 In the last video, we have seen that the underlying translational symmetry of a crystal can be represented using Bravais lattices. And because crystals can form different repeating patterns, so we also have different corresponding Bravais lattices, right? Now in this video, we will try to put a name to these different Bravais lattices, to these different patterns, so that we can talk and communicate about them much more effectively. Now to do that, we think about the unit cell that makes up the lattice. So in this video, we are going to try and understand what a unit cell is and which unit cell should be chosen to describe a particular lattice. So let's jump right into the video. Let us take a look at this particular two-dimensional lattice. Now if we were to name this lattice, what would you have done? Well, we can think of this lattice to be made up of these squares, right? We can take this particular square and we can translate it. And in this way, via translation, we can cover up the whole lattice. So all we did was we thought of a particular unit that on repetition can cover up the whole lattice. So this particular unit is called the unit cell and a unit cell should always be so selected such that on translation it can cover up the whole lattice. Now because this lattice can be thought to be made up of squares, so we can like go ahead and call this a square lattice. Now are there other ways of describing this lattice using some different unit cell? Can we describe this lattice using say a triangle as my unit cell? Can a triangle on translation cover up this whole lattice? You can pause the video and think about this for a moment. Well, if we took this triangle and if we translated it, if we did that, we will realize that there will always be these gaps that are left behind, right? So a triangle on translation does not cover up a whole two-dimensional space. There will always be these gaps left behind. So a triangle cannot be considered to be a unit cell. Now that the triangle is out of the picture, what about using this parallelogram as a unit cell? Well, of course we can use it, right? If we take this parallelogram and if we translate it and because this lattice is infinite in all directions, so this parallelogram can cover up the entire space of the lattice, right? So even this parallelogram can be considered as the unit cell. Now because this lattice can now be thought to be made up of this oblique shaped parallelograms, so instead of calling it a square lattice, we might have called it an oblique lattice instead, right? Now besides this parallelogram and the square, there are also many other ways of selecting a unit cell. We can for example take this rectangle made by joining all these lattice points. We can think of this as the unit cell because clearly this rectangle on translation can cover up the whole lattice or we might have simply chosen a bigger square or maybe a longer parallelogram. The choices are actually pretty limitless because all these shapes on translation can cover up this infinite lattice. So even all of this can be thought of as the unit cell. However, unlike the square and the oblique, which has lattice points only at the corners, all these other unit cells has lattice points at the corners but also at some additional places, right? Now all such unit cells that have lattice points only at the corners, all such unit cells are called the primitive unit cells. While all others which have lattice points at some other positions also, besides the ones at the corners, all such unit cells are not primitive. Now because there can be many different non-primitive unit cells, so therefore we do not focus much on them and instead we generally use these primitive unit cells to describe our overall lattice. However, the non-primitive unit cells do play a role sometimes and we will talk more about this in a future video. Now can you think of some other primitive unit cells that can describe this lattice? Well actually there are a few more, right? We can think of this lattice to be made up of this kind of oblique unit cells or maybe even these ones which are like more oblique. So there are many such ways but we will go ahead and bunch all of these together and call them obliques. So because this particular lattice can either be thought to be made up of squares or obliques, so we should either call it a square lattice or an oblique lattice. So what do we call it? Do we call it square or do we call it oblique? We have to make a decision, right? And this decision actually depends upon the unit cell that best describes the symmetry of the overall lattice. So what do we mean by this? Let's try and understand. So what exactly is a square? Well besides the fact that in a square all the sides are equal and all angles are 90 degrees, so let's take a square and try to rotate it along this particular axis. If I do that we will see that the square repeats itself after 90 degrees, right? In other words if I start from my original position and if I rotate this square along this axis by 360 degrees then the square will repeat itself one, two, three and four times, right? So we say that this axis has an order four and we call it a C4 axis of symmetry. Now a square also has other axis of symmetry like this one and if we rotate the square by 360 degrees along this axis the square will repeat itself two times. So we call this axis as C2 axis of symmetry. So a square has C4 and C2 axis of symmetry. What about an oblique? Well if I rotate the oblique by 360 degrees along this particular axis then the oblique does not repeat itself after 90 degrees. In fact it repeats itself only after 180 degrees and so during a full 360 degree rotation around this particular axis it repeats itself only two times. So in an oblique this axis is not a C4 axis but instead it's a C2 axis of symmetry. Now if we try rotating the oblique around this axis then we will see that the oblique repeats itself only after 360 degrees. Now even an asymmetrical object repeats after 360 degrees, right? So this is not an axis of symmetry. So clearly a square is much more symmetrical compared to an oblique, right? Now if we come back to our original lattice and if we try to rotate it and do remember that these lattices are infinite in all directions. So if I rotate it, the lattice will repeat itself after 90 degrees, right? In other words we can say that this particular lattice has a C4 axis of symmetry and because a square possesses this symmetry while a parallelogram does not so a square better reflects the global symmetry of the lattice so we will call this a square lattice. Well what about this particular lattice? Even this lattice can have both a square as well as a parallelogram as its unit lattice, right? So would you call this a square lattice or would you call this an oblique lattice? Well if I took this particular lattice and tried rotating it and do remember that this lattice is actually infinite in all directions so if I try rotating this lattice the lattice will actually repeat itself after 90 degrees, right? So you can see that this square has repeated itself while the oblique has not repeated itself. So because this lattice is infinite in all directions the global symmetry of the lattice is better described by this square rather than this oblique so even out here we will call this a square lattice. So we can now conclude and say that if there is more than one unit cell that can describe the overall lattice we should actually choose the more symmetrical unit cell as the more symmetrical unit cell will better describe the global symmetry of the lattice. So now that we have understood what a unit cell is and which unit cell should be chosen to describe a particular lattice in the next video we are going to talk about different Bravais lattices in two dimension and three dimension and we are going to classify them into different categories. So see you in the next video.