Find angle between planes (011) and (001)

[jerjer]

Please help me!
Find angle between planes (011) and (001)?

 

[Simon Bridge]

Welcome to PF:
https://www.physicsforums.com/showthread.php?t=197071

 

[jerjer]

Thanks spo much!
So according to that
to find the angle btw planes (011) and (001) in a cubic crystal (they are perpendicular) I need to normalize vectors.

Normalizing vectors:
ll v ll = sqrt( 0^2 +1^2+1^2)= sqrt(2)

llwll = sqrt (0^2 + 0^2 +1^2)= 1


v vector normalized:
x/1.41= 0/1.41= 0
y/1.41= 0.71
z/1.41= 0.71
v = 0.71j +0.71 k

w vector normalized:
x/1=0/1= 0
y/1=0/1= 0
z/1=1/1=1
w = k

v dot w= 0.71+0.71= 1.41

then, the angle theta between planes (011) and (001)
theta= v dot w/( llvll * llwll)
theta= inverse of cosine ( 1.41/( sqrt (2)) (sqrt(1))= 1.41/ sqrt (2) (1))
theta= inverse cosine (0.997)
theta= 4.4

DOes this make sense?
if I do inverse cosine of 0.997 I get theta= 4.4
but I do inverse cosine of 1 I get angle is 0

not sure what I'm doing wrong =( please some help!

 

[Simon Bridge]

(011) and (001) in a cubic crystal (they are perpendicular)

... how do you figure that?

v dot w= 0.71+0.71= 1.41

...don't think so. How did you get this result?

Note: It helps to explicitly keep √2 like that instead of converting to a decimal.

theta= v dot w/( llvll * llwll)

... yes - though ||v||=||w||=1 because you just normalized them didn't you?

To understand this approach:
The strategy is to find a vector perpendicular to each plane - related to the Miller indices how?
The angle between the planes is the angle between these two vectors.

I don't think you need to normalize them - just turns the dot product into the cosine of the angle.
The problem wants you to understand what the Miller notation is telling you.