Find angle between planes (011) and (001)

1. Jan 27, 2012

jerjer

Find angle between planes (011) and (001)?

2. Jan 28, 2012

Simon Bridge

3. Jan 28, 2012

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!!

4. Jan 28, 2012

Simon Bridge

... how do you figure that?
...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.
... 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.

Last edited: Jan 28, 2012