Conceptual question on miller planes

Physics Q&A
1

Dear course team,

I have a quick question on Miller planes, to check whether I understand this correctly.
In the lecture notes, it is mentioned that

The plane designated by Miller indices (u,v,w) intersects lattice vector a1 at |a1|u, a2 at |a2|v and a3 at |a3|w.

However, I was wondering whether these lattice vectors should be primitive lattice vectors or not. In the last exam, we were given the conventional unit cell of an FCC lattice. Thinking I was doing the right thing, I chose to express the miller planes in terms of the FCC primitive lattice vectors, but this seemed to make the problem a whole lot harder. Can we just assume that the miller planes are based off of the conventional unit cell?

2

For that statement to be true, the Miller planes and the Miller indices should be based on the same set of lattice vectors (so if primitive, then both primitive).

In the last exam, if memory serves me right, the Miller planes were indeed corresponding to the conventional unit cell, and that one is indeed easier to use.