Weiss Zone law and its applications

Weiss Zone law and its applications
Erratum: At 14.25 the Plane ODE should be (11 -1) with C as the origin. I have made a mistake in writing it as (-1 11) in the green text below the right figure. However, the subsequent calculation uses the correct indices (11 -1).

[@waqasmuneer7951]

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[@IZTOK_LOVRIN]

Very good teacher! You connnect well with the students when drawing alsongside with them. I learned alot. Thank you professor and greetings from Slovenia!

[@blzKrg]

so, in general do [u v w] and [-u -v -w] represent the same direction but in opposite sense?

[@muralikrishnay2734]

Yeah, those are colinear too

[@livethelifewithpk007]

Good Morning Sir, in the equation 3 you mentioned u=-v, but it could be v=-u. if it is v=-u then we will have miller indices like [u -u 0] which turns out to be as [1 -1 0] (can't put bar over a number).

[@introductiontomaterialsscience]

Thanks for asking. Yes, that is also possible. Both [-1 1 0] or [1 -1 0] are right answers. These two indices are actually representing opposite senses along the same direction. Since we are only interested in the line of intersection and not the sense, either of them is the correct answer.

[@livethelifewithpk007]

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[@jayakrishnaadapa8842]

I am also thinking the same it got clear with your wonderful reply sir thank you

[@blzKrg]

@@introductiontomaterialsscience so, in general do [u v w] and [-u -v -w] represent the same direction but in opposite sense?

[@rajeshprasadlectures]

@@blzKrg Yes.

[@shivbhole2761]

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[@buildsuccesstea1844]

In 18：17 and for the Miller Induce of ODB with C as orgin ，why the minus is put in the first position but not the third one？

[@buildsuccesstea1844]

Sorry，should be ODE but not ODB

[@introductiontomaterialsscience]

@@buildsuccesstea1844 This is indeed a mistake. Thanks for pointing this out. I had missed taking note of this earlier. I have now put an erratum in the description.

[@knightarora]

sir in 1:48 you have stated "(is parallel to)" how is it parallel sir ! eg. if (110) and [-1 1 1] is this two parallel ?

[@introductiontomaterialsscience]

Yes, the direction [-1 1 1] either lies in the plane (111) or is parallel to it. You can check it by drawing.

[@sauravuppoor2409]

At 16:39 Is it necessary to show that PQ is the common dirrection. Why cant we just say that AB is parallel to DE and hence AB/DE is the common direction since both will have same miller indices?

[@introductiontomaterialsscience]

Thanks. I think that will be a better and quicker way :-)

[@kaushalyakumarihami1394]

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[@muralikrishnay2734]

Preparing for isro exam?

[@qmtv5772]

Dear Students, ODE is (11-1) not (-111), please note it..... (Video 14:23)

[@shinshin6595]

it looks a writing error

[@qmtv5772]

@@shinshin6595 yes, writing mitake

[@-RajarshiKashyapSarmah]

Absolute gold!!

[@harikrishnan3112]

Sir with C as origin the miller indices for plane ODE must be (1 1 1bar) but how can it be (1bar 1 1)

[@introductiontomaterialsscience]

This is indeed a mistake. Thanks for pointing this out. I have now put an erratum in the description.

[@harikrishnan3112]

@@introductiontomaterialsscience Thank you so much sir

[@deepkalariya6906]

@@introductiontomaterialsscience Thank you sir

[@BPranoy]

@@introductiontomaterialsscience Professor please pin this comment to the top.

[@ShuvamNayak]

Sir, how Weiss law is applicable to other crystal structure? The law depends on the dot product of the line and the normal line perpendicular to plane giving us the dot product equal to zero. But in other crystal structure, I won't know the miller indices of the line normal to the plane.

[@introductiontomaterialsscience]

There is way to prove it without using the dot product. It can then be shown that it is applicable to all crystal structures.

