A porous amorphous carbon microsphere with Ag particles inside and Au particles on the outside, thus separating the different metals, (a) its transmission electron microscopy (TEM) image and (b) a computer simulation that helped analyze the structure quantitatively, revealing the very low density of the carbon.

 A carbon micro sphere with Ag nanoparticles partially hollowed out and replaced by Pd on the outside of each nanoparticle, leading to a complex structure where the different metals are close together without constituting an alloy, (a) the TEM image and (b) a computer simulation of the replacement process which revealed that the TEM is very misleading toward the percentage of the Ag being replaced by Pd. The impression of very large cavities arises even at small replacement ratios (here only 1/3 of the original nanoparticles' volume has been removed).

 Chemical locomotion of a Pt/Au nano rod in H2O2 solution (public domain image, wikipedia).

 Pd nano shells, (a) SEM of complete spheres and (b) TEM of incomplete ones. In catalysis, the ugliest compounds with the broadest size distributions are often the most active, like these incomplete shells, which outperform their nicer looking, more narrowly size dispersed counterparts.

 Simulated terminal length distributions of a fractionation that repeatedly halves (here up to four times) until fragments are shorter than the limit length (300 nm). The red hatched curve is from initial lengths around 440 nm. The blue curve is from a very broad initial distribution (1 µ

 m standard deviation). Its shape looks like a section cut out of a broad distribution's long tail and together with statistical noise leads to a peak at a misleadingly short length.

 (a) Lengths vs. diameters of wire fragments after sonication. The gray line is the usual method's estimate of the aspect ratio a = Llim/d

  the statistical error seems to be larger than the whole terminal range Λ

  (blue). The improved analysis uses the lower and uppermost slopes b and B. The statistical error is only the spread around the limits of the terminal range (yellow wedge shaped areas). Computationally facilitated image analysis allows analyzing a lot of fragments and can be adapted easily for different purposes, for example (b) to determine the average network link thickness in nano-foam.

 A TEM of a metal thin-film (a)

  automatic image recognition cannot yet distinguish twinning dislocations from domain boundaries. We use Adobe Photoshop to mark the scale bar (green), multiply twinned crystal dislocations of interest with blue, singly twinned boundaries with red lines, and then analyze only the image layer containing the markings (b).

 Section of a TEM of a metal thin-film (a) and the same section's image layer containing the markings (b). Mathematical graph analysis automatically finds and labels every branching point (c) and calculates all angles. This has helped to show the importance of two-fold over five-fold twins in ultra hard metallic thin films.