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them to predict the detailed shape of the nanoparticles as a function of particle
size. This prediction makes a precise connection between the diameter of a Ru
nanoparticle and the number of highly desirable reactive sites for breaking N 2
bonds on the nanoparticle. Finally, all of these calculations were used to
develop an overall model that describes how the individual reaction rates for
the many different kinds of metal atoms on the nanoparticle's surfaces
couple together to define the overall reaction rate under realistic reaction con-
ditions. At no stage in this process was any experimental data used to fit or
adjust the model, so the final result was a truly predictive description of the
reaction rate of a complex catalyst. After all this work was done, Honkala
et al. compared their predictions to experimental measurements made with
Ru nanoparticle catalysts under reaction conditions similar to industrial con-
ditions. Their predictions were in stunning quantitative agreement with the
experimental outcome.
1.2.2 Embrittlement of Metals by Trace Impurities
It is highly likely that as you read these words you are within 1 m of a large
number of copper wires since copper is the dominant metal used for carrying
electricity between components of electronic devices of all kinds. Aside from
its low cost, one of the attractions of copper in practical applications is that it is
a soft, ductile metal. Common pieces of copper (and other metals) are almost
invariably polycrystalline, meaning that they are made up of many tiny
domains called grains that are each well-oriented single crystals. Two neigh-
boring grains have the same crystal structure and symmetry, but their orien-
tation in space is not identical. As a result, the places where grains touch
have a considerably more complicated structure than the crystal structure of
the pure metal. These regions, which are present in all polycrystalline materials,
are called grain boundaries.
It has been known for over 100 years that adding tiny amounts of certain
impurities to copper can change the metal from being ductile to a material
that will fracture in a brittle way (i.e., without plastic deformation before the
fracture). This occurs, for example, when bismuth (Bi) is present in copper
(Cu) at levels below 100 ppm. Similar effects have been observed with lead
(Pb) or mercury (Hg) impurities. But how does this happen? Qualitatively,
when the impurities cause brittle fracture, the fracture tends to occur at grain
boundaries, so something about the impurities changes the properties of
grain boundaries in a dramatic way. That this can happen at very low concen-
trations of Bi is not completely implausible because Bi is almost completely
insoluble in bulk Cu. This means that it is very favorable for Bi atoms to seg-
regate to grain boundaries rather than to exist inside grains, meaning that the
 
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