Coherence and multiple scattering in "Z-contrast" images

Hollow-cone dark-field images from crystalline silicon were examined as a function of thickness and scattering angle. We find that both coherent scattering and multiple scattering can cause the intensity to depend non-linearly on thickness, even for high-angle scattering events. A simple method for estimating the effect of multiple elastic scattering in thick specimens is provided. We show theoretically, that a coherence volume exists around each scatterer whose dimensions depend inversely on scattering angle. The coherence volume has a narrow "cigar" shape, elongated along the optic axis. The narrowness ensures that inter-atomic-column interferences, such as zero-order Laue zone Bragg reflections, are suppressed, whereas the elongation permits intra-atomic-column interference (or columnar diffraction). In high-resolution "Z-contrast" images, this bias towards columnar diffraction acts to enhance the signal from atom columns.