The unit cell is not a triangle, but a rhombus (two triangles), so its area is b*h. Note the red outline of the "2D repeat unit" at 13:20 is a rhombus. I hope this helps.
@@EngineeringandDesignSolutions i know its been a few years... but is the triangle itself not an equilateral triangle, and to use just area of equilateral triangle instead? or was that just for fcc only and does not apply to bcc?
Not sure if you were confused or if it's a typo, but it's a = (4root3/3)R. Keeping the "R" in there is important to answer your question. If you watch the lecture on BCC linear density ruclips.net/video/aPC8YwHNrL0/видео.html, I go through it pretty carefully. 1. In short, though the "R" is the atomic radius and the atoms only "touch" along the 3D diagonal from the front-left-bottom corner to the back-right-top corner through the middle atom. There are four radii ("4R") that such a path goes through. 2. The side of the cube has a length of just "a". 3. Doing the geometry, the diagonal along the xy-plane is a*root2. 4. The diagonal along the "4R" path from step 1 is a*root3. 5. We set 4R = a*root3 = 3*a/root3. 6. a then solves for 4root3/3)R My bet is that step 4 is a sticking point, but it's best to show that visually, not typing, so if it's still a tough spot, just watch that video from 9:00 to about 13:30. I hope this helps. Thanks for watching and commenting!
Engineering and Design Solutions I'm lost on step 5. How does 4R = a*√(3) = (3*a)/√(3)? Where did the 3 in the last step come from? In the video from the link it says that a = 4R/√(3) not a=4R√(3)/3.
I used a proprietary site from a publisher that is now not available at all. It was pretty cool but it was a bit glitchy from using Adobe Flash. I should do my own using 3D CAD...
The (111) plane could be defined by an equilateral triangle of three atoms, yes. I think what you are asking about is why four atoms are shown to be the "repeating unit". It is because one "triangle" of three atoms may have an atom in the middle that is a bit behind/below the plane (indicated in light blue) and the next one over has one a bit in front/above the plane (indicated in pink). Also, they are at 60 / 180 degrees to each other. Thus, the second does not actually repeat the first. However, if the two are combined, they contain all the elements (4 atoms plus one in front and one behind) and are oriented like all the others. In other news, yes, you could still calculate the planar density with a single triangle! I hope this helps. Thanks for posting!
Yeah ..... it's already confusing to me , and now got again confused seeing this .... I think not only me , everyone over every space has forgotten geometry
@@moupiamukherjee1713 not sure if you already got it but he used bh since it's a rhombus. If you want, you could think of it as two equilateral triangles having bh/2 as the area so bh/2 + bh/2 would be equal to (bh + bh)/2 or 2bh/2 which is just bh. It became "sqrt2 ah" because the base is equals to "sqrt2 a" and h is "h". Hope this helps!
@@judy-chan4536 Hi sorry had an exam yesterday! But to answer the question, you can actually do that. By using the area of the triangle we'll have: [1] A = 1/2 b * h [2] A = 1/2 * (sqr rt 2)a * (a)(sqr rt 3/2) By doing those we'll get: [3] 1/2 (a^2)(sqrt 2)(sqrt 3/2) But we can't stop there, since the repeating unit is inside a rhombus and there's two equilateral triangles, we multiply [3] by 2 [4] 2 * (1/2) (a^2)(sqrt 2)(sqrt 3/2)
when he calculated the second vector he didnt multiply his "a" by root of 2 according to his unit length formula.Is it another different way of calculating LD?
That's because the second vector traversed the edge of the cube, which has a length of "a". The first vector went from corner-to-corner; that distance is a*(sqrt(2))). I hope this helps!
Very clear and well paced! Thanks.
I still don`t understand why you`re saying that we have two atoms for the first example
Thank you man,didnt understand in class but now i do,thanks a lot.
Why did you use (base)(height) = Triangle area
instead of (base)(height)/2 = Triangle Area
at 13:20
The unit cell is not a triangle, but a rhombus (two triangles), so its area is b*h. Note the red outline of the "2D repeat unit" at 13:20 is a rhombus.
I hope this helps.
@@EngineeringandDesignSolutions i know its been a few years... but is the triangle itself not an equilateral triangle, and to use just area of equilateral triangle instead? or was that just for fcc only and does not apply to bcc?
@@judy-chan4536 I know its been a few years, but it is a equilateral triangle
@@houch8002 i know its been a few years but it is a triangle
How do you get the a = 4root3 over 3 from a square?
Not sure if you were confused or if it's a typo, but it's a = (4root3/3)R. Keeping the "R" in there is important to answer your question. If you watch the lecture on BCC linear density ruclips.net/video/aPC8YwHNrL0/видео.html, I go through it pretty carefully.
