Not sure of the cell vector. In what context do you use it? But lattice vector is a precisely defined concept: a vector from one lattice point to another lattice point. If by cell vector, you mean basis vectors defining a cell, then these are three special non coplanar lattice translations that span a unit cell.
One application we make of this is in determining the reciprocal lattice of FCC. Since reciprocal lattice is defined in terms of primitive basis of real lattice, it is important to find one. ruclips.net/video/A1V8J68afsA/видео.html
Very good explaination, Sir. But there is a mistake at @8.23 in this video. Contribution of each cornered atom in primitive unit cell is not 1/8. Although total number of atoms in one primitive unit cell is 1. Plz correct me if I am wrong.
Thank you for observing this. You are indeed right as all corners do not include the same solid angle. But for the purpose of calculation of effective number it works out fine to think that the contribution is 1/8 from all corners. More correctly, this is average contribution from each corner. Let us look at it differently. Focus on one corner (corner focus). Eight unit cells share this corner. And amount of sphere in each of these unit cells is not the same. Consider one particular unit cel out of these 8. Now focus on a unit cell (unit cell focus). This has eight corners and different parts of sphere is included in the unit cell at each of these corners. One of these corners will have exactly the same part of sphere included in the unit cell. So eight corners of one unit cell have one to one correspondence with eight unit cells at one corner. And as eight unit cells at one corner include one atom, eight corners of one unit cell also include one atom. I agree all this is a lot of hand-waving. A more precise proof of the statement will require adding all the solid angles of a parallelepiped unit cell. And I hope, that analogous to the theorem for 2D parallelogram, where the angles sum to 360 degrees giving a complete circle, there must be a theorem for 3D parallelopiped where all the 8 solid angles sum to 4 Pi steradians, giving a full sphere.
I literally love the way, how you clearly explained the primitive cell. Thank you so much!
Thanks for your time and effort for making such wonderful videos for young and old minds. We can only request you to keep doing more such videos.
Best teaching ever in this topic . Statements were clear accurate and understanding . How easily it is described ! Loved it . Inspired by you 🙏♥️
Sir please make a video on peritectic and peritectoid reactions
Thank you sir for this beautiful lecture
Thank you for the clear explanation, sir..
Very nice conceptual class sir , thanks 👍
What is the difference between cell vector and lattice vector?
Not sure of the cell vector. In what context do you use it? But lattice vector is a precisely defined concept: a vector from one lattice point to another lattice point. If by cell vector, you mean basis vectors defining a cell, then these are three special non coplanar lattice translations that span a unit cell.
This was very helpful! Thanks :)
Very clear explanation. Thank you :-)
sir, what is the application of these concepts,where will we use this?
One application we make of this is in determining the reciprocal lattice of FCC. Since reciprocal lattice is defined in terms of primitive basis of real lattice, it is important to find one.
ruclips.net/video/A1V8J68afsA/видео.html
only if our professor could have been like you :/
Very good explaination, Sir. But there is a mistake at @8.23 in this video. Contribution of each cornered atom in primitive unit cell is not 1/8. Although total number of atoms in one primitive unit cell is 1. Plz correct me if I am wrong.
Thank you for observing this. You are indeed right as all corners do not include the same solid angle. But for the purpose of calculation of effective number it works out fine to think that the contribution is 1/8 from all corners. More correctly, this is average contribution from each corner.
Let us look at it differently. Focus on one corner (corner focus). Eight unit cells share this corner. And amount of sphere in each of these unit cells is not the same. Consider one particular unit cel out of these 8. Now focus on a unit cell (unit cell focus). This has eight corners and different parts of sphere is included in the unit cell at each of these corners. One of these corners will have exactly the same part of sphere included in the unit cell.
So eight corners of one unit cell have one to one correspondence with eight unit cells at one corner. And as eight unit cells at one corner include one atom, eight corners of one unit cell also include one atom.
I agree all this is a lot of hand-waving. A more precise proof of the statement will require adding all the solid angles of a parallelepiped unit cell. And I hope, that analogous to the theorem for 2D parallelogram, where the angles sum to 360 degrees giving a complete circle, there must be a theorem for 3D parallelopiped where all the 8 solid angles sum to 4 Pi steradians, giving a full sphere.
Pls upload for primitive unit cell of HCP structure
The conventional cell of the HCP structure is itself primitive.
thank you so much
Thanks Rajesh