The directions are symmetry equivalent. i.e.there is some symmetry operation of the crystal which takes one direction to the other. For example [100] and [001] in a cubic crystal because you can rotate [100] into [001] by 90 degrees around the four-fold-axis along [010]. In tetragonal crystal [010] is not a four-fold axis. So this rotation is not a symmetry rotation. Therefore in tetragonal crystal [100] and [001] are not equivalent, i.e., not sy,mmetry equivalent.
miller indices for direction only represent the orientation of the direction and not its position or sense. So what do you mean by the sense of direction? In the video you did explain that sense means the positive and negative direction of a line about the origin, say it does not represent positive x-axis and negative x-axis, but in the latter part we learn that [100] is for +ve x-axis and [bar-1,00] as -ve x-axis direction. Please, somebody, clarify the meaning of orientation and the sense.
There are actually two approaches: to regard sense or to disregard it. If we disregard the sense then [100] and [-100] represent the same direction. If we regard sense, then of course, [100] and [-100] are opposite directions.
It depends on the choice of coordinate axis directions. For negative x axis, if you choose it as the coordinate axis direction, you can take miller indices as [100] instead of [bar1 0 0]
Both things are same in this case as it is one- dimensional. But if you would talk for [111] and [bar1 1 1] then both directions make the different sense surely. So here it makes the sense of using bar.
Sir in the second example the direction which u calculated as [1/2 1/2 1] ,I m getting it as [0 1/2 1] please check it again and tell me if I m wrong there.
The problem is related to representing 3D on 2D. I am assuming that the direction goes from the corner to the top face centre. You are assuming that the direction is lying on the back face and going from the corner to the centre of the top edge. With your interpretation what you are getting is correct.
@@introductiontomaterialsscience sir please make videos on other topics of physics , your video are great and they contain concept unlike other teacher on TH-cam .
[001] is a translational symmetry of the tetragonal crystal. But it is not symmetry equivalent to [001] and [010] directions. This can be seen in two ways: 1) The shortest translation along [001] is of length c whereas that along [100] 0r [010] is of length a. 2) [001] is the direction of unique 4-fols axis in the crystal. [100] or [010] do not have this symmetry.
Sir in example no. 2 you take x as -1 and y as -1 but we said that mille indices in parallel direction have same indices so how this condition is satified in this case ?
The OA vector is starting from the origin and going to the centre of the top face. 1/2 a +1/2 b brings one from the origin to the centre of the bottom face. then 1c takes us to the centre of the top face.
Thanks for fetching and eye holding lectures ,,,,the thing i wanna from you is that you complete the all aspects of metallurgy ,,,,for. ,,, accordingly Gate
hello please answer anyone to my question i.e why I need learn about these Miller or these lattices and unit cells simply about crystallography because these all are just imaginations where these Miller indices are to be used please give any one applications for my understanding purpose
Your question is indeed interesting. One of the most important applications of Miller indices is one of the most important devices that you and I using to communicate: the computers. As you know computer technology is based on Si wafers. And these Si wafers have to have specific crystal orientations (111) or (100). It is important to crystals of these specific orientations and then slice them in correct orientations. It is also important for further processing of wafer to make VLSI circuits. If (111) wafers are processed in an (100) line all the products will be a waste. You can check the following websites and videos: th-cam.com/video/IRoIXjxIcBQ/w-d-xo.html th-cam.com/video/vXk6Uhq74nU/w-d-xo.html www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_5/illustr/i5_2_4.pdf You make me realize that I could have mentioned some applications like this in my video.
Best material science teacher. GOD BLESS YOU, sir
A big thanks to you professor. I have cleared my exam just learning from your lectures ..thanks a lot and stay safe and healthy 🙏
These lectures are absolute wonder, with detailed explanation, which is even not mentioned in many famous books we study in bsc, 👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻
nice lecture sir, your presentation was simple to understand and covered all points. Thank u sir
Excellent. At least I figured out the confusing puzzles around me for two years through watching your videos.
Sir the way you you teaching directly penetrate our heart🙏🙏,A thousand of thanks sir🙏May all lectures teaches like you🤔😶😞😞.
Great sir , hats of directly hitting the concept .
How I find the coordinates of another point on the dircetion in terms of a,b,c?
Sir, what is meant when you say these 4 directions only are Equivalent?
How should I conceive equivalence ?
The directions are symmetry equivalent. i.e.there is some symmetry operation of the crystal which takes one direction to the other. For example [100] and [001] in a cubic crystal because you can rotate [100] into [001] by 90 degrees around the four-fold-axis along [010]. In tetragonal crystal [010] is not a four-fold axis. So this rotation is not a symmetry rotation. Therefore in tetragonal crystal [100] and [001] are not equivalent, i.e., not sy,mmetry equivalent.
