Miller indices?

Question

Does anyone know what the Miller indices of the Y-Z plane (x equal to zero) is?

Is this a trick question from my professor?

What would be the Y and Z intercepts of the Y-Z plane?

Answer 1

It's always nice to see a question that checks how well you understand related concepts. Crystals posses translational symmetry, so you are free to translate the origin by any integer number of lattice constants along the a,b,or c axes. Please note that a,b and c are not orthogonal in general, but have included angles alpha, beta and gamma. Miller indices describe the reciprocal lattice, so you must consider coordinates in one unit cell. By translational symmetry x=0 is equivalent to x=1 and the required Miller indicies are (100). The International Tables for X-Ray Crystallography is the primary reference for crystallographers worldwide and highly recommended.

Answer 2

That would be (infinity,0,0). See source.

The Miller indices are given by the reciprocals of the intercepts of the plane in question divided by the unit cell dimensions (i.e., the reciprocals of the coordinates of the intercepts where the units of measurement along an axis are the dimensions of the unit cell along that axis).

In this case, the intercept with the x-axis is at x=0, and the intercepts with the z and y axes are at infinity (i.e., the plane never intersects these axes). If the unit cell dimensions are a,b,c, then the Miller indices are given by:

(1/(0/a), 1/(infinity/b), 1/(infinity/c)) =
(infinity, 0,0)

Answer 3

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