Miller Indices for Crystal Structures

How to calculate miller indices of planes and directions in a crystal structure

[@JohnDoe-eo8gi]

10 years of helping people solve Material Science problems. Thank you!

[@Trikkie87]

You sir, have some love and cookies and chocolate and all that is good in life. Where i couldnt for the love get it by the books explanation, after watching this tutorial 1 time im suddenly a miller indices expert. #faithinmaterialsciencesrestored

[@Snagoot]

this is literally the same 2 questions i have for my first assessment. thank you

[@reignofhope]

and it's official, I not only don't care about school anymore, I actively resent it.

[@claramelb7476]

Hahahahaha I feel you!

[@beowulf20s]

Wonderful explanation. I have not seen this procedure explained better.

[@Korppuli]

Wow, I solved my homework thanks to this video. THANK YOU!

[@AraujoMatt]

For crystal planes we consider all parallel planes to have the same indices. If a plane intersects the origin, it is more simple to calculate the indices of the plane by either translating it from the origin or choosing a different coordinate system. This way we avoid calculating a normal vector using more complicated math. In the drawing, the plane that is drawn will never intersect the y-axis because it is parallel to it. Therefore its intersect is zero. The reciprocal or zero is zero.

[@AraujoMatt]

Khairy, Thanks for your comment. The Miller indices indicates a vector normal to the plane. There is no y-component to the normal vector of this plane so it must be zero. Quoting "Materials Science and Engineering", Callister and Rethwisch, 8th Ed: "A plane that parallels an axis may be considered to have an infinite intercept, and, therefore, a zero index."

[@g.maleksmith8430]

Do you think you could explain why it intersects the y axis at -(2/3) and not (2/3)? Thanks

[@tmac13in34]

+G.Malek Smith I think he meant why you intersect the z-axis at (-2/3) and not (2/3) not y-axis.

[@tjaartopperman4468]

You probably mean the z-intersection. That is where both x and y are zero. At x =1 we have z = 2/3, and at z = 0 we have x = 1/2 as shown. So you have: x = 1, 1/2,...,... and z = 2/3, 0,...,... . If we expand the series one step, then x = 1, 1/2, 0,..., and z would expand to 2/3, 0, -2/3,...,... So at x=0, and y=0, we have z = -2/3, which is our answer. No value of y will ever affect x and z since the plane is parallel to the y-axis, and that is why we can just force y to 0.

[@tw0million]

super helpful for exam review. thanks!

[@arinjayakhare3013]

Wonderful Explanation

[@mbekafaku4371]

awesome explanation

[@elyssa8552]

May I ask why at 6:41 the intercept of z is - 2/3? Is it possible to imagine the plane going upwards instead? Thanks!

[@majorblazer6908]

If the plane goes upwards it would not intersect the z axis. So your only option is extending it downwards

[@elyssa8552]

@@majorblazer6908 Oh I get it! Thanks alot!

[@suziee_ai2024]

could you actually draw another cube that shows the line above projected from the origin?

[@GautamKumar-cr7tw]

I thought it would be (403) and not (403bar). Could you please explain and correct me if I'm wrong.

[@fikremariamgedefaw9808]

the recprocal of 0= 1/0= is infinity

[@abdelrahmangamalmahdy]

he should have written infinity and then converted it to be zero

[@LNasterio]

The plane explanation was good, however the direction part was very confusing... I felt like I missed out part of the video???

[@ip_v1]

Has a bit of a mistake by taking the y intercept for the 2nd example plane at 0 instead of infinity but ok...

[@AraujoMatt]

Fatih, perhaps that wasn't the best explanation. The indices are the normal vector(or one of the normal vectors) to all planes parallel to this plane. We don't want to calculate the normal because then we need an Equation for the plane and cross products etc. As I understand it we use the idea of a limit to say it intersects y at Infinity. 1 over infinity is 0. I just keep in mind what the normal vector must look like...in this case, It has no y component

[@sanjidaakter54]

how to draw planner structure having indices (001);(110);(110)

[@HighTech636]

Great explanation.

[@shitpostadmiralty2921]

It's 1am, my materials HW is due in 7 hours... I cause my own anguish.

[@fatihaltunay591]

You dont explain how the plane doesnt intersect the y axes. Please explain it...

[@abdullahghumman5714]

reciprocal of 0 is infinity.......bro y intercept is actually infinity!!!!

[@cami_6622]

2021 hadir

[@jeenyus720]

You sound like microsoft sam. I like you, you're alright with me.

[@shrivathsagkumar]

bro y did you take -2/3

[@Martyr9991]

+shrivathsa g kumar I'm assuming you're asking about the second example for the y-intercept. If you continued the plane downwards, it would intersect at -2/3. You can see this by looking at the line created on the x-z plane. Starting on the x axis, going one half x in one direction causes a positive 2/3 so going the opposite direction, going one half the opposite direction will cause a -2/3 which is also where it intercepts the z plane/axis.

[@shrivathsagkumar]

Thanks a lot .

[@gameshow360]

Sir miller indices solution send

[@anumishra1905]

plz explain in hindi also

[@anumishra1905]

plz explain in hindi also