How did you arrive at the planes on the sides of the square? I think you really teach some portions very well and do not do justice to some topics. The square lattice is one example that you make it too abstract
suppose we keep an hexagonal motif on the square (2D) lattice ; will there be a 2 fold axis passing through the centre of the hexagon ? maybe a more general query will be which elements survive ? I'm able to find some mirror planes only , not sure about them too
A very interesting question indeed. It took some time for me to analyse it in detail. Two-fold is common to 4-fold of square lattice and 6-fold of the hexagon. Thus it will always survive. There are in general three possibilities: 1. A pair of orthogonal mirrors of hexagon coinciding with the the edges of the square. In this case the two-fold and this set of mirrors will survive. 2. A pair of orthogonal mirrors of hexagon coinciding with the the diagonals of the square. In this case the two-fold and this set of mirrors will survive. 3. No coincidence between mirrors of the square and the hexagon. In this case only the two-fold survives. These three cases lead to three different plane groups (out of 17 possible two-dimensional plane groups. This topic has not been covered in this set of lectures.
Consider a square as a unit cell. Repeat it to generate other squares such that they share the edges and vertices. You get the tiling of the plane by squares. The vertices of this tiling form a square lattice.
will the symmetry of the unit cell be equal to the symmetry of lattice or they are different. As in square unit cell (in 2D) will those 2 fold symmetry and 4 fold symmetry about vertices be retained as it is in square lattice?
Not necessarily. One can choose an arbitrary unit cell not showing the symmetry of the lattice. For example, in the 2D square lattice, you can select a parallelogram unit cell that will not have the 4-fold symmetry. Conventionally one chooses a unit cell showing as much symmetry as possible of the lattice. But this is not always necessary.
No, it can be a finite object also. For example a cube has many point symmetries like rotations and reflections. But a single cube itself is niether a lattice nor a crystal.
Sir your handwriting is fabulous. I wish i could have that too! And your teaching skill is outstanding...
Best teacher in material science ... almost everything discussed
keep the content coming sir you will get a million subs.
it is government funded videos,he does not need subscribers.
I like you name
Thank you sir , really nicely explained.
very clear explanation. this tutorial series is very helpful
How did you arrive at the planes on the sides of the square? I think you really teach some portions very well and do not do justice to some topics. The square lattice is one example that you make it too abstract
Could you please explain your question a bit more. i will try to explain.
suppose we keep an hexagonal motif on the square (2D) lattice ; will there be a 2 fold axis passing through the centre of the hexagon ? maybe a more general query will be which elements survive ? I'm able to find some mirror planes only , not sure about them too
A very interesting question indeed. It took some time for me to analyse it in detail. Two-fold is common to 4-fold of square lattice and 6-fold of the hexagon. Thus it will always survive. There are in general three possibilities:
1. A pair of orthogonal mirrors of hexagon coinciding with the the edges of the square. In this case the two-fold and this set of mirrors will survive.
2. A pair of orthogonal mirrors of hexagon coinciding with the the diagonals of the square. In this case the two-fold and this set of mirrors will survive.
3. No coincidence between mirrors of the square and the hexagon. In this case only the two-fold survives.
These three cases lead to three different plane groups (out of 17 possible two-dimensional plane groups. This topic has not been covered in this set of lectures.
👍🏻👍🏻👍🏻👍🏻
Thank you sir
Prof, what is square lattice?! I did not get the actual gist of what square lattice really is.. Could u please elaborate?
Consider a square as a unit cell. Repeat it to generate other squares such that they share the edges and vertices. You get the tiling of the plane by squares. The vertices of this tiling form a square lattice.
😀😀😀😀🙏🙏🙏
Thank u sir
2:15 can we have symmetry abt diagonal in rectangle??
You can try it. Diagonal does not act as mirror.
A 2 fold rotational symmetry.
will the symmetry of the unit cell be equal to the symmetry of lattice or they are different. As in square unit cell (in 2D) will those 2 fold symmetry and 4 fold symmetry about vertices be retained as it is in square lattice?
Not necessarily. One can choose an arbitrary unit cell not showing the symmetry of the lattice. For example, in the 2D square lattice, you can select a parallelogram unit cell that will not have the 4-fold symmetry. Conventionally one chooses a unit cell showing as much symmetry as possible of the lattice. But this is not always necessary.
Sir, wont there be 4 fold about mid point of nearest neighbour lattice points
No, there it is two-fold.
@@rajeshprasadlectures yes sir. Its obvious, don't know why I got confused. Thanks a lot for replying and thanks for wonderful lectures sir.
i dont understand the point group part, can anyone help me?
it will include all non translational symmetry
Sir ,
if any system has point symmetry then can we say that that system is lattice or crystal ?
No, it can be a finite object also. For example a cube has many point symmetries like rotations and reflections. But a single cube itself is niether a lattice nor a crystal.
@@introductiontomaterialsscience thank you sir 😊