[@indugupta4266]

Dear Sir, Miller indices for common direction AB is [1bar 1 0] if we consider A as an origin to define AB Direction, if we consider B as an origin then what would be the Miller indices of AB Direction? Is it [1 1bar 0]??

[@introductiontomaterialsscience]

If AB is [-1 1 0] then BA is of course [1 -1 0]. But this is considering AB and BA as vectors. But if we consider the entire line without considering the sense, then both are equivalent and either of them represents the entire line.

[@indugupta4266]

@@introductiontomaterialsscience Okay Sir. Thank you very much.

[@anuragdatta3403]

Hello sir, I have a general question. If the type of crystal is not mentioned, are we supposed to consider a primary cubic crystal?

[@introductiontomaterialsscience]

Weiss zone law is applicable to all crystals. Thus in the application of this law, it does not matter what is the crystal system.

[@anuragdatta3403]

I mean, not just in Weiss Zone Law..... If I'm given the Miller Indices of Direction, and the type of crystal is not specified, will I consider a primary cubic crystal?

[@introductiontomaterialsscience]

@@anuragdatta3403 Since you asked on this video, I assumed it to be related to the Weiss zone law. In general, you cannot assume it to be cubic. The answer to any question related to length, direction or interplanar distances depends upon the crystal system. Take for an example, the angle between [100] and [010]. For a cubic system the answer is 90°. For hexagonal system it is 120°.

[@anuragdatta3403]

Okay sir.
Thank you so much!
Your explanations are really amazing.

[@yelsinmendezcamacho8483]

Great explanation! can the problem of common direction be solved by applying the cross product between the two planes?

[@introductiontomaterialsscience]

Yes. mathematically the two methods are equivalent. But the justification for using cross product is a bit more involved for non cubic crystal systems. It requires the use of reciprocal vectors which I have not discussed in this course.

[@pritom7298]

Thanks sir. Take love

[@manthankapopara3895]

Sir, what will be the common direction to [2 3 5] and [1 1 -1]

[@introductiontomaterialsscience]

[8, -7, 1] as can be obtained by application of Weiss Zone Law.

[@pranav9339]

@@introductiontomaterialsscience how to do this geometrically professor? Unlike the case of this video, ( 2 3 5) and (1 1 -1) does have any direction coinciding or parallel.

[@introductiontomaterialsscience]

@@pranav9339 As large numbers like 5, 7, 8 are involved it would not be easy, although possible, to do this geometrically.

[@pranav9339]

@@introductiontomaterialsscience Thanks a lot prof.

[@ruchiray8557]

Amazing video

[@saurav1916]

I think it should have been pointed out that weiss zone law is nothing but same as vector law that dot product of two perpendicular vector is zero.
Here two vector being the direction( [uvw] ) and the plane(vector perpendicular to plane (hkl) ).

[@introductiontomaterialsscience]

This simple explanation will work only for cubic crystal system as only for cubic crystals [hkl] vector is normal to (hkl) plane. It is not true in general. For example [100] direction is not perpendicular to (100) plane in a hexagonal crystal. However, the law itself is true in general, for all crystal systems.

[@saurav1916]

@@introductiontomaterialsscience thanks for pointing out the flaw in logic.
I think...
Yes, the word "perpendicular" can only be used in case of cubic as only cubic system is cartesian but intuitively thinking about it we can say that the dot product of two basis vector is zero and therefore the vector law holds.
Or another way, lets imagine that all the other crystal systems are just modified cubic system (like what linear transformation in matrix does to 3d space) then the vector law holds for direction[abc] and the plane(pqr).

[@introductiontomaterialsscience]

@@saurav1916 As I mentioned in my earlier answer, the key step required in a proof based on dot product is that [hkl] direction is perpendicular to (hkl) plane. This is not true in general. However, [hkl] direction in reciprocal space is indeed perpendicular to the (hkl) plane in real space. This fact can be used to give a proof based on dot products. But you then need the introduction of reciprocal space.

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