The phase difference between successive Bragg planes is 2π radians or 360°. For an atom translated one unit cell length in the a-direction, i.e., from x = 0 to x = 1, the phase difference would be 2πh radians. For the 310 planes below, this amounts to a phase difference of 2π(3) = 6π radians.

For an atom translated a fraction of a unit cell translation, the phase difference will be that fraction of the phase difference for a unit cell translation. Thus, for atom 2 (at x = ¹/₃), the phase difference, relative to the origin, would be 2π(3)(¹/₃) = 2π. In three dimensions the phase difference due to atom j at fractional co-ordinates x_j, y_j, z_j is

2π(hx_j + ky_j + lz_j)
In crystallography, it is customary to express atom positions using dimensionless, fractional co-ordinates.


Return