Solution (source code)

= Solution

The resolved periodic contrast comes principally from <electron phase contrast>: transmitted and diffracted <electron> waves interfere after passing through the image-forming optics. The resulting intensity depends on specimen thickness, orientation, defocus and the <contrast transfer function>; bright dots cannot automatically be labelled gold-atom positions without image simulation. The surrounding nonperiodic background is consistent with an amorphous support or contamination, but its chemistry is not determined by contrast alone.

The particle contains differently oriented fringe regions, and the <Fourier transform> has several opposing spot pairs with an approximately pentagonal/tenfold composite appearance. Together with the faceted outline, this is \b[consistent with a multiply twinned <gold> particle, plausibly a decahedral arrangement], rather than one perfect cubic lattice with fivefold rotational symmetry. Opposite Fourier spots occur because the recorded image intensity is real; counting ten spots is not itself proof of a tenfold crystal. Overlapping domains, contrast-transfer effects and a slightly off-axis view can complicate the pattern. A tilt series or spatially windowed transforms across individual domains would test the twinning interpretation. The stability of such particles involves a competition among surface, twin-boundary and elastic strain energies.<Stability of Multiply-Twinned Particles by Shozo Ino>[J. Phys. Soc. Jpn. 27 (1969), pp.941–953, abstract: decahedral/icosahedral particle energetics]{ref}