Miller Indices Calculation Question

[rtellez700]

Homework Statement

Give the Miller indices of the plane that is define by the two directions [111] and [2$\overline{1}$3]?

Homework Equations

h~1/a
k~1/b
l~1/c

The Attempt at a Solution

I know how to solve for miller indices once you know the the intercepts of the plane. So I found the equation for the plane but it happens to cross through the origin. I know that I am either suppose to move the origin or move the plane to a parallel position. How do i know where this position is? Or can any position i choose be correct?

 

[KataKoniK]

Hello! In order to determine the Miller indices of a plane, you need to have at least two non-parallel directions that lie on the plane. In this case, you have the [111] and [2\overline{1}3] directions, which are not parallel. So, you can use the equation h~1/a, k~1/b, l~1/c to solve for the Miller indices. However, as you mentioned, the plane may pass through the origin, which means that one of the intercepts will be zero. In this case, you can either choose a different position for the plane or use a different set of directions to determine the Miller indices. Remember, the Miller indices represent the relative spacing between planes in a crystal lattice, so the position of the plane is not as important as the directions that define it. I hope this helps!