@@introductiontomaterialsscience it's clear now, thanks to you sir.
miller indices for direction only represent the orientation of the direction and not its position or sense. So what do you mean by the sense of direction?
In the video you did explain that sense means the positive and negative direction of a line about the origin, say it does not represent positive x-axis and negative x-axis, but in the latter part we learn that [100] is for +ve x-axis and [bar-1,00] as -ve x-axis direction. Please, somebody, clarify the meaning of orientation and the sense.
There are actually two approaches: to regard sense or to disregard it. If we disregard the sense then [100] and [-100] represent the same direction. If we regard sense, then of course, [100] and [-100] are opposite directions.
It depends on the choice of coordinate axis directions. For negative x axis, if you choose it as the coordinate axis direction, you can take miller indices as [100] instead of [bar1 0 0]
Both things are same in this case as it is one- dimensional. But if you would talk for [111] and [bar1 1 1] then both directions make the different sense surely. So here it makes the sense of using bar.
@@rajeshprasad101 sir ap technical
Sir in the second example the direction which u calculated as [1/2 1/2 1] ,I m getting it as
[0 1/2 1] please check it again and tell me if I m wrong there.
The problem is related to representing 3D on 2D. I am assuming that the direction goes from the corner to the top face centre. You are assuming that the direction is lying on the back face and going from the corner to the centre of the top edge. With your interpretation what you are getting is correct.
Yes I also agree with u
What is the Significance of the Miller Indices of Family of symmetry-related direction and Miller Indices of Family of symmetry-related plane ??
All symmetry-related directions/planes have the same physical properties. For example all symmetry-related directions have the same Young's modulus.
@@introductiontomaterialsscience sir please make videos on other topics of physics , your video are great and they contain concept unlike other teacher on TH-cam .
your videos are good....besides material science ...for other mechanical engineering related topics which videos i shall refer..Please reply
Nptel is great source as whole mit ocw is a great source too
I didn't get the second example sir
why [001] does not represent transnational symmetry in tetragonal unit cell.?
[001] is a translational symmetry of the tetragonal crystal. But it is not symmetry equivalent to [001] and [010] directions. This can be seen in two ways:
1) The shortest translation along [001] is of length c whereas that along [100] 0r [010] is of length a.
2) [001] is the direction of unique 4-fols axis in the crystal. [100] or [010] do not have this symmetry.
If I take a different unitcell for the same lattice, will I get different miller indices?
Yes, Miller indices depend upon the chosen unit cell.
Sir in example no. 2 you take x as -1 and y as -1 but we said that mille indices in parallel direction have same indices so how this condition is satified in this case ?
I didn't get it please
Plz clarify the meaning.... orientation of line in this sense..?
Thank you so much professor 🎉❤
sir, i did not understand the example. why did u take 1/2 a , 1/2 b, and for c u took 1, how?? can u plz explain?
The OA vector is starting from the origin and going to the centre of the top face. 1/2 a +1/2 b brings one from the origin to the centre of the bottom face. then 1c takes us to the centre of the top face.
@@rajeshprasad101 thank u so much sir!!
how can i download class material?
Thanks for fetching and eye holding lectures ,,,,the thing i wanna from you is that you complete the all aspects of metallurgy ,,,,for. ,,, accordingly Gate
Nice explanation sir ji
Why z axis abset in tetragonal
hello please answer anyone to my question i.e why I need learn about these Miller or these lattices and unit cells simply about crystallography because these all are just imaginations where these Miller indices are to be used please give any one applications for my understanding purpose
Your question is indeed interesting. One of the most important applications of Miller indices is one of the most important devices that you and I using to communicate: the computers. As you know computer technology is based on Si wafers. And these Si wafers have to have specific crystal orientations (111) or (100). It is important to crystals of these specific orientations and then slice them in correct orientations. It is also important for further processing of wafer to make VLSI circuits. If (111) wafers are processed in an (100) line all the products will be a waste. You can check the following websites and videos:
th-cam.com/video/IRoIXjxIcBQ/w-d-xo.html
th-cam.com/video/vXk6Uhq74nU/w-d-xo.html
www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_5/illustr/i5_2_4.pdf
You make me realize that I could have mentioned some applications like this in my video.
Thanks professor
Thank you sir.
Thank so much sir ....🙏
Thank You Sir
Great sir
very nice explanation sir
Thank you Sir ❤️❤️❤️❤️
ty sir
I didn't get it please
Awesome
thank you very much sir......
Thnku sir
👍👍👍👍
Thanku sir
it will be 2 2 1 in second example..
ME 07
Ty sir