1. In short, though the "R" is the atomic radius and the atoms only "touch" along the 3D diagonal from the front-left-bottom corner to the back-right-top corner through the middle atom. There are four radii ("4R") that such a path goes through.
2. The side of the cube has a length of just "a".
3. Doing the geometry, the diagonal along the xy-plane is a*root2.
4. The diagonal along the "4R" path from step 1 is a*root3.
5. We set 4R = a*root3 = 3*a/root3.
6. a then solves for 4root3/3)R
My bet is that step 4 is a sticking point, but it's best to show that visually, not typing, so if it's still a tough spot, just watch that video from 9:00 to about 13:30.
I hope this helps. Thanks for watching and commenting!
Engineering and Design Solutions I'm lost on step 5. How does 4R = a*√(3) = (3*a)/√(3)? Where did the 3 in the last step come from? In the video from the link it says that a = 4R/√(3) not a=4R√(3)/3.
@@Cutepeaches210 at the beginning,that confused my head too.but it is only calculus.multiply both numerator and denominator with square root 3. :)
Why number of atoms is 2?
since no. of radii traversed = 4
You are all very welcome!
brings a lot of memories!
hey can i get the link to the website you used to rotate cell
I used a proprietary site from a publisher that is now not available at all. It was pretty cool but it was a bit glitchy from using Adobe Flash. I should do my own using 3D CAD...
You can use ovito software
10:44 This is where you lost me. Would the (111) plane not just be a triangle? What am I missing here?
The (111) plane could be defined by an equilateral triangle of three atoms, yes. I think what you are asking about is why four atoms are shown to be the "repeating unit". It is because one "triangle" of three atoms may have an atom in the middle that is a bit behind/below the plane (indicated in light blue) and the next one over has one a bit in front/above the plane (indicated in pink). Also, they are at 60 / 180 degrees to each other. Thus, the second does not actually repeat the first. However, if the two are combined, they contain all the elements (4 atoms plus one in front and one behind) and are oriented like all the others.
In other news, yes, you could still calculate the planar density with a single triangle!
I hope this helps.
Thanks for posting!
isnt the area= 1/2bh? why is it in sqrt2 ah? shouldt it be 1/2 sqrt2 ah?
Yeah ..... it's already confusing to me , and now got again confused seeing this .... I think not only me , everyone over every space has forgotten geometry
@@moupiamukherjee1713 not sure if you already got it but he used bh since it's a rhombus. If you want, you could think of it as two equilateral triangles having bh/2 as the area so bh/2 + bh/2 would be equal to (bh + bh)/2 or 2bh/2 which is just bh.
It became "sqrt2 ah" because the base is equals to "sqrt2 a" and h is "h". Hope this helps!
@@mimikyamko7220 why not use the area of equilateral triangle a^2root3/4 outright instead of base*height?
@@judy-chan4536 Hi sorry had an exam yesterday! But to answer the question, you can actually do that. By using the area of the triangle we'll have:
[1] A = 1/2 b * h
[2] A = 1/2 * (sqr rt 2)a * (a)(sqr rt 3/2)
By doing those we'll get:
[3] 1/2 (a^2)(sqrt 2)(sqrt 3/2)
But we can't stop there, since the repeating unit is inside a rhombus and there's two equilateral triangles, we multiply [3] by 2
[4] 2 * (1/2) (a^2)(sqrt 2)(sqrt 3/2)
@@judy-chan4536 let me know if you have any more questions.
Can i ask how a became 0.405 nm? please answer,
Given by question
Okay!. at first i guess it came from the atomic radius and somewhat apply some atoms
Software name?
VMSE
can you give me that link of pdf
Not sure what you are referring to, but thanks for watching!
u are a great engineer
Great 👍
I want to learn how we calculate 'a' but it was written already.
from where did you get this pdf ??
drive.google.com/drive/folders/1ZgFR4AxTfOVzl25othZRi9nmhQMY2tso
greatly thanks for you bro :)
Thanks for the video
I need this pdf please and thanks for this explanation
Which is ur app
I don't understand - app for what?
@@EngineeringandDesignSolutions the app you are using to show 3D projection.....
when he calculated the second vector he didnt multiply his "a" by root of 2 according to his unit length formula.Is it another different way of calculating LD?
That's because the second vector traversed the edge of the cube, which has a length of "a". The first vector went from corner-to-corner; that distance is a*(sqrt(2))).
I hope this helps!
saved my life
It is wrong.2D circle number is important in linear density like planar one.
very helpful!!! :)
Glad to be of service!
First example, isnt that suppose to be 4 atoms
better explained than my professor
thank man,!
thanks a lot