This was absolutely helpful, studied crystallography so much times from different professors, reference books but never got good understanding like this. Now, I understood why in XRD the miller indices planes are taken. Its all make sense now.
Thank you for the clear drawing and the neat notes!! I was getting rusty with some of the earlier concepts and was having a hard time envisioning the plane!
I was analyzing my TEM data and now matching it with my XRD data, however can you please tell that which peak I should consider from XRD data majorly so that I can correlate interplanar spacing by both XRD and TEM.
Sir , what will happen if the miller indices of planes are not same or in other words, planes are not parallel? How will we calculate the interplanar spacing????
Sir I think at 6:45, OA will be equal to a/h if ,and only if, we had not scaled the Miller indexes by some factor to make it an integer. I mean, to find h if we just do reciprocal of the number of a's required to span x- intercept, only then will OA be equal to a/h. Please correct me if i am wrong.
You are right. When we define Miller indices we reduce to smallest integers, making (200) as (100). This is fine if we are not worrying about dhkl. But when we think of dhkl we do not use such reductions and consider (200) and (100) as distinct. For example, d200=a/2 and d100=a in cubic crystal.
For Miller indices, you need to take reciprocals of 'intercepts in terms of respective lattice parameters". Thus the intercepts a/h. b/k and c/l have to be divided by a, b and c respectively to give relative intercepts 1/h. 1/k and 1/l. taking the reciprocals of the relative intercepts we get the Miller indices (hkl).
@@introductiontomaterialsscience sir according to you, we need to divide the edge length "a" by the corresponding length of intercept in order to get Miller index "h". But in books( for example SSP BY CHARLES KITTEN) ,they do the same but they also scale it to the nearest integer. If we also scale it then OA ≠ a/h. So according to the definition of h, do we have to scale it or not?
@@rajeshprasadlectures Sir I think at 6:45, OA will be equal to a/h if ,and only if, we had not scaled the Miller indexes by some factor to make it an integer. I mean, to find h if we just do reciprocal of x- intercept, only then will OA be equal to a/h. Please correct me if i am wrong.
Sir, how can we say that the distance between origin and plane is the same as the distance between two successive planes passing through corners.? Can you please explain this?
This really part of the definition of interplanar spacing. Consider any given Miller Indices (hkl). This gives a plane with intercepts a/h, b/k, c/l. By definition, any plane parallel to this will also have the same Miller indices. Thus with this definition alone we cannot define dhkl uniquely. So after having the first plane with intercepts a/h, b/k, c/l we take as the next plane one passing through the origin and parallel to this plane and define the distance between them as dhkl. And then we repeat these planes at dhkl to have a set of parallel (hkl) planes with spacing dhkl. I hope I have made it clear.
If only the interplanar spacing is given, nothing can be done. If lattice parameters are also given then you have a relationship giving interplanar spacing in terms of miller indices and lattice parameters. Still, since there are three Miller indices and only one equation, a solution is not guaranteed. But in the case of a cubic crystal, it is possible to get a solution because you can determine h^2+k^2+l^2. Given this value, one can determine the family {hkl}. for example if h^2+k^2+l^2=3 then you can say that {hkl}={111}. But within this family, a specific plane (hkl) cannot be determined. For example, it can be (111) or (-1 1 1) among other possibilities.
This is a espectacular explication, thanks so much professor. (From Colombia)
This was absolutely helpful, studied crystallography so much times from different professors, reference books but never got good understanding like this. Now, I understood why in XRD the miller indices planes are taken. Its all make sense now.
Thank you for the clear drawing and the neat notes!! I was getting rusty with some of the earlier concepts and was having a hard time envisioning the plane!
I was analyzing my TEM data and now matching it with my XRD data, however can you please tell that which peak I should consider from XRD data majorly so that I can correlate interplanar spacing by both XRD and TEM.
Sir , what will happen if the miller indices of planes are not same or in other words, planes are not parallel? How will we calculate the interplanar spacing????
This can be found out using simple pythagoras theorem by projecting in all three planes XY, YZ, ZX
Thank You Sir. You are the best
Sir I think at 6:45, OA will be equal to a/h if ,and only if, we had not scaled the Miller indexes by some factor to make it an integer. I mean, to find h if we just do reciprocal of the number of a's required to span x- intercept, only then will OA be equal to a/h. Please correct me if i am wrong.
