Definition of atomic planes

1. Aug 26, 2008

Narcol2000

Atomic planes are defined as the reciprocal quantities 1/u' , 1/v' and 1/w' transformed to the smallest three integers (here the plane intersects the crystal lattice at the unit-cell axes u'a,v'b and w'c).

My question is, why are reciprocal quantities used? This is something that has bugged me for a very long time... it seems pretty arbitrary to me.

2. Aug 27, 2008

Gokul43201

Staff Emeritus
It's not arbitrary.

For any general plane described by the equation, $ax+by+cz+d=0$, verify that the intercepts are given by: -d/a, -d/b and -d/c.

That's the origin of the Miller Indices - they describe the coefficients a,b,c in the equation of the plane (or the direction cosines of its normal).

3. Aug 29, 2008

Narcol2000

Thanks for the tip, it makes sense now, I just hate learning things without knowing the reason behind it.