- #1

Chillguy

- 13

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## Homework Statement

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.

## Homework Equations

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

## The Attempt at a Solution

In the fcc case

[tex] d=\frac{2\pi}{hb_1+kb_2+lb_3}\\

b_1=\frac{2\pi}{a}(y-x+z)[/tex]

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?