# Homework Help: A crystallography problem using 3D geometry

1. Dec 6, 2017

### hzx

1. The problem statement, all variables and given/known data
Three close-packed planes of atoms are stacked to form fcc lattice. The stacking sequence of the three planes can be altered to form the hexagonal close packed structure by sliding the third plane by the vector r over the second. If the planes in the fcc structure are all (111) planes, what is the translation vector r in terms of unit vectors [100], [010], and [001] of the fcc lattice?

2. Relevant equations

3. The attempt at a solution
Unit vectors [100], [010], and [001] of the fcc lattice can be expressed as a, b, and c (any arbitrary origin point O would work).
The problem can be converted to finding relative position of one atom from hcp from an arbitrary origin point O defined using fcc lattice.

2. Dec 11, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.