Answer to Question #133591 in Physics for Jai Narayan

Question

In an orthorhombic crystal a lattice plane makes intercepts of 2a, 3b and 4c on the
three axes. Write down the Miller indices for this plane.

Answer 1

The intercepts on XYZ space are at X=2, Y=3, Z=4.

Find reciprocals:

1/2, 1/3, 1/4.

What is the least common numerator for these numbers? 12.

Multiply the reciprocals by their LON to obtain Miller indexes:

$$12\cdot\frac{1}{2}=6,\\\space\\ 12\cdot\frac{1}{3}=4,\\\space\\ 12\cdot\frac{1}{4}=3.$$

Miller indexes are (6,4,3).