When I hear someone talking about a (100) plane or a (111) plane or an (hkl) in general, my first thought is, is the system cubic. The reason I think this is because I tend NOT to think of the planes associated with their miller indices, but the vectors that are normal to planes. In cubic systems, [hkl] vectors are normal to their corresponding (hkl) planes. Hence, direct space (hkl) planes are parallel to their reciprocal space counterparts. In cubic systems, these relationships are true.
I think this is a bad way to think of the relationship between Direct and Reciprocal space, as not all systems are cubic and I fumble when dealing with other sorts of lattices. Does anyone have some advice of a more fundamental way to view the relationship between the two spaces? Preferably, one that is quite intuitive. I realize they are Fourier Transforms of one another. I am sorry if this is a silly question.
For example, in an HCP system, how should I envision the (hkl) plane? It is not normal to the [hkl] vector? is there no simple intuitive way to see such things? I can certainly do the math I suppose.