Miller Indices (Solid State Physics)

[SeanGillespie]

Homework Statement

A simple cubic crystal with lattice parameter 0.5 nm has a plane which intersects atoms at the points (-0.5,-0.5,0), (1,-0.5,0.5) and (1,2.5,-1.5), where the coordinates have units of nm.

What are the miller indices of the plane?

Having read the relevant chapters of three different books I am still none the wiser, and have been unable to find a similar solution to this problem.

I am truly stuck and have no idea how to begin this question; I'm hoping someone can guide me through the process to a solution.

 

[beyondlight]

How to find millerindices:

1) Choose origo in some arbitrary point.

2) Choose a plane that DOES NOT intersect origo. Find the intersection in the x-axis and the y-axis. Lets say (1,2).

3) Invert (1,0.5)

4) Extend so that you get integers (2,1)

Your millierindices are then (h, k)= (2,1)

Im not so god at it. I only know how it works on a simple basis. The point with millerindices i think are that if you choose a "miller-plane" (h,k,l) then if that intersects origo, then the plane intersects x-axis at a/h, y-axis at a/k and the z-axis at a/l. a is the width of the cubic structure.