You are right. When we define Miller indices we reduce to smallest integers, making (200) as (100). This is fine if we are not worrying about dhkl. But when we think of dhkl we do not use such reductions and consider (200) and (100) as distinct. For example, d200=a/2 and d100=a in cubic crystal.
@@introductiontomaterialsscience i got it sir. Thanks for the help.
if OA=a/h, OB=b/k OC=c/l, miller indice (h/a k/b l/c). these are not equal to (hkl)???
For Miller indices, you need to take reciprocals of 'intercepts in terms of respective lattice parameters". Thus the intercepts a/h. b/k and c/l have to be divided by a, b and c respectively to give relative intercepts 1/h. 1/k and 1/l. taking the reciprocals of the relative intercepts we get the Miller indices (hkl).
Thank you!!
@@introductiontomaterialsscience 7:31 Sir once can you explain how you got OA= a/h if edge length of cube is a?
@@Krishna-in3ni By definition, if the first Miller index is h then the first intercept is a/h.
@@introductiontomaterialsscience sir according to you, we need to divide the edge length "a" by the corresponding length of intercept in order to get Miller index "h". But in books( for example SSP BY CHARLES KITTEN) ,they do the same but they also scale it to the nearest integer. If we also scale it then OA ≠ a/h. So according to the definition of h, do we have to scale it or not?
Nice and concise. Thank you!
thanks sir. bravo
Thank you so much sir
Thank you so much professor!
Abdul Kalam voice sir
Thanks for that. How can we prove the interplanar spacing relation in the case of a hexagonal lattice?
You can derive it using the concept of reciprocal lattice. I will do a video on it soon.
@@rajeshprasadlectures Sir I think at 6:45, OA will be equal to a/h if ,and only if, we had not scaled the Miller indexes by some factor to make it an integer. I mean, to find h if we just do reciprocal of x- intercept, only then will OA be equal to a/h. Please correct me if i am wrong.
why cant sir use the black board
Thank u so much for detailed explanation 🙏🙏🙏🙏🙏
Sir, how can we say that the distance between origin and plane is the same as the distance between two successive planes passing through corners.? Can you please explain this?
This really part of the definition of interplanar spacing. Consider any given Miller Indices (hkl). This gives a plane with intercepts a/h, b/k, c/l. By definition, any plane parallel to this will also have the same Miller indices. Thus with this definition alone we cannot define dhkl uniquely. So after having the first plane with intercepts a/h, b/k, c/l we take as the next plane one passing through the origin and parallel to this plane and define the distance between them as dhkl. And then we repeat these planes at dhkl to have a set of parallel (hkl) planes with spacing dhkl. I hope I have made it clear.
@@introductiontomaterialsscience yes sir, i got it. Thank you so much.
What is the interplanar spacing for BCC and fcc lattice?
this is awesome sir
what does it mean for plane to pass though corners ? no where in derivation you took plane to be passing through corners
Plane is passing through the corners of the unit cell.. The unit cell is not drawn.. We are assuming it
Sir How do you calculate the miller indices given the inter planar spacing ? Thank you :)
If only the interplanar spacing is given, nothing can be done. If lattice parameters are also given then you have a relationship giving interplanar spacing in terms of miller indices and lattice parameters. Still, since there are three Miller indices and only one equation, a solution is not guaranteed. But in the case of a cubic crystal, it is possible to get a solution because you can determine h^2+k^2+l^2. Given this value, one can determine the family {hkl}. for example if h^2+k^2+l^2=3 then you can say that {hkl}={111}. But within this family, a specific plane (hkl) cannot be determined. For example, it can be (111) or (-1 1 1) among other possibilities.
Sir did you not teach numerical?
Best explanation of topic 💯
Superb
What for hexagonal shape?
Thankyou Sir
Good to see Ethiopian here :)
Thank you very much sir
How do you define 'adjacent' planes?
The parallel plane in the adjacent unit cell passing through its corners
My hero
Good lecture.
Thank you sir
Marvellous
awesome
Great
God bless you
Amrita ece(E,F,G) guys say 👋
👍👍👍👍
How it can be proved that (hkl) perpendicular to [hkl]?
Please answer me sir with my RUclips account