# Lattice Planes

1. Feb 20, 2015

### Chillguy

1. The problem statement, all variables and given/known data
Prove that the lattice planes with the greatest densities of points are the {111} planes in a fcc bravis lattice and the {110} planes in a bcc bravis lattice.

2. Relevant equations
d/v=points per unit area where d is the spacing of planes and v is the unit volume.

3. The attempt at a solution
In the fcc case
$$d=\frac{2\pi}{hb_1+kb_2+lb_3}\\ b_1=\frac{2\pi}{a}(y-x+z)$$
Which is in terms of the reciprocal space. So we simply need to maximize this value. Does this immediately tell us it is in the {111} miller index because the reciprocal is given in terms of 3 coordinates?

2. Feb 26, 2015