While it is interesting to observe changes in the kinetics for an individual NP over time under reaction conditions, the absolute kinetics for different NPs cannot be compared directly because every NP is different in size, surface area, and distribution of surface sites. To facilitate comparisons between different NPs, and with data for bulk surfaces, it is useful to convert the absolute rates to rates normalized to the NP surface area in Da/second/nm 2 . The problem is that while we know the NP mass quite precisely, we generally have little information on the NP shape. Freshly trapped NPs are usually cleaned by pre-heating to high T NP to desorb oxides or other contaminants, subliming a few monolayers-worth of material from the surface. For some materials (e.g. Si) pre-heating can be done above the bulk T melt , and in those cases it is reasonable to assume that the melted NPs are spherical, and the NPs are generally large enough that it is also reasonable to assume the bulk density, allowing the surface area to be estimated with reasonable accuracy from the mass. Some materials (e.g. carbon) cannot be melted in the trap because melting occurs only at elevated pressures. Others (e.g. Hf, T melt = 2506 K ) could be melted in situ in principle, but actually reaching the bulk T melt for a trapped NP is difficult because thermionic emission and sublimation become so fast above 2400 K that it is difficult to maintain stable trapping. For such NPs, electron microscopy of the NP feedstock gives some insight into typical shapes, but the detailed shapes of the individual trapped NPs are generally unknown. Therefore, for want of information, we typically assume spherical shape, resulting in lower limits for the estimated NP surface areas, and therefore upper limits on the area-normalized rates.