What is the first step when converting Miller indices to a plane intercept representation?

• A. Take reciprocal and plot the point
• B. Encase in parentheses
• C. Multiply across by LCM
• D. Find intercepts

Answer: (A)

The main idea is that Miller indices encode where a plane cuts the crystal axes via reciprocal distances. If a plane intercepts the a-axis at a/h, the b-axis at b/k, and the c-axis at c/l, then the Miller indices h, k, l are the reciprocals of those intercept fractions (in units of the lattice parameters). So the first step to convert to an intercept representation is to take the reciprocals: 1/h, 1/k, 1/l. These reciprocals give the intercepts along the axes (in lattice-parameter units). After that, you can clear fractions by multiplying by a common factor to obtain simple integer intercepts, but that clearing is a subsequent step. Note that if any index is zero, that indicates the plane is parallel to that axis (an infinite intercept), which is why it’s treated separately in the plotting.