Question

Calculate the miller indices of the following and draw the diagrams (1 2 1) (2 1 2) (1 11) (2 4 2)

Answer 1

The notation (1 2 1) (2 1 2) (1 11) (2 4 2) represents a plane. Miller Indices are the reciprocals of the parameters of each crystal face. Thus, the points corresponding to such planes in notation $(r_1,r_2,r_3)$ can be calculated as reciprocals:

$$(1 2 1)=(1/1,1/2,1/1)=(1,0.5,1)\\ (212)=(1/2,1/1,1/2)=(0.5,1,0.5)\\ (111)=(111),\\ (242)=(0.5,0.25,0.5).$$

Draw them: