corner peg atom broke okay, so there are many like the most part of the atoms is outside the unit cell corner peg atom there the most part of that atom is outside the unit cell, so we have to count only that part which is within the unit cell, so you tell me one thing with this corner see when you do this question in the exam then I will be better examination also see what cube model and it will be easy for you to do that, now suppose the atoms are present at that corner okay now how many cubes you can draw from that corner, how many cubes you can draw only one, why a cube here will be here, so 4 in this plane and 4 in the top also, so when you take this entire 8 cubes this will be the center of that cube, so it means what the atoms present at this corner is distributed in among 8 cubes right, that's why the contribution in one cube is, here if I ask you what is the effective number of the atoms, 8 corners and the contribution of one corner is 1 by 8, so 8 into 1 by 8 is 1 okay, so we have to do all these conclusions, we have to do separately, this is same but you should know the contribution corner to k contribution, ok, but there are one thing which we will discuss before this write down, there are next line, there are 7 primitive unit cell, there are 7 primitive unit cell possible, there are 7 primitive unit cell possible and their variations are and their variations are as follows and their variations are as follows, so I will draw this table, on this table they have asked question once, this all these possible variations we call it as Bravier's lattice, they have asked how many Bravier's lattice is possible, write down here, so I will draw the table you copy it down, this you have to memorize, the first column I will write down here, crystal lattice, then the possible variations edge length axial distance also we call it as an axial angles, so we are taking the reference of this, this is x, y and z, edge length on x axis is k and opposite angle is alpha, it is b and this is beta, c and this is gamma, because we will have to take the reference of this, so we will take this as c, this is gamma and this is b, this is beta, because actually what happens I have will draw this table with reference of this, if you change this a, b and c the entire thing will change, so copy down as it is, the length on y axis is c and opposite angle is gamma, z axis is b, beta, a and alpha, so the first crystal lattice we write down, we have cubic crystal lattice, the first one is cubic, now in cubic the different possible variations are, we can have primitive unit cell, primitive unit cell I will write it as PRM for reference, primitive unit cell and we can have body centered BC or we can have face centered, only these three possible variations we have, what is the edge length for cubic, cubic of a is equals to b is equals to c and what is the axial angles, all three angles are 90, alpha, beta, gamma, 90, this is the first thing, now the next one is tetragonal, the possible variations is primitive PRM and body centered, only two possible variations here, primitive and body centered, the edge length is a is equals to b does not equals to c and the angle is all three angles are equal to 90, tetragonal, the next one is orthorhombic, orthorhombic, orthorhombic all four possible variations are there, primitive, possible, body centered possible, face centered possible, in centered possible, all four possible variations we have and here the three edges are different, a does not equals to b does not equals to c, but the angles are still 90 degree, the next one is hexagonal, hexagonal we have only one variations we have that is primitive, only one variations and then the edge length is a is equals to b does not equals to c, alpha, beta is 90, but gamma is one but b, rhombohedral or we also call it as trigonal, rhombohedral or trigonal in this only we have one possible variations that is primitive, a is equals to b is equals to c, alpha is equals to beta is equals to gamma, but it is not equal to 90 degree, monoclinic, the second last one monoclinic, two possible variations primitive and in centered, a does not equals to b does not equals to c, alpha gamma is 90 and beta is not equal to 90, the last one is triclinic, the only possible is primitive, a does not equals to b, does not equals to c, alpha does not equals to beta, does not equals to gamma, does not equals to this are the possible variations. Now, I say I have given this in a pattern, if you remember this you can write on this easily, first one all three are equal, last one is not equal all three are different then reverse, the last one is not equal all three are equal and the for the last two are not equal, it does not equals to b does not equals to c, because they will ask this they will give you for author and wrong way, what is the this like this they have given four options we need to choose this, for example a question many times this here also you will get this question, bit sad, whatever example you write c, j it is not it will not come most probably because very straight forward ok, but in other example you definitely get this ok, and C i t with d i y all these things you have to memorize this h length and xl, so it is in a order I will suggest you to memorize this and then you can write on this, first three all three angles are equal and directly gamma is 120 not equal to 90, now the possible variation like I said three here, three plus two, five plus four, nine ten, then eleven, thirteen and fourteen, that is why we have fourteen that is what this question also ask many times, how many possible variations are there that is possible that is fourteen answers, got it ok, and all these edge length and x and i angles based on this, x axis where we have a, y axis c and b z to b, a to the opposite of alpha, b to the opposite of beta, c to the opposite of alpha ok, if they change this in the exam if they give you this axis also, if they change this a here, c here, v here like that the entire thing will change ok, so that is why it is important.