Atomic step contrast from forbidden reflections

Diffraction contrast from weak 1/3 {422} reflections, observed in 〈111〉 diffraction patterns from gold, has been explained in terms of atomic steps on the (111) surface. It has been assumed from structure factor considerations that these reflections extinguish at an integral number n of complete unit cells, i.e. after every third (111) atomic layer. We show that this assumption is not valid unless the crystal is oriented with this reflection in the exact Bragg orientation. As the crystal is tilted away from the Bragg condition, extinction of the 1/3 {422} beam no longer occurs when the crystal is an integral number of unit cells thick. For tilts of about 5° from the zone axis, extinction may occur for instance after every sixth (111) layer. This phenomenon is explained using a kinematic scattering argument based on the multislice approach, where the phase of the scattered amplitude between successive layers depends on tilt from the 〈111〉 zone axis. Experiment is correlated with dynamical many-beam multislice calculations.