Angle between planes in orthorhombic crystal

[daskywalker]

Homework Statement

In an orthorhombic crystal the angle between (1 1 0) and (1 -1 0) is 38o and the angle between (001) and (201) is 65o. What is the angle between (211) and (2 -1 1) ?

Homework Equations

equation of direction cosines

The Attempt at a Solution

I found the b/a ratio by replacing unknown variable b in (110) and (1-10) and known cosine value of 38 degrees. I tried to use similar approach to solve for c/a with the other two planes (001) and (201) but I am not sure how to continue

 

[nate808]

from there to find the angle between (211) and (2 -1 1).

To find the angle between (211) and (2 -1 1), we can use the formula for the angle between two planes in a crystal system. This formula is given by:

cosθ = (h1h2 + k1k2 + l1l2)/√(h1^2 + k1^2 + l1^2)√(h2^2 + k2^2 + l2^2)

Where (h1, k1, l1) and (h2, k2, l2) are the Miller indices of the two planes.

In this case, we have (h1, k1, l1) = (2,1,1) and (h2, k2, l2) = (2,-1,1).

Plugging these values into the formula, we get:

cosθ = (2*2 + 1*(-1) + 1*1)/√(2^2 + 1^2 + 1^2)√(2^2 + (-1)^2 + 1^2) = 4/√6√6 = 4/6 = 2/3

Solving for θ, we get:

θ = cos^-1(2/3) = 48.2o

Therefore, the angle between (211) and (2 -1 1) is 48.2o.